A Review of the Combination of Experimental Measurements and Fibril-Reinforced Modeling for Investigation of Articular Cartilage and Chondrocyte Response to Loading
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paper_title: Normal and pathological adaptations of articular cartilage to joint loading

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Joints are functional units that transmit mechanical loads between contacting bones during normal daily or specialized activities, e.g., sports. All components of the joint, i.e. articular cartilage, bone, muscles, ligaments/tendons and nerves, participate in load transmission. Failure in any of these components can cause joint malfunction, which, in turn, may lead to accumulation of damage in other joint components. Mechanical forces have great influence on the synthesis and rate of turnover of articular cartilage molecules, such as proteoglycans (PGs). Regular cyclic loading of the joint enhances PG synthesis and makes cartilage stiff. On the other hand, loading appears to have less evident effects on the articular cartilage collagen fibril network. Continuous compression of the cartilage diminishes PG synthesis and causes damage of the tissue through necrosis. The prevailing view is that osteoarthrosis (OA) starts from the cartilage surface through PG depletion and fibrillation of the superficial collagen network. It has also been suggested that the initial structural changes take place in the subchondral bone, especially when the joint is exposed to an impact type of loading. This in turn would create an altered stress pattern on joint surfaces, which leads to structural damage and mechanical failure of articular cartilage. The importance of the neuromuscular system to the initiation and progression of OA is still poorly understood. Many surgical extra- and intra-articular procedures have been used for the treatment of OA. Although some of the new methods, such as autologous chondrocyte transplantation and mosaicplasty, have given good clinical results, it is reasonable to emphasize that the methods still are experimental and more controlled studies are needed.
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paper_title: Further insights into the structural principles governing the function of articular cartilage.

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Abstract ::: A new experimental technique involving the observation of an artificial notch propagating through articular cartilage has been used to examine the biomechanical properties of this tissue. By predetermining both the orientation of the notch and its location with respect to the primary functional zones a more rigorous description of the structure/function relationships in cartilage has been achieved. The principal findings are: A primary 'strain-locking' role for the superficial zone has been demonstrated experimentally in articular cartilage. Comparison of the behaviour of radial and transverse notches has revealed a primary structural anisotropy in the general matrix. This is strong evidence in support of the morphological model proposed in a recent paper by the present author. A range of mechanical responses is shown to be reflected consistently in structural features considered to arise principally from variations in the degree of crosslinking between the overall radial configuration of collagen fibres. It is possible to separate mechanically the collagen fibres from the general matrix and the bonding relationship between them is time-dependent. Measurement of loads required to propagate a radial notch suggest (a) that the strength of the fibres and/or that of the crosslinks between fibres increases with depth through the cartilage thickness, and (b) that the radial columns of chondrocytes typical of the deep zone do not represent planes of significantly reduced strength relative to the adjacent matrix. A major structural discontinuity exists in normal articular cartilage in a plane parallel to and below the articular surface. It is argued that this plane represents a major change in overall orientation of the collagen fibres. Finally, by applying the experimental techniques described in this paper both to degenerative articular cartilage and to healthy articular cartilage in which the primary components have been selectively degraded enzymatically it should be possible to gain a more precise picture of the structural origin of malfunction in this tissue.
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paper_title: Cell deformation behavior in mechanically loaded rabbit articular cartilage 4 weeks after anterior cruciate ligament transection

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OBJECTIVE ::: Chondrocyte stresses and strains in articular cartilage are known to modulate tissue mechanobiology. Cell deformation behavior in cartilage under mechanical loading is not known at the earliest stages of osteoarthritis. Thus, the aim of this study was to investigate the effect of mechanical loading on volume and morphology of chondrocytes in the superficial tissue of osteoarthritic cartilage obtained from anterior cruciate ligament transected (ACLT) rabbit knee joints, 4 weeks after intervention. ::: ::: ::: METHODS ::: A unique custom-made microscopy indentation system with dual-photon microscope was used to apply controlled 2 MPa force-relaxation loading on patellar cartilage surfaces. Volume and morphology of chondrocytes were analyzed before and after loading. Also global and local tissue strains were calculated. Collagen content, collagen orientation and proteoglycan content were quantified with Fourier transform infrared microspectroscopy, polarized light microscopy and digital densitometry, respectively. ::: ::: ::: RESULTS ::: Following the mechanical loading, the volume of chondrocytes in the superficial tissue increased significantly in ACLT cartilage by 24% (95% confidence interval (CI) 17.2-31.5, P < 0.001), while it reduced significantly in contralateral group tissue by -5.3% (95% CI -8.1 to -2.5, P = 0.003). Collagen content in ACLT and contralateral cartilage were similar. PG content was reduced and collagen orientation angle was increased in the superficial tissue of ACLT cartilage compared to the contralateral cartilage. ::: ::: ::: CONCLUSIONS ::: We found the novel result that chondrocyte deformation behavior in the superficial tissue of rabbit articular cartilage is altered already at 4 weeks after ACLT, likely because of changes in collagen fibril orientation and a reduction in PG content.
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paper_title: A biphasic viscohyperelastic fibril-reinforced model for articular cartilage: formulation and comparison with experimental data.

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Experiments in articular cartilage have shown highly nonlinear stress-strain curves under finite deformations, nonlinear tension-compression response as well as intrinsic viscous effects of the proteoglycan matrix and the collagen fibers. A biphasic viscohyperelastic fibril-reinforced model is proposed here, which is able to describe the intrinsic viscoelasticity of the fibrillar and nonfibrillar components of the solid phase, the nonlinear tension-compression response and the nonlinear stress-strain curves under tension and compression. A viscohyperelastic constitutive equation was used for the matrix and the fibers encompassing, respectively, a hyperelastic function used previously for the matrix and a hyperelastic law used before to represent biological connective tissues. This model, implemented in an updated Lagrangian finite element code, displayed good ability to follow experimental stress-strain equilibrium curves under tension and compression for human humeral cartilage. In addition, curve fitting of experimental reaction force and lateral displacement unconfined compression curves showed that the inclusion of viscous effects in the matrix allows the description of experimental data with material properties for the fibers consistent with experimental tensile tests, suggesting that intrinsic viscous effects in the matrix of articular cartilage plays an important role in the mechanical response of the tissue.
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paper_title: Gd-DTPA2− as a measure of cartilage degradation

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Glycosaminoglycans (GAGs) are the main source of tissue fixed charge density (FCD) in cartilage, and are lost early in arthritic diseases. We tested the hypothesis that, like Na + , the charged contrast agent Gd-DTPA 2- (and hence proton T 1 ) could be used to measure tissue FCD and hence GAG concentration. NMR spectroscopy studies of cartilage explants demonstrated that there was a strong correlation (r > 0.96) between proton T 1 in the presence of Gd-DTPA 2- and tissue sodium and GAG concentrations. An ideal one-compartment electrochemical (Donnan) equilibrium model was examined as a means of quantifying FCD from Gd-DTPA 2- concentration, yielding a value 50% less but linearly correlated with the validated method of quantifying FCD from Na + . These data could be used as the basis of an empirical model with which to quantify FCD from Gd-DTPA 2- concentration, or a more sophisticated physical model could be developed. Spatial distributions of FCD were easily observed in T,-weighted MRI studies of trypsin and interleukin-1 induced cartilage degradation, with good histological correlation. Therefore, equilibration of the tissue in Gd-DTPA 2- gives us the opportunity to directly image (through T, weighting) the concentration of GAG, a major and critically important macromolecule in cartilage. Pilot clinical studies demonstrated Gd-DTPA 2- penetration into cartilage, suggesting that this technique is clinically feasible.
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paper_title: Stress–relaxation of human patellar articular cartilage in unconfined compression: Prediction of mechanical response by tissue composition and structure

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Abstract Mechanical properties of articular cartilage are controlled by tissue composition and structure. Cartilage function is sensitively altered during tissue degeneration, in osteoarthritis (OA). However, mechanical properties of the tissue cannot be determined non-invasively. In the present study, we evaluate the feasibility to predict, without mechanical testing, the stress–relaxation response of human articular cartilage under unconfined compression. This is carried out by combining microscopic and biochemical analyses with composition-based mathematical modeling. Cartilage samples from five cadaver patellae were mechanically tested under unconfined compression. Depth-dependent collagen content and fibril orientation, as well as proteoglycan and water content were derived by combining Fourier transform infrared imaging, biochemical analyses and polarized light microscopy. Finite element models were constructed for each sample in unconfined compression geometry. First, composition-based fibril-reinforced poroviscoelastic swelling models, including composition and structure obtained from microscopical and biochemical analyses were fitted to experimental stress–relaxation responses of three samples. Subsequently, optimized values of model constants, as well as compositional and structural parameters were implemented in the models of two additional samples to validate the optimization. Theoretical stress–relaxation curves agreed with the experimental tests ( R =0.95–0.99). Using the optimized values of mechanical parameters, as well as composition and structure of additional samples, we were able to predict their mechanical behavior in unconfined compression, without mechanical testing ( R =0.98). Our results suggest that specific information on tissue composition and structure might enable assessment of cartilage mechanics without mechanical testing.
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paper_title: The effects of selective matrix degradation on the short-term compressive properties of adult human articular cartilage.

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The effects of proteoglycan and collagen digestion on the transient response of human articular cartilage when tested in unconfined compression were determined. Small cylindrical specimens of cartilage, isolated from the femoral head of the hip joint and from the femoral condyles of the knee joint, were subjected to a suddenly applied compressive load using a test apparatus designed to yield a transient oscillatory response. From this response values of the elastic stiffness and the viscous damping coefficient were determined. Cathepsin D and cathepsin B1 were used to digest the proteoglycan in some specimens, while in other specimens leukocyte elastase was used to attack the non-helical terminal regions of the Type II tropocollagen molecules and possibly the Type IX collagen molecule and thereby disturb the integrity of the collagen mesh. The results showed that proteoglycan digestion alone reduced the viscous damping coefficient but it did not significantly alter the elastic stiffness as determined from the oscillatory response. In contrast, the action of elastase reduced both the damping coefficient and the elastic stiffness of the cartilage. The results demonstrated the role of proteoglycans in regulating fluid transport in cartilage and hence controlling the time-dependent viscous properties. The elastic stiffness was shown to be dependent on the integrity of the collagen fibre network and not on the proteoglycans.
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paper_title: A composition-based cartilage model for the assessment of compositional changes during cartilage damage and adaptation

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Summary Objective The composition of articular cartilage changes with progression of osteoarthritis. Since compositional changes are associated with changes in the mechanical properties of the tissue, they are relevant for understanding how mechanical loading induces progression. The objective of this study is to present a computational model of articular cartilage which enables to study the interaction between composition and mechanics. Methods Our previously developed fibril-reinforced poroviscoelastic swelling model for articular cartilage was combined with our tissue composition-based model. In the combined model both the depth- and strain-dependencies of the permeability are governed by tissue composition. All local mechanical properties in the combined model are directly related to the local composition of the tissue, i.e., to the local amounts of proteoglycans and collagens and to tissue anisotropy. Results Solely based on the composition of the cartilage, we were able to predict the equilibrium and transient response of articular cartilage during confined compression, unconfined compression, indentation and two different 1D-swelling tests, simultaneously. Conclusion Since both the static and the time-dependent mechanical properties have now become fully dependent on tissue composition, the model allows assessing the mechanical consequences of compositional changes seen during osteoarthritis without further assumptions. This is a major step forward in quantitative evaluations of osteoarthritis progression.
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paper_title: Confocal microscopy indentation system for studying in situ chondrocyte mechanics

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Abstract Chondrocytes synthesize extracellular matrix molecules, thus they are essential for the development, adaptation and maintenance of articular cartilage. Furthermore, it is well accepted that the biosynthetic activity of chondrocytes is influenced by the mechanical environment. Therefore, their response to mechanical stimuli has been studied extensively. Much of the knowledge in this area of research has been derived from testing of isolated cells, cartilage explants, and fixed cartilage specimens: systems that differ in important aspects from chondrocytes embedded in articular cartilage and observed during loading conditions. In this study, current model systems have been improved by working with the intact cartilage in real time. An indentation system was designed on a confocal microscope that allows for simultaneous loading and observation of chondrocytes in their native environment. Cell mechanics were then measured under precisely controlled loading conditions. The indentation system is based on a light transmissible cylindrical glass indentor of 0.17 mm thickness and 1.64 mm diameter that is aligned along the focal axis of the microscope and allows for real time observation of live cells in their native environment. The system can be used to study cell deformation and biological responses, such as calcium sparks, while applying prescribed loads on the cartilage surface. It can also provide novel information on the relationship between cell loading and cartilage adaptive/degenerative processes in the intact tissue.
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paper_title: Importance of collagen orientation and depth-dependent fixed charge densities of cartilage on mechanical behavior of chondrocytes.

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The collagen network and proteoglycan matrix of articular cartilage are thought to play an important role in controlling the stresses and strains in and around chondrocytes, in regulating the biosynthesis of the solid matrix, and consequently in maintaining the health of diarthrodial joints. Understanding the detailed effects of the mechanical environment of chondrocytes on cell behavior is therefore essential for the study of the development, adaptation, and degeneration of articular cartilage. Recent progress in macroscopic models has improved our understanding of depth-dependent properties of cartilage. However, none of the previous works considered the effect of realistic collagen orientation or depth-dependent negative charges in microscopic models of chondrocyte mechanics. The aim of this study was to investigate the effects of the collagen network and fixed charge densities of cartilage on the mechanical environment of the chondrocytes in a depth-dependent manner. We developed an anisotropic, inhomogeneous, microstructural fibril-reinforced finite element model of articular cartilage for application in unconfined compression. The model consisted of the extracellular matrix and chondrocytes located in the superficial, middle, and deep zones. Chondrocytes were surrounded by a pericellular matrix and were assumed spherical prior to tissue swelling and load application. Material properties of the chondrocytes, pericellular matrix, and extracellular matrix were obtained from the literature. The loading protocol included a free swelling step followed by a stress-relaxation step. Results from traditional isotropic and transversely isotropic biphasic models were used for comparison with predictions from the current model. In the superficial zone, cell shapes changed from rounded to elliptic after free swelling. The stresses and strains as well as fluid flow in cells were greatly affected by the modulus of the collagen network. The fixed charge density of the chondrocytes, pericellular matrix, and extracellular matrix primarily affected the aspect ratios (height/ width) and the solid matrix stresses of cells. The mechanical responses of the cells were strongly location and time dependent. The current model highlights that the collagen orientation and the depth-dependent negative fixed charge densities of articular cartilage have a great effect in modulating the mechanical environment in the vicinity of chondrocytes, and it provides an important improvement over earlier models in describing the possible pathways from loading of articular cartilage to the mechanical and biological responses of chondrocytes.
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paper_title: Regulatory volume decrease (RVD) by isolated and in situ bovine articular chondrocytes

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Articular chondrocytes in vivo are exposed to a changing osmotic environment under both physiological (static load) and pathological (osteoarthritis) conditions. Such changes to matrix hydration could alter cell volume in situ and influence matrix metabolism. However the ability of chondrocytes to regulate their volume in the face of osmotic perturbations have not been studied in detail. We have investigated the regulatory volume decrease (RVD) capacity of bovine articular chondrocytes within, and isolated from the matrix, before and following acute hypotonic challenge. Cell volumes were determined by visualising fluorescently-labelled chondrocytes using confocal laser scanning microscopy (CLSM) at 21°C. Chondrocytes in situ were grouped into superficial (SZ), mid (MZ), and deep zones (DZ). When exposed to 180mOsm or 250mOsm hypotonic challenge, cells in situ swelled rapidly (within ∼90 sec). Chondrocytes then exhibited rapid RVD (t1/2 ∼ 8 min), with cells from all zones returning to ∼3% of their initial volume after 20 min. There was no significant difference in the rates of RVD between chondrocytes in the three zones. Similarly, no difference in the rate of RVD was observed for an osmotic shock from 280 to 250 or 180mOsm. Chondrocytes isolated from the matrix into medium of 380mOsm and then exposed to 280mOsm showed an identical RVD response to that of in situ cells. The RVD response of in situ cells was inhibited by REV 5901. The results suggested that the signalling pathways involved in RVD remained intact after chondrocyte isolation from cartilage and thus it was likely that there was no role for cell-matrix interactions in mediating RVD. © 2001 Wiley-Liss, Inc.
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paper_title: Biomechanical properties of knee articular cartilage

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Structure and properties of knee articular cartilage are adapted to stresses exposed on it during physiological activ- ities. In this study, we describe site- and depth-dependence of the biomechanical properties of bovine knee articular cartilage. We also investigate the effects of tissue structure and composition on the biomechanical parameters as well as characterize experimentally and numerically the compression-tension nonlinearity of the cartilage matrix. In vitro mechano-optical mea- surements of articular cartilage in unconfined compression geometry are conducted to obtain material parameters, such as thickness, Young's and aggregate modulus or Poisson's ratio of the tissue. The experimental results revealed significant site- and depth-dependent variations in recorded parameters. After enzymatic modification of matrix collagen or proteoglycans our results show that collagen primarily controls the dynamic tissue response while proteoglycans affect more the static properties. Experimental measurements in compression and tension suggest a nonlinear compression-tension behavior of articular carti- lage in the direction perpendicular to articular surface. Fibril reinforced poroelastic finite element model was used to capture the experimentally found compression-tension nonlinearity of articular cartilage.
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paper_title: Is classical consolidation theory applicable to articular cartilage deformation?

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In this paper, classical consolidation theory has been used to investigate the time-dependent response of articular cartilage to static loading. An experimental technique was developed to measure simultaneously the matrix internal pressure and creep strain under conditions of one-dimensional consolidation. This is the first measurement of the internal stress state of loaded cartilage. It is demonstrated that under static compression the applied load is shared by the components of the matrix (i.e. water, the proteoglycans, and the collagen fibrillar meshwork), during which time a maximum hydrostatic excess pore pressure is developed as initial water exudation occurs. This pressure decays as water is further exuded from the matrix and effective consolidation begins with a progressive transfer of the applied stress from water to the collagen fibrils and proteoglycan gel. Consolidation is completed when the hydrostatic excess pore pressure is reduced to zero and the solid components sustain in full the applied load.
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paper_title: Physical properties of rabbit articular cartilage after transection of the anterior cruciate ligament

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The effect of unilateral transection of the anterior cruciate ligament on the confined compression and swelling properties of the distal femoral articular cartilage of skeletally mature rabbits at 9 weeks after surgery was determined. Gross morphological grading of the transected and contralateral control distal femora stained with India ink confirmed that cartilage degeneration had been induced by ligament transection. Osteochondral cores, 1.8 mm in diameter, were harvested from the medial femoral condyles. The modulus, permeability, and electrokinetic (streaming potential) coefficient of the articular cartilage of the osteochondral cores were assessed by confined compression creep experiments. The properties (mean ± SD) of control cartilage were: confined compression modulus, 0.75 ± 0.28 MPa; hydraulic permeability, 0.63 ± 0.28 × 10−15 m2/Pa*sec; and electrokinetic coefficient, 0.16 ± 0.31 ± 10−9 V/Pa. In transected knees, the modulus was reduced by 18% (p = 0.04), while the permeability and electrokinetic coefficient were not detectably altered. The change in modulus was accompanied by a trend (p = 0.07) toward a decrease (-11%) in the glycosaminoglycan density within the tissue, a significant increase (p <0.001) in the water content of the cartilage after equilibration in 1 × phosphate buffered saline from 70.3 ± 4.1% in control knees to 75.2 ± 4.0% in transected knees, and little further swelling after tissue equilibration in hypotonic saline. The compressive modulus of the cartilage from both control and transected knees was positively correlated with the density of tissue glycosaminoglycan. The alterations in the physical properties of the articular cartilage after transection of the anterior cruciate ligament in the rabbit show trends similar to those observed in human and other animal models of osteoarthritis and provide further support for the use of this model in the study of cartilage degeneration.
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paper_title: Modeling the Matrix of Articular Cartilage Using a Continuous Fiber Angular Distribution Predicts Many Observed Phenomena

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A number of theoretical frameworks embodying the disparity between tensile and compressive properties of cartilage have been proposed, accounting for the collagen fibers implicitly [1,2] or explicitly [3–5]. These models generally propose discrete fiber families to describe the collagen matrix. They are able to capture the most salient features of the cartilage mechanical response, namely, the tension-compression nonlinearity of the stress-strain curve [6].Copyright © 2009 by ASME
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paper_title: Depth-dependent Compressive Equilibrium Properties of Articular Cartilage Explained by its Composition

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For this study, we hypothesized that the depth-dependent compressive equilibrium properties of articular cartilage are the inherent consequence of its depth-dependent composition, and not the result of depth-dependent material properties. To test this hypothesis, our recently developed fibril-reinforced poroviscoelastic swelling model was expanded to include the influence of intra- and extra-fibrillar water content, and the influence of the solid fraction on the compressive properties of the tissue. With this model, the depth-dependent compressive equilibrium properties of articular cartilage were determined, and compared with experimental data from the literature. The typical depth-dependent behavior of articular cartilage was predicted by this model. The effective aggregate modulus was highly strain-dependent. It decreased with increasing strain for low strains, and increases with increasing strain for high strains. This effect was more pronounced with increasing distance from the articular surface. The main insight from this study is that the depth-dependent material behavior of articular cartilage can be obtained from its depth-dependent composition only. This eliminates the need for the assumption that the material properties of the different constituents themselves vary with depth. Such insights are important for understanding cartilage mechanical behavior, cartilage damage mechanisms and tissue engineering studies.
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paper_title: Implementation of subject‐specific collagen architecture of cartilage into a 2D computational model of a knee joint—data from the osteoarthritis initiative (OAI)

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A subject-specific collagen architecture of cartilage, obtained from T2 mapping of 3.0 T magnetic resonance imaging (MRI; data from the Osteoarthritis Initiative), was implemented into a 2D finite element model of a knee joint with fibril-reinforced poroviscoelastic cartilage properties. For comparison, we created two models with alternative collagen architectures, addressing the potential inaccuracies caused by the nonoptimal estimation of the collagen architecture from MRI. Also two models with constant depth-dependent zone thicknesses obtained from literature were created. The mechanical behavior of the models were analyzed and compared under axial impact loading of 846N. Compared to the model with patient-specific collagen architecture, the cartilage model without tangentially oriented collagen fibrils in the superficial zone showed up to 69% decrease in maximum principal stress and fibril strain and 35% and 13% increase in maximum principal strain and pore pressure, respectively, in the superficial layers of the cartilage. The model with increased thickness for the superficial and middle zones, as obtained from the literature, demonstrated at most 73% increase in stress, 143% increase in fibril strain, and 26% and 23% decrease in strain and pore pressure, respectively, in the intermediate cartilage. The present results demonstrate that the computational model of a knee joint with the collagen architecture of cartilage estimated from patient-specific MRI or literature lead to different stress and strain distributions. The findings also suggest that minor errors in the analysis of collagen architecture from MRI, for example due to the analysis method or MRI resolution, can lead to alterations in knee joint stresses and strains. © 2012 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 31:10–22, 2012
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paper_title: Complex nature of stress inside loaded articular cartilage

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Abstract We show that in the early stages of loading of the cartilage matrix extensive water exudation and related physicochemical and structural changes give rise to a distinctly consolidatable system. By enzymatically modifying the pre-existing osmotic condition of the normal matrix and measuring its hydrostatic excess pore pressure, we have studied the exact influence of physicochemistry on the consolidation of cartilage. We argue that the attainment of a certain minimum level of swelling stiffness of the solid skeleton, which is developed at the maximum hydrostatic excess pore pressure of the fluid, controls the effective consolidation of articular cartilage. Three related but distinct stresses are developed during cartilage deformation, namely (1) the swelling stress in the coupled proteoglycan/collagen skeleton in the early stages of deformation, (2) the hydrostatic excess pore pressure carried by the fluid component, and (3) the effective stress generated on top of the minimum value of the swelling stress in the consolidation stages following the attainment of the fluid's maximum pore pressure. The minimum value of the swelling pressure is in turn generated over and above the intrinsic osmotic pressure in the unloaded matrix. The response of the hyaluronidase-digested matrix relative to its intact state again highlights the important influence of the osmotic pressure and the coefficient of permeability, both of which are related to the volume fraction of proteoglycans on cartilage deformation, and therefore its ability to function as an effective stress-redistributing layer above the subchondral bone.
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paper_title: The collagenous architecture of articular cartilage--a synthesis of ultrastructure and mechanical function.

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The fibrillar ultrastructure within the general matrix of articular cartilage has been examined in the stressed root region of predetermined notches propagating under tension in directions both perpendicular and parallel to the articular surface. From the different ultrastructural responses induced by the 2 notch geometries, it has been possible to further clarify the relationship between structure and load bearing function in normal articular cartilage, and identify features of the collagenous architecture that seem directly related to a loss of load bearing function associated with both osteoarthritis and nonprogressive degeneration.
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paper_title: A hyperelastic biphasic fibre-reinforced model of articular cartilage considering distributed collagen fibre orientations: continuum basis, computational aspects and applications

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Cartilage is a multi-phase material composed of fluid and electrolytes (68-85% by wet weight), proteoglycans (5-10% by wet weight), chondrocytes, collagen fibres and other glycoproteins. The solid ...
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paper_title: Traversing the intact/fibrillated joint surface: a biomechanical interpretation

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Cartilage taken from the osteoarthritic bovine patellae was used to investigate the progression of change in the collagenous architecture associated with the development of fibrillated lesions. Differential interference contrast optical microscopy using fully hydrated radial sections revealed a continuity in the alteration of the fibrillar architecture in the general matrix consistent with the progressive destructuring of a native radial arrangement of fibrils repeatedly interconnected in the transverse direction via a non-entwinement-based linking mechanism. This destructuring is shown to occur in the still intact regions adjacent to the disrupted lesion thus rendering them more vulnerable to radial rupture. Two contrasting modes of surface rupture were observed and these are explained in terms of the absence or presence of a skewed structural weakening of the intermediate zone. A mechanism of surface rupture initiation based on simple bi-layer theory is proposed to account for the intensification of surface ruptures observed in the intact regions on advancing towards the fibrillation front. Focusing specifically on the primary collagen architecture in the cartilage matrix, this study proposes a pathway of change from intact to overt disruption within a unified structural framework.
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paper_title: Stress-sharing between the fluid and solid components of articular cartilage under varying rates of compression

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This paper investigates the factors affecting the mechanical behavior of the articular matrix with special emphasis on the effect of compressive strain-rate on the short and long term responses of the fluid and the solid components. The relationships expressed in the general theory of one-dimensional consolidation are generalized to account for strain-rate in the deformation process with the result that the stiffness due to the fluid and the solid components, and a parameter representing the degree of drag, can be calculated explicity
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paper_title: Chondrocyte deformation and local tissue strain in articular cartilage: A confocal microscopy study

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It is well accepted that mechanical forces can modulate the metabolic activity of chondrocytes, although the specific mechanisms of mechanical signal transduction in articular cartilage are still unknown. One proposed pathway through which chondrocytes may perceive changes in their mechanical environment is directly through cellular deformation. An important step toward understanding the role of chondrocyte deformation in signal transduction is to determine the changes in the shape and volume of chondrocytes during applied compression of the tissue. Recently, a technique was developed for quantitative morphometry of viable chondrocytes within the extracellular matrix using three-dimensional confocal scanning laser microscopy. In the present study, this method was used to quantify changes in chondrocyte morphology and local tissue deformation in the surface, middle, and deep zones in explants of canine articular cartilage subjected to physiological levels of matrix deformation. The results indicated that at 15% surface-to-surface equilibrium strain in the tissue, a similar magnitude of local tissue strain occurs in the middle and deep zones. In the surface zone, local strains of 19% were observed, indicating that the compressive stiffness of the surface zone is significantly less than that of the middle and deep zones. With this degree of tissue deformation, significant decreases in cellular height of 26, 19, and 20% and in cell volume of 22, 16, and 17% were observed in the surface, middle, and deep zones, respectively. The deformation of chondrocytes in the surface zone was anisotropic, with significant lateral expansion occurring in the direction perpendicular to the local split-line pattern. When compression was removed, there was complete recovery of cellular morphology in all cases. These observations support the hypothesis that deformation of chondrocytes or a change in their volume may occur during in vivo joint loading and may have a role in the mechanical signal transduction pathway of articular cartilage.
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paper_title: Maturation of collagen fibril network structure in tibial and femoral cartilage of rabbits.

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OBJECTIVE ::: The structure and composition of articular cartilage change during development and growth, as well as in response to varying loading conditions. These changes modulate the functional properties of cartilage. We studied maturation-related changes in the collagen network organization of cartilage as a function of tissue depth. ::: ::: ::: DESIGN ::: Articular cartilage from the tibial medial plateaus and femoral medial condyles of female New Zealand white rabbits was collected from six age-groups: 4 weeks (n=30), 6 weeks (n=30), 3 months (n=24), 6 months (n=24), 9 months (n=27) and 18 months (n=19). Collagen fibril orientation, parallelism (anisotropy) and optical retardation were analyzed with polarized light microscopy. Differences in the development of depth-wise collagen organization in consecutive age-groups and the two joint locations were compared statistically. ::: ::: ::: RESULTS ::: The collagen fibril network of articular cartilage undergoes significant changes during maturation. The most prominent changes in collagen architecture, as assessed by orientation, parallelism and retardation were noticed between the ages of 4 and 6 weeks in tibial cartilage and between 6 weeks and 3 months in femoral cartilage, i.e., orientation became more perpendicular-to-surface, and parallelism and retardation increased with changes being most prominent in the deep zone. At the age of 6 weeks, tibial cartilage had a more perpendicular-to-surface orientation in the middle and deep zones than femoral cartilage (P<0.001) and higher parallelism throughout the tissue depth (P<0.001), while femoral cartilage exhibited more parallel-to-surface orientation (P<0.01) above the deep zone after maturation. Optical retardation of collagen was higher in tibial than in femoral cartilage at the ages of 4 and 6 weeks (P<0.001), while at older ages, retardation below the superficial zone in the femoral cartilage became higher than in the tibial cartilage. ::: ::: ::: CONCLUSIONS ::: During maturation, there is a significant modulation of collagen organization in articular cartilage which occurs earlier in tibial than in femoral cartilage, and is most pronounced in the deep zone.
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paper_title: A Study of the Structural Response of Wet Hyaline Cartilage to Various Loading Situations

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A direct view has been obtained of the manner in which the fibrous components and chondrocytes in hyaline cartilage respond to the application of uniaxial tensile loading and plane-strain compressive loading.A micro-mechanical testing device has been developed which inserts directly into the stage of a high-resolution optical microscope fitted with Nomarski interference contrast and this has permitted simultaneous morphological and mechanical observations to be conducted on articular cartilage maintained in its wet functional condition.Aligned and crimped fibrous arrays surround the deeper chondrocytes and can be observed to undergo well-defined geometric changes with applied stress. It is thought that these arrays may act as displacement or strain sensors transmitting mechanical information from the bulk matrix to their associated cells thus inducing a specific metabolic response.The process of tissue recovery following sustained high levels of compressive loading can also be observed with this experimen...
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paper_title: Comparison of single-phase isotropic elastic and fibril-reinforced poroelastic models for indentation of rabbit articular cartilage.

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Classically, single-phase isotropic elastic (IE) model has been used for in situ or in vivo indentation analysis of articular cartilage. The model significantly simplifies cartilage structure and properties. In this study, we apply a fibril-reinforced poroelastic (FRPE) model for indentation to extract more detailed information on cartilage properties. Specifically, we compare the information from short-term (instantaneous) and long-term (equilibrium) indentations, as described here by IE and FRPE models. Femoral and tibial cartilage from rabbit (age 0-18 months) knees (n=14) were tested using a plane-ended indenter (diameter=0.544 mm). Stepwise creep tests were conducted to equilibrium. Single-phase IE solution for indentation was used to derive instantaneous modulus and equilibrium (Young's) modulus for the samples. The classical and modified Hayes' solutions were used to derive values for the indentation moduli. In the FRPE model, the indentation behavior was sample-specifically described with three material parameters, i.e. fibril network modulus, non-fibrillar matrix modulus and permeability. The instantaneous and fibril network modulus, and the equilibrium Young's modulus and non-fibrillar matrix modulus showed significant (p<0.01) linear correlations of R(2)=0.516 and 0.940, respectively (Hayes' solution) and R(2)=0.531 and 0.960, respectively (the modified Hayes' solution). No significant correlations were found between the non-fibrillar matrix modulus and instantaneous moduli or between the fibril network modulus and the equilibrium moduli. These results indicate that the instantaneous indentation modulus (IE model) provides information on tensile stiffness of collagen fibrils in cartilage while the equilibrium modulus (IE model) is a significant measure for stiffness of PG matrix. Thereby, this study highlights the feasibility of a simple indentation analysis.
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paper_title: Fourier transform infrared imaging spectroscopy investigations in the pathogenesis and repair of cartilage.

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Significant complications in the management of osteoarthritis (OA) are the inability to identify early cartilage changes during the development of the disease, and the lack of techniques to evaluate the tissue response to therapeutic and tissue engineering interventions. In recent studies several spectroscopic parameters have been elucidated by Fourier transform infrared imaging spectroscopy (FT-IRIS) that enable evaluation of molecular and compositional changes in human cartilage with progressively severe OA, and in repair cartilage from animal models. FT-IRIS permits evaluation of early-stage matrix changes in the primary components of cartilage, collagen and proteoglycan on histological sections at a spatial resolution of approximately 6.25 microm. In osteoarthritic cartilage, the collagen integrity, monitored by the ratio of peak areas at 1338 cm(-1)/Amide II, was found to correspond to the histological Mankin grade, the gold standard scale utilized to evaluate cartilage degeneration. Apparent matrix degradation was observable in the deep zone of cartilage even in the early stages of OA. FT-IRIS studies also found that within the territorial matrix of the cartilage cells (chondrocytes), proteoglycan content increased with progression of cartilage degeneration while the collagen content remained the same, but the collagen integrity decreased. Regenerative (repair) tissue from microfracture treatment of an equine cartilage defect showed significant changes in collagen distribution and loss in proteoglycan content compared to the adjacent normal cartilage, with collagen fibrils demonstrating a random orientation in most of the repair tissue. These studies demonstrate that FT-IRIS is a powerful technique that can provide detailed ultrastructural information on heterogeneous tissues such as diseased cartilage and thus has great potential as a diagnostic modality for cartilage degradation and repair.
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paper_title: Mechanical characterization of articular cartilage by combining magnetic resonance imaging and finite-element analysis—a potential functional imaging technique

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Magnetic resonance imaging (MRI) provides a method for non-invasive characterization of cartilage composition and structure. We aimed to see whether T1 and T2 relaxation times are related to proteoglycan (PG) and collagen-specific mechanical properties of articular cartilage. Specifically, we analyzed whether variations in the depthwise collagen orientation, as assessed by the laminae obtained from T2 profiles, affect the mechanical characteristics of cartilage. After MRI and unconfined compression tests of human and bovine patellar cartilage samples, fibril-reinforced poroviscoelastic finite-element models (FEM), with depthwise collagen orientations implemented from quantitative T2 maps (3 laminae for human, 3–7 laminae for bovine), were constructed to analyze the non-fibrillar matrix modulus (PG specific), fibril modulus (collagen specific) and permeability of the samples. In bovine cartilage, the non-fibrillar matrix modulus (R = −0.64, p < 0.05) as well as the initial permeability (R = 0.70, p < 0.05) correlated with T1. In bovine cartilage, T2 correlated positively with the initial fibril modulus (R = 0.62, p = 0.05). In human cartilage, the initial fibril modulus correlated negatively (R = −0.61, p < 0.05) with T2. Based on the simulations, cartilage with a complex collagen architecture (5 or 7 laminae), leading to high bulk T2 due to magic angle effects, provided higher compressive stiffness than tissue with a simple collagen architecture (3 laminae). Our results suggest that T1 reflects PG-specific mechanical properties of cartilage. High T2 is characteristic to soft cartilage with a classical collagen architecture. Contradictorily, high bulk T2 can also be found in stiff cartilage with a multilaminar collagen fibril network. By emerging MRI and FEM, the present study establishes a step toward functional imaging of articular cartilage.
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paper_title: MRI assessment of cartilage ultrastructure

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In T2-weighted MRI images joint cartilage can appear laminated. The multilaminar appearance is visualized as zones of different intensity. This appearance is based on the dipolar interaction of water molecules within cartilage zones of different collageneous network structures. Therefore, the MR visualization of zones of anisotropic arrangement of the collagen fibers depends upon their orientation to the static magnetic field (magic-angle effect). The aim of this article is to demonstrate the potential of high-resolution MRI for characterizing cartilage network structuring and biomechanical properties. Information equivalent to that from polarization light microscopy can be derived noninvasively. Based on NMR microscopic (microMRI) data, potential new possibilities of MRI for quantitative assessment of collagen structuring and intracartilagenous load distribution are presented. These methods use MR intensity angle dependence and load influence on cartilage visualization. Alternatively to the determination of mechanical parameters from cartilage deformation, it is demonstrated that stress distribution and biomechanical properties can be derived in principle from the local intensity variation of anisotropic fiber orientation zones. The limitations with respect to a clinical application of the proposed methods are discussed.
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paper_title: Biochemical (and Functional) Imaging of Articular Cartilage

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Over the coming decades nondestructive biochemical imaging by magnetic resonance imaging (MRI) will provide an adjunct or surrogate for the destructive histologic and biochemical assays used today. A number of MRI methods demonstrate image contrast that, although influenced by the biochemical composition, is not normally specific to a particular measure of the biochemical state. The most widely used of these is T2-weighted imaging, which variably reveals collagen ultrastructure, hydration (or collagen content), and, to a lesser extent, glycosaminoglycan (GAG) concentration (each of these biochemical metrics is an important determinant of the functional integrity of cartilage). The lack of specificity of this technique (and others discussed herein) confounds efforts to improve strategies for evaluating cartilage. However, three methods permit a very specific measure of the cartilage biochemical state. Each of these three methods, explored in detail in this article, is rooted in a biophysical theory that relates the image signal intensity to a specific biochemical feature. Proton-density imaging directly measures water content (hydration), a parameter that might increase approximately 5% with significant degeneration. Magic-angle imaging, in which the angle dependence of T2 is measured, can provide a specific measure of collagen (or macromolecular) ultrastructure. The difficulty in getting the angle dependence presently precludes its use clinically. Delayed gadolinium-enhanced MRI of cartilage provides a specific measure of the distribution of GAGs. This method measures the distribution of a charged contrast agent, which in turn reflects the distribution of charge associated with GAG. This technique can be used in a clinical setting, and ongoing studies will explore its utility in monitoring therapeutic efficacy and disease progression. Although none of these techniques are presently in routine clinical use, emerging data provide promise that the future will see patient-specific biochemical analysis of cartilage, an outcome almost unimaginable 20 years ago.
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paper_title: Articular cartilage superficial zone collagen birefringence reduced and cartilage thickness increased before surface fibrillation in experimental osteoarthritis

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Objectives—To investigate articular cartilage collagen network, thickness of birefringent cartilage zones, and glycosaminoglycan concentration in macroscopically normal looking knee joint cartilage of young beagles subjected to experimental slowly progressive osteoarthritis (OA). Methods—OA was induced by a tibial 30° valgus osteotomy in 15 female beagles at the age of 3 months. Fifteen sisters were controls. Cartilage specimens were collected seven (Group 1) and 18 months (Group 2) postoperatively. Collagen induced optical path diVerence and cartilage zone thickness measurements were determined from histological sections of articular cartilage with smooth and intact surface by computer assisted quantitative polarised light microscopy. Volume density of cartilage collagen fibrils was determined by image analysis from transmission electron micrographs and content of glycosaminoglycans by quantitative digital densitometry from histological sections. Results—In the superficial zone of the lateral tibial and femoral cartilage,the collagen induced optical path diVerence (birefringence) decreased by 19 to 71% (p < 0.05) seven months postoperatively.This suggests that severe superficial collagen fibril network deterioration took place, as 18 months postoperatively, macroscopic and microscopic OA was present in many cartilage areas. Thickness of the uncalcified cartilage increased while the superficial zone became thinner in the same sites. In operated dogs, glycosaminoglycan content first increased (Group 1) in the lateral tibial condyle and then decreased (Group 2) (p < 0.05). Conclusion—In this OA model, derangement of the superficial zone collagen network was the probable reason for birefringence reduction. This change occurred well before macroscopic OA. (Ann Rheum Dis 1998;57:237‐245)
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paper_title: Effect of superficial collagen patterns and fibrillation of femoral articular cartilage on knee joint mechanics-a 3D finite element analysis.

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Collagen fibrils of articular cartilage have specific depth-dependent orientations and the fibrils bend in the cartilage surface to exhibit split-lines. Fibrillation of superficial collagen takes place in osteoarthritis. We aimed to investigate the effect of superficial collagen fibril patterns and collagen fibrillation of cartilage on stresses and strains within a knee joint. A 3D finite element model of a knee joint with cartilage and menisci was constructed based on magnetic resonance imaging. The fibril-reinforced poroviscoelastic material properties with depth-dependent collagen orientations and split-line patterns were included in the model. The effects of joint loading on stresses and strains in cartilage with various split-line patterns and medial collagen fibrillation were simulated under axial impact loading of 1000 N. In the model, the collagen fibrils resisted strains along the split-line directions. This increased also stresses along the split-lines. On the contrary, contact and pore pressures were not affected by split-line patterns. Simulated medial osteoarthritis increased tissue strains in both medial and lateral femoral condyles, and contact and pore pressures in the lateral femoral condyle. This study highlights the importance of the collagen fibril organization, especially that indicated by split-line patterns, for the weight-bearing properties of articular cartilage. Osteoarthritic changes of cartilage in the medial femoral condyle created a possible failure point in the lateral femoral condyle. This study provides further evidence on the importance of the collagen fibril organization for the optimal function of articular cartilage.
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paper_title: Indentation diagnostics of cartilage degeneration.

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OBJECTIVE ::: Mechanical indentation and ultrasound (US) indentation instruments have been introduced for quantitative assessment of cartilage properties in vivo. In this study, we compared capabilities of these instruments to determine properties of healthy and spontaneously degenerated human patellar cartilage in situ and to diagnose the early stages of osteoarthritis (OA). ::: ::: ::: DESIGN ::: Six anatomical sites were localized from human patellae (N=14). By determining the force by which the tissue resists constant deformation (F(IND)), a mechanical indentation instrument was used to measure the compressive dynamic stiffness of cartilage. Further, the dynamic modulus (E(US)) and the US reflection coefficient of cartilage surface (R(US)) were measured with an US indentation instrument. For reference, Young's modulus and dynamic modulus were determined from cartilage disks using unconfined compression geometry. Proteoglycan and collagen contents of samples were analyzed microscopically. The samples were divided into three categories (healthy, early degeneration, and advanced degeneration) based on the Osteoarthritis Research Society International (OARSI) OA-grading. ::: ::: ::: RESULTS ::: Parameters R(US), E(US) and F(IND) were significantly associated with the histological, compositional and mechanical properties of cartilage (|r|=0.28-0.72, n=73-75, P<0.05). Particularly, R(US) was able to discern degeneration of the samples with high sensitivity (0.77) and specificity (0.98). All parameters, except R(US,) showed statistically significant site-dependent variation in healthy cartilage. ::: ::: ::: CONCLUSIONS ::: US reflection measurement shows potential for diagnostics of early OA as no site-matched reference values are needed. In addition, the high linear correlations between indentation and reference measurements suggest that these arthroscopic indentation instruments can be used for quantitative evaluation of cartilage mechanical properties, e.g., after cartilage repair surgery.
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paper_title: In situ compressive stiffness, biochemical composition, and structural integrity of articular cartilage of the human knee joint

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Abstract Objective Reduction of compressive stiffness of articular cartilage has been reported as one of the first signs of cartilage degeneration. For the measurement of in situ compressive stiffness, a hand-held indentation probe has recently been developed and baseline data for macroscopically normal knee joint cartilage were provided. However, the histological stage of degeneration of the measured cartilage was not known. The purpose of this study was to investigate whether there is a relationship between the in situ measured compressive stiffness, the histological stage of degeneration, and the biochemical composition of articular cartilage. Design Instantaneous compressive stiffness was measured for the articular cartilage of 24 human cadaver knees. Additionally, biochemical composition (total proteoglycan and collagen content) and histological appearance (according to the Mankin score) were assessed for each measurement location. Results Despite visually normal surfaces, various histological signs of degeneration were present. A high correlation between Mankin score and cartilage stiffness was observed for the lateral patellar groove ( R 2 =0.81), the medial ( R 2 =0.83) and the lateral femoral condyle ( R 2 =0.71), whereas a moderate correlation was found for the medial patellar groove ( R 2 =0.44). No correlation was observed between biochemical composition and cartilage compressive stiffness. Conclusions Our results are in agreement with others and show that the instantaneous compressive stiffness is primarily dependent on the integrity of the extracellular matrix, and not on the content of the major cartilage constituents. The high correlation between stiffness and Mankin score in mild osteoarthrosis suggests that the stage of cartilage degeneration can be assessed quantitatively with the hand-held indentation probe. Moderate and severe case of osteoarthrosis remains to be investigated.
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paper_title: A nonlinear biphasic fiber-reinforced porohyperviscoelastic model of articular cartilage incorporating fiber reorientation and dispersion.

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A nonlinear biphasic fiber-reinforced porohyperviscoelastic (BFPHVE) model of articular cartilage incorporating fiber reorientation effects during applied load was used to predict the response of ovine articular cartilage at relatively high strains (20%). The constitutive material parameters were determined using a coupled finite element-optimization algorithm that utilized stress relaxation indentation tests at relatively high strains. The proposed model incorporates the strain-hardening, tension-compression, permeability, and finite deformation nonlinearities that inherently exist in cartilage, and accounts for effects associated with fiber dispersion and reorientation and intrinsic viscoelasticity at relatively high strains. A new optimization cost function was used to overcome problems associated with large peak-to-peak differences between the predicted finite element and experimental loads that were due to the large strain levels utilized in the experiments. The optimized material parameters were found to be insensitive to the initial guesses. Using experimental data from the literature, the model was also able to predict both the lateral displacement and reaction force in unconfined compression, and the reaction force in an indentation test with a single set of material parameters. Finally, it was demonstrated that neglecting the effects of fiber reorientation and dispersion resulted in poorer agreement with experiments than when they were considered. There was an indication that the proposed BFPHVE model, which includes the intrinsic viscoelasticity of the nonfibrillar matrix (proteoglycan), might be used to model the behavior of cartilage up to relatively high strains (20%). The maximum percentage error between the indentation force predicted by the FE model using the optimized material parameters and that measured experimentally was 3%.
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paper_title: The Effect of Matrix Tension-Compression Nonlinearity and Fixed Negative Charges on Chondrocyte Responses in Cartilage

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Thorough analyses of the mechano-electrochemical interaction between articular cartilage matrix and the chondrocytes are crucial to understanding of the signal transduction mechanisms that modulate the cell metabolic activities and biosynthesis. Attempts have been made to model the chondrocytes embedded in the collagen-proteoglycan extracellular matrix to determine the distribution of local stress-strain field, fluid pressure and the time-dependent deformation of the cell. To date, these models still have not taken into account a remarkable characteristic of the cartilage extracellular matrix given rise from organization of the collagen fiber architecture, now known as the tension-compression nonlinearity (TCN) of the tissue, as well as the effect of negative charges attached to the proteoglycan molecules, and the cell cytoskeleton that interacts with mobile ions in the interstitial fluid to create osmotic and electro-kinetic events in and around the cells. In this study, we proposed a triphasic, multi-scale, finite element model incorporating the Conewise Linear Elasticity that can describe the various known coupled mechanical, electrical and chemical events, while at the same time representing the TCN of the extracellular matrix. The model was employed to perform a detailed analysis of the chondrocytes' deformational and volume responses, and to quantitatively describe the mechano-electrochemical environment of these cells. Such a model describes contributions of the known detailed micro-structural and composition of articular cartilage. Expectedly, results from model simulations showed substantial effects of the matrix TCN on the cell deformational and volume change response. A low compressive Poisson's ratio of the cartilage matrix exhibiting TCN resulted in dramatic recoiling behavior of the tissue under unconfined compression and induced significant volume change in the cell. The fixed charge density of the chondrocyte and the pericellular matrix were also found to play an important role in both the time-dependent and equilibrium deformation of the cell. The pericellular matrix tended to create a uniform osmolarity around the cell and overall amplified the cell volume change. It is concluded that the proposed model can be a useful tool that allows detailed analysis of the mechano-electrochemical interactions between the chondrocytes and its surrounding extracellular matrix, which leads to more quantitative insights in the cell mechano-transduction.
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paper_title: Depth-wise progression of osteoarthritis in human articular cartilage: investigation of composition, structure and biomechanics

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Summary Objective Osteoarthritis (OA) is characterized by the changes in structure and composition of articular cartilage. However, it is not fully known, what is the depth-wise change in two major components of the cartilage solid matrix, i.e., collagen and proteoglycans (PGs), during OA progression. Further, it is unknown how the depth-wise changes affect local tissue strains during compression. Our aim was to address these issues. Methods Data from the previous microscopic and biochemical measurements of the collagen content, distribution and orientation, PG content and distribution, water content and histological grade of normal and degenerated human patellar articular cartilage ( n =73) were reanalyzed in a depth-wise manner. Using this information, a composition-based finite element (FE) model was used to estimate tissue function solely based on its composition and structure. Results The orientation angle of collagen fibrils in the superficial zone of cartilage was significantly less parallel to the surface ( P P P Conclusion For the first time, depth-wise point-by-point statistical comparisons of structure and composition of human articular cartilage were conducted. The present results indicated that early OA is primarily characterized by the changes in collagen orientation and PG content in the superficial zone, while collagen content does not change until OA has progressed to its late stage. Our simulation results suggest that impact loads in OA joint could create a risk for tissue failure and cell death.
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paper_title: Fourier transform infrared imaging and MR microscopy studies detect compositional and structural changes in cartilage in a rabbit model of osteoarthritis.

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Assessment of subtle changes in proteoglycan (PG) and collagen, the primary macromolecular components of cartilage, which is critical for diagnosis of the early stages of osteoarthritis (OA), has so far remained a challenge. In this study we induced osteoarthritic cartilage changes in a rabbit model by ligament transection and medial meniscectomy and monitored disease progression by infrared fiber optic probe (IFOP) spectroscopy, Fourier transform infrared imaging spectroscopy (FT-IRIS), and magnetic resonance imaging (MRI) microscopy. IFOP studies combined with chemometric partial least-squares analysis enabled us to monitor progressive cartilage surface changes from two to twelve weeks post-surgery. FT-IRIS studies of histological sections of femoral condyle cartilage revealed that compared with control cartilage the OA cartilage had significantly reduced PG content 2 and 4 weeks post-surgery, collagen fibril orientation changes 2 and 4 weeks post-surgery, and changes in collagen integrity 2 and 10 weeks post-surgery, but no significant changes in collagen content at any time. MR microscopy studies revealed reduced fixed charge density (FCD), indicative of reduced PG content, in the OA cartilage, compared with controls, 4 weeks post-surgery. A non-significant trend toward higher apparent MT exchange rate, k(m), was also found in the OA cartilage at this time point, suggesting changes in collagen structural features. These two MR findings for FCD and k(m) parallel the FT-IRIS findings of reduced PG content and altered collagen integrity, respectively. MR microscopy studies of the cartilage at the 12-week time point also found a trend toward longer T (2) values and reduced anisotropy in the deep zone of the OA cartilage, consistent with increased hydration and less ordered collagen. These studies reveal that FT-IRIS and MR microscopy provide complementary data on compositional changes in articular cartilage in the early stages of osteoarthritic degradation.
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paper_title: A novel method for determination of collagen orientation in cartilage by Fourier transform infrared imaging spectroscopy (FT-IRIS).

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OBJECTIVE ::: The orientation of collagen molecules is an important determinant of their functionality in connective tissues. The objective of the current study is to establish a method to determine the alignment of collagen molecules in histological sections of cartilage by polarized Fourier transform infrared imaging spectroscopy (FT-IRIS), a method based on molecular vibrations. ::: ::: ::: METHODS ::: Polarized FT-IRIS data obtained from highly oriented tendon collagen were utilized to calibrate the derived spectral parameters. The ratio of the integrated areas of the collagen amide I/II absorbances was used as an indicator of collagen orientation. These data were then applied to FT-IRIS analysis of the orientation of collagen molecules in equine articular cartilage, in equine repair cartilage after microfracture treatment, and in human osteoarthritic cartilage. Polarized light microscopy (PLM), the most frequently utilized technique to evaluate collagen fibril orientation in histological sections, was performed on picrosirius red-stained sections for comparison. ::: ::: ::: RESULTS AND CONCLUSION ::: Thicknesses of each zone of normal equine cartilage (calculated based on differences in collagen orientation) were equivalent as determined by PLM and FT-IRIS. Comparable outcomes were obtained from the PLM and FT-IRIS analyses of repair and osteoarthritis tissues, whereby similar zonal variations in collagen orientation were apparent for the two methods. However, the PLM images of human osteoarthritic cartilage showed less obvious zonal discrimination and orientation compared to the FT-IRIS images, possibly attributable to the FT-IRIS method detecting molecular orientation changes prior to their manifestation at the microscopic level.
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paper_title: Characterization of articular cartilage by combining microscopic analysis with a fibril-reinforced finite-element model.

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Load-bearing characteristics of articular cartilage are impaired during tissue degeneration. Quantitative microscopy enables in vitro investigation of cartilage structure but determination of tissue functional properties necessitates experimental mechanical testing. The fibril-reinforced poroviscoelastic (FRPVE) model has been used successfully for estimation of cartilage mechanical properties. The model includes realistic collagen network architecture, as shown by microscopic imaging techniques. The aim of the present study was to investigate the relationships between the cartilage proteoglycan (PG) and collagen content as assessed by quantitative microscopic findings, and model-based mechanical parameters of the tissue. Site-specific variation of the collagen network moduli, PG matrix modulus and permeability was analyzed. Cylindrical cartilage samples (n=22) were harvested from various sites of the bovine knee and shoulder joints. Collagen orientation, as quantitated by polarized light microscopy, was incorporated into the finite-element model. Stepwise stress-relaxation experiments in unconfined compression were conducted for the samples, and sample-specific models were fitted to the experimental data in order to determine values of the model parameters. For comparison, Fourier transform infrared imaging and digital densitometry were used for the determination of collagen and PG content in the same samples, respectively. The initial and strain-dependent fibril network moduli as well as the initial permeability correlated significantly with the tissue collagen content. The equilibrium Young's modulus of the nonfibrillar matrix and the strain dependency of permeability were significantly associated with the tissue PG content. The present study demonstrates that modern quantitative microscopic methods in combination with the FRPVE model are feasible methods to characterize the structure-function relationships of articular cartilage.
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paper_title: Mechanically induced calcium signaling in chondrocytes in situ.

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Changes in intracellular calcium (Ca(2+)) concentration, also known as Ca(2+) signaling, have been widely studied in articular cartilage chondrocytes to investigate pathways of mechanotransduction. Various physical stimuli can generate an influx of Ca(2+) into the cell, which in turn is thought to trigger a range of metabolic and signaling processes. In contrast to most studies, the approach used in this study allows for continuous real time recording of calcium signals in chondrocytes in their native environment. Therefore, interactions of cells with the extracellular matrix (ECM) are fully accounted for. Calcium signaling was quantified for dynamic loading conditions and at different temperatures. Peak magnitudes of calcium signals were greater and of shorter duration at 37°C than at 21°C. Furthermore, Ca(2+) signals were involved in a greater percentage of cells in the dynamic compared to the relaxation phases of loading. In contrast to the time-delayed signaling observed in isolated chondrocytes seeded in agarose gel, Ca(2+) signaling in situ is virtually instantaneous in response to dynamic loading. These differences between in situ and in vitro cell signaling responses might provide crucial insight into the role of the ECM in providing pathways of mechanotransduction in the intact cartilage that are absent in isolated cells seeded in gel constructs.
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paper_title: Changes in spatial collagen content and collagen network architecture in porcine articular cartilage during growth and maturation

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Summary Objectives The present study was designed to reveal changes in the collagen network architecture and collagen content in cartilage during growth and maturation of pigs. Methods Femoral groove articular cartilage specimens were collected from 4-, 11- and 21-month-old domestic pigs ( n =12 in each group). The animal care conditions were kept constant throughout the study. Polarized light microscopy was used to determine the collagen fibril network birefringence, fibril orientation and parallelism. Infrared spectroscopy was used to monitor changes in the spatial collagen content in cartilage tissue. Results During growth, gradual alterations were recorded in the collagen network properties. At 4 months of age, a major part of the collagen fibrils was oriented parallel to the cartilage surface throughout the tissue. However, the fibril orientation changed considerably as skeletal maturation progressed. At 21 months of age, the fibrils of the deep zone cartilage ran predominantly at right angles to the cartilage surface. The collagen content increased and its depthwise distribution changed during growth and maturation. A significant increase of the collagen network birefringence was observed in the deep tissue at the age of 21 months. Conclusions The present study revealed dynamic changes of the collagen network during growth and maturation of the pigs. The structure of the collagen network of young pigs gradually approached a network with the classical Benninghoff architecture. The probable explanation for the alterations is growth of the bone epiphysis with simultaneous adaptation of the cartilage to increased joint loading. The maturation of articular cartilage advances gradually with age and offers, in principle, the possibility to influence the quality of the tissue, especially by habitual joint loading. These observations in porcine cartilage may be of significance with respect to the maturation of human articular cartilage.
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paper_title: Uncertainties in indentation testing of articular cartilage: A fibril-reinforced poroviscoelastic study

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Indentation testing provides a quantitative technique to evaluate mechanical characteristics of articular cartilage in situ and in vivo. Traditionally, analytical solutions proposed by Hayes et al. [Hayes WC, Keer LM, Herrmann G, Mockros LF. A mathematical analysis for indentation tests of articular cartilage. J Biomech 1972;5(5):541-51] have been applied for the analysis of indentation measurements, and due to their practicality, they have been used for clinical diagnostics. Using this approach, the elastic modulus is derived based on scaling factors which depend on cartilage thickness, indenter radius and Poisson's ratio, and the cartilage model is assumed isotropic and homogeneous, thereby greatly simplifying the true tissue characteristics. The aim was to investigate the validity of previous model assumptions for indentation testing. Fibril-reinforced poroviscoelastic cartilage (FRPVE) model including realistic tissue characteristics was used to simulate indentation tests. The effects of cartilage inhomogeneity, anisotropy, and indentation velocity on the indentation response were evaluated, and scaling factors from the FRPVE analysis were derived. Subsequently, the validity of scaling factors obtained using the traditional and the FRPVE analyses was studied by calculating indentation moduli for bovine cartilage samples, and comparing these values to those obtained experimentally in unconfined compression testing. Collagen architecture and compression velocity had significant effects on the indentation response. Isotropic elastic analysis gave significantly higher (30-107%) Young's moduli for indentation compared to unconfined compression testing. Modification of Hayes' scaling factors by accounting for cartilage inhomogeneity and anisotropy improved the agreement of Young's moduli obtained for the two test configurations by 14-28%. These results emphasize the importance of realistic cartilage structure and mechanical properties in the indentation analysis. Although it is not possible to fully describe tissue inhomogeneity and anisotropy with just the Young's modulus and Poisson's ratio, accounting for inhomogeneity and anisotropy in these two parameters may help to improve the in vivo characterization of tissue using arthroscopic indentation testing.
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paper_title: Nondestructive imaging of human cartilage glycosaminoglycan concentration by MRI

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Despite the compelling need mandated by the prevalence and morbidity of degenerative cartilage diseases, it is extremely difficult to study disease progression and therapeutic efficacy, either in vitro or in vivo (clinically). This is partly because no techniques have been available for nondestructively visualizing the distribution of functionally important macromolecules in living cartilage. Here we describe and validate a technique to image the glycosaminoglycan concentration ([GAG]) of human cartilage nondestructively by magnetic resonance imaging (MRI). The technique is based on the premise that the negatively charged contrast agent gadolinium diethylene triamine pentaacetic acid (Gd(DTPA)2-) will distribute in cartilage in inverse relation to the negatively charged GAG concentration. Nuclear magnetic resonance spectroscopy studies of cartilage explants demonstrated that there was an approximately linear relationship between T1 (in the presence of Gd(DTPA)2-) and [GAG] over a large range of [GAG]. Furthermore, there was a strong agreement between the [GAG] calculated from [Gd(DTPA)2-] and the actual [GAG] determined from the validated methods of calculations from [Na+] and the biochemical DMMB assay. Spatial distributions of GAG were easily observed in T1-weighted and T1-calculated MRI studies of intact human joints, with good histological correlation. Furthermore, in vivo clinical images of T1 in the presence of Gd(DTPA)2- (i.e., GAG distribution) correlated well with the validated ex vivo results after total knee replacement surgery, showing that it is feasible to monitor GAG distribution in vivo. This approach gives us the opportunity to image directly the concentration of GAG, a major and critically important macromolecule in human cartilage. Magn Reson Med 41:857–865, 1999. © 1999 Wiley-Liss, Inc.
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paper_title: A fibril-reinforced poroviscoelastic swelling model for articular cartilage.

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From a mechanical point of view, the most relevant components of articular cartilage are the tight and highly organized collagen network together with the charged proteoglycans. Due to the fixed charges of the proteoglycans, the cation concentration inside the tissue is higher than in the surrounding synovial fluid. This excess of ion particles leads to an osmotic pressure difference, which causes swelling of the tissue. The fibrillar collagen network resists straining and swelling pressures. This combination makes cartilage a unique, highly hydrated and pressurized tissue, enforced with a strained collagen network. Many theories to explain articular cartilage behavior under loading, expressed in computational models that either include the swelling behavior or the properties of the anisotropic collagen structure, can be found in the literature. The most common tests used to determine the mechanical quality of articular cartilage are those of confined compression, unconfined compression, indentation and swelling. All theories currently available in the literature can explain the cartilage response occurring in some of the above tests, but none of them can explain these for all of the tests. We hypothesized that a model including simultaneous mathematical descriptions of (1) the swelling properties due to the fixed-change densities of the proteoglycans and (2) the anisotropic viscoelastic collagen structure, can explain all these test simultaneously. To study this hypothesis we extended our fibril-reinforced poroviscoelastic finite element model with our biphasic swelling model. We have shown that the newly developed fibril-reinforced poroviscoelastic swelling (FPVES) model for articular cartilage can simultaneously account for the reaction force during swelling, confined compression, indentation and unconfined compression as well as the lateral deformation during unconfined compression. Using this theory it is possible to analyze the link between the collagen network and the swelling properties of articular cartilage.
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paper_title: The Pericellular Matrix as a Transducer of Biomechanical and Biochemical Signals in Articular Cartilage

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: The pericellular matrix (PCM) is a narrow tissue region surrounding chondrocytes in articular cartilage, which together with the enclosed cell(s) has been termed the “chondron.” While the function of this region is not fully understood, it is hypothesized to have important biological and biomechanical functions. In this article, we review a number of studies that have investigated the structure, composition, mechanical properties, and biomechanical role of the chondrocyte PCM. This region has been shown to be rich in proteoglycans (e.g., aggrecan, hyaluronan, and decorin), collagen (types II, VI, and IX), and fibronectin, but is defined primarily by the presence of type VI collagen as compared to the extracellular matrix (ECM). Direct measures of PCM properties via micropipette aspiration of isolated chondrons have shown that the PCM has distinct mechanical properties as compared to the cell or ECM. A number of theoretical and experimental studies suggest that the PCM plays an important role in regulating the microenvironment of the chondrocyte. Parametric studies of cell–matrix interactions suggest that the presence of the PCM significantly affects the micromechanical environment of the chondrocyte in a zone-dependent manner. These findings provide support for a potential biomechanical function of the chondrocyte PCM, and furthermore, suggest that changes in the PCM and ECM properties that occur with osteoarthritis may significantly alter the stress-strain and fluid environments of the chondrocytes. An improved understanding of the structure and function of the PCM may provide new insights into the mechanisms that regulate chondrocyte physiology in health and disease.
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paper_title: Contribution of postnatal collagen reorientation to depth-dependent mechanical properties of articular cartilage

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The collagen fibril network is an important factor for the depth-dependent mechanical behaviour of adult articular cartilage (AC). Recent studies show that collagen orientation is parallel to the articular surface throughout the tissue depth in perinatal animals, and that the collagen orientations transform to a depth-dependent arcade-like structure in adult animals. Current understanding on the mechanobiology of postnatal AC development is incomplete. In the current paper, we investigate the contribution of collagen fibril orientation changes to the depth-dependent mechanical properties of AC. We use a composition-based finite element model to simulate in a 1-D confined compression geometry the effects of ten different collagen orientation patterns that were measured in developing sheep. In initial postnatal life, AC is mostly subject to growth and we observe only small changes in depth-dependent mechanical behaviour. Functional adaptation of depth-dependent mechanical behaviour of AC takes place in the second half of life before puberty. Changes in fibril orientation alone increase cartilage stiffness during development through the modulation of swelling strains and osmotic pressures. Changes in stiffness are most pronounced for small stresses and for cartilage adjacent to the bone. We hypothesize that postnatal changes in collagen fibril orientation induce mechanical effects that in turn promote these changes. We further hypothesize that a part of the depth-dependent postnatal increase in collagen content in literature is initiated by the depth-dependent postnatal increase in fibril strain due to collagen fibril reorientation.
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paper_title: CHONDROCYTES IN AGAROSE CULTURE SYNTHESIZE A MECHANICALLY FUNCTIONAL EXTRACELLULAR MATRIX

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The ability of chondrocytes from calf articular cartilage to synthesize and assemble a mechanically functional cartilage-like extracellular matrix was quantified in high cell density (∼ 107 cell/ml) agarose gel culture. The time evolution of chondrocyte proliferation, proteoglycan synthesis and loss to the media, and total deposition of glycosaminoglycan (GAG)-containing matrix within agarose gels was characterized during 10 weeks in culture. To assess whether the matrix deposited within the agarose gel was mechanically and electromechanically functional, we measured in parallel cultures the time evolution of dynamic mechanical stiffness and oscillatory streaming potential in uniaxial confined compression, and determined the intrinsic equilibrium modulus, hydraulic permeability, and electrokinetic coupling coefficient of the developing cultures. Biosynthetic rates were initially high, but by 1 month had fallen to a level similar to that found in the parent calf articular cartilage from which the cells were extracted. The majority of the newly synthesized proteoglycans remained in the gel. Histological sections showed matrix rich in proteoglycans and collagen fibrils developing around individual cells. The equilibrium modulus, dynamic stiffness, and oscillatory streaming potential rose to many times (>5X) their initial values at the start of the culture; the hydraulic permeability decreased to a fraction (∼1/10) that of the cell-laden porous agarose at the beginning of the culture. By day 35 of culture, DNA concentration (cell density), GAG concentration, stiffness, and streaming potential were all ∼25% that of calf articular cartilage. The frequency dependence of the dynamic stiffness and potential was similar to that of calf articular cartilage. Together, these results suggested the formation of mechanically functional matrix.
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paper_title: T2relaxation reveals spatial collagen architecture in articular cartilage: A comparative quantitative MRI and polarized light microscopic study

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It has been suggested that orientational changes in the collagen network of articular cartilage account for the depthwise T2 anisotropy of MRI through the magic angle effect. To investigate the relationship between laminar T2 appearance and collagen organization (anisotropy), bovine osteochondral plugs (N = 9) were T2 mapped at 9.4T with cartilage surface normal to the static magnetic field. Collagen fibril arrangement of the same samples was studied with polarized light microscopy, a quantitative technique for probing collagen organization by analyzing its ability to rotate plane polarized light, i.e., birefringence (BF). Depthwise variation of safranin O-stained proteoglycans was monitored with digital densitometry. The spatially varying cartilage T2 followed the architectural arrangement of the collagen fibril network: a linear positive correlation between T2 and the reciprocal of BF was established in each sample, with r = 0.91 +/- 0.02 (mean +/- SEM, N = 9). The current results reveal the close connection between the laminar T2 structure and the collagen architecture in histologic zones.
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paper_title: Mechanical loading of in situ chondrocytes in lapine retropatellar cartilage after anterior cruciate ligament transection

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The aims of this study were (i) to quantify chondrocyte mechanics in fully intact articular cartilage attached to its native bone and (ii) to compare the chondrocyte mechanics for cells in healthy and early osteoarthritis (OA) tissue. We hypothesized that cells in the healthy tissue would deform less for given articular surface pressures than cells in the early OA tissue because of a loss of matrix integrity in early OA and the associated loss of structural integrity that is thought to protect chondrocytes. Chondrocyte dynamics were quantified by measuring the deformation response of the cells to controlled loading of fully intact cartilage using a custom-designed confocal indentation system. Early OA was achieved nine weeks following transection of the anterior cruciate ligament (ACL) in rabbit knees. Experiments were performed on the retropatellar cartilage of early OA rabbit knees (four joints and 48 cells), the corresponding intact contralateral control knees (four joints and 48 cells) and knees from normal control rabbits (four joints and 48 cells). Nine weeks following ACL transection, articular cartilage of the experimental joints showed substantial increases in thickness, and progression towards OA as assessed using histological grading. Local matrix strains in the superficial zone were greater for the experimental (38 ± 4%) compared with the contralateral (27 ± 5%) and normal (28 ± 4%) joints (p = 0.04). Chondrocyte deformations in the axial and depth directions were similar during indentation loading for all experimental groups. However, cell width increased more for the experimental cartilage chondrocytes (12 ± 1%) than the contralateral (6 ± 1%) and normal control chondrocytes (6 ± 1%; p < 0.001). On average, chondrocyte volume increased with indentation loading in the early OA cartilage (8 ± 3%, p = 0.001), while it decreased for the two control groups (−8 ± 2%, p = 0.002 for contralateral and −8 ± 1%, p = 0.004 for normal controls). We conclude from these results that our hypothesis of cell deformations in the early OA tissue was only partially supported: specifically, changes in chondrocyte mechanics in early OA were direction-specific with the primary axial deformations remaining unaffected despite vastly increased average axial matrix deformations. Surprisingly, chondrocyte deformations increased in early OA in specific transverse directions which have received little attention to date but might be crucial to chondrocyte signalling in early OA.
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paper_title: MR Imaging of Normal and Matrix-depleted Cartilage: Correlation with Biomechanical Function and Biochemical Composition

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PURPOSE: To correlate articular cartilage function, as reflected in biomechanical properties and biochemical composition, with magnetic resonance (MR) imaging parameters of normal articular cartilage and cartilage partially depleted of matrix components. MATERIALS AND METHODS: Normal articular cartilage from 12 porcine patellae was evaluated biomechanically, biochemically, and with MR imaging (with and without gadolinium enhancement). The patellae were then enzymatically treated to deplete the matrix of either collagen or proteoglycan and then reevaluated biomechanically, biochemically, and with MR imaging. Correlations between cartilaginous tissue function and MR imaging parameters were made. Analysis of variance was performed to assess the effect of enzymatic treatment on measured parameters. Linear correlations among the MR imaging, biochemical, and biomechanical parameters were performed to determine the strengths of the relationships. P < .05 indicated statistically significant differences. RESULTS: ...
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paper_title: Detecting structural changes in early experimental osteoarthritis of tibial cartilage by microscopic magnetic resonance imaging and polarised light microscopy

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Objectives: To detect changes in the collagen fibril network in articular cartilage in a canine experimental model of early osteoarthritis (OA) using microscopic magnetic resonance imaging (µMRI) and polarised light microscopy (PLM). ::: ::: Methods: Eighteen specimens from three pairs of the medial tibia of an anterior cruciate ligament transection canine model were subjected to µMRI and PLM study 12 weeks after surgery. For each specimen, the following experiments were carried out: (a) two dimensional µMRI images of T2 relaxation at four orientations; (b) the tangent Young's modulus; and (c) two dimensional PLM images of optical retardance and fibril angle. Disease induced changes in tissue were examined across the depth of the cartilage at a µMRI resolution of 13.7–23.1 µm. ::: ::: Results: Several distinct changes from T2 weighted images of cartilage in OA tibia were seen. For the specimens that were covered at least in part by the meniscus, the significant changes in µMRI included a clear shift in the depth of maximum T2 (21–36%), a decrease in the superficial zone thickness (37–38%), and an increase in cartilage total thickness (15–27%). These µMRI changes varied topographically in the tibia surface because they were not significant in completely exposed locations in medial tibia. The µMRI results were confirmed by the PLM measurements and correlated well with the mechanical measurements. ::: ::: Conclusion: Both µMRI and PLM can detect quantitatively changes in collagen fibre architecture in early OA and resolve topographical variations in cartilage microstructure of canine tibia.
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paper_title: Contribution of tissue composition and structure to mechanical response of articular cartilage under different loading geometries and strain rates

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Mechanical function of articular cartilage in joints between articulating bones is dependent on the composition and structure of the tissue. The mechanical properties of articular cartilage are traditionally tested in compression using one of the three loading geometries, i.e., confined compression, unconfined compression or indentation. The aim of this study was to utilize a composition-based finite element model in combination with a fractional factorial design to determine the importance of different cartilage constituents in the mechanical response of the tissue, and to compare the importance of the tissue constituents with different loading geometries and loading rates. The evaluated parameters included water and collagen fraction as well as fixed charge density on cartilage surface and their slope over the tissue thickness. The thicknesses of superficial and middle zones, as based on the collagen orientation, were also included in the evaluated parameters. A three-level resolution V fractional factorial design was used. The model results showed that inhomogeneous composition plays only a minor role in indentation, though that role becomes more significant in confined compression and unconfined compression. In contrast, the collagen architecture and content had a more profound role in indentation than with two other loading geometries. These differences in the mechanical role of composition and structure between the loading geometries were emphasized at higher loading rates. These findings highlight how the results from mechanical tests of articular cartilage under different loading conditions are dependent upon tissue composition and structure.
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paper_title: Mechanical behavior of articular cartilage quantitative changes with enzymatic alteration of the proteoglycan fraction.

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The in-vitro viscoelastic mechanical response of normal rabbit articular cartilage is strongly dependent on the quantity and integrity of the proteoglycan fraction of the tissue matrix. Experimental results demonstrate that specific functional relationships exist between shear moduli, retardation time spectra, and proteoglycan content. Quantitative enzymolysis of the proteoglycan fraction of the tissue alters the form of these relationships in a fashion consistent with the altered physiochemical make-up of the tissue. The observed changes in mechanical behavior with controlled enzymolysis are similar to those associated with the early stages of osteoarthritis, rheumatoid arthritis, joint sepsis, and synovitis in animal models.
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paper_title: Hypotonic challenge modulates cell volumes differently in the superficial zone of intact articular cartilage and cartilage explant

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The objective of this study was to evaluate the effect of sample preparation on the biomechanical behaviour of chondrocytes. We compared the volumetric and dimensional changes of chondrocytes in the superficial zone (SZ) of intact articular cartilage and cartilage explant before and after a hypotonic challenge. Calcein-AM labelled SZ chondrocytes were imaged with confocal laser scanning microscopy through intact cartilage surfaces and through cut surfaces of cartilage explants. In order to clarify the effect of tissue composition on cell volume changes, Fourier Transform Infrared microspectroscopy was used for estimating the proteoglycan and collagen contents of the samples. In the isotonic medium (300 mOsm), there was a significant difference (p < 0.05) in the SZ cell volumes and aspect ratios between intact cartilage samples and cartilage explants. Changes in cell volumes at both short-term (2 min) and long-term (2 h) time points after the hypotonic challenge (180 mOsm) were significantly different (p < 0.05) between the groups. Further, proteoglycan content was found to correlate significantly (r 2 = 0.63, p < 0.05) with the cell volume changes in cartilage samples with intact surfaces. Collagen content did not correlate with cell volume changes. The results suggest that the biomechanical behaviour of chondrocytes following osmotic challenge is different in intact cartilage and in cartilage explant. This indicates that the mechanobiological responses of cartilage and cell signalling may be significantly dependent on the integrity of the mechanical environment of chondrocytes.
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paper_title: Fibril reinforced poroelastic model predicts specifically mechanical behavior of normal, proteoglycan depleted and collagen degraded articular cartilage

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Abstract Degradation of collagen network and proteoglycan (PG) macromolecules are signs of articular cartilage degeneration. These changes impair cartilage mechanical function. Effects of collagen degradation and PG depletion on the time-dependent mechanical behavior of cartilage are different. In this study, numerical analyses, which take the compression-tension nonlinearity of the tissue into account, were carried out using a fibril reinforced poroelastic finite element model. The study aimed at improving our understanding of the stress-relaxation behavior of normal and degenerated cartilage in unconfined compression. PG and collagen degradations were simulated by decreasing the Young's modulus of the drained porous (nonfibrillar) matrix and the fibril network, respectively. Numerical analyses were compared to results from experimental tests with chondroitinase ABC (PG depletion) or collagenase (collagen degradation) digested samples. Fibril reinforced poroelastic model predicted the experimental behavior of cartilage after chondroitinase ABC digestion by a major decrease of the drained porous matrix modulus (−64±28%) and a minor decrease of the fibril network modulus (−11±9%). After collagenase digestion, in contrast, the numerical analyses predicted the experimental behavior of cartilage by a major decrease of the fibril network modulus (−69±5%) and a decrease of the drained porous matrix modulus (−44±18%). The reduction of the drained porous matrix modulus after collagenase digestion was consistent with the microscopically observed secondary PG loss from the tissue. The present results indicate that the fibril reinforced poroelastic model is able to predict specifically characteristic alterations in the stress-relaxation behavior of cartilage after enzymatic modifications of the tissue. We conclude that the compression-tension nonlinearity of the tissue is needed to capture realistically the mechanical behavior of normal and degenerated articular cartilage.
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paper_title: Cartilage failure in osteoarthritis: Relevance of normal structure and function. A review

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Osteoarthritis is a multifactorial condition of diverse etiology affecting synovial joints, in which the final common pathway is destruction and loss of articular cartilage (and changes in other joint structures), which normally protects the bone against compressive and shearing forces. Known causes of secondary osteoarthritis can be grouped into those that cause abnormal stresses and those that produce an abnormal cartilage. The resulting imbalance between tissue texture and mechanical environment may eventually lead to cartilage destruction. ::: ::: The histopathology of cartilage fibrillation is described and related to its normal structure, particularly collagen fibril orientation. Load carriage in normal cartilage involves an interaction between the fibril mesh, proteoglycan, and water. Possible defects in normal matrix organization may lead to failure of this mechanism and to structural breakdown of the cartilage. Biochemical changes in the matrix in early osteoarthritis, particularly in experimental models, are described. The initial change, before loss of proteoglycan or fibril breakage, is an increased water content. A similar change is seen in normal cartilage after brief exercise. There may be a mechanism common to both the normal reversible change (thus providing a means for adaption to changed stresses) and the pathological prolonged change. ::: ::: Chondrocyte metabolism and its modification in early degenerative change are described. Factors regulating metabolism include nutrition, growth factors and cytokines, ionic constitution of the matrix, and mechanical stimuli. Known causes of secondary osteoarthritis may act via these factors to cause changes in cell metabolism that play a part in the initiation and ongoing pathogenesis of cartilage failure.
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paper_title: Computer simulation of damage on distal femoral articular cartilage after meniscectomies

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It is commonly accepted that total or partial meniscectomies cause wear of articular cartilages that leads to severe damage in a period of few years. This also produces alteration of the biomechanical environment and increases articular instability, with a progressive and degenerative arthrosic pathology. Due to these negative consequences, total meniscectomy technique has been avoided, with a clear preference for partial meniscectomies. Despite the better results obtained with this latter technique, it has been demonstrated that the knee still suffers progressive long-term wear, which alters the properties of the surface of articular cartilage. In this paper, a phenomenological isotropic damage model of articular cartilage is presented and implemented in a finite element code. We hypothesized that there is a relation between the increase of shear stress and cartilage degeneration. To confirm the hypothesis, the obtained results were compared to experimental ones. It is used to investigate the effect of meniscectomies on articular damage in the human knee joint. Two different situations were compared for the tibio-femoral joint: healthy and after meniscectomy. The distribution of damaged regions and the damage level distribution resulted qualitatively similar to experimental results, showing, for instance that, after meniscectomy, significant degeneration occurs in the lateral compartment. A noteworthy result was that patterns of damage in a total meniscectomy model give better agreement to clinical results when using relative increases in shear stress, rather than an absolute shear stress criterion. The predictions for partial meniscectomies indicated the relative severity of the procedures.
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paper_title: Experimental Verification of the Roles of Intrinsic Matrix Viscoelasticity and Tension-Compression Nonlinearity in the Biphasic Response of Cartilage

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A biphasic-CLE-QLV model proposed in our recent study [2001, J. Biomech. Eng., 123, pp. 410-417] extended the biphasic theory of Mow et al. [1980, J. Biomech. Eng., 102, pp. 73-84] to include both tension-compression nonlinearity and intrinsic viscoelasticity of the cartilage solid matrix by incorporating it with the conewise linear elasticity (CLE) model [1995, J. Elasticity, 37, pp. 1-38] and the quasi-linear viscoelasticity (QLV) model [Biomechanics: Its foundations and objectives, Prentice Hall, Englewood Cliffs, 1972]. This model demonstrates that a simultaneous prediction of compression and tension experiments of articular cartilage, under stress-relaxation and dynamic loading, can be achieved when properly taking into account both flow-dependent and flow-independent viscoelastic effects, as well as tension-compression nonlinearity. The objective of this study is to directly test this biphasic-CLE-QLV model against experimental data from unconfined compression stress-relaxation tests at slow and fast strain rates as well as dynamic loading. Twelve full-thickness cartilage cylindrical plugs were harvested from six bovine glenohumeral joints and multiple confined and unconfined compression stress-relaxation tests were performed on each specimen. The material properties of specimens were determined by curve-fitting the experimental results from the confined and unconfined compression stress relaxation tests. The findings of this study demonstrate that the biphasic-CLE-QLV model is able to describe the strain-rate-dependent mechanical behaviors of articular cartilage in unconfined compression as attested by good agreements between experimental and theoretical curvefits (r 2 =0.966±0.032 for testing at slow strain rate; r 2 =0.998±0.002 for testing at fast strain rate) and predictions of the dynamic response (r 2 =0.91±0.06). This experimental study also provides supporting evidence for the hypothesis that both tension-compression nonlinearity and intrinsic viscoelasticity of the solid matrix of cartilage are necessary for modeling the transient and equilibrium responses of this tissue in tension and compression. Furthermore, the biphasic-CLE-QLV model can produce better predictions of the dynamic modulus of cartilage in unconfined dynamic compression than the biphasic-CLE and biphasic poroviscoelastic models, indicating that intrinsic viscoelasticity and tension-compression nonlinearity of articular cartilage may play important roles in the load-support mechanism of cartilage under physiologic loading.
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paper_title: ON THE FUNDAMENTAL FLUID TRANSPORT MECHANISMS THROUGH NORMAL AND PATHOLOGICAL ARTICULAR CARTILAGE DURING FUNCTION-II. THE ANALYSIS, SOLUTION AND CONCLUSIONS*?

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Abstract The articulating process of synovial joints is represented by a spatially fixed cyclically time varying normal surface traction applied over a layered model of the cartilage-subchondral bone system. A two-phase mechanically interacting mixture is used to represent the solid matrix and the interstitial fluid of the cartilage continuum. The resulting equations of motion may be reduced to the currently employed physical laws used to describe the transport of fluid through the tissue, i.e. Darcy's law and Biot's consolidation equations. These equations were simplified by an order of magnitude analysis, and the resulting equations were solved by a double Fourier-Laplace transform procedure. The analytical solution shows that the fluid transport mechanism is strongly dependent upon a nondimensional parameter defined by ϵ 12 = Nk h 2 ω . This parameter is the ratio of the force required to deform the tissue as a whole to the force of frictional resistance due to the rate of movement of the interstitial fluid relative to the solid matrix. It is found that during normal function of healthy articular cartilage the consolidation effects will dominate the movement of interstitial fluid. In degenerative cartilage, as characterized by increasing the surface porosity and permeability and a decrease in tissue stiffness, the direct pressure effects, i.e. Darcy's law, becomes comparable to those of consolidation.
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paper_title: A Transversely Isotropic Biphasic Model for Unconfined Compression of Growth Plate and Chondroepiphysis

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Using the biphasic theory for hydrated soft tissues (Mow et al., 1980) and a transversely isotropic elastic model for the solid matrix, an analytical solution is presented for the unconfined compression of cylindrical disks of growth plate tissues compressed between two rigid platens with a frictionless interface. The axisymmetric case where the plane of transverse isotropy is perpendicular to the cylindrical axis is studied, and the stress-relaxation response to imposed step and ramp displacements is solved. This solution is then used to analyze experimental data from unconfined compression stress-relaxation tests performed on specimens from bovine distal ulnar growth plate and chondroepiphysis to determine the biphasic material parameters. The transversely isotropic biphasic model provides an excellent agreement between theory and experimental results, better than was previously achieved with an isotropic model, and can explain the observed experimental behavior in unconfined compression of these tissues.
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paper_title: Cartilage is poroelastic, not viscoelastic (including and exact theorem about strain energy and viscous loss, and an order of magnitude relation for equilibration time)

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Abstract Cartilage is often called viscoelastic, yet when strain lags stress in cartilage it is not primarily because of effects within the material of the cartilage skeleton itself. It is because the cartilage skeleton is bathed in fluid. Except in pure shear deformation, attaining equilibrium strain requires that pore fluid flow within the cartilage. Viscous forces retard this flow. This behavior is known as poroelastic. The equilibrium time is of the order L 2 (Yσ) , where Y is the Young's modulus, σ the permeability of the cartilage, and L is the length of the path along which liquid flows during equilibration. I show that this is true for any consolidation experiment, whatever the direction of consolidation and the direction of liquid flow. In the course of this demonstration I prove that if load is applied abruptly to a Hookean material and is thereafter held constant, the strain energy at equilibrium equals the energy dissipated in the material during equilibration.
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paper_title: Partial Meniscectomy Changes Fluid Pressurization in Articular Cartilage in Human Knees

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Partial meniscectomy is believed to change the biomechanics of the knee joint through alterations in the contact of articular cartilages and menisci. Although fluid pressure plays an important role in the load support mechanism of the knee, the fluid pressurization in the cartilages and menisci has been ignored in the finite element studies of the mechanics of meniscectomy. In the present study, a 3D fibril-reinforced poromechanical model of the knee joint was used to explore the fluid flow dependent changes in articular cartilage following partial medial and lateral meniscectomies. Six partial longitudinal meniscectomies were considered under relaxation, simple creep, and combined creep loading conditions. In comparison to the intact knee, partial meniscectomy not only caused a substantial increase in the maximum fluid pressure but also shifted the location of this pressure in the femoral cartilage. Furthermore, these changes were positively correlated to the size of meniscal resection. While in the intact joint, the location of the maximum fluid pressure was dependent on the loading conditions, in the meniscectomized joint the location was predominantly determined by the site of meniscal resection. The partial meniscectomy also reduced the rate of the pressure dissipation, resulting in even larger difference between creep and relaxation times as compared to the case of the intact knee. The knee joint became stiffer after meniscectomy because of higher fluid pressure at knee compression followed by slower pressure dissipation. The present study indicated the role of fluid pressurization in the altered mechanics of meniscectomized knees.
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paper_title: The role of viscoelasticity of collagen fibers in articular cartilage: theory and numerical formulation.

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The relative importance of fluid-dependent and fluid-independent transient mechanical behavior in articular cartilage was examined for tensile and unconfined compression testing using a fibril reinforced model. The collagen matrix of articular cartilage was modeled as viscoelastic using a quasi-linear viscoelastic formulation with strain-dependent elastic modulus, while the proteoglycan matrix was considered as linearly elastic. The collagen viscoelastic properties were obtained by fitting experimental data from a tensile test. These properties were used to investigate unconfined compression testing, and the sensitivity of the properties was also explored. It was predicted that the stress relaxation observed in tensile tests was not caused by fluid pressurization at the macroscopic level. A multi-step tensile stress relaxation test could be approximated using a hereditary integral in which the elastic fibrillar modulus was taken to be a linear function of the fibrillar strain. Applying the same formulation to the radial fibers in unconfined compression, stress relaxation could not be simulated if fluid pressurization were absent. Collagen viscoelasticity was found to slightly weaken fluid pressurization in unconfined compression, and this effect was relatively more significant at moderate strain rates. Therefore, collagen viscoelasticity appears to play an import role in articular cartilage in tensile testing, while fluid pressurization dominates the transient mechanical behavior in compression. Collagen viscoelasticity plays a minor role in the mechanical response of cartilage in unconfined compression if significant fluid flow is present.
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paper_title: On the fundamental fluid transport mechanisms through normal and pathological articular cartilage during function—I the formulation

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Abstract The fundamental fluid transport mechanisms associated with articular cartilage are important toward the understanding of the biomechanical processes involved in the physiology of normal and pathological synovial joints. Phenomenologically, articular cartilage is viewed as a mixture of two mechanically interacting continua, i.e. a solid matrix phase and a liquid phase composed of water. In synovial joints the liquid phase may be transported through the solid matrix by a direct pressure gradient as a result of the squeeze film action of synovial fluid during articulation and as a result of the consolidation of the solid matrix. The mechanically interacting mixture is composed of a solid. defined by an elastic internal energy function, and an incompressible liquid. The accompanying frictional resistance of relative motion is considered by a linear diffusive dissipation term. The equations of motion for each phase and the total mixture were derived from the extended Hamilton's Principle, where the Rayleigh dissipative resistance is considered as a generalized body force field. This procedure yields, as special cases, the classical Darcy's Law for the liquid transport due to direct pressure gradients, as well as Biot's consolidation equations for the liquid transport due to the dilatation of the solid phase.
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paper_title: A composition-based cartilage model for the assessment of compositional changes during cartilage damage and adaptation

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Summary Objective The composition of articular cartilage changes with progression of osteoarthritis. Since compositional changes are associated with changes in the mechanical properties of the tissue, they are relevant for understanding how mechanical loading induces progression. The objective of this study is to present a computational model of articular cartilage which enables to study the interaction between composition and mechanics. Methods Our previously developed fibril-reinforced poroviscoelastic swelling model for articular cartilage was combined with our tissue composition-based model. In the combined model both the depth- and strain-dependencies of the permeability are governed by tissue composition. All local mechanical properties in the combined model are directly related to the local composition of the tissue, i.e., to the local amounts of proteoglycans and collagens and to tissue anisotropy. Results Solely based on the composition of the cartilage, we were able to predict the equilibrium and transient response of articular cartilage during confined compression, unconfined compression, indentation and two different 1D-swelling tests, simultaneously. Conclusion Since both the static and the time-dependent mechanical properties have now become fully dependent on tissue composition, the model allows assessing the mechanical consequences of compositional changes seen during osteoarthritis without further assumptions. This is a major step forward in quantitative evaluations of osteoarthritis progression.
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paper_title: A Conewise Linear Elasticity Mixture Model for the Analysis of Tension-Compression Nonlinearity in Articular Cartilage

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A biphasic mixture model is developed which can account for the observed tension-compression nonlinearity of cartilage by employing the continuum-based Conewise Linear Elasticity (CLE) model of Curnier et al. (J Elasticity 37:1–38, 1995) to describe the solid phase of the mixture. In this first investigation, the orthotropic octantwise linear elasticity model was reduced to the more specialized case of cubic symmetry, to reduce the number of elastic constants from twelve to four. Confined and unconfined compression stress-relaxation, and torsional shear testing were performed on each of nine bovine humeral head articular cartilage cylindrical plugs from 6 month old calves. Using the CLE model with cubic symmetry, the aggregate modulus in compression and axial permeability were obtained from confined compression (H−A =0.64±0.22 MPa, kz = 3.62 ± .97 × 10−16 m4/N.s, r2 =0.95±0.03), the tensile modulus, compressive Poisson ratio and radial permeability were obtained from unconfined compression (E+Y = 12.75 ± 1.56 MPa, ν− =0.03±0.01, kr =6.06±2.10×10−16 m4/N.s, r2 =0.99±0.00), and the shear modulus was obtained from torsional shear (µ=0.17±0.06 MPa). The model was also employed to successfully predict the interstitial fluid pressure at the center of the cartilage plug in unconfined compression (r2 =0.98±0.01). The results of this study demonstrate that the integration of the CLE model with the biphasic mixture theory can provide a model of cartilage which can successfully curvefit three distinct testing configurations while producing material parameters consistent with previous reports in the literature.
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paper_title: Biomechanical properties of knee articular cartilage

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Structure and properties of knee articular cartilage are adapted to stresses exposed on it during physiological activ- ities. In this study, we describe site- and depth-dependence of the biomechanical properties of bovine knee articular cartilage. We also investigate the effects of tissue structure and composition on the biomechanical parameters as well as characterize experimentally and numerically the compression-tension nonlinearity of the cartilage matrix. In vitro mechano-optical mea- surements of articular cartilage in unconfined compression geometry are conducted to obtain material parameters, such as thickness, Young's and aggregate modulus or Poisson's ratio of the tissue. The experimental results revealed significant site- and depth-dependent variations in recorded parameters. After enzymatic modification of matrix collagen or proteoglycans our results show that collagen primarily controls the dynamic tissue response while proteoglycans affect more the static properties. Experimental measurements in compression and tension suggest a nonlinear compression-tension behavior of articular carti- lage in the direction perpendicular to articular surface. Fibril reinforced poroelastic finite element model was used to capture the experimentally found compression-tension nonlinearity of articular cartilage.
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paper_title: Is classical consolidation theory applicable to articular cartilage deformation?

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In this paper, classical consolidation theory has been used to investigate the time-dependent response of articular cartilage to static loading. An experimental technique was developed to measure simultaneously the matrix internal pressure and creep strain under conditions of one-dimensional consolidation. This is the first measurement of the internal stress state of loaded cartilage. It is demonstrated that under static compression the applied load is shared by the components of the matrix (i.e. water, the proteoglycans, and the collagen fibrillar meshwork), during which time a maximum hydrostatic excess pore pressure is developed as initial water exudation occurs. This pressure decays as water is further exuded from the matrix and effective consolidation begins with a progressive transfer of the applied stress from water to the collagen fibrils and proteoglycan gel. Consolidation is completed when the hydrostatic excess pore pressure is reduced to zero and the solid components sustain in full the applied load.
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paper_title: The Apparent Viscoelastic Behavior of Articular Cartilage—The Contributions From the Intrinsic Matrix Viscoelasticity and Interstitial Fluid Flows

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Articular cartilage was modeled rheologically as a biphasic poroviscoelastic material. A specific integral-type linear viscoelastic model was used to describe the constitutive relation of the collagen-proteoglycan matrix in shear. For bulk deformation, the matrix was assumed either to be linearly elastic, or viscoelastic with an identical reduced relaxation spectrum as in shear. The interstitial fluid was considered to be incompressible and inviscid. The creep and the rate-controlled stress-relaxation experiments on articular cartilage under confined compression were analyzed using this model. Using the material data available in the literature, it was concluded that both the interstitial fluid flow and the intrinsic matrix viscoelasticity contribute significantly to the apparent viscoelastic behavior of this tissue under confined compression.
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paper_title: Biomechanics of the knee joint in flexion under various quadriceps forces.

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Bioemchanics of the entire knee joint including tibiofemoral and patellofemoral joints were investigated at different flexion angles (0 degrees to 90 degrees ) and quadriceps forces (3, 137, and 411 N). In particular, the effect of changes in location and magnitude of restraining force that counterbalances the isometric extensor moment on predictions was investigated. The model consisted of three bony structures and their articular cartilage layers, menisci, principal ligaments, patellar tendon, and quadriceps muscle. Quadriceps forces significantly increased the anterior cruciate ligament, patellar tendon, and contact forces/areas as well as the joint resistant moment. Joint flexion, however, substantially diminished them all with the exception of the patellofemoral contact force/area that markedly increased in flexion. When resisting extensor moment by a force applied on the tibia, the force in cruciate ligaments and tibial translation significantly altered as a function of magnitude and location of the restraining force. Quadriceps activation generated large ACL forces at full extension suggesting that post ACL reconstruction exercises should avoid large quadriceps exertions at near full extension angles. In isometric extension exercises against a force on the tibia, larger restraining force and its more proximal location to the joint substantially decreased forces in the anterior cruciate ligament at small flexion angles whereas they significantly increased forces in the posterior cruciate ligament at larger flexion angles.
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paper_title: Time-Dependent Nanomechanics of Cartilage

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In this study, atomic force microscopy-based dynamic oscillatory and force-relaxation indentation was employed to quantify the time-dependent nanomechanics of native (untreated) and proteoglycan (PG)-depleted cartilage disks, including indentation modulus Eind, force-relaxation time constant t, magnitude of dynamic complex modulus jE*j, phase angle d between force and indentation depth, storage modulus E 0 , and loss modulus E 00 . At ~2 nm dynamic deformation amplitude, jE*j increased significantly with frequency from 0.22 5 0.02 MPa (1 Hz) to 0.77 5 0.10 MPa (316 Hz), accompanied by an increase in d (energy dissipation). At this length scale, the energy dissipation mechanisms were deconvoluted: the dynamic frequency dependence was primarily governed by the fluid-flow-induced poroelasticity, whereas the long-time force relaxation reflected flow-independent viscoelasticity. After PG depletion, the change in the frequency response of jE*j and d was consistent with an increase in cartilage local hydraulic permeability. Although untreated disks showed only slight dynamic amplitude-dependent behavior, PG-depleted disks showed great amplitude-enhanced energy dissipation, possibly due to additional viscoelastic mechanisms. Hence, in addition to functioning as a primary determinant of cartilage compressive stiffness and hydraulic permeability, the presence of aggrecan minimized the amplitude dependence of jE*j at nanometer-scale deformation.
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paper_title: Tensile and compressive properties of healthy and osteoarthritic human articular cartilage

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Osteoarthritis (OA) is a disease affecting articular cartilage and the underlying bone, resulting from many biological and mechanical interacting factors which change the extracellular matrix (ECM) and cells and lead to increasing levels of cartilage degeneration, like softening, fibrillation, ulceration and cartilage loss. The early diagnosis of the disease is fundamental to prevent pain, further tissue degeneration and reduce hospital costs. Although morphological modifications can be detected by modern non-invasive diagnostic techniques, they may not be evident in the early stages of OA. The mechanical properties of articular cartilage are related to its composition and structure and are sensitive to even small changes in the ECM that could occur in early OA. The aim of the present study was to compare the mechanical properties of healthy and OA cartilage using a combined experimental-numerical approach. Experimental assessments consisted of step wise confined and unconfined compression and tension stress relaxation tests on disks (for compression) or strips (for tension) of cartilage obtained from human femoral heads discarded from the operating room after total hip replacement. The numerical model was based on the biphasic theory and included the tension-compression non-linearity. Considering OA samples vs normal samples, the static compressive modulus was 55-68% lower, the permeability was 60-80% higher, the dynamic compressive modulus was 59-64% lower, the static tension modulus was 72-83% lower. The model successfully simulated the experimental tests performed on healthy and OA cartilage and was used in combination with the experimental tests to evaluate the role of different ECM components in the mechanical response of normal and OA cartilage.
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paper_title: A cross-validation of the biphasic poroviscoelastic model of articular cartilage in unconfined compression, indentation, and confined compression.

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The biphasic poroviscoelastic (BPVE) model was curve fit to the simultaneous relaxation of reaction force and lateral displacement exhibited by articular cartilage in unconfined compression (n=18). Model predictions were also made for the relaxation observed in reaction force during indentation with a porous plane-ended metal indenter (n=4), indentation with a nonporous plane ended metal indenter (n=4), and during confined compression (n=4). Each prediction was made using material parameters resulting from curve fits of the unconfined compression response of the same tissue. The BPVE model was able to account for both the reaction force and the lateral displacement during unconfined compression very well. Furthermore, model predictions for both indentation and confined compression also followed the experimental data well. These results provide substantial evidence for the efficacy of the biphasic poroviscoelastic model for articular cartilage, as no successful cross-validation of a model simulation has been demonstrated using other mathematical models.
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paper_title: The viscoelastic shear behavior of normal rabbit articular cartilage.

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Abstract A theoretical solution ‡ for the indentation of a layered medium by an axisymmetric plane-ended ram has been applied in the in vitro study of the mechanical properties of the articular surface of the distal femur of the rabbit. Experimental results directly yield shear moduli and retardation spectra which are invariant with respect to cartilage thickness and applied stress within the stress range used. The success of this theory, coupled with the simplicity and reproducibility of the test, suggests that this method has wide applicability in the study of experimentally or pathologically altered cartilage.
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paper_title: Equivalence Between Short-Time Biphasic and Incompressible Elastic Material Responses

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Porous-permeable tissues have often been modeled using porous media theories such as the biphasic theory. This study examines the equivalence of the short-time biphasic and incompressible elastic responses for arbitrary deformations and constitutive relations from first principles. This equivalence is illustrated in problems of unconfined compression of a disk, and of articular contact under finite deformation, using two different constitutive relations for the solid matrix of cartilage, one of which accounts for the large disparity observed between the tensile and compressive moduli in this tissue. Demonstrating this equivalence under general conditions provides a rationale for using available finite element codes for incompressible elastic materials as a practical substitute for biphasic analyses, so long as only the short-time biphasic response is sought. In practice, an incompressible elastic analysis is representative of a biphasic analysis over the short-term response deltat<<Delta(2) / //parallelC(4)//K//, where Delta is a characteristic dimension, C(4) is the elasticity tensor, and K is the hydraulic permeability tensor of the solid matrix. Certain notes of caution are provided with regard to implementation issues, particularly when finite element formulations of incompressible elasticity employ an uncoupled strain energy function consisting of additive deviatoric and volumetric components.
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paper_title: The permeability of articular cartilage under compressive strain and at high pressures

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The permeability of bovine articular cartilage was measured in an apparatus designed to permit this measurement while the fluid pressure gradient across the cartilage and the axial compressive strain applied to the cartilage were varied independently. For all of the pressure gradients tested the permeability of the cartilage decreased as the compressive strain increased. From previous work, it was postulated that joint lubrication is accomplished first by fluid exudation into the joint space. both at the leading edge of the moving contact area and between portions of the opposing cartilaginous surfaces, and second by imbibition of the expelled fluid back into the cartilage toward the trailing edge of the contact area caused by the "elastic" recovery of the tissue. The present work extends this model to include the condition that the permeability of cartilage is dependent on the extent to which it is deformed.
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paper_title: Viscoelastic shear properties of articular cartilage and the effects of glycosidase treatments

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The objectives of this study were to determine the viscoelastic shear properties of articular cartilage and to investigate the effects of the alteration of proteoglycan structure on these shear properties. Glycosidase treatments (chondroitinase ABC and Streptomyces hyaluronidase) were used to alter the proteoglycan structure and content of the tissue. The dynamic viscoelastic shear properties of control and treated tissues were measured and statistically compared. Specifically, cylindrical bovine cartilage specimens were subjected to oscillatory shear deformation of small amplitude (γo = 0.001 radian) over a physiological range of frequencies (0.01–20 Hz) and at various compressive strains (5, 9, 12, and 16%). The dynamic complex shear modulus was calculated from the measurements. The experimental results show that the solid matrix of normal articular cartilage exhibits intrinsic viscoelastic properties in shear over the range of frequencies tested. These viscoelastic shear properties were found to be dependent on compressive strains. Our data also provide significant insights into the structure-function relationships for articular cartilage. Significant correlations were found between the material properties (the magnitude of dynamic shear modulus, the phase shift angle, and the equilibrium compressive modulus), and the biochemical compositions of the cartilage (collagen, proteoglycan, and water contents). The shear modulus was greatly reduced when the proteoglycans were degraded by either chondroitinase ABC or Streptomyces hyaluronidase. The results suggest that the ability of collagen to resist tension elastically provides the stiffness of the cartilage matrix in shear and its elastic energy storage capability. Proteoglycans enmeshed in the collagen matrix inflate the collagen network and induce a tensile prestress in the collagen fibrils. This interaction of the collagen and proteoglycan within the cartilage matrix provides the complex mechanism that allows the tissue to resist shear deformation.
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paper_title: Stress-sharing between the fluid and solid components of articular cartilage under varying rates of compression

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This paper investigates the factors affecting the mechanical behavior of the articular matrix with special emphasis on the effect of compressive strain-rate on the short and long term responses of the fluid and the solid components. The relationships expressed in the general theory of one-dimensional consolidation are generalized to account for strain-rate in the deformation process with the result that the stiffness due to the fluid and the solid components, and a parameter representing the degree of drag, can be calculated explicity
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paper_title: Technical Note: Modelling Soft Tissue Using Biphasic Theory - A Word of Caution.

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In recent years the biphasic approach initiated by Mow and coworkers, has been very popular in modelling soft, hydrated, cartilage tissues as well as other soft tissues, such as the brain. This work points out that due to the inherent inability of biphasic models in their present form to account for stress-strain rate dependence resulting from the viscoelasticity of the solid phase, the applicability of these models is limited to the loading conditions producing large relative velocities of phases.
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paper_title: Analysis of partial meniscectomy and ACL reconstruction in knee joint biomechanics under a combined loading

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Abstract Background Despite partial meniscectomies and ligament reconstructions as treatments of choice for meniscal and ligament injuries, respectively, the knee joint osteoarthritis persists. Methods A detailed nonlinear finite element model of the knee joint was developed to evaluate biomechanics of the tibiofemoral joint under 200 N drawer load with and without 1500 N compression preload. The model incorporated composite structure of cartilage and meniscus. The effects on joint response and articular contact pressure of unilateral partial meniscectomy, of changes in prestrain or material properties of the anterior cruciate ligament and of their combination were investigated. Findings Compressive preload further increases anterior cruciate ligament strains/forces in drawer loading. Partial meniscectomy and perturbations in anterior cruciate ligament prestrain/material properties, alone or combined, substantially alter the load transfer via covered and uncovered areas of cartilage as well as contact pressure distribution on cartilage. Partial meniscectomy especially when combined with a slacker anterior cruciate ligament diminish the load via affected meniscus generating unloaded regions on the cartilage. Interpretation Partial meniscectomy concurrent with a slack anterior cruciate ligament substantially alter cartilage contact pressures. These alterations further intensify in the event of greater external forces, larger meniscal resections and total anterior cruciate ligament rupture, thus suggesting a higher risk of joint degeneration.
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paper_title: Effects of proteoglycan extraction on the tensile behavior of articular cartilage

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We undertook an interdisciplinary biomechanical and biochemical study to explore the extent and manner in which the total pool of proteoglycans influences the kinetic and static behavior of bovine articular cartilage in tension. Two biomechanical tests were used: (a) the viscoelastic creep test and (b) a slow constant-rate uniaxial tension test; and two enzymatic proteoglycan extraction procedures were used: (a) chondroitinase ABC treatment and (b) a sequential enzymatic treatment with chondroitinase ABC, trypsin, and Streptomyces hyaluronidase. We found that the viscoelastic creep response of all cartilage specimens may be divided into two distinct phases: an initial phase (less than 15 s), characterized by a rapid increase in strain following load application, and a late phase (15 s less than or equal to t less than 25,000 s), characterized by a more gradual increase in strain. A major finding of this study is that the kinetics of the creep response is greatly influenced by the glycosaminoglycan content of the tissue. For untreated and control specimens, the initial response comprises about 50% of the total strain, while for chondroitinase ABC and sequentially extracted specimens, the initial response comprises up to 83% of the total strain. Furthermore, most untreated and control specimens did not reach equilibrium within the 25,000 s test period, while enzymatically digested specimens often reached equilibrium in less than 100 s. Thus, we conclude that through their physical restraints on collagen, the bulk of proteoglycan present in the tissue acts to retard fibrillar reorganization and alignment under tensile loading, thereby effectively preventing sudden extension of the collagen network. In contrast, the results of our slow constant-rate uniaxial tension experiment show that essentially complete extraction of proteoglycan glycosaminoglycans does not affect the intrinsic tensile stiffness and strength of cartilage specimens or the collagen network in a significant manner. Hence, an important function of the bulk proteoglycans (i.e., the large aggregating type) in cartilage is to retard the rate of stretch and alignment when a tensile load is suddenly applied. This mechanism may be useful in protecting the cartilage collagen network during physiological situations, where sudden impact forces are imposed on a joint.
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paper_title: Biphasic Poroviscoelastic Simulation of the Unconfined Compression of Articular Cartilage: I—Simultaneous Prediction of Reaction Force and Lateral Displacement

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This study investigated the ability of the linear biphasic poroelastic (BPE) model and the linear biphasic poroviscoelastic (BPVE) model to simultaneously predict the reaction force and lateral displacement exhibited by articular cartilage during stress relaxation in unconfined compression. Both models consider articular cartilage as a binary mixture of a porous incompressible solid phase and an incompressible inviscid fluid phase. The BPE model assumes the solid phase is elastic, while the BPVE model assumes the solid phase is viscoelastic. In addition, the efficacy of two additional models was also examined, i.e., the transversely isotropic BPE (TIBPE) model, which considers transverse isotropy of the solid matrix within the framework of the linear BPE model assumptions, and a linear viscoelastic solid (LVE) model, which assumes that the viscoelastic behavior of articular cartilage is solely governed by the intrinsic viscoelastic nature of the solid matrix, independent of the imerstitial fluid flow. It was found that the BPE model was able to accurately account for the lateral displacement, but unable to fit the short-term reaction force data of all specimens tested. The TIBPE model was able to account for either the lateral displacement or the reaction force, but not both simultaneously. The LVE model was able to account for the complete reaction force, but unable to fit the lateral displacement measured experimentally. The BPVE model was able to completely account for both lateral displacement and reaction force for all specimens tested. These results suggest that both the fluid flow-dependent and fluid flow-independent viscoelastic mechanisms are essential for a complete simulation of the viscoelastic phenomena of articular cartilage.
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paper_title: A VISCOELASTIC MODEL FOR COLLAGEN FIBRES

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The viscoelastic behaviour of collagen fibres of different lengths was studied by developing simulation models. These models were found to explain the creep and stress-relaxation behaviour of the collagen fibres.
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paper_title: A Phenomenological Approach Toward Patient-Specific Computational Modeling of Articular Cartilage Including Collagen Fiber Tracking

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To model the cartilage morphology and the material response, a phenomenological and patient-specific simulation approach incorporating the collagen fiber fabric is proposed. Cartilage tissue respon ...
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paper_title: Cartilage stress-relaxation proceeds slower at higher compressive strains.

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Articular cartilage is the connective tissue which covers bone surfaces and deforms during in vivo activity. Previous research has investigated flow-dependent cartilage viscoelasticity, but relatively few studies have investigated flow-independent mechanisms. This study investigated polymer dynamics as an explanation for the molecular basis of flow-independent cartilage viscoelasticity. Polymer dynamics predicts that stress-relaxation will proceed more slowly at higher volumetric concentrations of polymer. Stress-relaxation tests were performed on cartilage samples after precompression to different strain levels. Precompression increases the volumetric concentration of cartilage biopolymers, and polymer dynamics predicts an increase in relaxation time constant. Stress-relaxation was slower for greater precompression. There was a significant correlation between the stress-relaxation time constant and cartilage volumetric concentration. Estimates of the flow-dependent timescale suggest that flow-dependent relaxation occurs on a longer timescale than presently observed. These results are consistent with polymer dynamics as a mechanism of cartilage viscoelasticity.
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paper_title: Cartilage Stresses in the Human Hip Joint

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The total surface stress measured in vitro on acetabular cartilage when step-loaded by an instrumented hemiprosthesis are partitioned into fluid and cartilage network stresses using a finite element model of the cartilage layer and measurements of the layer consolidation. The finite element model is based on in situ measurements of cartilage geometry and constitutive properties. Unique instrumentation was em­ ployed to collect the geometry and constitutive properties and pressure and con­ solidation data. When loaded, cartilage consolidates and exudes its interstitial fluid through and from its solid network into the interarticular gap. The finite element solutions include the spatial distributions of fluid and network stresses, the normal flow velocities into the gap, and the contact network stresses at the cartilage surface, all versus time. Even after long-duration application of physiological-level force, fluid pressure supports 90 percent of the load with the cartilage network stresses remaining well below the drained modulus of cartilage. The results support the "weeping" mechanism of joint lubrication proposed by McCutchen.
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paper_title: The nonlinear interaction between cartilage deformation and interstitial fluid flow

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Abstract The movement of interstitial fluid through articular cartilage and its influence on the creep behavior of the tissue due to a unit step load function has been investigated. Experimental results are presented to show that the hydraulic permeability of articular cartilage depends on both the axial compressive strain on the tissue sample, as well as the driving pressure difference maintained across the specimen. These experimental results have been utilized in a known theory of a deformable and permeable material used to describe the behavior of articular cartilage. The creep-like behavior of the cartilage in compression has been analytically treated. It has been determined that the nonlinear interaction between the hydraulic permeability of the tissue and the compressive strain on the tissue retards the progress of the consolidation of the cartilage during uniaxial compression. However, the equilibrium displacement of the articular surface as t → ∞ depends only on the elastic constant of the parallel spring and dashpot viscoelastic behavior of the solid component of the tissue.
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paper_title: Structure-Function Relationships in Enzymatically Modified Articular Cartilage

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The present study is aimed at revealing structure-function relationships of bovine patellar articular cartilage. Collagenase, chondroitinase ABC and elastase were used for controlled and selective enzymatic modifications of cartilage structure, composition and functional properties. The effects of the enzymatic degradations were quantitatively evaluated using quantitative polarized light microscopy, digital densitometry of safranin O-stained sections as well as with biochemical and biomechanical techniques. The parameters related to tissue composition and structure were correlated with the indentation stiffness of cartilage. In general, tissue alterations after enzymatic digestions were restricted to the superficial cartilage. All enzymatic degradations induced superficial proteoglycan (PG) depletion. Collagenase also induced detectable superficial collagen damage, though without causing cartilage fibrillation or tissue swelling. Quantitative microscopic techniques were more sensitive than biochemical methods in detecting these changes. The Young's modulus of cartilage decreased after enzymatic treatments indicating significant softening of the tissue. The PG concentration of the superficial zone proved to be the major determinant of the Young's modulus (r(2) = 0.767, n = 72, p < 0.001). Results of the present study indicate that specific enzymatic degradations of the tissue PGs and collagen can provide reproducible experimental models to clarify the structure-function relationships of cartilage. Effects of these models mimic the changes observed in early osteoarthrosis. Biomechanical testing and quantitative microscopic techniques proved to be powerful tools for detecting the superficial structural and compositional changes while the biochemical measurements on the whole uncalcified cartilage were less sensitive.
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paper_title: Effect of superficial collagen patterns and fibrillation of femoral articular cartilage on knee joint mechanics-a 3D finite element analysis.

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Collagen fibrils of articular cartilage have specific depth-dependent orientations and the fibrils bend in the cartilage surface to exhibit split-lines. Fibrillation of superficial collagen takes place in osteoarthritis. We aimed to investigate the effect of superficial collagen fibril patterns and collagen fibrillation of cartilage on stresses and strains within a knee joint. A 3D finite element model of a knee joint with cartilage and menisci was constructed based on magnetic resonance imaging. The fibril-reinforced poroviscoelastic material properties with depth-dependent collagen orientations and split-line patterns were included in the model. The effects of joint loading on stresses and strains in cartilage with various split-line patterns and medial collagen fibrillation were simulated under axial impact loading of 1000 N. In the model, the collagen fibrils resisted strains along the split-line directions. This increased also stresses along the split-lines. On the contrary, contact and pore pressures were not affected by split-line patterns. Simulated medial osteoarthritis increased tissue strains in both medial and lateral femoral condyles, and contact and pore pressures in the lateral femoral condyle. This study highlights the importance of the collagen fibril organization, especially that indicated by split-line patterns, for the weight-bearing properties of articular cartilage. Osteoarthritic changes of cartilage in the medial femoral condyle created a possible failure point in the lateral femoral condyle. This study provides further evidence on the importance of the collagen fibril organization for the optimal function of articular cartilage.
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paper_title: Biomechanics: Mechanical Properties of Living Tissues

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Prefaces. 1. Introduction: A sketch of the History and Scope of the Field. 2. The Meaning of the Constitutive Equation. 3. The Flow Properties of Blood. 4. Mechanics of Erythrocytes, Leukocytes, and Other Cells. 5. Interaction of Red Blood Cells with Vessel Wall, and Wall Shear with Endothelium. 6 Bioviscoelastic Fluids. Bioviscoelastic Solids. 8. Mechanical Properties and Active Remodeling of Blood Vessels. 9. Skeletal Muscle. 10. Heart Muscle. 11. Smooth Muscles. 12. Bone and Cartilage. Indices
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paper_title: Confined and unconfined stress relaxation of cartilage: appropriateness of a transversely isotropic analysis

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Abstract Previous studies have shown that stress relaxation behavior of calf ulnar growth plate and chondroepiphysis cartilage can be described by a linear transverse isotropic biphasic model. The model provides a good fit to the observed unconfined compression transients when the out-of-plane Poisson's ratio is set to zero. This assumption is based on the observation that the equilibrium stress in the axial direction ( σ z ) is the same in confined and unconfined compression, which implies that the radial stress σ r =0 in confined compression. In our study, we further investigated the ability of the transversely isotropic model to describe confined and unconfined stress relaxation behavior of calf cartilage. A series of confined and unconfined stress relaxation tests were performed on calf articular cartilage (4.5 mm diameter, ∼3.3 mm height) in a displacement-controlled compression apparatus capable of measuring σ z and σ r . In equilibrium, σ r >0 and σ z in confined compression was greater than in unconfined compression. Transient data at each strain were fitted by the linear transversely isotropic biphasic model and the material parameters were estimated. Although the model could provide good fits to the unconfined transients, the estimated parameters overpredicted the measured σ r . Conversely, if the model was constrained to match equilibrium σ r , the fits were poor. These findings suggest that the linear transversely isotropic biphasic model could not simultaneously describe the observed stress relaxation and equilibrium behavior of calf cartilage.
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paper_title: Determination of collagen-proteoglycan interactions in vitro.

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The objective of this study was to characterize the physical interactions of the molecular networks formed by mixtures of collagen and proteoglycan in vitro. Pure proteoglycan aggrecan solutions, collagen (type II) suspensions and mixtures of these molecules in varying proportions and concentrations were subjected to viscometric flow measurements using a cone-on-plate viscometer. Linear viscoelastic and non-Newtonian flow properties of these solutions and suspensions were described using a second-order statistical network theory for polymeric fluids (Zhu et al., 1991, J. Biomechanics24, 1007–1018). This theory provides a set of material coefficients which relate the macroscopic flow behavior of the fluid to an idealized molecular network structure. The results indicated distinct differences between the flow properties of pure collagen suspensions and those of pure proteoglycan solutions. The collagen network showed much greater shear stiffness and more effective energy storage capability than the proteoglycan network. The relative proportion of collagen to proteoglycan is the dominant factor in determining the flow behavior of the mixtures. Analysis of the statistical network theory indicated that the collagen in a collagen-proteoglycan mixture enhances molecular interactions by increasing the amount of entanglement interactions and/or the strength of interaction, while aggrecan acts to reduce the number and/or strength of molecular interactions. These results characterize the physical interactions between type II collagen and aggrecan and provide some insight into their potential roles in giving articular cartilage its mechanical behavior.
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paper_title: A nonlinear biphasic fiber-reinforced porohyperviscoelastic model of articular cartilage incorporating fiber reorientation and dispersion.

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A nonlinear biphasic fiber-reinforced porohyperviscoelastic (BFPHVE) model of articular cartilage incorporating fiber reorientation effects during applied load was used to predict the response of ovine articular cartilage at relatively high strains (20%). The constitutive material parameters were determined using a coupled finite element-optimization algorithm that utilized stress relaxation indentation tests at relatively high strains. The proposed model incorporates the strain-hardening, tension-compression, permeability, and finite deformation nonlinearities that inherently exist in cartilage, and accounts for effects associated with fiber dispersion and reorientation and intrinsic viscoelasticity at relatively high strains. A new optimization cost function was used to overcome problems associated with large peak-to-peak differences between the predicted finite element and experimental loads that were due to the large strain levels utilized in the experiments. The optimized material parameters were found to be insensitive to the initial guesses. Using experimental data from the literature, the model was also able to predict both the lateral displacement and reaction force in unconfined compression, and the reaction force in an indentation test with a single set of material parameters. Finally, it was demonstrated that neglecting the effects of fiber reorientation and dispersion resulted in poorer agreement with experiments than when they were considered. There was an indication that the proposed BFPHVE model, which includes the intrinsic viscoelasticity of the nonfibrillar matrix (proteoglycan), might be used to model the behavior of cartilage up to relatively high strains (20%). The maximum percentage error between the indentation force predicted by the FE model using the optimized material parameters and that measured experimentally was 3%.
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paper_title: Experimental Verification and Theoretical Prediction of Cartilage Interstitial Fluid Pressurization At an Impermeable Contact Interface in Confined Compression

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Interstitial fluid pressurization has long been hypothesized to play a fundamental role in the load support mechanism and frictional response of articular cartilage. However, to date, few experimental studies have been performed to verify this hypothesis from direct measurements. The first objective of this study was to investigate experimentally the hypothesis that cartilage interstitial fluid pressurization does support the great majority of the applied load, in the testing configurations of confined compression creep and stress relaxation. The second objective was to investigate the hypothesis that the experimentally observed interstitial fluid pressurization could also be predicted using the linear biphasic theory of Mow et al. (J. Biomech. Engng ASME, 102, 73-84, 1980). Fourteen bovine cartilage samples were tested in a confined compression chamber fitted with a microchip piezoresistive transducer to measure interstitial fluid pressure, while simultaneously measuring (during stress relaxation) or prescribing (during creep) the total stress. It was found that interstitial fluid pressure supported more than 90% of the total stress for durations as long as 725 +/- 248 s during stress relaxation (mean +/- S.D., n = 7), and 404 +/- 229 s during creep (n = 7). When comparing experimental measurements of the time-varying interstitial fluid pressure against predictions from the linear biphasic theory, nonlinear coefficients of determination r2 = 0.871 +/- 0.086 (stress relaxation) and r2 = 0.941 +/- 0.061 (creep) were found. The results of this study provide some of the most direct evidence to date that interstitial fluid pressurization plays a fundamental role in cartilage mechanics; they also indicate that the mechanism of fluid load support in cartilage can be properly predicted from theory.
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paper_title: Computational biomechanics of articular cartilage of human knee joint: effect of osteochondral defects.

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Articular cartilage and its supporting bone functional conditions are tightly coupled as injuries of either adversely affects joint mechanical environment. The objective of this study was set to quantitatively investigate the extent of alterations in the mechanical environment of cartilage and knee joint in presence of commonly observed osteochondral defects. An existing validated finite element model of a knee joint was used to construct a refined model of the tibial lateral compartment including proximal tibial bony structures. The response was computed under compression forces up to 2000 N while simulating localized bone damage, cartilage-bone horizontal split, bone overgrowth and absence of deep vertical collagen fibrils. Localized tibial bone damage increased overall joint compliance and substantially altered pattern and magnitude of contact pressures and cartilage strains in both tibia and femur. These alterations were further exacerbated when bone damage was combined with base cartilage split and absence of deep vertical collagen fibrils. Local bone boss markedly changed contact pressures and strain patterns in neighbouring cartilage. Bone bruise/fracture and overgrowth adversely perturbed the homeostatic balance in the mechanical environment of articulate cartilage surrounding and opposing the lesion as well as the joint compliance. As such, they potentially contribute to the initiation and development of post-traumatic osteoarthritis.
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paper_title: The biphasic poroviscoelastic behavior of articular cartilage: role of the surface zone in governing the compressive behavior.

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Surface fibrillation of articular cartilage is an early sign of degenerative changes in the development of osteoarthritis. To assess the influence of the surface zone on the viscoelastic properties of cartilage under compressive loading, we prepared osteochondral plugs from skeletally mature steers, with and without the surface zone of articular cartilage, for study in the confined compression creep experiment. The relative contributions of two viscoelastic mechanisms, i.e. a flow-independent mechanism [Hayes and Bodine, J. Biomechanics 11, 407-419 (1978)], and a flow-dependent mechanism [Mow et al. J. biomech. Engng 102, 73-84 (1980)], to the compressive creep response of these two types of specimens were determined using the biphasic poroviscoelastic theory proposed by Mak. [J. Biomechanics 20, 703-714 (1986)]. From the experimental results and the biphasic poroviscoelastic theory, we found that frictional drag associated with interstitial fluid flow and fluid pressurization are the dominant mechanisms of load support in the intact specimens, i.e. the flow-dependent mechanisms alone were sufficient to describe normal articular cartilage compressive creep behavior. For specimens with the surface removed, we found an increased creep rate which was derived from an increased tissue permeability, as well as significant changes in the flow-independent parameters of the viscoelastic solid matrix. permeability, as well as significant changes in the flow-independent parameters of the viscoelastic solid matrix. From these tissue properties and the biphasic poroviscoelastic theory, we determined that the flow-dependent mechanisms of load support, i.e. frictional drag and fluid pressurization, were greatly diminished in cartilage without the articular surface. Calculations based upon these material parameters show that for specimens with the surface zone removed, the cartilage solid matrix became more highly loaded during the early stages of creep. This suggests that an important function of the articular surface is to provide for a low fluid permeability, and thereby serve to restrict fluid exudation and increase interstitial fluid pressurization. Thus, it is likely that with increasing severity of damage to the articular surface, load support in cartilage under compression shifts from the flow-dependent modes of fluid drag and pressurization to increased solid matrix stress. This suggests that it is important to maintain the integrity of the articular surface in preserving normal compressive behavior of the tissue and normal load carriage in the joint.
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paper_title: Failure locus of the anterior cruciate ligament: 3D finite element analysis

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Anterior cruciate ligament (ACL) disruption is a common injury that is detrimental to an athlete's quality of life. Determining the mechanisms that cause ACL injury is important in order to develop proper interventions. A failure locus defined as various combinations of loadings and movements, internal/external rotation of femur and valgus and varus moments at a 25o knee flexion angle leading to ACL failure was obtained. The results indicated that varus and valgus movements were more dominant to the ACL injury than femoral rotation. Also, Von Mises stress in the lateral tibial cartilage during the valgus ACL injury mechanism was 83% greater than that of the medial cartilage during the varus mechanism of ACL injury. The results of this study could be used to develop training programmes focused on the avoidance of the described combination of movements which may lead to ACL injury.
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paper_title: Computational biodynamics of human knee joint in gait: from muscle forces to cartilage stresses.

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Using a validated finite element model of the intact knee joint we aim to compute muscle forces and joint response in the stance phase of gait. The model is driven by reported in vivo kinematics-kinetics data and ground reaction forces in asymptomatic subjects. Cartilage layers and menisci are simulated as depth-dependent tissues with collagen fibril networks. A simplified model with less refined mesh and isotropic depth-independent cartilage is also considered to investigate the effect of model accuracy on results. Muscle forces and joint detailed response are computed following an iterative procedure yielding results that satisfy kinematics/kinetics constraints while accounting at deformed configurations for muscle forces and passive properties. Predictions confirm that muscle forces and joint response alter substantially during the stance phase and that a simplified joint model may accurately be used to estimate muscle forces but not necessarily contact forces/areas, tissue stresses/strains, and ligament forces. Predictions are in general agreement with results of earlier studies. Performing the analyses at 6 periods from beginning to the end (0%, 5%, 25%, 50%, 75% and 100%), hamstrings forces peaked at 5%, quadriceps forces at 25% whereas gastrocnemius forces at 75%. ACL Force reached its maximum of 343 N at 25% and decreased thereafter. Contact forces reached maximum at 5%, 25% and 75% periods with the medial compartment carrying a major portion of load and experiencing larger relative movements and cartilage strains. Much smaller contact stresses were computed at the patellofemoral joint. This novel iterative kinematics-driven model is promising for the joint analysis in altered conditions.
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paper_title: A Fibril-Network-Reinforced Biphasic Model of Cartilage in Unconfined Compression

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Cartilage mechanical function relies on a composite structure of a collagen fibrillar network entrapping a proteoglycan matrix. Previous biphasic or poroelastic models of this tissue, which have approximated its composite structure using a homogeneous solid phase, have experienced difficulties in describing measured material responses. Progress to date in resolving these difficulties has demonstrated that a constitutive low that is successful for one test geometry (confined compression) is not necessarily successful for another (unconfined compression). In this study, we hypothesize that an alternative fibril-reinforced composite biphasic representation of cartilage can predict measured material responses and explore this hypothesis by developing and solving analytically a fibril-reinforced biphasic model for the case of uniaxial unconfined compression with frictionless compressing platens. The fibrils were considered to provide stiffness in tension only. The lateral stiffening provided by the fibril network dramatically increased the frequency dependence of disk rigidity in dynamic sinusoidal compression and the magnitude of the stress relaxation transient, in qualitative agreement with previously published data. Fitting newly obtained experimental stress relaxation data to the composite model allowed extraction of mechanical parameters from these tests, such as the rigidity of the fibril network, in addition to the elastic constants and the hydraulic permeability of the remaining matrix. Model calculations further highlight a potentially important difference between homogeneous and fibril-reinforced composite models. In the latter type of model, the stresses carried by different constituents can be dissimilar, even in sign (compression versus tension) even though strains can be identical. Such behavior, resulting only from a structurally physiological description, could have consequences in the efforts to understand the mechanical signals that determine cellular and extracellular biological responses to mechanical loads in cartilage.
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paper_title: Flow-independent viscoelastic properties of articular cartilage matrix.

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Abstract A sinusoidal shear generator developed by Miles (1962) is used to measure viscoelastic complex shear moduli for bovine articular cartilage. The shear loading mode uncouples the measurement of matrix properties from the flow of interstitial fluid and thus provides flow-independent measurements which are highly sensitive to biochemical alteration of the matrix constituents. Increased cross-linking causes significant increases in the matrix storage modulus while proteoglycan depletion and collagenase digestion cause significant decreases. Highly significant differences in complex shear moduli are also observed between the proteoglycan depletion group and the collagenase digestion group.
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paper_title: An Analysis of the Unconfined Compression of Articular Cartilage

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Analytical solutions have been obtained for the internal deformation and fluid-flow fields and the externally observable creep, stress relaxation, and constant strain-rate behaviors which occur during the unconfined compression of a cylindrical specimen of a fluid-filled, porous, elastic solid, such as articular cartilage, between smooth, impermeable plates. Instantaneously, the "biphasic" continuum deforms without change in volume and behaves like an incompressible elastic solid of the same shear modulus. Radial fluid flow then allows the internal fluid pressure to equilibrate with the external environment. The equilibrium response is controlled by the Young's modulus and Poisson's ratio of the solid matrix.
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paper_title: Failure criterion of collagen fiber: Viscoelastic behavior simulated by using load control data

paper_content:

A nonlinear Zener model is developed to model the viscoelastic behavior of collagen fibers, a building block of the biological soft tissues in the skeletal system. The effects of the strain rate dependency, the loading history, rest, and recovery on the stress-strain relationship of collagen fibers were investigated using the Zener model. The following loading conditions were simulated: (1) the stress relaxation after cyclic loading, (2) the constant strain rate loading before and after cyclic loading (stabilization) and post recovery, and (3) the constant strain rate loading over a wide range of loading rates. In addition, we explored the critical values of stress and strain using different failure criteria at different strain rates. Four major findings were derived from these simulations. First of all, the stress relaxation is larger with a smaller number cycles of preloading. Second, the strain rate sensitivity diminishes after the stabilization and recovery from resting. Third, the stress-strain curve is dependent on the strain rate except for extreme loading conditions (very fast or slow rates of loading). Finally, the strain energy density (SED) criteria may be a more practical failure criterion than the ultimate stress or strain criterion for collagen fiber. These results provide the basis for interpretation of the viscoelastic and failure behaviors of complex structures such as spinal functional units with more economical CPU than full finite element modeling of the whole structure would have required.
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paper_title: Stresses in the local collagen network of articular cartilage: a poroviscoelastic fibril-reinforced finite element study.

paper_content:

Osteoarthritis (OA) is a multifactorial disease, resulting in diarthrodial joint wear and eventually destruction. Swelling of cartilage, which is proportional to the amount of collagen damage, is an initial event of cartilage degeneration, so damage to the collagen fibril network is likely to be one of the earliest signs of OA cartilage degeneration. We propose that the local stresses and strains in the collagen fibrils, which cause the damage, cannot be determined dependably without taking the local arcade-like collagen-fibril structure into account. We investigate this using a poroviscoelastic fibril-reinforced FEA model. The constitutive fibril properties were determined by fitting numerical data to experimental results of unconfined compression and indentation tests on samples of bovine patellar articular cartilage. It was demonstrated that with this model the stresses and strains in the collagen fibrils can be calculated. It was also exhibited that fibrils with different orientations at the same location can be loaded differently, depending on the local architecture of the collagen network. To the best of our knowledge, the present model is the first that can account for these features. We conclude that the local stresses and strains in the articular cartilage are highly influenced by the local morphology of the collagen-fibril network.
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paper_title: A physical model for the time-dependent deformation of articular cartilage.

paper_content:

A physical analogue was developed to simulate the time-dependent deformation of articular cartilage. The analogue was constructed from a matrix of water-saturated sponge material whose permeability could be varied, and was constrained so as to allow one-dimensional deformation under both static and dynamic compressive loading. Simultaneous measurements were made of the applied stress, matrix excess pore pressure and matrix strain. The results obtained reinforce the view that under static and low strain-rate loading conditions, a consolidatable system like cartilage sustains the applied stress through a stress-sharing mechanism between matrix water and the solid skeleton. However, at high strain-rates load-bearing is dominated by a mechanism in which the matrix water is immobilized and the excess pore pressure rises to almost that of the applied stress, thus suggesting that the constituents of the matrix act as a single functional entity to support the applied load. The model supports the description of cartilage as a poro-visco-hyperelastic material.
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paper_title: A fibril-reinforced poroviscoelastic swelling model for articular cartilage.

paper_content:

From a mechanical point of view, the most relevant components of articular cartilage are the tight and highly organized collagen network together with the charged proteoglycans. Due to the fixed charges of the proteoglycans, the cation concentration inside the tissue is higher than in the surrounding synovial fluid. This excess of ion particles leads to an osmotic pressure difference, which causes swelling of the tissue. The fibrillar collagen network resists straining and swelling pressures. This combination makes cartilage a unique, highly hydrated and pressurized tissue, enforced with a strained collagen network. Many theories to explain articular cartilage behavior under loading, expressed in computational models that either include the swelling behavior or the properties of the anisotropic collagen structure, can be found in the literature. The most common tests used to determine the mechanical quality of articular cartilage are those of confined compression, unconfined compression, indentation and swelling. All theories currently available in the literature can explain the cartilage response occurring in some of the above tests, but none of them can explain these for all of the tests. We hypothesized that a model including simultaneous mathematical descriptions of (1) the swelling properties due to the fixed-change densities of the proteoglycans and (2) the anisotropic viscoelastic collagen structure, can explain all these test simultaneously. To study this hypothesis we extended our fibril-reinforced poroviscoelastic finite element model with our biphasic swelling model. We have shown that the newly developed fibril-reinforced poroviscoelastic swelling (FPVES) model for articular cartilage can simultaneously account for the reaction force during swelling, confined compression, indentation and unconfined compression as well as the lateral deformation during unconfined compression. Using this theory it is possible to analyze the link between the collagen network and the swelling properties of articular cartilage.
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paper_title: The Role of Flow-Independent Viscoelasticity in the Biphasic Tensile and Compressive Responses of Articular Cartilage

paper_content:

A long-standing challenge in the biomechanics of connective tissues (e.g., articular cartilage, ligament, tendon) has been the reported disparities between their tensile and compressive properties. In general, the intrinsic tensile properties of the solid matrices of these tissues are dictated by the collagen content and microstructural architecture, and the intrinsic compressive properties are dictated by their proteoglycan content and molecular organization as well as water content. These distinct materials give rise to a pronounced and experimentally well-documented nonlinear tension ‐compression stress‐ strain responses, as well as biphasic or intrinsic extracellular matrix viscoelastic responses. While many constitutive models of articular cartilage have captured one or more of these experimental responses, no single constitutive law has successfully described the uniaxial tensile and compressive responses of cartilage within the same framework. The objective of this study was to combine two previously proposed extensions of the biphasic theory of Mow et al. [1980, ASME J. Biomech. Eng.,102, pp. 73‐84] to incorporate tension‐compression nonlinearity as well as intrinsic viscoelasticity of the solid matrix of cartilage. The biphasic-conewise linear elastic model proposed by Soltz and Ateshian [2000, ASME J. Biomech. Eng.,122, pp. 576‐586] and based on the bimodular stressstrain constitutive law introduced by Curnier et al. [1995, J. Elasticity,37, pp. 1‐38], as well as the biphasic poroviscoelastic model of Mak [1986, ASME J. Biomech. Eng., 108, pp. 123‐130], which employs the quasi-linear viscoelastic model of Fung [1981, Biomechanics: Mechanical Properties of Living Tissues, Springer-Verlag, New York], were combined in a single model to analyze the response of cartilage to standard testing configurations. Results were compared to experimental data from the literature and it was found that a simultaneous prediction of compression and tension experiments of articular cartilage, under stress-relaxation and dynamic loading, can be achieved when properly taking into account both flow-dependent and flow-independent viscoelasticity effects, as well as tension‐compression nonlinearity. @DOI: 10.1115/1.1392316#
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paper_title: Mechanical behavior of articular cartilage: quantitative changes with alteration of ionic environment.

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The in vitro viscoelastic mechanical response of normal rabbit articular cartilage is quantitatively altered by changes in the ionic concentration of the test environment. Experimental results indicate that specific functional relationships exist between shear moduli, retardation time spectra and ionic concentration. The forms of these relationships are consistent with the structure and physio-chemical composition of the tissue.
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paper_title: Knee joint biomechanics in closed-kinetic-chain exercises.

paper_content:

Effective management of knee joint disorders demands appropriate rehabilitation programs to restore function while strengthening muscles. Excessive stresses in cartilage/menisci and forces in ligaments should be avoided to not exacerbate joint condition after an injury or reconstruction. Using a validated 3D nonlinear finite element model, detailed biomechanics of the entire joint in closed-kinetic-chain squat exercises are investigated at different flexion angles, weights in hands, femur-tibia orientations and coactivity in hamstrings. Predictions are in agreement with results of earlier studies. Estimation of small forces in cruciate ligaments advocates the use of squat exercises at all joint angles and external loads. In contrast, large contact stresses, especially at the patellofemoral joint, that approach cartilage failure threshold in compression suggest avoiding squatting at greater flexion angles, joint moments and weights in hands. Current results are helpful in comprehensive evaluation and design of effective exercise therapies and trainings with minimal risk to various components.
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paper_title: Experimental determination of the linear biphasic constitutive coefficients of human fetal proximal femoral chondroepiphysis.

paper_content:

The mechanical properties of the cartilaginous regions of the proximal femoral epiphysis are an important factor in load transmission through the hip joint of young children. Cylindrical test specimens excised from the chondroepiphysis of human stillborn femoral heads were subjected to uniaxial loading in peripherally-unconfined compression, using a ramp/plateau input strain history. The corresponding load vs time curves were analyzed in terms of a recent analytical solution for a linear biphasic material (the well-known KLM model), allowing calculation of that model's three fundamental constitutive coefficients (permeability, equilibrium modulus and solid-phase Poisson ratio) for this material. The numerical algorithm developed to evaluate the biphasic solution yielded very precise replication of previously published KLM parametric plots. When fitted to experimental load histories, however, the model provided only a rather loose approximation of specimen behavior, due apparently to a substantial underestimation of the transient response component associated with interstitial fluid transport. Averaged over the series, the best-fit values for permeability (2.51 X 10(-15) m4 Ns-1) and equilibrium modulus (0.699 MPa) were in the range of values accepted for human adult articular cartilage. A consequence of the coarseness of the analytical curve fits was that a solid-phase Poisson ratio of 0.0 was inferred for all specimens. The permeability vs equilibrium modulus exhibited a nearly linear (r = 0.74) inverse relationship similar to that reported for adult articular cartilage.
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paper_title: Influence of patellofemoral articular geometry and material on mechanics of the unresurfaced patella.

paper_content:

Patellar resurfacing during knee replacement is still under debate, with several studies reporting higher incidence of anterior knee pain in unresurfaced patellae. Congruency between patella and femur impacts the mechanics of the patellar cartilage and strain in the underlying bone, with higher stresses and strains potentially contributing to cartilage wear and anterior knee pain. The material properties of the articulating surfaces will also affect load transfer between femur and patella. The purpose of this study was to evaluate the mechanics of the unresurfaced patella and compare with natural and resurfaced conditions in a series of finite element models of the patellofemoral joint. In the unresurfaced analyses, three commercially available implants were compared, in addition to an 'ideal' femoral component which replicated the geometry, but not the material properties, of the natural femur. Hence, the contribution of femoral component material properties could be assessed independently from geometry changes. The ideal component tracked the kinematics and patellar bone strain of the natural knee, but had consistently inferior contact mechanics. In later flexion, compressive patellar bone strain in unresurfaced conditions was substantially higher than in resurfaced conditions. Understanding how femoral component geometry and material properties in unresurfaced knee replacement alters cartilage contact mechanics and bone strain may aid in explaining why the incidence of anterior knee pain is higher in the unresurfaced population, and ultimately contribute to identifying criteria to pre-operatively predict which patients are suited to an unresurfaced procedure and reducing the incidence of anterior knee pain in the unresurfaced patient population.
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paper_title: Importance of the superficial tissue layer for the indentation stiffness of articular cartilage

paper_content:

Indentation testing is a widely used technique for nondestructive mechanical analysis of articular cartilage. Although cartilage shows an inhomogeneous, layered structure with anisotropic mechanical properties, most theoretical indentation models assume material homogeneity and isotropy. In the present study, quantitative polarized light microscopy (PLM) measurements from canine cartilage were utilized to characterize thickness and structure of the superficial, collageneous tissue layer as well as to reveal its relation to experimental indentation measurements. In addition to experimental analyses, a layered, transversely isotropic finite element (FE) model was developed and the effect of superficial (tangential) tissue layer with high elastic modulus in the direction parallel to articular surface on the indentation response was studied. The experimental indentation stiffness was positively correlated with the relative thickness of the superficial cartilage layer. Also the optical retardation, which reflects the degree of parallel organization of collagen fibrils as well as collagen content, was related to indentation stiffness. FE results indicated effective stiffening of articular cartilage under indentation due to high transverse modulus of the superficial layer. The present results suggest that indentation testing is an efficient technique for the characterization of the superficial degeneration of articular cartilage.
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paper_title: Nonlinear analysis of cartilage in unconfined ramp compression using a fibril reinforced poroelastic model.

paper_content:

OBJECTIVE ::: To develop a biomechanical model for cartilage which is capable of capturing experimentally observed nonlinear behaviours of cartilage and to investigate effects of collagen fibril reinforcement in cartilage. ::: ::: ::: DESIGN ::: A sequence of 10 or 20 steps of ramp compression/relaxation applied to cartilage disks in uniaxial unconfined geometry is simulated for comparison with experimental data. ::: ::: ::: BACKGROUND ::: Mechanical behaviours of cartilage, such as the compression-offset dependent stiffening of the transient response and the strong relaxation component, have been previously difficult to describe using the biphasic model in unconfined compression. ::: ::: ::: METHODS ::: Cartilage is modelled as a fluid-saturated solid reinforced by an elastic fibrillar network. The latter, mainly representing collagen fibrils, is considered as a distinct constituent embedded in a biphasic component made up mainly of proteoglycan macromolecules and a fluid carrying mobile ions. The Young's modulus of the fibrillar network is taken to vary linearly with its tensile strain but to be zero for compression. Numerical computations are carried out using a finite element procedure, for which the fibrillar network is discretized into a system of spring elements. ::: ::: ::: RESULTS ::: The nonlinear fibril reinforced poroelastic model is capable of describing the strong relaxation behaviour and compression-offset dependent stiffening of cartilage in unconfined compression. Computational results are also presented to demonstrate unique features of the model, e.g. the matrix stress in the radial direction is changed from tensile to compressive due to presence of distinct fibrils in the model. ::: ::: ::: RELEVANCE ::: Experimentally observed nonlinear behaviours of cartilage are successfully simulated, and the roles of collagen fibrils are distinguished by using the proposed model. Thus this study may lead to a better understanding of physiological responses of individual constituents of cartilage to external loads, and of the roles of mechanical loading in cartilage remodelling and pathology.
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paper_title: Fibril reinforced poroelastic model predicts specifically mechanical behavior of normal, proteoglycan depleted and collagen degraded articular cartilage

paper_content:

Abstract Degradation of collagen network and proteoglycan (PG) macromolecules are signs of articular cartilage degeneration. These changes impair cartilage mechanical function. Effects of collagen degradation and PG depletion on the time-dependent mechanical behavior of cartilage are different. In this study, numerical analyses, which take the compression-tension nonlinearity of the tissue into account, were carried out using a fibril reinforced poroelastic finite element model. The study aimed at improving our understanding of the stress-relaxation behavior of normal and degenerated cartilage in unconfined compression. PG and collagen degradations were simulated by decreasing the Young's modulus of the drained porous (nonfibrillar) matrix and the fibril network, respectively. Numerical analyses were compared to results from experimental tests with chondroitinase ABC (PG depletion) or collagenase (collagen degradation) digested samples. Fibril reinforced poroelastic model predicted the experimental behavior of cartilage after chondroitinase ABC digestion by a major decrease of the drained porous matrix modulus (−64±28%) and a minor decrease of the fibril network modulus (−11±9%). After collagenase digestion, in contrast, the numerical analyses predicted the experimental behavior of cartilage by a major decrease of the fibril network modulus (−69±5%) and a decrease of the drained porous matrix modulus (−44±18%). The reduction of the drained porous matrix modulus after collagenase digestion was consistent with the microscopically observed secondary PG loss from the tissue. The present results indicate that the fibril reinforced poroelastic model is able to predict specifically characteristic alterations in the stress-relaxation behavior of cartilage after enzymatic modifications of the tissue. We conclude that the compression-tension nonlinearity of the tissue is needed to capture realistically the mechanical behavior of normal and degenerated articular cartilage.
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paper_title: A fibril reinforced nonhomogeneous poroelastic model for articular cartilage: inhomogeneous response in unconfined compression.

paper_content:

The depth dependence of material properties of articular cartilage, known as the zonal differences, is incorporated into a nonlinear fibril-reinforced poroelastic model developed previously in order to explore the significance of material heterogeneity in the mechanical behavior of cartilage. The material variations proposed are based on extensive observations. The collagen fibrils are modeled as a distinct constituent which reinforces the other two constituents representing proteoglycans and water. The Young's modulus and Poisson's ratio of the drained nonfibrillar matrix are so determined that the aggregate compressive modulus for confined geometry fits the experimental data. Three nonlinear factors are considered, i.e. the effect of finite deformation, the dependence of permeability on dilatation and the fibril stiffening with its tensile strain. Solutions are extracted using a finite element procedure to simulate unconfined compression tests. The features of the model are then demonstrated with an emphasis on the results obtainable only with a nonhomogeneous model, showing reasonable agreement with experiments. The model suggests mechanical behaviors significantly different from those revealed by homogeneous models: not only the depth variations of the strains which are expected by qualitative analyses, but also, for instance, the relaxation-time dependence of the axial strain which is normally not expected in a relaxation test. Therefore, such a nonhomogeneous model is necessary for better understanding of the mechanical behavior of cartilage.
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paper_title: The Generalized Consolidation of Articular Cartilage: An Investigation of Its Near-Physiological Response to Static Load

paper_content:

This paper presents a study of the response of articular cartilage to compression whilst measuring simultaneously its strain and fluid excess pore pressure using a newly developed experimental apparatus for testing the tissue in its unconfined state. This has provided a comparison of the load-induced responses of the cartilage matrix under axial, radial and 3-D consolidation regimes. Our results demonstrate that the patterns of the hydrostatic excess pore pressure for axial and 3-D consolidation are similar, but differ significantly from that obtained under the more physiologically relevant condition in which the matrix exhibits radial consolidation when loaded either through a non-porous polished stainless steel indenter or an opposing cartilage disc. Based on the transient strain characteristics obtained under axial and unconfined compression we argue that consolidation is indeed the controlling mechanism of cartilage biomechanical function.
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paper_title: Stress–relaxation of human patellar articular cartilage in unconfined compression: Prediction of mechanical response by tissue composition and structure

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Abstract Mechanical properties of articular cartilage are controlled by tissue composition and structure. Cartilage function is sensitively altered during tissue degeneration, in osteoarthritis (OA). However, mechanical properties of the tissue cannot be determined non-invasively. In the present study, we evaluate the feasibility to predict, without mechanical testing, the stress–relaxation response of human articular cartilage under unconfined compression. This is carried out by combining microscopic and biochemical analyses with composition-based mathematical modeling. Cartilage samples from five cadaver patellae were mechanically tested under unconfined compression. Depth-dependent collagen content and fibril orientation, as well as proteoglycan and water content were derived by combining Fourier transform infrared imaging, biochemical analyses and polarized light microscopy. Finite element models were constructed for each sample in unconfined compression geometry. First, composition-based fibril-reinforced poroviscoelastic swelling models, including composition and structure obtained from microscopical and biochemical analyses were fitted to experimental stress–relaxation responses of three samples. Subsequently, optimized values of model constants, as well as compositional and structural parameters were implemented in the models of two additional samples to validate the optimization. Theoretical stress–relaxation curves agreed with the experimental tests ( R =0.95–0.99). Using the optimized values of mechanical parameters, as well as composition and structure of additional samples, we were able to predict their mechanical behavior in unconfined compression, without mechanical testing ( R =0.98). Our results suggest that specific information on tissue composition and structure might enable assessment of cartilage mechanics without mechanical testing.
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paper_title: High-resolution diffusion tensor imaging of human patellar cartilage: Feasibility and preliminary findings

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MR diffusion tensor imaging (DTI) was used to analyze the microstructural properties of articular cartilage. Human patellar cartilage-on-bone samples were imaged at 9.4T using a diffusion-weighted SE sequence (12 gradient directions, resolution = 39 x 78 x 1500 microm(3)). Voxel-based maps of the mean diffusivity, fractional anisotropy (FA), and eigenvectors were calculated. The mean diffusivity decreased from the surface (1.45 x 10(-3) mm(2)/s) to the tide mark (0.68 x 10(-3) mm(2)/s). The FA was low (0.04-0.28) and had local maxima near the surface and in the portion of the cartilage corresponding to the radial layer. The eigenvector corresponding to the largest eigenvalue showed a distinct zonal pattern, being oriented tangentially and radially in the upper and lower portions of the cartilage, respectively. The findings correspond to current scanning electron microscopy (SEM) data on the zonal architecture of cartilage. The eigenvector maps appear to reflect the alignment of the collagenous fibers in cartilage. In view of current efforts to develop and evaluate structure-modifying therapeutic approaches in osteoarthritis (OA), DTI may offer a tool to assess the structural properties of cartilage.
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paper_title: Depth-dependent Compressive Equilibrium Properties of Articular Cartilage Explained by its Composition

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For this study, we hypothesized that the depth-dependent compressive equilibrium properties of articular cartilage are the inherent consequence of its depth-dependent composition, and not the result of depth-dependent material properties. To test this hypothesis, our recently developed fibril-reinforced poroviscoelastic swelling model was expanded to include the influence of intra- and extra-fibrillar water content, and the influence of the solid fraction on the compressive properties of the tissue. With this model, the depth-dependent compressive equilibrium properties of articular cartilage were determined, and compared with experimental data from the literature. The typical depth-dependent behavior of articular cartilage was predicted by this model. The effective aggregate modulus was highly strain-dependent. It decreased with increasing strain for low strains, and increases with increasing strain for high strains. This effect was more pronounced with increasing distance from the articular surface. The main insight from this study is that the depth-dependent material behavior of articular cartilage can be obtained from its depth-dependent composition only. This eliminates the need for the assumption that the material properties of the different constituents themselves vary with depth. Such insights are important for understanding cartilage mechanical behavior, cartilage damage mechanisms and tissue engineering studies.
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paper_title: A hyperelastic biphasic fibre-reinforced model of articular cartilage considering distributed collagen fibre orientations: continuum basis, computational aspects and applications

paper_content:

Cartilage is a multi-phase material composed of fluid and electrolytes (68-85% by wet weight), proteoglycans (5-10% by wet weight), chondrocytes, collagen fibres and other glycoproteins. The solid ...
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paper_title: Structural Analysis of Articular Cartilage Using Multiphoton Microscopy: Input for Biomechanical Modeling

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The 3-D morphology of chicken articular cartilage was quantified using multiphoton microscopy (MPM) for use in continuum-mechanical modeling. To motivate this morphological study we propose aspects of a new, 3-D finite strain constitutive model for articular cartilage focusing on the essential load-bearing morphology: an inhomogeneous, poro-(visco)elastic solid matrix reinforced by an anisotropic, (visco)elastic dispersed fiber fabric which is saturated by an incompressible fluid residing in strain-dependent pores. Samples of fresh chicken cartilage were sectioned in three orthogonal planes and imaged using MPM, specifically imaging the collagen fibers using second harmonic generation. Employing image analysis techniques based on Fourier analysis, we derived the principal directionality and dispersion of the collagen fiber fabric in the superficial layer. In the middle layer, objective thresholding techniques were used to extract the volume fraction occupied by extracellular collagen matrix. In conjunction with information available in the literature, or additional experimental testing, we show how this data can be used to derive a 3-D map of the initial solid volume fraction and Darcy permeability.
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paper_title: On the anisotropy and inhomogeneity of permeability in articular cartilage

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Articular cartilage is known to be anisotropic and inhomogeneous because of its microstructure. In particular, its elastic properties are influenced by the arrangement of the collagen fibres, which are orthogonal to the bone-cartilage interface in the deep zone, randomly oriented in the middle zone, and parallel to the surface in the superficial zone. In past studies, cartilage permeability has been related directly to the orientation of the glycosaminoglycan chains attached to the proteoglycans which constitute the tissue matrix. These studies predicted permeability to be isotropic in the undeformed configuration, and anisotropic under compression. They neglected tissue anisotropy caused by the collagen network. However, magnetic resonance studies suggest that fluid flow is “directed” by collagen fibres in biological tissues. Therefore, the aim of this study was to express the permeability of cartilage accounting for the microstructural anisotropy and inhomogeneity caused by the collagen fibres. Permeability is predicted to be anisotropic and inhomogeneous, independent of the state of strain, which is consistent with the morphology of the tissue. Looking at the local anisotropy of permeability, we may infer that the arrangement of the collagen fibre network plays an important role in directing fluid flow to optimise tissue functioning.
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paper_title: A human knee joint model considering fluid pressure and fiber orientation in cartilages and menisci

paper_content:

Abstract Articular cartilages and menisci are generally considered to be elastic in the published human knee models, and thus the fluid-flow dependent response of the knee has not been explored using finite element analysis. In the present study, the fluid pressure and site-specific collagen fiber orientation in the cartilages and menisci were implemented into a finite element model of the knee using fibril-reinforced modeling previously proposed for articular cartilage. The geometry of the knee was obtained from magnetic resonance imaging of a healthy young male. The bones were considered to be elastic due to their greater stiffness compared to that of the cartilages and menisci. The displacements obtained for fast ramp compression were essentially same as those for instantaneous compression of equal magnitude with the fluid being trapped in the tissues, which was expected. However, a clearly different pattern of displacements was predicted by an elastic model using a greater Young's modulus and a Poisson's ratio for nearly incompressible material. The results indicated the influence of fluid pressure and fiber orientation on the deformation of articular cartilage in the knee. The fluid pressurization in the femoral cartilage was somehow affected by the site-specific fiber directions. The peak fluid pressure in the femoral condyles was reduced by three quarters when no fibril reinforcement was assumed. The present study indicates the necessity of implementing the fluid pressure and anisotropic fibril reinforcement in articular cartilage for a more accurate understanding of the mechanics of the knee.
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paper_title: Stresses in the local collagen network of articular cartilage: a poroviscoelastic fibril-reinforced finite element study.

paper_content:

Osteoarthritis (OA) is a multifactorial disease, resulting in diarthrodial joint wear and eventually destruction. Swelling of cartilage, which is proportional to the amount of collagen damage, is an initial event of cartilage degeneration, so damage to the collagen fibril network is likely to be one of the earliest signs of OA cartilage degeneration. We propose that the local stresses and strains in the collagen fibrils, which cause the damage, cannot be determined dependably without taking the local arcade-like collagen-fibril structure into account. We investigate this using a poroviscoelastic fibril-reinforced FEA model. The constitutive fibril properties were determined by fitting numerical data to experimental results of unconfined compression and indentation tests on samples of bovine patellar articular cartilage. It was demonstrated that with this model the stresses and strains in the collagen fibrils can be calculated. It was also exhibited that fibrils with different orientations at the same location can be loaded differently, depending on the local architecture of the collagen network. To the best of our knowledge, the present model is the first that can account for these features. We conclude that the local stresses and strains in the articular cartilage are highly influenced by the local morphology of the collagen-fibril network.
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paper_title: Characterization of articular cartilage by combining microscopic analysis with a fibril-reinforced finite-element model.

paper_content:

Load-bearing characteristics of articular cartilage are impaired during tissue degeneration. Quantitative microscopy enables in vitro investigation of cartilage structure but determination of tissue functional properties necessitates experimental mechanical testing. The fibril-reinforced poroviscoelastic (FRPVE) model has been used successfully for estimation of cartilage mechanical properties. The model includes realistic collagen network architecture, as shown by microscopic imaging techniques. The aim of the present study was to investigate the relationships between the cartilage proteoglycan (PG) and collagen content as assessed by quantitative microscopic findings, and model-based mechanical parameters of the tissue. Site-specific variation of the collagen network moduli, PG matrix modulus and permeability was analyzed. Cylindrical cartilage samples (n=22) were harvested from various sites of the bovine knee and shoulder joints. Collagen orientation, as quantitated by polarized light microscopy, was incorporated into the finite-element model. Stepwise stress-relaxation experiments in unconfined compression were conducted for the samples, and sample-specific models were fitted to the experimental data in order to determine values of the model parameters. For comparison, Fourier transform infrared imaging and digital densitometry were used for the determination of collagen and PG content in the same samples, respectively. The initial and strain-dependent fibril network moduli as well as the initial permeability correlated significantly with the tissue collagen content. The equilibrium Young's modulus of the nonfibrillar matrix and the strain dependency of permeability were significantly associated with the tissue PG content. The present study demonstrates that modern quantitative microscopic methods in combination with the FRPVE model are feasible methods to characterize the structure-function relationships of articular cartilage.
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paper_title: Deep vertical collagen fibrils play a significant role in mechanics of articular cartilage.

paper_content:

The primary orientation of collagen fibrils alters along the cartilage depth; being horizontal in the superficial zone, random in the transitional zone, and vertical in the deep zone. Commonly used confined and unconfined (when with no underlying bone) testing configurations cannot capture the mechanical role of deep vertical fibril network. To determine this role in cartilage mechanics, an axisymmetric nonlinear fibril-reinforced poroelastic model of tibial cartilage plateaus was developed accounting for depth-dependent properties and distinct fibril networks with physical material properties. Both creep and relaxation indentation models were analyzed which results were found equivalent in the transient period but diverged in post-transient periods. Vertical fibrils played a significant role at the transient period in dramatically increasing the stiffness of the tissue and in protecting the solid matrix against large distortions and strains at the subchondral junction. This role, however, disappeared both with time and at loading rates slower than those expected in physiological activities such as walking. The vertical fibrils demonstrated a chevron-type deformation pattern that was further accentuated with time in creep loading. Damages to deep vertical collagen fibril network or their firm anchorage to the bone, associated with bone bruises, for example, would weaken the transient stiffness and place the tissue at higher risk of failure particularly at the deep zone.
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paper_title: Strain-rate Dependent Stiffness of Articular Cartilage in Unconfined Compression

paper_content:

The stiffness of articular cartilage is a nonlinear function of the strain amplitude and strain rate as well as the loading history, as a consequence of the flow of interstitial water and the stiffening of the collagen fibril network. This paper presents a full investigation of the interplay between the fluid kinetics and fibril stiffening of unconfined cartilage disks by analyzing over 200 cases with diverse material properties. The lower and upper elastic limits of the stress (under a given strain) are uniquely established by the instantaneous and equilibrium stiffness (obtained numerically for finite deformations and analytically for small deformations). These limits could be used to determine safe loading protocols in order that the stress in each solid constituent remains within its own elastic limit. For a given compressive strain applied at a low rate, the loading is close to the lower limit and is mostly borne directly by the solid constituents (with little contribution from the fluid). In contrast, however in case of faster compression, the extra loading is predominantly transported to the fibrillar matrix via rising fluid pressure with little increase of stress in the nonfibrillar matrix. The fibrillar matrix absorbs the loading increment by self-stiffening: the quicker the loading the faster the fibril stiffening until the upper elastic loading limit is reached. This self-protective mechanism prevents cartilage from damage since the fibrils are strong in tension. The present work demonstrates the ability of the fibril reinfored poroelastic models to describe the strain rate dependent behavior of articular cartilage in unconfined compression using a mechanism of fibril stiffening mainly induced by the fluid flow.
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paper_title: A Transversely Isotropic Biphasic Model for Unconfined Compression of Growth Plate and Chondroepiphysis

paper_content:

Using the biphasic theory for hydrated soft tissues (Mow et al., 1980) and a transversely isotropic elastic model for the solid matrix, an analytical solution is presented for the unconfined compression of cylindrical disks of growth plate tissues compressed between two rigid platens with a frictionless interface. The axisymmetric case where the plane of transverse isotropy is perpendicular to the cylindrical axis is studied, and the stress-relaxation response to imposed step and ramp displacements is solved. This solution is then used to analyze experimental data from unconfined compression stress-relaxation tests performed on specimens from bovine distal ulnar growth plate and chondroepiphysis to determine the biphasic material parameters. The transversely isotropic biphasic model provides an excellent agreement between theory and experimental results, better than was previously achieved with an isotropic model, and can explain the observed experimental behavior in unconfined compression of these tissues.
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paper_title: A composition-based cartilage model for the assessment of compositional changes during cartilage damage and adaptation

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Summary Objective The composition of articular cartilage changes with progression of osteoarthritis. Since compositional changes are associated with changes in the mechanical properties of the tissue, they are relevant for understanding how mechanical loading induces progression. The objective of this study is to present a computational model of articular cartilage which enables to study the interaction between composition and mechanics. Methods Our previously developed fibril-reinforced poroviscoelastic swelling model for articular cartilage was combined with our tissue composition-based model. In the combined model both the depth- and strain-dependencies of the permeability are governed by tissue composition. All local mechanical properties in the combined model are directly related to the local composition of the tissue, i.e., to the local amounts of proteoglycans and collagens and to tissue anisotropy. Results Solely based on the composition of the cartilage, we were able to predict the equilibrium and transient response of articular cartilage during confined compression, unconfined compression, indentation and two different 1D-swelling tests, simultaneously. Conclusion Since both the static and the time-dependent mechanical properties have now become fully dependent on tissue composition, the model allows assessing the mechanical consequences of compositional changes seen during osteoarthritis without further assumptions. This is a major step forward in quantitative evaluations of osteoarthritis progression.
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paper_title: Deformation of Chondrocytes in Articular Cartilage under Compressive Load: A Morphological Study

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The main function of articular cartilage is to transmit load. The objective of this study was to describe the deformation of chondrocytes under static loading and its relation to collagen matrix deformation. Whole intact rabbit knee joints were loaded statically with either high or low magnitude and long or short duration. Specimens were cryopreserved while under load and prepared for morphological evaluation by field emission scanning electron microscopy. With this method an immediate preservation of the chondrocyte in its loaded state was possible. Static compression of articular cartilage produced a zone-specific deformation of chondrocyte shape, depending on the magnitude and duration of load. Under high-force and long-duration loading, the chondrocytes showed considerable deformation concomitant with the highly deformed collagen fibres. Chondrocyte deformation occurred mostly in the transitional and upper radial zones and less in the lower layers. There was no significant change of the chondrocyte shape in the tangential zone under high- or low-force short-duration loading. These results show that the chondrocytes undergo significant changes in shape ex vivo and that they are sensitive to differences in the magnitude and duration of loads being applied. Chondrocyte deformation is strongly linked to the deformation of the surrounding cartilage collagen matrix.
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paper_title: A Conewise Linear Elasticity Mixture Model for the Analysis of Tension-Compression Nonlinearity in Articular Cartilage

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A biphasic mixture model is developed which can account for the observed tension-compression nonlinearity of cartilage by employing the continuum-based Conewise Linear Elasticity (CLE) model of Curnier et al. (J Elasticity 37:1–38, 1995) to describe the solid phase of the mixture. In this first investigation, the orthotropic octantwise linear elasticity model was reduced to the more specialized case of cubic symmetry, to reduce the number of elastic constants from twelve to four. Confined and unconfined compression stress-relaxation, and torsional shear testing were performed on each of nine bovine humeral head articular cartilage cylindrical plugs from 6 month old calves. Using the CLE model with cubic symmetry, the aggregate modulus in compression and axial permeability were obtained from confined compression (H−A =0.64±0.22 MPa, kz = 3.62 ± .97 × 10−16 m4/N.s, r2 =0.95±0.03), the tensile modulus, compressive Poisson ratio and radial permeability were obtained from unconfined compression (E+Y = 12.75 ± 1.56 MPa, ν− =0.03±0.01, kr =6.06±2.10×10−16 m4/N.s, r2 =0.99±0.00), and the shear modulus was obtained from torsional shear (µ=0.17±0.06 MPa). The model was also employed to successfully predict the interstitial fluid pressure at the center of the cartilage plug in unconfined compression (r2 =0.98±0.01). The results of this study demonstrate that the integration of the CLE model with the biphasic mixture theory can provide a model of cartilage which can successfully curvefit three distinct testing configurations while producing material parameters consistent with previous reports in the literature.
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paper_title: A viscoelastic model for fiber-reinforced composites at finite strains: Continuum basis, computational aspects and applications

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Abstract This paper presents a viscoelastic model for the fully three-dimensional stress and deformation response of fiber-reinforced composites that experience finite strains. The composites are thought to be (soft) matrix materials which are reinforced by two families of fibers so that the mechanical properties of the composites depend on two fiber directions. The relaxation and/or creep response of each compound of the composite is modeled separately and the global response is obtained by an assembly of all contributions. We develop novel closed-form expressions for the fourth-order elasticity tensor (tangent moduli) in full generality. Constitutive models for orthotropic, transversely isotropic and isotropic hyperelastic materials at finite strains with or without dissipation are included as special cases. In order to clearly show the good performance of the constitutive model, we present 3D and 2D numerical simulations of a pressurized laminated circular tube which shows an interesting `stretch inversion phenomenon' in the low pressure domain. Numerical results are in good qualitative agreement with experimental data and approximate the observed strongly anisotropic physical response with satisfying accuracy. A third numerical example is designed to illustrate the anisotropic stretching process of a fiber-reinforced rubber bar and the subsequent relaxation behavior at finite strains. The material parameters are chosen so that thermodynamic equilibrium is associated with the known homogeneous deformation state.
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paper_title: The collagenous architecture of articular cartilage--a synthesis of ultrastructure and mechanical function.

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The fibrillar ultrastructure within the general matrix of articular cartilage has been examined in the stressed root region of predetermined notches propagating under tension in directions both perpendicular and parallel to the articular surface. From the different ultrastructural responses induced by the 2 notch geometries, it has been possible to further clarify the relationship between structure and load bearing function in normal articular cartilage, and identify features of the collagenous architecture that seem directly related to a loss of load bearing function associated with both osteoarthritis and nonprogressive degeneration.
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paper_title: Mechanical characterization of articular cartilage by combining magnetic resonance imaging and finite-element analysis—a potential functional imaging technique

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Magnetic resonance imaging (MRI) provides a method for non-invasive characterization of cartilage composition and structure. We aimed to see whether T1 and T2 relaxation times are related to proteoglycan (PG) and collagen-specific mechanical properties of articular cartilage. Specifically, we analyzed whether variations in the depthwise collagen orientation, as assessed by the laminae obtained from T2 profiles, affect the mechanical characteristics of cartilage. After MRI and unconfined compression tests of human and bovine patellar cartilage samples, fibril-reinforced poroviscoelastic finite-element models (FEM), with depthwise collagen orientations implemented from quantitative T2 maps (3 laminae for human, 3–7 laminae for bovine), were constructed to analyze the non-fibrillar matrix modulus (PG specific), fibril modulus (collagen specific) and permeability of the samples. In bovine cartilage, the non-fibrillar matrix modulus (R = −0.64, p < 0.05) as well as the initial permeability (R = 0.70, p < 0.05) correlated with T1. In bovine cartilage, T2 correlated positively with the initial fibril modulus (R = 0.62, p = 0.05). In human cartilage, the initial fibril modulus correlated negatively (R = −0.61, p < 0.05) with T2. Based on the simulations, cartilage with a complex collagen architecture (5 or 7 laminae), leading to high bulk T2 due to magic angle effects, provided higher compressive stiffness than tissue with a simple collagen architecture (3 laminae). Our results suggest that T1 reflects PG-specific mechanical properties of cartilage. High T2 is characteristic to soft cartilage with a classical collagen architecture. Contradictorily, high bulk T2 can also be found in stiff cartilage with a multilaminar collagen fibril network. By emerging MRI and FEM, the present study establishes a step toward functional imaging of articular cartilage.
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paper_title: A VISCOELASTIC MODEL FOR COLLAGEN FIBRES

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The viscoelastic behaviour of collagen fibres of different lengths was studied by developing simulation models. These models were found to explain the creep and stress-relaxation behaviour of the collagen fibres.
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paper_title: A Phenomenological Approach Toward Patient-Specific Computational Modeling of Articular Cartilage Including Collagen Fiber Tracking

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To model the cartilage morphology and the material response, a phenomenological and patient-specific simulation approach incorporating the collagen fiber fabric is proposed. Cartilage tissue respon ...
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paper_title: Decreased birefringence of the superficial zone collagen network in the canine knee (stifle) articular cartilage after long distance running training, detected by quantitative polarised light microscopy.

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OBJECTIVE: To investigate the effects of a one year programme of running training (up to 40 km/day for 15 weeks) on the spatial orientation pattern of collagen and glycosaminoglycans in articular cartilage in different parts of the knee (stifle) and shoulder joints of young beagle dogs. METHODS: Area specific measurements of the optical path difference (= retardation, gamma) and the cartilage zone thickness were performed using conventional procedures and a new computer based quantitative polarised light microscopy method. Transmission electron microscopy was used to determine the zonal volume density of collagen fibrils. The concentrations of collagen and hydroxypyridinium crosslinks were investigated biochemically. RESULTS: Running training decreased gamma by 24-34% (p < 0.05) in the superficial zone of the lateral femoral condyle articular cartilage and at the centre of the tibial condyles. Gamma of glycosaminoglycans decreased by 26% (p < 0.05) in the superficial zone of the lateral condyle of the femur, but at the same site the volume density of collagen fibrils was unchanged. Neither the collagen concentration nor the concentration of hydroxypyridinium crosslinks was altered as a result of running. In both control and runner dogs, the thickness and gamma values of the superficial zone were greater in the humerus and the femur than in the tibia. CONCLUSION: Endurance type running exercise in beagles caused a reduction in the superficial zone birefringence of the articular cartilage, which indicates either a disorganisation or a reorientation of the superficial zone collagen network. Articular cartilage showed marked variability of collagen network organisation over the different knee (stifle) joint articular surfaces.
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paper_title: Effect of superficial collagen patterns and fibrillation of femoral articular cartilage on knee joint mechanics-a 3D finite element analysis.

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Collagen fibrils of articular cartilage have specific depth-dependent orientations and the fibrils bend in the cartilage surface to exhibit split-lines. Fibrillation of superficial collagen takes place in osteoarthritis. We aimed to investigate the effect of superficial collagen fibril patterns and collagen fibrillation of cartilage on stresses and strains within a knee joint. A 3D finite element model of a knee joint with cartilage and menisci was constructed based on magnetic resonance imaging. The fibril-reinforced poroviscoelastic material properties with depth-dependent collagen orientations and split-line patterns were included in the model. The effects of joint loading on stresses and strains in cartilage with various split-line patterns and medial collagen fibrillation were simulated under axial impact loading of 1000 N. In the model, the collagen fibrils resisted strains along the split-line directions. This increased also stresses along the split-lines. On the contrary, contact and pore pressures were not affected by split-line patterns. Simulated medial osteoarthritis increased tissue strains in both medial and lateral femoral condyles, and contact and pore pressures in the lateral femoral condyle. This study highlights the importance of the collagen fibril organization, especially that indicated by split-line patterns, for the weight-bearing properties of articular cartilage. Osteoarthritic changes of cartilage in the medial femoral condyle created a possible failure point in the lateral femoral condyle. This study provides further evidence on the importance of the collagen fibril organization for the optimal function of articular cartilage.
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paper_title: Analysis of articular cartilage as a composite using nonlinear membrane elements for collagen fibrils.

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To develop a composite fibre-reinforced model of the cartilage, membrane shell elements were introduced to represent collagen fibrils reinforcing the isotropic porous solid matrix filled with fluid. Nonlinear stress-strain curve of pure collagen fibres and collagen volume fraction were explicitly presented in the formulation of these membrane elements. In this composite model, in accordance with tissue structure, the matrix and fibril membrane network experienced dissimilar stresses despite identical strains in the fibre directions. Different unconfined compression and indentation case studies were performed to determine the distinct role of membrane collagen fibrils in nonlinear poroelastic mechanics of articular cartilage. The importance of nonlinear fibril membrane elements in the tissue relaxation response as well as in temporal and spatial variations of pore pressure and solid matrix stresses was demonstrated. By individual adjustments of the collagen volume fraction and collagen mechanical properties, the model allows for the simulation of alterations in the fibril network structure of the tissue towards modelling damage processes or repair attempts. The current model, which is based on a physiological description of the tissue structure, is promising in improvement of our understanding of the cartilage pathomechanics.
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paper_title: Nonlinear analysis of cartilage in unconfined ramp compression using a fibril reinforced poroelastic model.

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OBJECTIVE ::: To develop a biomechanical model for cartilage which is capable of capturing experimentally observed nonlinear behaviours of cartilage and to investigate effects of collagen fibril reinforcement in cartilage. ::: ::: ::: DESIGN ::: A sequence of 10 or 20 steps of ramp compression/relaxation applied to cartilage disks in uniaxial unconfined geometry is simulated for comparison with experimental data. ::: ::: ::: BACKGROUND ::: Mechanical behaviours of cartilage, such as the compression-offset dependent stiffening of the transient response and the strong relaxation component, have been previously difficult to describe using the biphasic model in unconfined compression. ::: ::: ::: METHODS ::: Cartilage is modelled as a fluid-saturated solid reinforced by an elastic fibrillar network. The latter, mainly representing collagen fibrils, is considered as a distinct constituent embedded in a biphasic component made up mainly of proteoglycan macromolecules and a fluid carrying mobile ions. The Young's modulus of the fibrillar network is taken to vary linearly with its tensile strain but to be zero for compression. Numerical computations are carried out using a finite element procedure, for which the fibrillar network is discretized into a system of spring elements. ::: ::: ::: RESULTS ::: The nonlinear fibril reinforced poroelastic model is capable of describing the strong relaxation behaviour and compression-offset dependent stiffening of cartilage in unconfined compression. Computational results are also presented to demonstrate unique features of the model, e.g. the matrix stress in the radial direction is changed from tensile to compressive due to presence of distinct fibrils in the model. ::: ::: ::: RELEVANCE ::: Experimentally observed nonlinear behaviours of cartilage are successfully simulated, and the roles of collagen fibrils are distinguished by using the proposed model. Thus this study may lead to a better understanding of physiological responses of individual constituents of cartilage to external loads, and of the roles of mechanical loading in cartilage remodelling and pathology.
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paper_title: A nonlinear biphasic fiber-reinforced porohyperviscoelastic model of articular cartilage incorporating fiber reorientation and dispersion.

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A nonlinear biphasic fiber-reinforced porohyperviscoelastic (BFPHVE) model of articular cartilage incorporating fiber reorientation effects during applied load was used to predict the response of ovine articular cartilage at relatively high strains (20%). The constitutive material parameters were determined using a coupled finite element-optimization algorithm that utilized stress relaxation indentation tests at relatively high strains. The proposed model incorporates the strain-hardening, tension-compression, permeability, and finite deformation nonlinearities that inherently exist in cartilage, and accounts for effects associated with fiber dispersion and reorientation and intrinsic viscoelasticity at relatively high strains. A new optimization cost function was used to overcome problems associated with large peak-to-peak differences between the predicted finite element and experimental loads that were due to the large strain levels utilized in the experiments. The optimized material parameters were found to be insensitive to the initial guesses. Using experimental data from the literature, the model was also able to predict both the lateral displacement and reaction force in unconfined compression, and the reaction force in an indentation test with a single set of material parameters. Finally, it was demonstrated that neglecting the effects of fiber reorientation and dispersion resulted in poorer agreement with experiments than when they were considered. There was an indication that the proposed BFPHVE model, which includes the intrinsic viscoelasticity of the nonfibrillar matrix (proteoglycan), might be used to model the behavior of cartilage up to relatively high strains (20%). The maximum percentage error between the indentation force predicted by the FE model using the optimized material parameters and that measured experimentally was 3%.
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paper_title: Effects of static axial strain on the tensile properties and failure mechanisms of self‐assembled collagen fibers

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Collagen fibers form the structural units of connective tissue throughout the body, transmitting force, maintaining shape, and providing a scaffold for cells. Our laboratory has studied collagen self-assembly since the 1970s. In this study, collagen fibers were self-assembled from molecular collagen solutions and then stretched to enhance alignment. Fibers were tested in uniaxial tension to study the mechanical properties and failure mechanisms. Results reported suggest that axial orientation of collagen fibrils can be achieved by stretching uncrosslinked collagen fibers. Stretching by about 30% not only results in decreased diameter and increased tensile strength but also leads to unusual failure mechanisms that inhibit crack propagation across the fiber. It is proposed that stretching serves to generate oriented fibrillar substructure in self-assembled collagen fibers. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 63: 1429–1440, 1997
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paper_title: Failure criterion of collagen fiber: Viscoelastic behavior simulated by using load control data

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A nonlinear Zener model is developed to model the viscoelastic behavior of collagen fibers, a building block of the biological soft tissues in the skeletal system. The effects of the strain rate dependency, the loading history, rest, and recovery on the stress-strain relationship of collagen fibers were investigated using the Zener model. The following loading conditions were simulated: (1) the stress relaxation after cyclic loading, (2) the constant strain rate loading before and after cyclic loading (stabilization) and post recovery, and (3) the constant strain rate loading over a wide range of loading rates. In addition, we explored the critical values of stress and strain using different failure criteria at different strain rates. Four major findings were derived from these simulations. First of all, the stress relaxation is larger with a smaller number cycles of preloading. Second, the strain rate sensitivity diminishes after the stabilization and recovery from resting. Third, the stress-strain curve is dependent on the strain rate except for extreme loading conditions (very fast or slow rates of loading). Finally, the strain energy density (SED) criteria may be a more practical failure criterion than the ultimate stress or strain criterion for collagen fiber. These results provide the basis for interpretation of the viscoelastic and failure behaviors of complex structures such as spinal functional units with more economical CPU than full finite element modeling of the whole structure would have required.
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paper_title: Stresses in the local collagen network of articular cartilage: a poroviscoelastic fibril-reinforced finite element study.

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Osteoarthritis (OA) is a multifactorial disease, resulting in diarthrodial joint wear and eventually destruction. Swelling of cartilage, which is proportional to the amount of collagen damage, is an initial event of cartilage degeneration, so damage to the collagen fibril network is likely to be one of the earliest signs of OA cartilage degeneration. We propose that the local stresses and strains in the collagen fibrils, which cause the damage, cannot be determined dependably without taking the local arcade-like collagen-fibril structure into account. We investigate this using a poroviscoelastic fibril-reinforced FEA model. The constitutive fibril properties were determined by fitting numerical data to experimental results of unconfined compression and indentation tests on samples of bovine patellar articular cartilage. It was demonstrated that with this model the stresses and strains in the collagen fibrils can be calculated. It was also exhibited that fibrils with different orientations at the same location can be loaded differently, depending on the local architecture of the collagen network. To the best of our knowledge, the present model is the first that can account for these features. We conclude that the local stresses and strains in the articular cartilage are highly influenced by the local morphology of the collagen-fibril network.
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paper_title: Characterization of articular cartilage by combining microscopic analysis with a fibril-reinforced finite-element model.

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Load-bearing characteristics of articular cartilage are impaired during tissue degeneration. Quantitative microscopy enables in vitro investigation of cartilage structure but determination of tissue functional properties necessitates experimental mechanical testing. The fibril-reinforced poroviscoelastic (FRPVE) model has been used successfully for estimation of cartilage mechanical properties. The model includes realistic collagen network architecture, as shown by microscopic imaging techniques. The aim of the present study was to investigate the relationships between the cartilage proteoglycan (PG) and collagen content as assessed by quantitative microscopic findings, and model-based mechanical parameters of the tissue. Site-specific variation of the collagen network moduli, PG matrix modulus and permeability was analyzed. Cylindrical cartilage samples (n=22) were harvested from various sites of the bovine knee and shoulder joints. Collagen orientation, as quantitated by polarized light microscopy, was incorporated into the finite-element model. Stepwise stress-relaxation experiments in unconfined compression were conducted for the samples, and sample-specific models were fitted to the experimental data in order to determine values of the model parameters. For comparison, Fourier transform infrared imaging and digital densitometry were used for the determination of collagen and PG content in the same samples, respectively. The initial and strain-dependent fibril network moduli as well as the initial permeability correlated significantly with the tissue collagen content. The equilibrium Young's modulus of the nonfibrillar matrix and the strain dependency of permeability were significantly associated with the tissue PG content. The present study demonstrates that modern quantitative microscopic methods in combination with the FRPVE model are feasible methods to characterize the structure-function relationships of articular cartilage.
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paper_title: A fibril-reinforced poroviscoelastic swelling model for articular cartilage.

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From a mechanical point of view, the most relevant components of articular cartilage are the tight and highly organized collagen network together with the charged proteoglycans. Due to the fixed charges of the proteoglycans, the cation concentration inside the tissue is higher than in the surrounding synovial fluid. This excess of ion particles leads to an osmotic pressure difference, which causes swelling of the tissue. The fibrillar collagen network resists straining and swelling pressures. This combination makes cartilage a unique, highly hydrated and pressurized tissue, enforced with a strained collagen network. Many theories to explain articular cartilage behavior under loading, expressed in computational models that either include the swelling behavior or the properties of the anisotropic collagen structure, can be found in the literature. The most common tests used to determine the mechanical quality of articular cartilage are those of confined compression, unconfined compression, indentation and swelling. All theories currently available in the literature can explain the cartilage response occurring in some of the above tests, but none of them can explain these for all of the tests. We hypothesized that a model including simultaneous mathematical descriptions of (1) the swelling properties due to the fixed-change densities of the proteoglycans and (2) the anisotropic viscoelastic collagen structure, can explain all these test simultaneously. To study this hypothesis we extended our fibril-reinforced poroviscoelastic finite element model with our biphasic swelling model. We have shown that the newly developed fibril-reinforced poroviscoelastic swelling (FPVES) model for articular cartilage can simultaneously account for the reaction force during swelling, confined compression, indentation and unconfined compression as well as the lateral deformation during unconfined compression. Using this theory it is possible to analyze the link between the collagen network and the swelling properties of articular cartilage.
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paper_title: Contact Analysis of Biphasic Transversely Isotropic Cartilage Layers and Correlations With Tissue Failure

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Failure of articular cartilage has been investigated experimentally and theoretically, but there is only partial agreement between observed failure and predicted regions of peak stresses. Since trauma and repetitive stress are implicated in the etiopathogenesis of osteoarthritis, it is important to develop cartilage models which correctly predict sites of high stresses. Cartilage is anisotropic and inhomogeneous, though it has been difficult to incorporate these complexities into engineering analyses. The objectives of this study are to demonstrate that a transversely isotropic, biphasic model of cartilage can provide agreement between predicted regions of high stresses and observed regions of cartilage failure and that with transverse isotropy cartilage stresses are more sensitive to convexity and concavity of the surfaces than with isotropy. These objectives are achieved by solving problems of diarthrodial joint contact by the finite-element method. Results demonstrate that transversely isotropic models predict peak stresses at the cartilage surface and the cartilage-bone interface, in agreement with sites of fissures following impact loading; isotropic models predict peak stresses only at the cartilage-bone interface. Also, when convex cartilage layers contacted concave layers in this study, the highest tensile stresses occur in the convex layer for transversely isotropic models; no such differences are found with isotropic models. The significance of this study is that it establishes a threshold of modeling complexity for articular cartilage that provides good agreement with experimental observations under impact loading and that surface curvatures significantly affect stress and strain within cartilage when using a biphasic transversely isotropic model.
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paper_title: Ultrastructural evidence for fibril-to-fibril associations in articular cartilage and their functional implication.

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This study presents ultrastructural evidence for the presence of a variety of fibril-to-fibril interactions or associations in the architecture of the general matrix of articular cartilage. These interactions are believed to serve a higher purpose of repeatedly constraining an overall radial arrangement of fibrils into an array of oblique interconnecting segments thus creating a three dimensional meshwork within which the hydrated ground substance is constrained. It is argued that any reduction in these interfibrillar interactions will allow the oblique fibril segments to revert to a low energy radial configuration, thus explaining the presence of such arrays prominent in various degenerate forms of articular cartilage.
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paper_title: Fibril reinforced poroelastic model predicts specifically mechanical behavior of normal, proteoglycan depleted and collagen degraded articular cartilage

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Abstract Degradation of collagen network and proteoglycan (PG) macromolecules are signs of articular cartilage degeneration. These changes impair cartilage mechanical function. Effects of collagen degradation and PG depletion on the time-dependent mechanical behavior of cartilage are different. In this study, numerical analyses, which take the compression-tension nonlinearity of the tissue into account, were carried out using a fibril reinforced poroelastic finite element model. The study aimed at improving our understanding of the stress-relaxation behavior of normal and degenerated cartilage in unconfined compression. PG and collagen degradations were simulated by decreasing the Young's modulus of the drained porous (nonfibrillar) matrix and the fibril network, respectively. Numerical analyses were compared to results from experimental tests with chondroitinase ABC (PG depletion) or collagenase (collagen degradation) digested samples. Fibril reinforced poroelastic model predicted the experimental behavior of cartilage after chondroitinase ABC digestion by a major decrease of the drained porous matrix modulus (−64±28%) and a minor decrease of the fibril network modulus (−11±9%). After collagenase digestion, in contrast, the numerical analyses predicted the experimental behavior of cartilage by a major decrease of the fibril network modulus (−69±5%) and a decrease of the drained porous matrix modulus (−44±18%). The reduction of the drained porous matrix modulus after collagenase digestion was consistent with the microscopically observed secondary PG loss from the tissue. The present results indicate that the fibril reinforced poroelastic model is able to predict specifically characteristic alterations in the stress-relaxation behavior of cartilage after enzymatic modifications of the tissue. We conclude that the compression-tension nonlinearity of the tissue is needed to capture realistically the mechanical behavior of normal and degenerated articular cartilage.
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paper_title: Importance of the superficial tissue layer for the indentation stiffness of articular cartilage

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Indentation testing is a widely used technique for nondestructive mechanical analysis of articular cartilage. Although cartilage shows an inhomogeneous, layered structure with anisotropic mechanical properties, most theoretical indentation models assume material homogeneity and isotropy. In the present study, quantitative polarized light microscopy (PLM) measurements from canine cartilage were utilized to characterize thickness and structure of the superficial, collageneous tissue layer as well as to reveal its relation to experimental indentation measurements. In addition to experimental analyses, a layered, transversely isotropic finite element (FE) model was developed and the effect of superficial (tangential) tissue layer with high elastic modulus in the direction parallel to articular surface on the indentation response was studied. The experimental indentation stiffness was positively correlated with the relative thickness of the superficial cartilage layer. Also the optical retardation, which reflects the degree of parallel organization of collagen fibrils as well as collagen content, was related to indentation stiffness. FE results indicated effective stiffening of articular cartilage under indentation due to high transverse modulus of the superficial layer. The present results suggest that indentation testing is an efficient technique for the characterization of the superficial degeneration of articular cartilage.
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paper_title: A Triphasic Theory for the Swelling and Deformation Behaviors of Articular Cartilage

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Swelling of articular cartilage depends on its fixed charge density and distribution, the stiffness of its collagen-proteoglycan matrix, and the ion concentrations in the interstitium. A theory for a tertiary mixture has been developed, including the two fluid-solid phases (biphasic), and an ion phase, representing cation and anion of a single salt, to describe the deformation and stress fields for cartilage under chemical and/or mechanical loads. This triphasic theory combines the physico-chemical theory for ionic and polyionic (proteoglycan) solutions with the biphasic theory for cartilage. The present model assumes the fixed charge groups to remain unchanged, and that the counter-ions are the cations of a single salt of the bathing solution. The momentum equation for the neutral salt and for the intersitial water are expressed in terms of their chemical potentials whose gradients are the driving forces for their movements. These chemical potentials depend on fluid pressure p, salt concentration c, solid matrix dilatation e and fixed charge density cF . For a uni-uni valent salt such as NaCl, they are given by μi = μo i + (RT/Mi )ln[γ± 2 c (c + c F )] and μW = μo w + [p − RTφ(2c + cF ) + Bw e]/ρT w , where R, T, Mi , γ± , φ, ρT w and Bw are universal gas constant, absolute temperature, molecular weight, mean activity coefficient of salt, osmotic coefficient, true density of water, and a coupling material coefficient, respectively. For infinitesimal strains and material isotropy, the stress-strain relationship for the total mixture stress is σ = − pI − Tc I + λs (trE)I + 2μs E, where E is the strain tensor and (λs ,μs ) are the Lame constants of the elastic solid matrix. The chemical-expansion stress (− Tc ) derives from the charge-to-charge repulsive forces within the solid matrix. This theory can be applied to both equilibrium and non-equilibrium problems. For equilibrium free swelling problems, the theory yields the well known Donnan equilibrium ion distribution and osmotic pressure equations, along with an analytical expression for the “pre-stress” in the solid matrix. For the confined-compression swelling problem, it predicts that the applied compressive stress is shared by three load support mechanisms: 1) the Donnan osmotic pressure; 2) the chemical-expansion stress; and 3) the solid matrix elastic stress. Numerical calculations have been made, based on a set of equilibrium free-swelling and confined-compression data, to assess the relative contribution of each mechanism to load support. Our results show that all three mechanisms are important in determining the overall compressive stiffness of cartilage.
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paper_title: A finite element formulation and program to study transient swelling and load-carriage in healthy and degenerate articular cartilage

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The theory of poroelasticity is extended to include physico-chemical swelling and used to predict the transient responses of normal and degenerate articular cartilage to both chemical and mechanical loading; with emphasis on isolating the influence of the major parameters which govern its deformation. Using a new hybrid element, our mathematical relationships were implemented in a purpose-built poroelastic finite element analysis algorithm (u-pi-c program) which was used to resolve the nature of the coupling between the mechanical and chemical responses of cartilage when subjected to ionic transport across its membranous skeleton. Our results demonstrate that one of the roles of the strain-dependent matrix permeability is to limit the rate of transmission of stresses from the fluid to the collagen-proteoglycan solid skeleton in the incipient stages of loading, and that the major contribution of the swelling pressure is that of preventing any excessive deformation of the matrix.
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paper_title: Structural and Compositional Changes in Peri- and Extracellular Matrix of Osteoarthritic Cartilage Modulate Chondrocyte Morphology

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It has not been shown how specific changes in composition and structure in the peri- and extracellular matrix (PCM and ECM) of human articular cartilage modulate cell morphology in different stages of osteoarthritis (OA). In the present study, cell morphology in the superficial tissue of normal, early OA and advanced OA human cartilage samples were measured from histological sections. Collagen and proteoglycan contents in the vicinity of chondrocytes were analyzed using Fourier transform infrared spectroscopy and digital densitometry. Determinants of the experimentally observed morphological changes of cells were studied using finite element analysis (FEA). From normal tissue to early OA, cell aspect ratio (height/width) remained constant (0.69 ± 0.11 and 0.69 ± 0.09, respectively). In advanced OA, cells became significantly (p < 0.05) more rounded (aspect ratio of 0.83 ± 0.13). Normalized collagen content in the PCM, i.e. collagen content in the PCM with respect to that in the ECM, was reduced significantly (p < 0.05) only in advanced OA. FEA indicated that reduced proteoglycan content and increased collagen fibrillation in the PCM and ECM, as well as reduced collagen content only in the PCM, primarily explained experimentally found changes in cell aspect ratio. Our results suggest that changes in composition and structure of the PCM and ECM in the superficial tissue of human articular cartilage modulate cell morphology differently in early and advanced OA.
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paper_title: A validation of the quadriphasic mixture theory for intervertebral disc tissue

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The swelling and shrinking behaviour of soft biological tissues is described by a quadriphasic mixture model. In this model four phases are distinguished: a charged solid, a fluid, cations and anions. A description of the set of coupled differential equations of this quadriphasic mixture model is given. These equations are solved by the finite element method using a weighted residual approach. The resulting non-linear integral equations are linearized and solved by the Newton-Raphson iteration procedure. We performed some confined swelling and compression experiments on intervertebral disc tissue. These experiments are simulated by a one-dimensional finite element implementation of this quadriphasic mixture model. In contrast to a triphasic mixture model, physically realistic diffusion coefficients can be used to fit the experiments when the fixed charge density is relatively large, because in the quadriphasic mixture model electrical phenomena are not neglected.
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paper_title: Stress–relaxation of human patellar articular cartilage in unconfined compression: Prediction of mechanical response by tissue composition and structure

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Abstract Mechanical properties of articular cartilage are controlled by tissue composition and structure. Cartilage function is sensitively altered during tissue degeneration, in osteoarthritis (OA). However, mechanical properties of the tissue cannot be determined non-invasively. In the present study, we evaluate the feasibility to predict, without mechanical testing, the stress–relaxation response of human articular cartilage under unconfined compression. This is carried out by combining microscopic and biochemical analyses with composition-based mathematical modeling. Cartilage samples from five cadaver patellae were mechanically tested under unconfined compression. Depth-dependent collagen content and fibril orientation, as well as proteoglycan and water content were derived by combining Fourier transform infrared imaging, biochemical analyses and polarized light microscopy. Finite element models were constructed for each sample in unconfined compression geometry. First, composition-based fibril-reinforced poroviscoelastic swelling models, including composition and structure obtained from microscopical and biochemical analyses were fitted to experimental stress–relaxation responses of three samples. Subsequently, optimized values of model constants, as well as compositional and structural parameters were implemented in the models of two additional samples to validate the optimization. Theoretical stress–relaxation curves agreed with the experimental tests ( R =0.95–0.99). Using the optimized values of mechanical parameters, as well as composition and structure of additional samples, we were able to predict their mechanical behavior in unconfined compression, without mechanical testing ( R =0.98). Our results suggest that specific information on tissue composition and structure might enable assessment of cartilage mechanics without mechanical testing.
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paper_title: A composition-based cartilage model for the assessment of compositional changes during cartilage damage and adaptation

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Summary Objective The composition of articular cartilage changes with progression of osteoarthritis. Since compositional changes are associated with changes in the mechanical properties of the tissue, they are relevant for understanding how mechanical loading induces progression. The objective of this study is to present a computational model of articular cartilage which enables to study the interaction between composition and mechanics. Methods Our previously developed fibril-reinforced poroviscoelastic swelling model for articular cartilage was combined with our tissue composition-based model. In the combined model both the depth- and strain-dependencies of the permeability are governed by tissue composition. All local mechanical properties in the combined model are directly related to the local composition of the tissue, i.e., to the local amounts of proteoglycans and collagens and to tissue anisotropy. Results Solely based on the composition of the cartilage, we were able to predict the equilibrium and transient response of articular cartilage during confined compression, unconfined compression, indentation and two different 1D-swelling tests, simultaneously. Conclusion Since both the static and the time-dependent mechanical properties have now become fully dependent on tissue composition, the model allows assessing the mechanical consequences of compositional changes seen during osteoarthritis without further assumptions. This is a major step forward in quantitative evaluations of osteoarthritis progression.
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paper_title: Importance of collagen orientation and depth-dependent fixed charge densities of cartilage on mechanical behavior of chondrocytes.

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The collagen network and proteoglycan matrix of articular cartilage are thought to play an important role in controlling the stresses and strains in and around chondrocytes, in regulating the biosynthesis of the solid matrix, and consequently in maintaining the health of diarthrodial joints. Understanding the detailed effects of the mechanical environment of chondrocytes on cell behavior is therefore essential for the study of the development, adaptation, and degeneration of articular cartilage. Recent progress in macroscopic models has improved our understanding of depth-dependent properties of cartilage. However, none of the previous works considered the effect of realistic collagen orientation or depth-dependent negative charges in microscopic models of chondrocyte mechanics. The aim of this study was to investigate the effects of the collagen network and fixed charge densities of cartilage on the mechanical environment of the chondrocytes in a depth-dependent manner. We developed an anisotropic, inhomogeneous, microstructural fibril-reinforced finite element model of articular cartilage for application in unconfined compression. The model consisted of the extracellular matrix and chondrocytes located in the superficial, middle, and deep zones. Chondrocytes were surrounded by a pericellular matrix and were assumed spherical prior to tissue swelling and load application. Material properties of the chondrocytes, pericellular matrix, and extracellular matrix were obtained from the literature. The loading protocol included a free swelling step followed by a stress-relaxation step. Results from traditional isotropic and transversely isotropic biphasic models were used for comparison with predictions from the current model. In the superficial zone, cell shapes changed from rounded to elliptic after free swelling. The stresses and strains as well as fluid flow in cells were greatly affected by the modulus of the collagen network. The fixed charge density of the chondrocytes, pericellular matrix, and extracellular matrix primarily affected the aspect ratios (height/ width) and the solid matrix stresses of cells. The mechanical responses of the cells were strongly location and time dependent. The current model highlights that the collagen orientation and the depth-dependent negative fixed charge densities of articular cartilage have a great effect in modulating the mechanical environment in the vicinity of chondrocytes, and it provides an important improvement over earlier models in describing the possible pathways from loading of articular cartilage to the mechanical and biological responses of chondrocytes.
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paper_title: Composition of the pericellular matrix modulates the deformation behaviour of chondrocytes in articular cartilage under static loading

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The aim was to assess the role of the composition changes in the pericellular matrix (PCM) for the chondrocyte deformation. For that, a three-dimensional finite element model with depth-dependent collagen density, fluid fraction, fixed charge density and collagen architecture, including parallel planes representing the split-lines, was created to model the extracellular matrix (ECM). The PCM was constructed similarly as the ECM, but the collagen fibrils were oriented parallel to the chondrocyte surfaces. The chondrocytes were modelled as poroelastic with swelling properties. Deformation behaviour of the cells was studied under 15% static compression. Due to the depth-dependent structure and composition of cartilage, axial cell strains were highly depth-dependent. An increase in the collagen content and fluid fraction in the PCMs increased the lateral cell strains, while an increase in the fixed charge density induced an inverse behaviour. Axial cell strains were only slightly affected by the changes in PCM composition. We conclude that the PCM composition plays a significant role in the deformation behaviour of chondrocytes, possibly modulating cartilage development, adaptation and degeneration. The development of cartilage repair materials could benefit from this information.
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paper_title: On the Thermodynamical Admissibility of the Triphasic Theory of Charged Hydrated Tissues

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The triphasic theory on soft charged hydrated tissues (Lai, W. M., Hou, J. S., and Mow, V. C., 1991, "A Triphasic Theory for the Swelling and Deformation Behaviors of Articular Cartilage," ASME J. Biomech. Eng., 113, pp. 245-258) attributes the swelling propensity of articular cartilage to three different mechanisms: Donnan osmosis, excluded volume effect, and chemical expansion stress. The aim of this study is to evaluate the thermodynamic plausibility of the triphasic theory. The free energy of a sample of articular cartilage subjected to a closed cycle of mechanical and chemical loading is calculated using the triphasic theory. It is shown that the chemical expansion stress term induces an unphysiological generation of free energy during each closed cycle of loading and unloading. As the cycle of loading and unloading can be repeated an indefinite number of times, any amount of free energy can be drawn from a sample of articular cartilage, if the triphasic theory were true. The formulation for the chemical expansion stress as used in the triphasic theory conflicts with the second law of thermodynamics.
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paper_title: Quadriphasic mechanics of swelling incompressible porous media

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A chemo-electro-mechanical formulation of quasi-static finite deformation of swelling incompressible porous media is derived from mixture theory. The model consists of an electrically charged porous solid saturated with a monovalent ionic solution. Incompressible and isothermal deformation is assumed. Hydration forces are neglected. The mixture as a whole is assumed locally electroneutral. Four phases following different kinematic paths are defined: solid, fluid, anions and cations. Balance laws are derived for each phase and for the mixture as a whole. A Lagrangian form of the second law of thermodynamics is derived for incompressible porous media and is used to derive the constitutive relationships of the medium. It is shown that the theory is consistent with Biot's theory for the limiting case without ionic effects and with Staverman's results for the limiting case without deformation.
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paper_title: Complex nature of stress inside loaded articular cartilage

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Abstract We show that in the early stages of loading of the cartilage matrix extensive water exudation and related physicochemical and structural changes give rise to a distinctly consolidatable system. By enzymatically modifying the pre-existing osmotic condition of the normal matrix and measuring its hydrostatic excess pore pressure, we have studied the exact influence of physicochemistry on the consolidation of cartilage. We argue that the attainment of a certain minimum level of swelling stiffness of the solid skeleton, which is developed at the maximum hydrostatic excess pore pressure of the fluid, controls the effective consolidation of articular cartilage. Three related but distinct stresses are developed during cartilage deformation, namely (1) the swelling stress in the coupled proteoglycan/collagen skeleton in the early stages of deformation, (2) the hydrostatic excess pore pressure carried by the fluid component, and (3) the effective stress generated on top of the minimum value of the swelling stress in the consolidation stages following the attainment of the fluid's maximum pore pressure. The minimum value of the swelling pressure is in turn generated over and above the intrinsic osmotic pressure in the unloaded matrix. The response of the hyaluronidase-digested matrix relative to its intact state again highlights the important influence of the osmotic pressure and the coefficient of permeability, both of which are related to the volume fraction of proteoglycans on cartilage deformation, and therefore its ability to function as an effective stress-redistributing layer above the subchondral bone.
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paper_title: Depth- and strain-dependent mechanical and electromechanical properties of full-thickness bovine articular cartilage in confined compression.

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Compression tests have often been performed to assess the biomechanical properties of full-thickness articular cartilage. We tested whether the apparent homogeneous strain-dependent properties, deduced from such tests, reflect both strain- and depth-dependent material properties. Full-thickness bovine articular cartilage was tested by oscillatory confined compression superimposed on a static offset up to 45%. and the data fit to estimate modulus, permeability, and electrokinetic coefficient assuming homogeneity. Additional tests on partial-thickness cartilage were then performed to assess depth- and strain-dependent properties in an inhomogeneous model, assuming three discrete layers (i = 1 starting from the articular surface, to i = 3 up to the subchondral bone). Estimates of the zero-strain equilibrium confined compression modulus (H(A0)), the zero-strain permeability (kp0) and deformation dependence constant (M), and the deformation-dependent electrokinetic coefficient (ke) differed among individual layers of cartilage and full-thickness cartilage. HiA0 increased from layer 1 to 3 (0.27 to 0.71 MPa), and bracketed the apparent homogeneous value (0.47 MPa). ki(p0) decreased from layer 1 to 3 (4.6 x 10(-15) to 0.50 x 10(-15) m2/Pa s) and was less than the homogeneous value (7.3 x 10(-15) m2/Pa s), while Mi increased from layer 1 to 3 (5.5 to 7.4) and became similar to the homogeneous value (8.4). The amplitude of ki(e) increased markedly with compressive strain, as did the homogeneous value: at low strain, it was lowest near the articular surface and increased to a peak in the middle-deep region. These results help to interpret the biomechanical assessment of full-thickness articular cartilage.
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paper_title: A Poroelastic Finite Element Formulation Including Transport and Swelling in Soft Tissue Structures

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A field theory is presented for the study of swelling in soft tissue structures that are modeled as poroelastic materials. As a first approximation, soft tissues are assumed to be linear isotropic materials undergoing infinitesimal strains. Material properties are identified that are necessary for the solution of initial boundary value problems where swelling and convection are significant. A finite element model is developed that includes the solid displacements, the relative fiuid displacements, and a representative concentration as the primary unknowns. A numerical example is presented based on a triphasic model. The finite model simulates a typical experimental protocol for soft tissue testing and demonstrates the interaction and coupling associated with relative fluid motion and swelling in a deforming poroelastic material. The theory and finite element model provide a starting point for nonlinear porohyperelastic transport-swelling analyses of soft tissue structures that include finite strains in anisotropic materials.
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paper_title: The kinetics of chemically induced nonequilibrium swelling of articular cartilage and corneal stroma.

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An electromechanical model for charged, hydrated tissues is developed to predict the kinetics of changes in swelling and isometric compressive stress induced by changes in bath salt concentration. The model focuses on ionic transport as the rate limiting step in chemically modulating electrical interactions between the charged macromolecules of the extracellular matrix. The swelling response to such changes in local interaction forces is determined by the relative rates of chemical diffusion and fluid redistribution in the tissue sample. We have tested the model by comparing the experimentally observed salt-induced stress relaxation response in bovine articular cartilage and corneal stroma to the response predicted by the model using constitutive relations for the concentration dependent material properties of the tissues reported in a related study. The qualitatively good agreement between our experimental measurements and the predictions of the model supports the physical basis of the model and demonstrates the model's ability to discriminate between the two soft connective tissues that were examined.
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paper_title: A finite element analysis methodology for representing the articular cartilage functional structure.

paper_content:

Recognising that the unique biomechanical properties of articular cartilage are a consequence of its structure, this paper describes a finite element methodology which explicitly represents this structure using a modified overlay element model. The validity of this novel concept was then tested by using it to predict the axial curling forces generated by cartilage matrices subjected to saline solutions of known molality and concentration in a novel experimental protocol. Our results show that the finite element modelling methodology accurately represents the intrinsic biomechanical state of the cartilage matrix and can be used to predict its transient load-carriage behaviour. We conclude that this ability to represent the intrinsic swollen condition of a given cartilage matrix offers a viable avenue for numerical analysis of degenerate articular cartilage and also those matrices affected by disease.
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paper_title: Physicochemical Properties of Cartilage in the Light of Ion Exchange Theory

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Ion exchange theory has been applied to articular cartilage. Relationships were derived between permeability, diffusivity, electrical conductivity, and streaming potential. Systematic measurements were undertaken on these properties. Experimental techniques are described and data tabulated. Theoretical correlations were found to hold within the experimental error. The concentration of fixed negatively-charged groups in cartilage was shown to be the most important parameter. Fixed charge density was found to increase with distance from the articular surface and this variation was reflected in the other properties.
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paper_title: A fibril-reinforced poroviscoelastic swelling model for articular cartilage.

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From a mechanical point of view, the most relevant components of articular cartilage are the tight and highly organized collagen network together with the charged proteoglycans. Due to the fixed charges of the proteoglycans, the cation concentration inside the tissue is higher than in the surrounding synovial fluid. This excess of ion particles leads to an osmotic pressure difference, which causes swelling of the tissue. The fibrillar collagen network resists straining and swelling pressures. This combination makes cartilage a unique, highly hydrated and pressurized tissue, enforced with a strained collagen network. Many theories to explain articular cartilage behavior under loading, expressed in computational models that either include the swelling behavior or the properties of the anisotropic collagen structure, can be found in the literature. The most common tests used to determine the mechanical quality of articular cartilage are those of confined compression, unconfined compression, indentation and swelling. All theories currently available in the literature can explain the cartilage response occurring in some of the above tests, but none of them can explain these for all of the tests. We hypothesized that a model including simultaneous mathematical descriptions of (1) the swelling properties due to the fixed-change densities of the proteoglycans and (2) the anisotropic viscoelastic collagen structure, can explain all these test simultaneously. To study this hypothesis we extended our fibril-reinforced poroviscoelastic finite element model with our biphasic swelling model. We have shown that the newly developed fibril-reinforced poroviscoelastic swelling (FPVES) model for articular cartilage can simultaneously account for the reaction force during swelling, confined compression, indentation and unconfined compression as well as the lateral deformation during unconfined compression. Using this theory it is possible to analyze the link between the collagen network and the swelling properties of articular cartilage.
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paper_title: General Theory of Three‐Dimensional Consolidation

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The settlement of soils under load is caused by a phenomenon called consolidation, whose mechanism is known to be in many cases identical with the process of squeezing water out of an elasticporous medium. The mathematical physical consequences of this viewpoint are established in the present paper. The number of physical constants necessary to determine the properties of the soil is derived along with the general equations for the prediction of settlements and stresses in three‐dimensional problems. Simple applications are treated as examples. The operational calculus is shown to be a powerful method of solution of consolidation problems.
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paper_title: Contribution of postnatal collagen reorientation to depth-dependent mechanical properties of articular cartilage

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The collagen fibril network is an important factor for the depth-dependent mechanical behaviour of adult articular cartilage (AC). Recent studies show that collagen orientation is parallel to the articular surface throughout the tissue depth in perinatal animals, and that the collagen orientations transform to a depth-dependent arcade-like structure in adult animals. Current understanding on the mechanobiology of postnatal AC development is incomplete. In the current paper, we investigate the contribution of collagen fibril orientation changes to the depth-dependent mechanical properties of AC. We use a composition-based finite element model to simulate in a 1-D confined compression geometry the effects of ten different collagen orientation patterns that were measured in developing sheep. In initial postnatal life, AC is mostly subject to growth and we observe only small changes in depth-dependent mechanical behaviour. Functional adaptation of depth-dependent mechanical behaviour of AC takes place in the second half of life before puberty. Changes in fibril orientation alone increase cartilage stiffness during development through the modulation of swelling strains and osmotic pressures. Changes in stiffness are most pronounced for small stresses and for cartilage adjacent to the bone. We hypothesize that postnatal changes in collagen fibril orientation induce mechanical effects that in turn promote these changes. We further hypothesize that a part of the depth-dependent postnatal increase in collagen content in literature is initiated by the depth-dependent postnatal increase in fibril strain due to collagen fibril reorientation.
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paper_title: A Comparison Between Mechano-Electrochemical and Biphasic Swelling Theories for Soft Hydrated Tissues

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Biological tissues like intervertebral discs and articular cartilage primarily consist of interstitial fluid, collagen fibrils and negatively charged proteoglycans. Due to the fixed charges of the proteoglycans, the total ion concentration inside the tissue is higher than in the surrounding synovial fluid (cation concentration is higher and the anion concentration is lower). This excess of ion particles leads to an osmotic pressure difference, which causes swelling of the tissue. In the last decade several mechano-electrochemical models, which include this mechanism, have been developed. As these models are complex and computationally expensive, it is only possible to analyze geometrically relatively small problems. Furthermore, there is still no commercial finite element tool that includes such a mechano-electrochemical theory. Lanir (Biorheology,24, pp. 173‐187, 1987) hypothesized that electrolyte flux in articular cartilage can be neglected in mechanical studies. Lanir’s hypothesis implies that the swelling behavior of cartilage is only determined by deformation of the solid and by fluid flow. Hence, the response could be described by adding a deformation-dependent pressure term to the standard biphasic equations. Based on this theory we developed a biphasic swelling model. The goal of the study was to test Lanir’s hypothesis for a range of material properties. We compared the deformation behavior predicted by the biphasic swelling model and a full mechano-electrochemical model for confined compression and 1D swelling. It was shown that, depending on the material properties, the biphasic swelling model behaves largely the same as the mechano-electrochemical model, with regard to stresses and strains in the tissue following either mechanical or chemical perturbations. Hence, the biphasic swelling model could be an alternative for the more complex mechano-electrochemical model, in those cases where the ion flux itself is not the subject of the study. We propose thumbrules to estimate the correlation between the two models for specific problems. @DOI: 10.1115/1.1835361#
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paper_title: Contribution of tissue composition and structure to mechanical response of articular cartilage under different loading geometries and strain rates

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Mechanical function of articular cartilage in joints between articulating bones is dependent on the composition and structure of the tissue. The mechanical properties of articular cartilage are traditionally tested in compression using one of the three loading geometries, i.e., confined compression, unconfined compression or indentation. The aim of this study was to utilize a composition-based finite element model in combination with a fractional factorial design to determine the importance of different cartilage constituents in the mechanical response of the tissue, and to compare the importance of the tissue constituents with different loading geometries and loading rates. The evaluated parameters included water and collagen fraction as well as fixed charge density on cartilage surface and their slope over the tissue thickness. The thicknesses of superficial and middle zones, as based on the collagen orientation, were also included in the evaluated parameters. A three-level resolution V fractional factorial design was used. The model results showed that inhomogeneous composition plays only a minor role in indentation, though that role becomes more significant in confined compression and unconfined compression. In contrast, the collagen architecture and content had a more profound role in indentation than with two other loading geometries. These differences in the mechanical role of composition and structure between the loading geometries were emphasized at higher loading rates. These findings highlight how the results from mechanical tests of articular cartilage under different loading conditions are dependent upon tissue composition and structure.
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paper_title: A finite element formulation and program to study transient swelling and load-carriage in healthy and degenerate articular cartilage

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The theory of poroelasticity is extended to include physico-chemical swelling and used to predict the transient responses of normal and degenerate articular cartilage to both chemical and mechanical loading; with emphasis on isolating the influence of the major parameters which govern its deformation. Using a new hybrid element, our mathematical relationships were implemented in a purpose-built poroelastic finite element analysis algorithm (u-pi-c program) which was used to resolve the nature of the coupling between the mechanical and chemical responses of cartilage when subjected to ionic transport across its membranous skeleton. Our results demonstrate that one of the roles of the strain-dependent matrix permeability is to limit the rate of transmission of stresses from the fluid to the collagen-proteoglycan solid skeleton in the incipient stages of loading, and that the major contribution of the swelling pressure is that of preventing any excessive deformation of the matrix.
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paper_title: Hyperelastic modelling of arterial layers with distributed collagen fibre orientations

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Constitutive relations are fundamental to the solution of problems in continuum mechanics, and are required in the study of, for example, mechanically dominated clinical interventions involving soft biological tissues. Structural continuum constitutive models of arterial layers integrate information about the tissue morphology and therefore allow investigation of the interrelation between structure and function in response to mechanical loading. Collagen fibres are key ingredients in the structure of arteries. In the media (the middle layer of the artery wall) they are arranged in two helically distributed families with a small pitch and very little dispersion in their orientation (i.e. they are aligned quite close to the circumferential direction). By contrast, in the adventitial and intimal layers, the orientation of the collagen fibres is dispersed, as shown by polarized light microscopy of stained arterial tissue. As a result, continuum models that do not account for the dispersion are not able to capture accurately the stress–strain response of these layers. The purpose of this paper, therefore, is to develop a structural continuum framework that is able to represent the dispersion of the collagen fibre orientation. This then allows the development of a new hyperelastic free-energy function that is particularly suited for representing the anisotropic elastic properties of adventitial and intimal layers of arterial walls, and is a generalization of the fibre-reinforced structural model introduced by Holzapfel & Gasser (Holzapfel & Gasser 2001 Comput. Meth. Appl. Mech. Eng. 190, 4379–4403) and Holzapfel et al. (Holzapfel et al. 2000 J. Elast. 61, 1–48). The model incorporates an additional scalar structure parameter that characterizes the dispersed collagen orientation. An efficient finite element implementation of the model is then presented and numerical examples show that the dispersion of the orientation of collagen fibres in the adventitia of human iliac arteries has a significant effect on their mechanical response.
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paper_title: Microstructural modeling of collagen network mechanics and interactions with the proteoglycan gel in articular cartilage

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Cartilage matrix mechanical function is largely determined by interactions between the collagen fibrillar network and the proteoglycan gel. Although the molecular physics of these matrix constituents have been characterized and modern imaging methods are capable of localized measurement of molecular densities and orientation distributions, theoretical tools for using this information for prediction of cartilage mechanical behavior are lacking. We introduce a means to model collagen network contributions to cartilage mechanics based upon accessible microstructural information (fibril density and orientation distributions) and which self-consistently follows changes in microstructural geometry with matrix deformations. The interplay between the molecular physics of the collagen network and the proteoglycan gel is scaled up to determine matrix material properties, with features such as collagen fibril pre-stress in free-swelling cartilage emerging naturally and without introduction of ad hoc parameters. Methods are developed for theoretical treatment of the collagen network as a continuum-like distribution of fibrils, such that mechanical analysis of the network may be simplified by consideration of the spherical harmonic components of functions of the fibril orientation, strain, and stress distributions. Expressions for the collagen network contributions to matrix stress and stiffness tensors are derived, illustrating that only spherical harmonic components of orders 0 and 2 contribute to the stress, while orders 0, 2, and 4 contribute to the stiffness. Depth- and compression-dependent equilibrium mechanical properties of cartilage matrix are modeled, and advantages of the approach are illustrated by exploration of orientation and strain distributions of collagen fibrils in compressed cartilage. Results highlight collagen-proteoglycan interactions, especially for very small physiological strains where experimental data are relatively sparse. These methods for determining matrix mechanical properties from measurable quantities at the microscale (composition, structure, and molecular physics) may be useful for investigating cartilage structure-function relationships relevant to load-bearing, injury, and repair.
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paper_title: A viscoelastic model for fiber-reinforced composites at finite strains: Continuum basis, computational aspects and applications

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Abstract This paper presents a viscoelastic model for the fully three-dimensional stress and deformation response of fiber-reinforced composites that experience finite strains. The composites are thought to be (soft) matrix materials which are reinforced by two families of fibers so that the mechanical properties of the composites depend on two fiber directions. The relaxation and/or creep response of each compound of the composite is modeled separately and the global response is obtained by an assembly of all contributions. We develop novel closed-form expressions for the fourth-order elasticity tensor (tangent moduli) in full generality. Constitutive models for orthotropic, transversely isotropic and isotropic hyperelastic materials at finite strains with or without dissipation are included as special cases. In order to clearly show the good performance of the constitutive model, we present 3D and 2D numerical simulations of a pressurized laminated circular tube which shows an interesting `stretch inversion phenomenon' in the low pressure domain. Numerical results are in good qualitative agreement with experimental data and approximate the observed strongly anisotropic physical response with satisfying accuracy. A third numerical example is designed to illustrate the anisotropic stretching process of a fiber-reinforced rubber bar and the subsequent relaxation behavior at finite strains. The material parameters are chosen so that thermodynamic equilibrium is associated with the known homogeneous deformation state.
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paper_title: Modeling the Matrix of Articular Cartilage Using a Continuous Fiber Angular Distribution Predicts Many Observed Phenomena

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A number of theoretical frameworks embodying the disparity between tensile and compressive properties of cartilage have been proposed, accounting for the collagen fibers implicitly [1,2] or explicitly [3–5]. These models generally propose discrete fiber families to describe the collagen matrix. They are able to capture the most salient features of the cartilage mechanical response, namely, the tension-compression nonlinearity of the stress-strain curve [6].Copyright © 2009 by ASME
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paper_title: A hyperelastic biphasic fibre-reinforced model of articular cartilage considering distributed collagen fibre orientations: continuum basis, computational aspects and applications

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Cartilage is a multi-phase material composed of fluid and electrolytes (68-85% by wet weight), proteoglycans (5-10% by wet weight), chondrocytes, collagen fibres and other glycoproteins. The solid ...
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paper_title: Analysis of articular cartilage as a composite using nonlinear membrane elements for collagen fibrils.

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To develop a composite fibre-reinforced model of the cartilage, membrane shell elements were introduced to represent collagen fibrils reinforcing the isotropic porous solid matrix filled with fluid. Nonlinear stress-strain curve of pure collagen fibres and collagen volume fraction were explicitly presented in the formulation of these membrane elements. In this composite model, in accordance with tissue structure, the matrix and fibril membrane network experienced dissimilar stresses despite identical strains in the fibre directions. Different unconfined compression and indentation case studies were performed to determine the distinct role of membrane collagen fibrils in nonlinear poroelastic mechanics of articular cartilage. The importance of nonlinear fibril membrane elements in the tissue relaxation response as well as in temporal and spatial variations of pore pressure and solid matrix stresses was demonstrated. By individual adjustments of the collagen volume fraction and collagen mechanical properties, the model allows for the simulation of alterations in the fibril network structure of the tissue towards modelling damage processes or repair attempts. The current model, which is based on a physiological description of the tissue structure, is promising in improvement of our understanding of the cartilage pathomechanics.
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paper_title: Nonlinear analysis of cartilage in unconfined ramp compression using a fibril reinforced poroelastic model.

paper_content:

OBJECTIVE ::: To develop a biomechanical model for cartilage which is capable of capturing experimentally observed nonlinear behaviours of cartilage and to investigate effects of collagen fibril reinforcement in cartilage. ::: ::: ::: DESIGN ::: A sequence of 10 or 20 steps of ramp compression/relaxation applied to cartilage disks in uniaxial unconfined geometry is simulated for comparison with experimental data. ::: ::: ::: BACKGROUND ::: Mechanical behaviours of cartilage, such as the compression-offset dependent stiffening of the transient response and the strong relaxation component, have been previously difficult to describe using the biphasic model in unconfined compression. ::: ::: ::: METHODS ::: Cartilage is modelled as a fluid-saturated solid reinforced by an elastic fibrillar network. The latter, mainly representing collagen fibrils, is considered as a distinct constituent embedded in a biphasic component made up mainly of proteoglycan macromolecules and a fluid carrying mobile ions. The Young's modulus of the fibrillar network is taken to vary linearly with its tensile strain but to be zero for compression. Numerical computations are carried out using a finite element procedure, for which the fibrillar network is discretized into a system of spring elements. ::: ::: ::: RESULTS ::: The nonlinear fibril reinforced poroelastic model is capable of describing the strong relaxation behaviour and compression-offset dependent stiffening of cartilage in unconfined compression. Computational results are also presented to demonstrate unique features of the model, e.g. the matrix stress in the radial direction is changed from tensile to compressive due to presence of distinct fibrils in the model. ::: ::: ::: RELEVANCE ::: Experimentally observed nonlinear behaviours of cartilage are successfully simulated, and the roles of collagen fibrils are distinguished by using the proposed model. Thus this study may lead to a better understanding of physiological responses of individual constituents of cartilage to external loads, and of the roles of mechanical loading in cartilage remodelling and pathology.
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paper_title: A finite element analysis methodology for representing the articular cartilage functional structure.

paper_content:

Recognising that the unique biomechanical properties of articular cartilage are a consequence of its structure, this paper describes a finite element methodology which explicitly represents this structure using a modified overlay element model. The validity of this novel concept was then tested by using it to predict the axial curling forces generated by cartilage matrices subjected to saline solutions of known molality and concentration in a novel experimental protocol. Our results show that the finite element modelling methodology accurately represents the intrinsic biomechanical state of the cartilage matrix and can be used to predict its transient load-carriage behaviour. We conclude that this ability to represent the intrinsic swollen condition of a given cartilage matrix offers a viable avenue for numerical analysis of degenerate articular cartilage and also those matrices affected by disease.
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paper_title: The role of interstitial fluid pressurization in articular cartilage lubrication

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Over the last two decades, considerable progress has been reported in the field of cartilage mechanics that impacts our understanding of the role of interstitial fluid pressurization on cartilage lubrication. Theoretical and experimental studies have demonstrated that the interstitial fluid of cartilage pressurizes considerably under loading, potentially supporting most of the applied load under various transient or steady-state conditions. The fraction of the total load supported by fluid pressurization has been called the fluid load support. Experimental studies have demonstrated that the friction coefficient of cartilage correlates negatively with this variable, achieving remarkably low values when the fluid load support is greatest. A theoretical framework that embodies this relationship has been validated against experiments, predicting and explaining various outcomes, and demonstrating that a low friction coefficient can be maintained for prolonged loading durations under normal physiological function. This paper reviews salient aspects of this topic, as well as its implications for improving our understanding of boundary lubrication by molecular species in synovial fluid and the cartilage superficial zone. Effects of cartilage degeneration on its frictional response are also reviewed.
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paper_title: A Microstructural Model of Elastostatic Properties of Articular Cartilage in Confined Compression

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A microstructural model of cartilage was developed to investigate the relative contribution of tissue matrix components to its elastostatic properties. Cartilage was depicted as a tensed collagen lattice pressurized by the Donnan osmotic swelling pressure of proteoglycans. As a first step in modeling the collagen lattice, two-dimensional networks of tensed, elastic, interconnected cables were studied as conceptual models. The models were subjected to the boundary conditions of confined compression and stress-strain curves and elastic moduli were obtained as a function of a two-dimensional equivalent of swelling pressure. Model predictions were compared to equilibrium confined compression moduli of calf cartilage obtained at different bath concentrations ranging from 0.01 to 0.50 M NaCl. It was found that a triangular cable network provided the most consistent correspondence to the experimental data. The model showed that the cartilage collagen network remained tensed under large confined compression strains and could therefore support shear stress. The model also predicted that the elastic moduli increased with increasing swelling pressure in a manner qualitatively similar to experimental observations. Although the model did not preclude potential contributions of other tissue components and mechanisms, the consistency of model predictions with experimental observations suggests that the cartilage collagen network, prestressed by proteoglycan swelling pressure, plays an important role in supporting compression.
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paper_title: Concerning the ultrastructural origin of large-scale swelling in articular cartilage

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The swelling behaviour of the general matrix of both normal and abnormally softened articular cartilage was investigated in the context of its relationship to the underlying subchondral bone, the articular surface, and with respect to the primary structural directions represented in its strongly anisotropic collagenous architecture. Swelling behaviours were compared by subjecting tissue specimens under different modes of constraint to a high swelling bathing solution of distilled water and comparing structural changes imaged at the macroscopic, microscopic and ultrastructural levels of resolution. Near zero swelling was observed in the isolated normal general matrix with minimal structural change. By contrast the similarly isolated softened general matrix exhibited large-scale swelling in both the transverse and radial directions. This difference in dimensional stability was attributed to fundamentally different levels of fibril interconnectivity between the 2 matrices. A model of structural transformation is proposed to accommodate fibrillar rearrangements associated with the large-scale swelling in the radial and transverse directions in the softened general matrix.
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paper_title: A Conewise Linear Elasticity Mixture Model for the Analysis of Tension-Compression Nonlinearity in Articular Cartilage

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A biphasic mixture model is developed which can account for the observed tension-compression nonlinearity of cartilage by employing the continuum-based Conewise Linear Elasticity (CLE) model of Curnier et al. (J Elasticity 37:1–38, 1995) to describe the solid phase of the mixture. In this first investigation, the orthotropic octantwise linear elasticity model was reduced to the more specialized case of cubic symmetry, to reduce the number of elastic constants from twelve to four. Confined and unconfined compression stress-relaxation, and torsional shear testing were performed on each of nine bovine humeral head articular cartilage cylindrical plugs from 6 month old calves. Using the CLE model with cubic symmetry, the aggregate modulus in compression and axial permeability were obtained from confined compression (H−A =0.64±0.22 MPa, kz = 3.62 ± .97 × 10−16 m4/N.s, r2 =0.95±0.03), the tensile modulus, compressive Poisson ratio and radial permeability were obtained from unconfined compression (E+Y = 12.75 ± 1.56 MPa, ν− =0.03±0.01, kr =6.06±2.10×10−16 m4/N.s, r2 =0.99±0.00), and the shear modulus was obtained from torsional shear (µ=0.17±0.06 MPa). The model was also employed to successfully predict the interstitial fluid pressure at the center of the cartilage plug in unconfined compression (r2 =0.98±0.01). The results of this study demonstrate that the integration of the CLE model with the biphasic mixture theory can provide a model of cartilage which can successfully curvefit three distinct testing configurations while producing material parameters consistent with previous reports in the literature.
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paper_title: Microstructural modeling of collagen network mechanics and interactions with the proteoglycan gel in articular cartilage

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Cartilage matrix mechanical function is largely determined by interactions between the collagen fibrillar network and the proteoglycan gel. Although the molecular physics of these matrix constituents have been characterized and modern imaging methods are capable of localized measurement of molecular densities and orientation distributions, theoretical tools for using this information for prediction of cartilage mechanical behavior are lacking. We introduce a means to model collagen network contributions to cartilage mechanics based upon accessible microstructural information (fibril density and orientation distributions) and which self-consistently follows changes in microstructural geometry with matrix deformations. The interplay between the molecular physics of the collagen network and the proteoglycan gel is scaled up to determine matrix material properties, with features such as collagen fibril pre-stress in free-swelling cartilage emerging naturally and without introduction of ad hoc parameters. Methods are developed for theoretical treatment of the collagen network as a continuum-like distribution of fibrils, such that mechanical analysis of the network may be simplified by consideration of the spherical harmonic components of functions of the fibril orientation, strain, and stress distributions. Expressions for the collagen network contributions to matrix stress and stiffness tensors are derived, illustrating that only spherical harmonic components of orders 0 and 2 contribute to the stress, while orders 0, 2, and 4 contribute to the stiffness. Depth- and compression-dependent equilibrium mechanical properties of cartilage matrix are modeled, and advantages of the approach are illustrated by exploration of orientation and strain distributions of collagen fibrils in compressed cartilage. Results highlight collagen-proteoglycan interactions, especially for very small physiological strains where experimental data are relatively sparse. These methods for determining matrix mechanical properties from measurable quantities at the microscale (composition, structure, and molecular physics) may be useful for investigating cartilage structure-function relationships relevant to load-bearing, injury, and repair.
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paper_title: A degeneration‐based hypothesis for interpreting fibrillar changes in the osteoarthritic cartilage matrix

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The collagen fibrillar architectures in the general matrix of cartilage slices removed from both normal and osteoarthritic femoral heads were examined by both differential interference light microscopy and scanning electron microscopy. Whereas the normal general matrix contained a finely differentiated pseudo-random weave of fibrils developed from an interconnected array of radial elements, the osteoarthritic general matrix was characterised by the presence of structurally distinct regions consisting of strongly aligned radial bundles of fibrils and associated intense tangles or ‘knotted’ features. Simple structural models were developed to explore possible transformation structures based on two different types of interconnectivity in the three-dimensional fibrillar network. These models support the hypothesis that the distinctive ultrastructural features of the osteoarthritic general matrix can develop as a consequence of largely passive degradative changes occurring in the fibrillar weave originally present in the normal matrix. This could, in principle, occur independently of any new structure that might develop as a consequence of any upregulation of collagen associated with the osteoarthritic process.
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paper_title: Is classical consolidation theory applicable to articular cartilage deformation?

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In this paper, classical consolidation theory has been used to investigate the time-dependent response of articular cartilage to static loading. An experimental technique was developed to measure simultaneously the matrix internal pressure and creep strain under conditions of one-dimensional consolidation. This is the first measurement of the internal stress state of loaded cartilage. It is demonstrated that under static compression the applied load is shared by the components of the matrix (i.e. water, the proteoglycans, and the collagen fibrillar meshwork), during which time a maximum hydrostatic excess pore pressure is developed as initial water exudation occurs. This pressure decays as water is further exuded from the matrix and effective consolidation begins with a progressive transfer of the applied stress from water to the collagen fibrils and proteoglycan gel. Consolidation is completed when the hydrostatic excess pore pressure is reduced to zero and the solid components sustain in full the applied load.
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paper_title: A comparison of the size distribution of collagen fibrils in connective tissues as a function of age and a possible relation between fibril size distribution and mechanical properties

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Data on the distribution of collagen fibril diameters in various connective tissues have been collected and analysed for common features. The diameter distributions of the collagen fibrils at birth and in the foetal stages of development are unimodal, whereas at maturity the mass-average diameter of the collagen fibrils is generally larger than at birth and the distributions of fibril sizes may be either unimodal or bimodal depending on the tissue. At senescence, few data are available but in most instances both the mean and mass-average diameters of the collagen fibrils are smaller than those at maturity and the fibril distributions are mainly bimodal. The division between tissues showing unimodal or bimodal fibril distributions at maturity does not simply relate to the type I collagen/type II collagen classification, to the distinction between orientated and unorientated material or indeed directly to the levels of stress and strain encountered by the tissue. However, there may prove to be a relation between a bimodal fibril diameter distribution at maturity and the maintenance over long periods of time of either high stress in stretched tissues or low stress in compressed tissues. It has also been noted that the width of the collagen fibril diameter distribution at birth differs between altricious and precocious animals. The ultimate tensile strength of a connective tissue and the mass-average diameter of the constituent collagen fibrils have been shown to have a positive correlation. Further, the form of the collagen fibril diameter distribution can be directly related to the mechanical properties of the tissue. In particular, it is postulated that the size distribution of the collagen fibrils is largely determined by two factors. First, if the tissue is primarily designed to have high tensile strength, then an increase in the diameter of the collagen fibrils will parallel an increase in the potential density of intrafibrillar covalent crosslinks. Consequently large collagen fibrils are predicted to have a greater tensile strength than small fibrils. Secondly, if the tissue is designed to be elastic and hence withstand creep, then a reduction in the diameter of the collagen fibrils will effectively increase the surface area per unit mass of the fibrils thus enhancing the probability of interfibrillar non-covalent crosslinks between the collagen fibrils and the components of the matrix. The idealized description given may indicate how the mechanical properties of a tissue may be interpreted in terms of the collagen fibril diameter distribution.
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paper_title: Nanomechanics of collagen fibrils under varying cross-link densities: Atomistic and continuum studies

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Abstract Collagen is a protein material with intriguing mechanical properties — it is highly elastic, shows large fracture strength and plays a crucial role in making Nature’s structural materials tough. Collagen based tissues consist of collagen fibrils, each of which is composed out of a staggered array of ultra-long tropocollagen molecules extending to several hundred nanometers. Albeit the macroscopic properties of collagen based tissues have been studied extensively, less is known about the nanomechanical properties of tropocollagen molecules and collagen fibrils, their elementary building blocks. In particular, the relationship between molecular properties and tissue properties remains a scarcely explored aspect of the science of collagen materials. Results of molecular multi-scale modeling of the nanomechanical properties of the large-strain deformation regime of collagen fibrils under varying cross-link densities are reported in this paper. The results confirm the significance of cross-links in collagen fibrils in improving its mechanical strength. Further, it is found that cross-links influence the nature of its large-deformation and fracture behavior. Cross-link deficient collagen fibrils show a highly dissipative deformation behavior with large yield regimes. Increasing cross-link densities lead to stronger fibrils that display an increasingly brittle deformation character. The simulation results are compared with recent nanomechanical experiments at the scale of tropocollagen molecules and collagen fibrils.
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paper_title: Depth-dependent confined compression modulus of full-thickness bovine articular cartilage.

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The objective of this study was to determine the equilibrium confined compression modulus of bovine articular cartilage as it varies with depth from the articular surface. Osteochondral samples were compressed by 8, 16, 24, and 32% of the cartilage thickness and allowed to equilibrate. Intratissue displacement within the cartilage was measured with use of fluorescently labeled chondrocyte nuclei as intrinsic, fiducial markers. Axial strain was then calculated in nine sequential 125 mm thick cartilage layers comprising the superficial 1,125 mm and in a 250 mmm thick layer of cartilage adjacent to the cartilage-bone interface. Adjacent osteochondral cores were also tested in confined compression to determine the equilibrium stresses required to achieve the same levels of compression. Stress-strain data for each layer of each sample were fit to a finite deformation stress-strain relation to determine the equilibrium confined compression modulus in each tissue layer. The compressive modulus increased significantly with depth from the articular surface and ranged from 0.079 ± 0.039 MPa in the superficial layer to 1.14 ± 0.44 MPa in the ninth layer. The deepest layer. 250 mm thick, had a modulus of 2.10 ± 2.69 MPa. These moduli were markedly different from the apparent “homogeneous” modulus for full-thickness cartilage (0.38 ± 0.12 MPa) and ranged from 21 to 560% of that value. The relatively low moduli and the compression-induced stiffening of the superficial layers suggest that these layers greatly affect the biomechanical behavior of cartilage, such as during confined compression testing. The delineation of the depth-dependent modulus provides a basis for detailed study of the relationship between the composition, structure, and function of cartilage in such processes as aging, repair, and degeneration.
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paper_title: The three-dimensional 'knit' of collagen fibrils in articular cartilage.

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TEM stereoscopy of thick sections has been used to reconstruct the 3-dimensional relationships of collagen fibrils in the general matrix of articular cartilage in its relaxed and deformed states. As well as identifying a variety of fibril interactions involving direct physical entwinement which are assumed to provide matrix cohesion the study also highlights the functional importance of the repeatedly kinked morphology exhibited by the radial fibrils. It is suggested that these fibril kinks, in accommodating local compressive strains that approach 100%, function as macro-molecular hinges and permit the collagen elements to undergo large spatial rearrangement without risk to their structural integrity.
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paper_title: Stress-sharing between the fluid and solid components of articular cartilage under varying rates of compression

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This paper investigates the factors affecting the mechanical behavior of the articular matrix with special emphasis on the effect of compressive strain-rate on the short and long term responses of the fluid and the solid components. The relationships expressed in the general theory of one-dimensional consolidation are generalized to account for strain-rate in the deformation process with the result that the stiffness due to the fluid and the solid components, and a parameter representing the degree of drag, can be calculated explicity
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paper_title: Collagen-collagen versus collagen-proteoglycan interactions in the determination of cartilage strength

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For articular cartilage to function as a stress-reducing layer in the joint, it must both deform to an appropriate level to achieve load-spreading as well as remain structurally coherent. Combined micromechanical and enzymatic studies of cartilage have demonstrated that the bulk of the extractable proteoglycans, while essential to the maintenance of compressive stiffness, contribute little to its cohesive strength. The study reported here clarifies fundamental aspects of the relationship between matrix components and the biomechanical function of cartilage.
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paper_title: Deformation of loaded articular cartilage prepared for scanning electron microscopy with rapid freezing and freeze-substitution fixation

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To investigate the effect of joint loading on collagen fibers in articular cartilage, 45 knees of adult rabbits were examined by scaning electron microscopy. The knees were loaded at the patella with a simulated “quadriceps force” of 0.5-4 times body weight for 0.5 or 25 minutes, plunge-frozen, and fixed by freezesubstitution with aldehydes. Six knees were loaded for 3 hours and then fixed conventionally. Fixed tibial plateaus were examined and then freeze-fractured through the area of tibiofemoral contact, dried, coated, and examined by scanning electron microscopy to assess the overall deformation of the tibial articular surface and matrix collagen fibers. With tissue prepared by conventional fixation used as a standard, the quality of fixation was graded by light and transmission electron microscopy of patellar cartilage taken from half of the freeze-fixed knees. In loaded specimens, an indentation was present where the femur contacted the tibial plateau. The diameter and apparent depth of the dent were proportional to the magnitude and duration of the load; no dent was seen in the controls. The thickness of the cartilage at the center of the indentation was reduced 15-80%. Meniscectomy always produced larger deformations in otherwise equivalent conditions. Icecrystal damage to cells was evident by transmission electron microscopy and scanning electron microscopy, but at magnifications as high as ×30,000 the collagen fibrils prepared by freeze-substitution and conventional aqueous methods were identical. In loaded regions, the collagen matrix of the tibial cartilage was deformed in two ways: (a) radial collagen fibers exhibited a periodic crimp, and (b) in regions where an indentation was created by the femoral condyle, the radial fibers were bent, in effect creating tangential zone where none had existed before. The radial fibers apparently are loaded axially and buckle under normal loads.
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paper_title: Structure-Function Relationships in Enzymatically Modified Articular Cartilage

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The present study is aimed at revealing structure-function relationships of bovine patellar articular cartilage. Collagenase, chondroitinase ABC and elastase were used for controlled and selective enzymatic modifications of cartilage structure, composition and functional properties. The effects of the enzymatic degradations were quantitatively evaluated using quantitative polarized light microscopy, digital densitometry of safranin O-stained sections as well as with biochemical and biomechanical techniques. The parameters related to tissue composition and structure were correlated with the indentation stiffness of cartilage. In general, tissue alterations after enzymatic digestions were restricted to the superficial cartilage. All enzymatic degradations induced superficial proteoglycan (PG) depletion. Collagenase also induced detectable superficial collagen damage, though without causing cartilage fibrillation or tissue swelling. Quantitative microscopic techniques were more sensitive than biochemical methods in detecting these changes. The Young's modulus of cartilage decreased after enzymatic treatments indicating significant softening of the tissue. The PG concentration of the superficial zone proved to be the major determinant of the Young's modulus (r(2) = 0.767, n = 72, p < 0.001). Results of the present study indicate that specific enzymatic degradations of the tissue PGs and collagen can provide reproducible experimental models to clarify the structure-function relationships of cartilage. Effects of these models mimic the changes observed in early osteoarthrosis. Biomechanical testing and quantitative microscopic techniques proved to be powerful tools for detecting the superficial structural and compositional changes while the biochemical measurements on the whole uncalcified cartilage were less sensitive.
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paper_title: Glycosaminoglycan network geometry may contribute to anisotropic hydraulic permeability in cartilage under compression.

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Resistance to fluid flow within cartilage extracellular matrix is provided primarily by a dense network of rod-like glycosaminoglycans (GAGs). If the geometrical organization of this network is random, the hydraulic permeability tensor of cartilage is expected to be isotropic. However, experimental data have suggested that hydraulic permeability may become anisotropic when the matrix is mechanically compressed, contributing to cartilage biomechanical functions such as lubrication. We hypothesized that this may be due to preferred GAG rod orientations and directionally-dependent reduction of inter-GAG spacings which reflect molecular responses to tissue deformations. To examine this hypothesis, we developed a model for effects of compression which allows the GAG rod network to deform consistently with tissue-scale deformations but while still respecting limitations imposed by molecular structure. This network deformation model was combined with a perturbation analysis of a classical analytical model for hydraulic permeability based on molecular structure. Finite element analyses were undertaken to ensure that this approach exhibited results similar to those emerging from more exact calculations. Model predictions for effects of uniaxial confined compression on the hydraulic permeability tensor were consistent with previous experimental results. Permeability decreased more rapidly in the direction perpendicular to compression than in the parallel direction, for matrix solid volume fractions associated with fluid transport in articular cartilage. GAG network deformations may therefore introduce anisotropy to the permeability (and other GAG-associated matrix properties) as physiological compression is applied, and play an important role in cartilage lubrication and other biomechanical functions.
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paper_title: Experimental Verification and Theoretical Prediction of Cartilage Interstitial Fluid Pressurization At an Impermeable Contact Interface in Confined Compression

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Interstitial fluid pressurization has long been hypothesized to play a fundamental role in the load support mechanism and frictional response of articular cartilage. However, to date, few experimental studies have been performed to verify this hypothesis from direct measurements. The first objective of this study was to investigate experimentally the hypothesis that cartilage interstitial fluid pressurization does support the great majority of the applied load, in the testing configurations of confined compression creep and stress relaxation. The second objective was to investigate the hypothesis that the experimentally observed interstitial fluid pressurization could also be predicted using the linear biphasic theory of Mow et al. (J. Biomech. Engng ASME, 102, 73-84, 1980). Fourteen bovine cartilage samples were tested in a confined compression chamber fitted with a microchip piezoresistive transducer to measure interstitial fluid pressure, while simultaneously measuring (during stress relaxation) or prescribing (during creep) the total stress. It was found that interstitial fluid pressure supported more than 90% of the total stress for durations as long as 725 +/- 248 s during stress relaxation (mean +/- S.D., n = 7), and 404 +/- 229 s during creep (n = 7). When comparing experimental measurements of the time-varying interstitial fluid pressure against predictions from the linear biphasic theory, nonlinear coefficients of determination r2 = 0.871 +/- 0.086 (stress relaxation) and r2 = 0.941 +/- 0.061 (creep) were found. The results of this study provide some of the most direct evidence to date that interstitial fluid pressurization plays a fundamental role in cartilage mechanics; they also indicate that the mechanism of fluid load support in cartilage can be properly predicted from theory.
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paper_title: Effects of static axial strain on the tensile properties and failure mechanisms of self‐assembled collagen fibers

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Collagen fibers form the structural units of connective tissue throughout the body, transmitting force, maintaining shape, and providing a scaffold for cells. Our laboratory has studied collagen self-assembly since the 1970s. In this study, collagen fibers were self-assembled from molecular collagen solutions and then stretched to enhance alignment. Fibers were tested in uniaxial tension to study the mechanical properties and failure mechanisms. Results reported suggest that axial orientation of collagen fibrils can be achieved by stretching uncrosslinked collagen fibers. Stretching by about 30% not only results in decreased diameter and increased tensile strength but also leads to unusual failure mechanisms that inhibit crack propagation across the fiber. It is proposed that stretching serves to generate oriented fibrillar substructure in self-assembled collagen fibers. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 63: 1429–1440, 1997
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paper_title: Direct Measurement of Glycosaminoglycan Intermolecular Interactions via High-Resolution Force Spectroscopy

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Intermolecular repulsion forces between negatively charged glycosaminoglycan (CS−GAG) macromolecules are a major determinant of cartilage biomechanical properties. It is thought that the electrostatic component of the total intermolecular interaction is responsible for 50−75% of the equilibrium elastic modulus of cartilage in compression, while other forces (e.g., steric, hydration, van der Waals, etc.) may also play a role. To investigate these forces, radiolabeled CS−GAG polymer chains, with a fully extended contour length of 35 nm, were chemically end-grafted to a planar surface to form model biomimetic polyelectrolyte “brush” layers whose environment (e.g., ionic strength, pH) was varied to mimic physiological conditions. The total intersurface force (≤nN) between the CS−GAG brushes and chemically modified probe tips (SO3- and OH) was measured as a function of tip−substrate separation distance in aqueous solution using the technique of high-resolution force spectroscopy (HRFS). These experiments showe...
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paper_title: The Role of Interstitial Fluid Pressurization and Surface Porosities on the Boundary Friction of Articular Cartilage

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Articular cartilage is the remarkable bearing material of diarthrodial joints. Experimental measurements of its friction coefficient under various configurations have demonstrated that it is load-dependent, velocity-dependent, and time-dependent, and it can vary from values as low as 0.002 to as high as 0.3 or greater. Yet, many studies have suggested that these frictional properties are not dependent upon the viscosity of synovial fluid. In this paper, a theoretical formulation of a boundary friction modelfor articular cartilage is described and verified directly against experimental results in the configuration of confined compression stress-relaxation. The mathematical formulation of the friction model can potentially explain many of the experimentally observed frictional responses in relation to the pressurization of the interstitial fluid inside cartilage during joint loading, and the equilibrium friction coefficient which prevails in the absence of such pressurization. In this proposed model, it is also hypothesized that surface porosities play a role in the regulation of the frictional response of cartilage. The good agreement between theoretical predictions and experimental results of this study provide support for the proposed boundary friction formulation.
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paper_title: Effect of dynamic loading on the frictional response of bovine articular cartilage.

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The objective of this study was to test the hypotheses that (1) the steady-state friction coefficient of articular cartilage is significantly smaller under cyclical compressive loading than the equilibrium friction coefficient under static loading, and decreases as a function of loading frequency; (2) the steady-state cartilage interstitial fluid load support remains significantly greater than zero under cyclical compressive loading and increases as a function of loading frequency. Unconfined compression tests with sliding of bovine shoulder cartilage against glass in saline were carried out on fresh cylindrical plugs (n=12), under three sinusoidal loading frequencies (0.05, 0.5 and 1 Hz) and under static loading; the time-dependent friction coefficient mu(eff) was measured. The interstitial fluid load support was also predicted theoretically. Under static loading mu(eff) increased from a minimum value (mu(min)=0.005+/-0.003) to an equilibrium value (mu(eq)=0.153+/-0.032). In cyclical compressive loading tests mu(eff) similarly rose from a minimum value (mu(min)=0.004+/-0.002, 0.003+/-0.001 and 0.003+/-0.001 at 0.05, 0.5 and 1 Hz) and reached a steady-state response oscillating between a lower-bound (mu(lb)=0.092+/-0.016, 0.083+/-0.019 and 0.084+/-0.020) and upper bound (mu(ub)=0.382+/-0.057, 0.358+/-0.059, and 0.298+/-0.061). For all frequencies it was found that mu(ub)>mu(eq) and mu(lb)<mu(eq)(p<0.05). Under cyclical compressive loading the interstitial fluid load support was found to oscillate above and below the static loading response, with suction occurring over a portion of the loading cycle at steady-state conditions. All theoretical predictions and most experimental results demonstrated little sensitivity to loading frequency. On the basis of these results, both hypotheses were rejected. Cyclical compressive loading is not found to promote lower frictional coefficients or higher interstitial fluid load support than static loading.
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paper_title: Relationship Between Mechanical Properties and Collagen Structure of Closed and Open Wounds

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Mechanical properties and collagen structure of excisional wounds left open are compared with wounds closed by clips. In both wound models, collagen fiber diameter increases with time post-wounding and is related to tensile strength. Clipped wounds show a higher ultimate tensile strength and tangent modulus compared with open wounds. In clipped wounds, newly deposited collagen appears as a biaxially oriented network as observed in normal skin. In open wounds a delay in the organization of the collagen network is observed and parallel wavy-shaped ribbons of collagen fibers are deposited. At long term, the high extensibility observed in open wounds may be due to the sliding of ribbons of collagen fibers past each other.
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paper_title: Experimental verification of the role of interstitial fluid pressurization in cartilage lubrication

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The objective of the current study was to measure the friction coefficient simultaneously with the interstitial fluid load support in bovine articular cartilage, while sliding against glass under a constant load. Ten visually normal 6-mm-diameter cartilage plugs harvested from the humeral head of four bovine shoulder joints (ages 2-4 months) were tested in a custom friction device under reciprocating linear motion (range of translation +/-2 mm; sliding velocity 1 mm/s), subjected to a 4.5 N constant load. The frictional coefficient was found to increase with time from a minimum value of mu min=0.010+/-0.007 (mean+/-SD) to a maximum value of 0.243+/-0.044 over a duration ranging from 920 to 19,870 s (median: 4,560 s). The corresponding interstitial fluid load support decreased from a maximum of 88.8+/-3.8% to 8.7+/-8.6%. A linear correlation was observed between the frictional coefficient and interstitial fluid load support (r2=0.96+/-0.03). These results support the hypothesis that the temporal variation of the frictional coefficient correlates negatively with the interstitial fluid load support and that consequently interstitial fluid load support is a primary mechanism regulating the frictional response in articular cartilage. Fitting the experimental data to a previously proposed biphasic boundary lubrication model for cartilage yielded an equilibrium friction coefficient of mu eq=0.284+/-0.044. The fraction of the apparent contact area over which the solid cartilage matrix was in contact with the glass slide was predicted at phi s=1.7+/-6.3%, significantly smaller than the solid volume fraction of the tissue, phi s=13.8+/-1.8%. The model predictions suggest that mixed lubrication prevailed at the contact interface under the loading conditions employed in this study.
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paper_title: Viscoelastic properties of proteoglycan subunits and aggregates in varying solution concentrations.

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Using a cone-on-plate mechanical spectrometer, we have measured the linear and non-linear rheological properties of cartilage proteoglycan solutions at concentrations similar to those found in situ. Solutions of bovine nasal cartilage proteoglycan subunits (22S) and aggregates (79S) were studied at concentrations ranging from 10 to 50 mg ml-1. We determined: (1) the complex viscoelastic shear modulus G (omega) under small amplitude (0.02 radians) oscillatory excitation at frequencies (omega) ranging from 1.0 to 20.0 Hz, (2) the non-linear shear rate (gamma) dependent apparent viscosity napp (gamma) in continuous shear, and (3) the non-linear shear rate dependent primary normal stress difference sigma 1 (gamma) in continuous shear. Both the apparent viscosity and normal stress difference were measured over four decades of shear rates ranging from 0.25 to 250 s-1. Analysis of the experimental results were performed using a variety of materially objective non-linear viscoelastic constitutive laws. We found that the non-linear, four-coefficient Oldroyd rate-type model was most effective for describing the measured flow characteristics of proteoglycan subunit and aggregate solutions. Values of the relaxation time lambda 1, retardation time lambda 2, zero shear viscosity no, and nonlinear viscosity parameter muo were computed for the aggregate and subunit solutions at all of the solute concentrations used. The four independent material coefficients showed marked dependence on the two different molecular conformations, i.e. aggregate or subunit, of proteoglycans in solution.
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paper_title: Ultrastructural evidence for fibril-to-fibril associations in articular cartilage and their functional implication.

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This study presents ultrastructural evidence for the presence of a variety of fibril-to-fibril interactions or associations in the architecture of the general matrix of articular cartilage. These interactions are believed to serve a higher purpose of repeatedly constraining an overall radial arrangement of fibrils into an array of oblique interconnecting segments thus creating a three dimensional meshwork within which the hydrated ground substance is constrained. It is argued that any reduction in these interfibrillar interactions will allow the oblique fibril segments to revert to a low energy radial configuration, thus explaining the presence of such arrays prominent in various degenerate forms of articular cartilage.
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paper_title: On the ultrastructure of softened cartilage: a possible model for structural transformation

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The fibrillar architecture in the general matrix of softened cartilage has been compared with that of the normal matrix using both Nomarski light microscopy and transmission electron microscopy with combined stereoscopic reconstruction. A pseudorandom network developed from an overall radial arrangement of collagen fibrils is the most fundamental ultrastructural characteristic of the normal general matrix. This, in turn, provides an efficient entrapment system for the swelling proteoglycans. Conversely, the most distinctive feature of the softened matrix is the presence of parallel and relatively unentwined fibrils, strongly aligned in the radial direction. The presence of an optically resolvable fibrous texture in the softened cartilage matrix indicates the presence of discrete bundles of closely packed and aligned fibrils at the ultrastructural level of organisation. The general absence of such texture in the normal cartilage general matrix is consistent with the much greater degree of interconnectedness and related short-range obliquity in the fibrillar architecture, hence the importance of the term pseudorandom network. A mechanism of structural transformation is proposed based on the important property of lateral interconnectivity in the fibrils which involves both entwinement and nonentwinement based interactions. The previously reported difference in intrinsic mechanical strength between the normal and softened matrices is consistent with the transformation model proposed in this study.
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paper_title: Assembly of type I collagen: fusion of fibril subunits and the influence of fibril diameter on mechanical properties.

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Abstract Structural stability of the extracellular matrix is primarily a consequence of fibrillar collagen and the extent of cross-linking. The relationship between collagen self-assembly, consequent fibrillar shape and mechanical properties remains unclear. Our laboratory developed a model system for the preparation of self-assembled type I collagen fibers with fibrillar substructure mimicking the hierarchical structures of tendon. The present study evaluates the effects of pH and temperature during self-assembly on fibrillar structure, and relates the structural effects of these treatments on the uniaxial tensile mechanical properties of self-assembled collagen fibers. Results of the analysis of fibril diameter distributions and mechanical properties of the fibers formed under the different incubation conditions indicate that fibril diameters grow via the lateral fusion of discrete ∼4 nm subunits, and that fibril diameter correlates positively with the low strain modulus. Fibril diameter did not correlate with either the ultimate tensile strength or the high strain elastic modulus, which suggests that lateral aggregation and consequently fibril diameter influences mechanical properties during small strain mechanical deformation. We hypothesize that self-assembly is mediated by the formation of fibrillar subunits that laterally and linearly fuse resulting in fibrillar growth. Lateral fusion appears important in generating resistance to deformation at low strain, while linear fusion leading to longer fibrils appears important in the ultimate mechanical properties at high strain.
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paper_title: Fibril reinforced poroelastic model predicts specifically mechanical behavior of normal, proteoglycan depleted and collagen degraded articular cartilage

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Abstract Degradation of collagen network and proteoglycan (PG) macromolecules are signs of articular cartilage degeneration. These changes impair cartilage mechanical function. Effects of collagen degradation and PG depletion on the time-dependent mechanical behavior of cartilage are different. In this study, numerical analyses, which take the compression-tension nonlinearity of the tissue into account, were carried out using a fibril reinforced poroelastic finite element model. The study aimed at improving our understanding of the stress-relaxation behavior of normal and degenerated cartilage in unconfined compression. PG and collagen degradations were simulated by decreasing the Young's modulus of the drained porous (nonfibrillar) matrix and the fibril network, respectively. Numerical analyses were compared to results from experimental tests with chondroitinase ABC (PG depletion) or collagenase (collagen degradation) digested samples. Fibril reinforced poroelastic model predicted the experimental behavior of cartilage after chondroitinase ABC digestion by a major decrease of the drained porous matrix modulus (−64±28%) and a minor decrease of the fibril network modulus (−11±9%). After collagenase digestion, in contrast, the numerical analyses predicted the experimental behavior of cartilage by a major decrease of the fibril network modulus (−69±5%) and a decrease of the drained porous matrix modulus (−44±18%). The reduction of the drained porous matrix modulus after collagenase digestion was consistent with the microscopically observed secondary PG loss from the tissue. The present results indicate that the fibril reinforced poroelastic model is able to predict specifically characteristic alterations in the stress-relaxation behavior of cartilage after enzymatic modifications of the tissue. We conclude that the compression-tension nonlinearity of the tissue is needed to capture realistically the mechanical behavior of normal and degenerated articular cartilage.
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paper_title: Structural and Compositional Changes in Peri- and Extracellular Matrix of Osteoarthritic Cartilage Modulate Chondrocyte Morphology

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It has not been shown how specific changes in composition and structure in the peri- and extracellular matrix (PCM and ECM) of human articular cartilage modulate cell morphology in different stages of osteoarthritis (OA). In the present study, cell morphology in the superficial tissue of normal, early OA and advanced OA human cartilage samples were measured from histological sections. Collagen and proteoglycan contents in the vicinity of chondrocytes were analyzed using Fourier transform infrared spectroscopy and digital densitometry. Determinants of the experimentally observed morphological changes of cells were studied using finite element analysis (FEA). From normal tissue to early OA, cell aspect ratio (height/width) remained constant (0.69 ± 0.11 and 0.69 ± 0.09, respectively). In advanced OA, cells became significantly (p < 0.05) more rounded (aspect ratio of 0.83 ± 0.13). Normalized collagen content in the PCM, i.e. collagen content in the PCM with respect to that in the ECM, was reduced significantly (p < 0.05) only in advanced OA. FEA indicated that reduced proteoglycan content and increased collagen fibrillation in the PCM and ECM, as well as reduced collagen content only in the PCM, primarily explained experimentally found changes in cell aspect ratio. Our results suggest that changes in composition and structure of the PCM and ECM in the superficial tissue of human articular cartilage modulate cell morphology differently in early and advanced OA.
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paper_title: Importance of collagen orientation and depth-dependent fixed charge densities of cartilage on mechanical behavior of chondrocytes.

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The collagen network and proteoglycan matrix of articular cartilage are thought to play an important role in controlling the stresses and strains in and around chondrocytes, in regulating the biosynthesis of the solid matrix, and consequently in maintaining the health of diarthrodial joints. Understanding the detailed effects of the mechanical environment of chondrocytes on cell behavior is therefore essential for the study of the development, adaptation, and degeneration of articular cartilage. Recent progress in macroscopic models has improved our understanding of depth-dependent properties of cartilage. However, none of the previous works considered the effect of realistic collagen orientation or depth-dependent negative charges in microscopic models of chondrocyte mechanics. The aim of this study was to investigate the effects of the collagen network and fixed charge densities of cartilage on the mechanical environment of the chondrocytes in a depth-dependent manner. We developed an anisotropic, inhomogeneous, microstructural fibril-reinforced finite element model of articular cartilage for application in unconfined compression. The model consisted of the extracellular matrix and chondrocytes located in the superficial, middle, and deep zones. Chondrocytes were surrounded by a pericellular matrix and were assumed spherical prior to tissue swelling and load application. Material properties of the chondrocytes, pericellular matrix, and extracellular matrix were obtained from the literature. The loading protocol included a free swelling step followed by a stress-relaxation step. Results from traditional isotropic and transversely isotropic biphasic models were used for comparison with predictions from the current model. In the superficial zone, cell shapes changed from rounded to elliptic after free swelling. The stresses and strains as well as fluid flow in cells were greatly affected by the modulus of the collagen network. The fixed charge density of the chondrocytes, pericellular matrix, and extracellular matrix primarily affected the aspect ratios (height/ width) and the solid matrix stresses of cells. The mechanical responses of the cells were strongly location and time dependent. The current model highlights that the collagen orientation and the depth-dependent negative fixed charge densities of articular cartilage have a great effect in modulating the mechanical environment in the vicinity of chondrocytes, and it provides an important improvement over earlier models in describing the possible pathways from loading of articular cartilage to the mechanical and biological responses of chondrocytes.
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paper_title: Composition of the pericellular matrix modulates the deformation behaviour of chondrocytes in articular cartilage under static loading

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The aim was to assess the role of the composition changes in the pericellular matrix (PCM) for the chondrocyte deformation. For that, a three-dimensional finite element model with depth-dependent collagen density, fluid fraction, fixed charge density and collagen architecture, including parallel planes representing the split-lines, was created to model the extracellular matrix (ECM). The PCM was constructed similarly as the ECM, but the collagen fibrils were oriented parallel to the chondrocyte surfaces. The chondrocytes were modelled as poroelastic with swelling properties. Deformation behaviour of the cells was studied under 15% static compression. Due to the depth-dependent structure and composition of cartilage, axial cell strains were highly depth-dependent. An increase in the collagen content and fluid fraction in the PCMs increased the lateral cell strains, while an increase in the fixed charge density induced an inverse behaviour. Axial cell strains were only slightly affected by the changes in PCM composition. We conclude that the PCM composition plays a significant role in the deformation behaviour of chondrocytes, possibly modulating cartilage development, adaptation and degeneration. The development of cartilage repair materials could benefit from this information.
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paper_title: The mechanical environment of the chondrocyte: a biphasic finite element model of cell-matrix interactions in articular cartilage.

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Abstract Mechanical compression of the cartilage extracellular matrix has a significant effect on the metabolic activity of the chondrocytes. However, the relationship between the stress–strain and fluid-flow fields at the macroscopic “tissue” level and those at the microscopic “cellular” level are not fully understood. Based on the existing experimental data on the deformation behavior and biomechanical properties of articular cartilage and chondrocytes, a multi-scale biphasic finite element model was developed of the chondrocyte as a spheroidal inclusion embedded within the extracellular matrix of a cartilage explant. The mechanical environment at the cellular level was found to be time-varying and inhomogeneous, and the large difference (∼3 orders of magnitude) in the elastic properties of the chondrocyte and those of the extracellular matrix results in stress concentrations at the cell–matrix border and a nearly two-fold increase in strain and dilatation (volume change) at the cellular level, as compared to the macroscopic level. The presence of a narrow “pericellular matrix” with different properties than that of the chondrocyte or extracellular matrix significantly altered the principal stress and strain magnitudes within the chondrocyte, suggesting a functional biomechanical role for the pericellular matrix. These findings suggest that even under simple compressive loading conditions, chondrocytes are subjected to a complex local mechanical environment consisting of tension, compression, shear, and fluid pressure. Knowledge of the local stress and strain fields in the extracellular matrix is an important step in the interpretation of studies of mechanical signal transduction in cartilage explant culture models.
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paper_title: Depth-dependent analysis of the role of collagen fibrils, fixed charges and fluid in the pericellular matrix of articular cartilage on chondrocyte mechanics.

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Abstract The pericellular matrix of articular cartilage has been shown to regulate the mechanical environment of chondrocytes. However, little is known about the mechanical role of collagen fibrils in the pericellular matrix, and how fibrils might help modulate strains acting on chondrocytes when cartilage is loaded. The primary objective was to clarify the effect of pericellular collagen fibrils on cell volume changes and strains during cartilage loading. Secondary objectives were to investigate the effects of pericellular fixed charges and fluid on cell responses. A microstructural model of articular cartilage, in which chondrocytes and pericellular matrices were represented with depth-dependent structural and morphological properties, was created. The extracellular matrix and pericellular matrices were modeled as fibril-reinforced, biphasic materials with swelling capabilities, while chondrocytes were assumed to be isotropic and biphasic with swelling properties. Collagen fibrils in the extracellular matrix were represented with an arcade-like architecture, whereas pericellular fibrils were assumed to run tangential to the cell surface. In the early stages of a stress–relaxation test, pericellular fibrils were found to sensitively affect cell volume changes, even producing a reversal from increasing to decreasing cell volume with increasing fibril stiffness in the superficial zone. Consequently, steady-state volume of the superficial zone cell decreased with increasing pericellular fibril stiffness. Volume changes in the middle and deep zone chondrocytes were smaller and opposite to those observed in the superficial zone chondrocyte. An increase in the pericellular fixed charge density reduced cell volumes substantially in every zone. The sensitivity of cell volume changes to pericellular fibril stiffness suggests that pericellular fibrils play an important, and as of yet largely neglected, role in regulating the mechanical environment of chondrocytes, possibly affecting matrix synthesis during cartilage development and degeneration, and affecting biosynthetic responses associated with articular cartilage loading.
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paper_title: A Study of the Structural Response of Wet Hyaline Cartilage to Various Loading Situations

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A direct view has been obtained of the manner in which the fibrous components and chondrocytes in hyaline cartilage respond to the application of uniaxial tensile loading and plane-strain compressive loading.A micro-mechanical testing device has been developed which inserts directly into the stage of a high-resolution optical microscope fitted with Nomarski interference contrast and this has permitted simultaneous morphological and mechanical observations to be conducted on articular cartilage maintained in its wet functional condition.Aligned and crimped fibrous arrays surround the deeper chondrocytes and can be observed to undergo well-defined geometric changes with applied stress. It is thought that these arrays may act as displacement or strain sensors transmitting mechanical information from the bulk matrix to their associated cells thus inducing a specific metabolic response.The process of tissue recovery following sustained high levels of compressive loading can also be observed with this experimen...
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paper_title: The Effect of Matrix Tension-Compression Nonlinearity and Fixed Negative Charges on Chondrocyte Responses in Cartilage

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Thorough analyses of the mechano-electrochemical interaction between articular cartilage matrix and the chondrocytes are crucial to understanding of the signal transduction mechanisms that modulate the cell metabolic activities and biosynthesis. Attempts have been made to model the chondrocytes embedded in the collagen-proteoglycan extracellular matrix to determine the distribution of local stress-strain field, fluid pressure and the time-dependent deformation of the cell. To date, these models still have not taken into account a remarkable characteristic of the cartilage extracellular matrix given rise from organization of the collagen fiber architecture, now known as the tension-compression nonlinearity (TCN) of the tissue, as well as the effect of negative charges attached to the proteoglycan molecules, and the cell cytoskeleton that interacts with mobile ions in the interstitial fluid to create osmotic and electro-kinetic events in and around the cells. In this study, we proposed a triphasic, multi-scale, finite element model incorporating the Conewise Linear Elasticity that can describe the various known coupled mechanical, electrical and chemical events, while at the same time representing the TCN of the extracellular matrix. The model was employed to perform a detailed analysis of the chondrocytes' deformational and volume responses, and to quantitatively describe the mechano-electrochemical environment of these cells. Such a model describes contributions of the known detailed micro-structural and composition of articular cartilage. Expectedly, results from model simulations showed substantial effects of the matrix TCN on the cell deformational and volume change response. A low compressive Poisson's ratio of the cartilage matrix exhibiting TCN resulted in dramatic recoiling behavior of the tissue under unconfined compression and induced significant volume change in the cell. The fixed charge density of the chondrocyte and the pericellular matrix were also found to play an important role in both the time-dependent and equilibrium deformation of the cell. The pericellular matrix tended to create a uniform osmolarity around the cell and overall amplified the cell volume change. It is concluded that the proposed model can be a useful tool that allows detailed analysis of the mechano-electrochemical interactions between the chondrocytes and its surrounding extracellular matrix, which leads to more quantitative insights in the cell mechano-transduction.
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paper_title: The Mechanical Behaviour of Chondrocytes Predicted with a Micro-structural Model of Articular Cartilage

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The integrity of articular cartilage depends on the proper functioning and mechanical stimulation of chondrocytes, the cells that synthesize extracellular matrix and maintain tissue health. The biosynthetic activity of chondrocytes is influenced by genetic factors, environmental influences, extracellular matrix composition, and mechanical factors. The mechanical environment of chondrocytes is believed to be an important determinant for joint health, and chondrocyte deformation in response to mechanical loading is speculated to be an important regulator of metabolic activity. In previous studies of chondrocyte deformation, articular cartilage was described as a biphasic material consisting of a homogeneous, isotropic, linearly elastic solid phase, and an inviscid fluid phase. However, articular cartilage is known to be anisotropic and inhomogeneous across its depth. Therefore, isotropic and homogeneous models cannot make appropriate predictions for tissue and cell stresses and strains. Here, we modelled articular cartilage as a transversely isotropic, inhomogeneous (TI) material in which the anisotropy and inhomogeneity arose naturally from the microstructure of the depth-dependent collagen fibril orientation and volumetric fraction, as well as the chondrocyte shape and volumetric fraction. The purpose of this study was to analyse the deformation behaviour of chondrocytes using the TI model of articular cartilage. In order to evaluate our model against experimental results, we simulated indentation and unconfined compression tests for nominal compressions of 15%. Chondrocyte deformations were analysed as a function of location within the tissue. The TI model predicted a non-uniform behaviour across tissue depth: in indentation testing, cell height decreased by 43% in the superficial zone and between 11 and 29% in the deep zone. In unconfined compression testing, cell height decreased by 32% in the superficial zone, 25% in the middle, and 18% in the deep zones. This predicted non-uniformity is in agreement with experimental studies. The novelty of this study is the use of a cartilage material model accounting for the intrinsic inhomogeneity and anisotropy of cartilage caused by its microstructure.
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paper_title: Remodeling of fracture callus in mice is consistent with mechanical loading and bone remodeling theory.

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During the remodeling phase of fracture healing in mice, the callus gradually transforms into a double cortex, which thereafter merges into one cortex. In large animals, a double cortex normally does not form. We investigated whether these patterns of remodeling of the fracture callus in mice can be explained by mechanical loading. Morphologies of fractures after 21, 28, and 42 days of healing were determined from an in vivo mid-diaphyseal femoral osteotomy healing experiment in mice. Bone density distributions from microCT at 21 days were converted into adaptive finite element models. To assess the effect of loading mode on bone remodeling, a well-established remodeling algorithm was used to examine the effect of axial force or bending moment on bone structure. All simulations predicted that under axial loading, the callus remodeled to form a single cortex. When a bending moment was applied, dual concentric cortices developed in all simulations, corresponding well to the progression of remodeling observed experimentally and resulting in quantitatively comparable callus areas of woven and lamellar bone. Effects of biological differences between species or other reasons cannot be excluded, but this study demonstrates how a difference in loading mode could explain the differences between the remodeling phase in small rodents and larger mammals.
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paper_title: The PTHrP–Ihh Feedback Loop in the Embryonic Growth Plate Allows PTHrP to Control Hypertrophy and Ihh to Regulate Proliferation

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Growth plate and long bone development is governed by biochemical signaling pathways of which the PTHrP–Ihh system is the best known. Other factors, such as BMPs, FGFs and mechanical loading, may interact with this system. This study aims at elucidating the relative importance of PTHrP and Ihh for controlling proliferation, and hypertrophy in fetal growth plate cartilage. We assessed the question why reduced Ihh expression leads to more pronounced effects on the number of non-hypertrophic cells and total bone formation, compared to PTHrP down-regulation.
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paper_title: The composition of engineered cartilage at the time of implantation determines the likelihood of regenerating tissue with a normal collagen architecture.

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The biomechanical functionality of articular cartilage is derived from both its biochemical composition and the architecture of the collagen network. Failure to replicate this normal Benninghoff architecture in regenerating articular cartilage may in turn predispose the tissue to failure. In this article, the influence of the maturity (or functionality) of a tissue-engineered construct at the time of implantation into a tibial chondral defect on the likelihood of recapitulating a normal Benninghoff architecture was investigated using a computational model featuring a collagen remodeling algorithm. Such a normal tissue architecture was predicted to form in the intact tibial plateau due to the interplay between the depth-dependent extracellular matrix properties, foremost swelling pressures, and external mechanical loading. In the presence of even small empty defects in the articular surface, the collagen architecture in the surrounding cartilage was predicted to deviate significantly from the native state,...
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paper_title: Prediction of collagen orientation in articular cartilage by a collagen remodeling algorithm

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Summary Objective Tissue engineering is a promising method to treat damaged cartilage. So far it has not been possible to create tissue-engineered cartilage with an appropriate structural organization. It is envisaged that cartilage tissue engineering will significantly benefit from knowledge of how the collagen fiber orientation is directed by mechanical conditions. The goal of the present study is to evaluate whether a collagen remodeling algorithm based on mechanical loading can be corroborated by the collagen orientation in healthy cartilage. Methods According to the remodeling algorithm, collagen fibrils align with a preferred fibril direction, situated between the positive principal strain directions. The remodeling algorithm was implemented in an axisymmetric finite element model of the knee joint. Loading as a result of typical daily activities was represented in three different phases: rest, standing and gait. Results In the center of the tibial plateau the collagen fibrils run perpendicular to the subchondral bone. Just below the articular surface they bend over to merge with the articular surface. Halfway between the center and the periphery, the collagen fibrils bend over earlier, resulting in a thicker superficial and transitional zones. Near the periphery fibrils in the deep zone run perpendicular to the articular surface and slowly bend over to angles of −45° and +45° with the articular surface. Conclusion The collagen structure as predicted with the collagen remodeling algorithm corresponds very well with the collagen structure in healthy knee joints. This remodeling algorithm is therefore considered to be a valuable tool for developing loading protocols for tissue engineering of articular cartilage.
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paper_title: Recent advances in mechanobiological modeling of bone regeneration

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Abstract Skeletal regeneration and bone fracture repair involves complex cellular and molecular events that result in new bone formation. Many of the critical steps during bone healing are dependent on the local mechanical environment in the healing tissue. Computational models are used together with mechano-regulation algorithms to predict the influence of mechanical stimuli on the tissue differentiation process during bone healing. This paper reviews the field of computational mechanobiology with focus on bone healing. The history of mechanoregulatory modeling is described, as well as the recent advances and current problems. Most recent advances have been focusing on integrating the mechano-regulatory algorithms with more sophisticated description of the cellular and molecular events. Achieving suitable validation for the models is the most significant challenge. Thus far, focus has been on corroborating mechanoregulatory models by comparing existing models with well characterized experimental data, identify shortcomings and further develop improved computational models of bone healing. Ultimately, these models can be used to help unraveling the basic principles of cell and tissue differentiation, optimization of implant design, and potentially to investigate treatments of non-union and other pathologies.
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paper_title: Mechanics of chondrocyte hypertrophy

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Chondrocyte hypertrophy is a characteristic of osteoarthritis and dominates bone growth. Intra- and extracellular changes that are known to be induced by metabolically active hypertrophic chondrocytes are known to contribute to hypertrophy. However, it is unknown to which extent these mechanical conditions together can be held responsible for the total magnitude of hypertrophy. The present paper aims to provide a quantitative, mechanically sound answer to that question. To address this aim requires a quantitative tool that captures the mechanical effects of collagen and proteoglycans, allows temporal changes in tissue composition, and can compute cell and tissue deformations. These requirements are met in our numerical model that is validated for articular cartilage mechanics, which we apply to quantitatively explain a range of experimental observations related to hypertrophy. After validating the numerical approach for studying hypertrophy, the model is applied to evaluate the direct mechanical effects of axial tension and compression on hypertrophy (Hueter-Volkmann principle) and to explore why hypertrophy is reduced in case of partially or fully compromised proteoglycan expression. Finally, a mechanical explanation is provided for the observation that chondrocytes do not hypertrophy when enzymatical collagen degradation is prohibited (S1Pcko knock-out mouse model). This paper shows that matrix turnover by metabolically active chondrocytes, together with externally applied mechanical conditions, can explain quantitatively the volumetric change of chondrocytes during hypertrophy. It provides a mechanistic explanation for the observation that collagen degradation results in chondrocyte hypertrophy, both under physiological and pathological conditions.
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paper_title: Determining the most important cellular characteristics for fracture healing using design of experiments methods.

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Computational models are employed as tools to investigate possible mechanoregulation pathways for tissue differentiation and bone healing. However, current models do not account for the uncertainty in input parameters, and often include assumptions about parameter values that are not yet established. The objective of this study was to determine the most important cellular characteristics of a mechanoregulatory model describing both cell phenotype-specific and mechanobiological processes that are active during bone healing using a statistical approach. The computational model included an adaptive two-dimensional finite element model of a fractured long bone. Three different outcome criteria were quantified: (1) ability to predict sequential healing events, (2) amount of bone formation at early, mid and late stages of healing and (3) the total time until complete healing. For the statistical analysis, first a resolution IV fractional factorial design (L(64)) was used to identify the most significant factors. Thereafter, a three-level Taguchi orthogonal array (L(27)) was employed to study the curvature (non-linearity) of the 10 identified most important parameters. The results show that the ability of the model to predict the sequences of normal fracture healing was predominantly influenced by the rate of matrix production of bone, followed by cartilage degradation (replacement). The amount of bone formation at early stages was solely dependent on matrix production of bone and the proliferation rate of osteoblasts. However, the amount of bone formation at mid and late phases had the rate of matrix production of cartilage as the most influential parameter. The time to complete healing was primarily dependent on the rate of cartilage degradation during endochondral ossification, followed by the rate of cartilage formation. The analyses of the curvature revealed a linear response for parameters related to bone, where higher rates of formation were more beneficial to healing. In contrast, parameters related to fibrous tissue and cartilage showed optimum levels. Some fibrous connective tissue- and cartilage formation was beneficial to bone healing, but too much of either tissue delayed bone formation. The identified significant parameters and processes are further confirmed by in vivo animal experiments in the literature. This study illustrates the potential of design of experiments methods for evaluating computational mechanobiological model parameters and suggests that further experiments should preferably focus at establishing values of parameters related to cartilage formation and degradation.
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paper_title: A computational model for collagen fibre remodelling in the arterial wall

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As the interaction between tissue adaptation and the mechanical condition within tissues is complex, mathematical models are desired to study this interrelation. In this study, a mathematical model is presented to investigate the interplay between collagen architecture and mechanical loading conditions in the arterial wall. It is assumed that the collagen fibres align along preferred directions, situated in between the principal stretch directions. The predicted fibre directions represent symmetrically arranged helices and agree qualitatively with morphometric data from literature. At the luminal side of the arterial wall, the fibres are oriented more circumferentially than at the outer side. The discrete transition of the fibre orientation at the media-adventitia interface can be explained by accounting for the different reference configurations of both layers. The predicted pressure-radius relations resemble experimentally measured sigma-shaped curves. As there is a strong coupling between the collagen architecture and the mechanical loading condition within the tissue, we expect that the presented model for collagen remodelling is useful to gain further insight into the processes involved in vascular adaptation, such as growth and smooth muscle tone adaptation.
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paper_title: Stress–relaxation of human patellar articular cartilage in unconfined compression: Prediction of mechanical response by tissue composition and structure

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Abstract Mechanical properties of articular cartilage are controlled by tissue composition and structure. Cartilage function is sensitively altered during tissue degeneration, in osteoarthritis (OA). However, mechanical properties of the tissue cannot be determined non-invasively. In the present study, we evaluate the feasibility to predict, without mechanical testing, the stress–relaxation response of human articular cartilage under unconfined compression. This is carried out by combining microscopic and biochemical analyses with composition-based mathematical modeling. Cartilage samples from five cadaver patellae were mechanically tested under unconfined compression. Depth-dependent collagen content and fibril orientation, as well as proteoglycan and water content were derived by combining Fourier transform infrared imaging, biochemical analyses and polarized light microscopy. Finite element models were constructed for each sample in unconfined compression geometry. First, composition-based fibril-reinforced poroviscoelastic swelling models, including composition and structure obtained from microscopical and biochemical analyses were fitted to experimental stress–relaxation responses of three samples. Subsequently, optimized values of model constants, as well as compositional and structural parameters were implemented in the models of two additional samples to validate the optimization. Theoretical stress–relaxation curves agreed with the experimental tests ( R =0.95–0.99). Using the optimized values of mechanical parameters, as well as composition and structure of additional samples, we were able to predict their mechanical behavior in unconfined compression, without mechanical testing ( R =0.98). Our results suggest that specific information on tissue composition and structure might enable assessment of cartilage mechanics without mechanical testing.
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paper_title: Depth- and strain-dependent mechanical and electromechanical properties of full-thickness bovine articular cartilage in confined compression.

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Compression tests have often been performed to assess the biomechanical properties of full-thickness articular cartilage. We tested whether the apparent homogeneous strain-dependent properties, deduced from such tests, reflect both strain- and depth-dependent material properties. Full-thickness bovine articular cartilage was tested by oscillatory confined compression superimposed on a static offset up to 45%. and the data fit to estimate modulus, permeability, and electrokinetic coefficient assuming homogeneity. Additional tests on partial-thickness cartilage were then performed to assess depth- and strain-dependent properties in an inhomogeneous model, assuming three discrete layers (i = 1 starting from the articular surface, to i = 3 up to the subchondral bone). Estimates of the zero-strain equilibrium confined compression modulus (H(A0)), the zero-strain permeability (kp0) and deformation dependence constant (M), and the deformation-dependent electrokinetic coefficient (ke) differed among individual layers of cartilage and full-thickness cartilage. HiA0 increased from layer 1 to 3 (0.27 to 0.71 MPa), and bracketed the apparent homogeneous value (0.47 MPa). ki(p0) decreased from layer 1 to 3 (4.6 x 10(-15) to 0.50 x 10(-15) m2/Pa s) and was less than the homogeneous value (7.3 x 10(-15) m2/Pa s), while Mi increased from layer 1 to 3 (5.5 to 7.4) and became similar to the homogeneous value (8.4). The amplitude of ki(e) increased markedly with compressive strain, as did the homogeneous value: at low strain, it was lowest near the articular surface and increased to a peak in the middle-deep region. These results help to interpret the biomechanical assessment of full-thickness articular cartilage.
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paper_title: Mechanical characterization of articular cartilage by combining magnetic resonance imaging and finite-element analysis—a potential functional imaging technique

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Magnetic resonance imaging (MRI) provides a method for non-invasive characterization of cartilage composition and structure. We aimed to see whether T1 and T2 relaxation times are related to proteoglycan (PG) and collagen-specific mechanical properties of articular cartilage. Specifically, we analyzed whether variations in the depthwise collagen orientation, as assessed by the laminae obtained from T2 profiles, affect the mechanical characteristics of cartilage. After MRI and unconfined compression tests of human and bovine patellar cartilage samples, fibril-reinforced poroviscoelastic finite-element models (FEM), with depthwise collagen orientations implemented from quantitative T2 maps (3 laminae for human, 3–7 laminae for bovine), were constructed to analyze the non-fibrillar matrix modulus (PG specific), fibril modulus (collagen specific) and permeability of the samples. In bovine cartilage, the non-fibrillar matrix modulus (R = −0.64, p < 0.05) as well as the initial permeability (R = 0.70, p < 0.05) correlated with T1. In bovine cartilage, T2 correlated positively with the initial fibril modulus (R = 0.62, p = 0.05). In human cartilage, the initial fibril modulus correlated negatively (R = −0.61, p < 0.05) with T2. Based on the simulations, cartilage with a complex collagen architecture (5 or 7 laminae), leading to high bulk T2 due to magic angle effects, provided higher compressive stiffness than tissue with a simple collagen architecture (3 laminae). Our results suggest that T1 reflects PG-specific mechanical properties of cartilage. High T2 is characteristic to soft cartilage with a classical collagen architecture. Contradictorily, high bulk T2 can also be found in stiff cartilage with a multilaminar collagen fibril network. By emerging MRI and FEM, the present study establishes a step toward functional imaging of articular cartilage.
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paper_title: Osteoarthritic changes in the biphasic mechanical properties of the chondrocyte pericellular matrix in articular cartilage.

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Abstract The pericellular matrix (PCM) is a narrow region of cartilaginous tissue that surrounds chondrocytes in articular cartilage. Previous modeling studies indicate that the mechanical properties of the PCM relative to those of the extracellular matrix (ECM) can significantly affect the stress–strain, fluid flow, and physicochemical environments of the chondrocyte, suggesting that the PCM plays a biomechanical role in articular cartilage. The goals of this study were to measure the mechanical properties of the PCM using micropipette aspiration coupled with a linear biphasic finite element model, and to determine the alterations in the mechanical properties of the PCM with osteoarthritis (OA). Using a recently developed isolation technique, chondrons (the chondrocyte and its PCM) were mechanically extracted from non-degenerate and osteoarthritic human cartilage. The transient mechanical behavior of the PCM was well-described by a biphasic model, suggesting that the viscoelastic response of the PCM is attributable to flow-dependent effects, similar to that of the ECM. With OA, the mean Young's modulus of the PCM was significantly decreased (38.7±16.2 kPa vs. 23.5±12.9 kPa, p 0.6). These findings suggest that the PCM may undergo degenerative processes with OA, similar to those occurring in the ECM. In combination with previous theoretical models of cell–matrix interactions in cartilage, our findings suggest that changes in the properties of the PCM with OA may have an important influence on the biomechanical environment of the chondrocyte.
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paper_title: Intraspecies and Interspecies Comparison of the Compressive Properties of the Medial Meniscus

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Quantification of the compressive material properties of the meniscus is of paramount importance, creating a “gold-standard” reference for future research. The purpose of this study was to determine compressive properties in six animal models (baboon, bovine, canine, human, lapine, and porcine) at six topographical locations. It was hypothesized that topographical variation of the compressive properties would be found in each animal model and that interspecies variations would also be exhibited. To test these hypotheses, creep and recovery indentation experiments were performed on the meniscus using a creep indentation apparatus and analyzed via a finite element optimization method to determine the material properties. Results show significant intraspecies and interspecies variation in the compressive properties among the six topographical locations, with the moduli exhibiting the highest values in the anterior portion. For example, the anterior location of the human meniscus has an aggregate modulus of 160 ± 40 kPa, whereas the central and posterior portions exhibit aggregate moduli of 100 ± 30 kPa. Interspecies comparison of the aggregate moduli identifies the lapine anterior location having the highest value (450 ± 120 kPa) and the human posterior location having the lowest (100 ± 30 kPa). These baseline values of compressive properties will be of help in future meniscal repair efforts.
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paper_title: Characterization of articular cartilage by combining microscopic analysis with a fibril-reinforced finite-element model.

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Load-bearing characteristics of articular cartilage are impaired during tissue degeneration. Quantitative microscopy enables in vitro investigation of cartilage structure but determination of tissue functional properties necessitates experimental mechanical testing. The fibril-reinforced poroviscoelastic (FRPVE) model has been used successfully for estimation of cartilage mechanical properties. The model includes realistic collagen network architecture, as shown by microscopic imaging techniques. The aim of the present study was to investigate the relationships between the cartilage proteoglycan (PG) and collagen content as assessed by quantitative microscopic findings, and model-based mechanical parameters of the tissue. Site-specific variation of the collagen network moduli, PG matrix modulus and permeability was analyzed. Cylindrical cartilage samples (n=22) were harvested from various sites of the bovine knee and shoulder joints. Collagen orientation, as quantitated by polarized light microscopy, was incorporated into the finite-element model. Stepwise stress-relaxation experiments in unconfined compression were conducted for the samples, and sample-specific models were fitted to the experimental data in order to determine values of the model parameters. For comparison, Fourier transform infrared imaging and digital densitometry were used for the determination of collagen and PG content in the same samples, respectively. The initial and strain-dependent fibril network moduli as well as the initial permeability correlated significantly with the tissue collagen content. The equilibrium Young's modulus of the nonfibrillar matrix and the strain dependency of permeability were significantly associated with the tissue PG content. The present study demonstrates that modern quantitative microscopic methods in combination with the FRPVE model are feasible methods to characterize the structure-function relationships of articular cartilage.
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paper_title: Inverse analysis of constitutive models: biological soft tissues.

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The paper describes a procedure for estimating the material parameters of biological soft tissue by fitting model prediction to experimental load-deformation data. This procedure minimizes the error between data and theoretical model prediction through systematically adjusting the parameters in the latter. The procedure uses commercially available software and is not specific to any particular model; nevertheless, for illustration purposes, we employ a six parameter fibril-reinforced poroelastic cartilage model. We are able to estimate any and all of these parameters by the procedure. Convergence of the parameters and convergence of the arbitrary initial stress relaxation to the data was demonstrated in all cases. Though we illustrate the optimization procedure here for unconfined compression only, it can be adapted easily to other experimental configurations such as confined compression, indentation and tensile test. Furthermore, the procedure can be applied in other areas of biomechanics where material parameters need to be extracted from experimental data.
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paper_title: Biomechanical, biochemical and structural correlations in immature and mature rabbit articular cartilage.

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OBJECTIVE ::: The structure and composition of articular cartilage change during development and growth. These changes lead to alterations in the mechanical properties of cartilage. In the present study, biomechanical, biochemical and structural relationships of articular cartilage during growth and maturation of rabbits are investigated. ::: ::: ::: DESIGN ::: Articular cartilage specimens from the tibial medial plateaus and femoral medial condyles of female New Zealand white rabbits were collected from seven age-groups; 0 days (n=29), 11 days (n=30), 4 weeks (n=30), 6 weeks (n=30), 3 months (n=24), 6 months (n=24) and 18 months (n=19). The samples underwent mechanical testing under creep indentation. From the mechanical response, instantaneous and equilibrium moduli were determined. Biochemical analyses of tissue collagen, hydroxylysylpyridinoline (HP) and pentosidine (PEN) cross-links in full thickness cartilage samples were conducted. Proteoglycans were investigated depth-wise from the tissue sections by measuring the optical density of Safranin-O-stained samples. Furthermore, depth-wise collagen architecture of articular cartilage was analyzed with polarized light microscopy. Finite element analyses of the samples from different age-groups were conducted to reveal tensile and compressive properties of the fibril network and the matrix of articular cartilage, respectively. ::: ::: ::: RESULTS ::: Tissue thickness decreased from approximately 3 to approximately 0.5mm until the age of 3 months, while the instantaneous modulus increased with age prior to peak at 4-6 weeks. A lower equilibrium modulus was observed before 3-month-age, after which the equilibrium modulus continued to increase. Collagen fibril orientation angle and parallelism index were inversely related to the instantaneous modulus, tensile fibril modulus and tissue thickness. Collagen content and cross-linking were positively related to the equilibrium compressive properties of the tissue. ::: ::: ::: CONCLUSIONS ::: During maturation, significant modulation of tissue structure, composition and mechanical properties takes place. Importantly, the present study provides insight into the mechanical, chemical and structural interactions that lead to functional properties of mature articular cartilage.
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paper_title: Fibril reinforced poroelastic model predicts specifically mechanical behavior of normal, proteoglycan depleted and collagen degraded articular cartilage

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Abstract Degradation of collagen network and proteoglycan (PG) macromolecules are signs of articular cartilage degeneration. These changes impair cartilage mechanical function. Effects of collagen degradation and PG depletion on the time-dependent mechanical behavior of cartilage are different. In this study, numerical analyses, which take the compression-tension nonlinearity of the tissue into account, were carried out using a fibril reinforced poroelastic finite element model. The study aimed at improving our understanding of the stress-relaxation behavior of normal and degenerated cartilage in unconfined compression. PG and collagen degradations were simulated by decreasing the Young's modulus of the drained porous (nonfibrillar) matrix and the fibril network, respectively. Numerical analyses were compared to results from experimental tests with chondroitinase ABC (PG depletion) or collagenase (collagen degradation) digested samples. Fibril reinforced poroelastic model predicted the experimental behavior of cartilage after chondroitinase ABC digestion by a major decrease of the drained porous matrix modulus (−64±28%) and a minor decrease of the fibril network modulus (−11±9%). After collagenase digestion, in contrast, the numerical analyses predicted the experimental behavior of cartilage by a major decrease of the fibril network modulus (−69±5%) and a decrease of the drained porous matrix modulus (−44±18%). The reduction of the drained porous matrix modulus after collagenase digestion was consistent with the microscopically observed secondary PG loss from the tissue. The present results indicate that the fibril reinforced poroelastic model is able to predict specifically characteristic alterations in the stress-relaxation behavior of cartilage after enzymatic modifications of the tissue. We conclude that the compression-tension nonlinearity of the tissue is needed to capture realistically the mechanical behavior of normal and degenerated articular cartilage.
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paper_title: Collagen network primarily controls Poisson's ratio of bovine articular cartilage in compression.

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The equilibrium Young's modulus of articular cartilage is known to be primarily determined by proteoglycans (PGs). However, the relation between the Poisson's ratio and the composition and structure of articular cartilage is more unclear. In this study, we determined Young's modulus and Poisson's ratio of bovine articular cartilage in unconfined compression. Subsequently, the same samples, taken from bovine knee (femoral, patellar and tibial cartilage) and shoulder (humeral cartilage) joints, were processed for quantitative microscopic analysis of PGs, collagen content, and collagen architecture. The Young's modulus, Poisson's ratio, PG content (estimated with optical density measurements), collagen content, and birefringence showed significant topographical variation (p < 0.05) among the test sites. Experimentally the Young's modulus was strongly determined by the tissue PG content (r = 0.86, p < 0.05). Poisson's ratio revealed a significant negative linear correlation (r = -0.59, p < 0.05) with the collagen content, as assessed by the Fourier transform infrared imaging. Finite element analyses, conducted using a fibril reinforced biphasic model, indicated that the mechanical properties of the collagen network strongly affected the Poisson's ratio. We conclude that Poisson's ratio of articular cartilage is primarily controlled by the content and organization of the collagen network.
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paper_title: Composition of the pericellular matrix modulates the deformation behaviour of chondrocytes in articular cartilage under static loading

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The aim was to assess the role of the composition changes in the pericellular matrix (PCM) for the chondrocyte deformation. For that, a three-dimensional finite element model with depth-dependent collagen density, fluid fraction, fixed charge density and collagen architecture, including parallel planes representing the split-lines, was created to model the extracellular matrix (ECM). The PCM was constructed similarly as the ECM, but the collagen fibrils were oriented parallel to the chondrocyte surfaces. The chondrocytes were modelled as poroelastic with swelling properties. Deformation behaviour of the cells was studied under 15% static compression. Due to the depth-dependent structure and composition of cartilage, axial cell strains were highly depth-dependent. An increase in the collagen content and fluid fraction in the PCMs increased the lateral cell strains, while an increase in the fixed charge density induced an inverse behaviour. Axial cell strains were only slightly affected by the changes in PCM composition. We conclude that the PCM composition plays a significant role in the deformation behaviour of chondrocytes, possibly modulating cartilage development, adaptation and degeneration. The development of cartilage repair materials could benefit from this information.
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paper_title: Collagen network of articular cartilage modulates fluid flow and mechanical stresses in chondrocyte.

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The extracellular matrix of articular cartilage modulates the mechanical signals sensed by the chondrocytes. In the present study, a finite element model (FEM) of the chondrocyte and its microenvironment was reconstructed using the information from fourier transform infrared imaging spectroscopy. This environment consisted of pericellular, territorial (mainly proteoglycans), and inter-territorial (mainly collagen) matrices. The chondrocyte, pericellular, and territorial matrix were assumedto be mechanically isotropic and poroelastic, whereas the inter-territorial matrix, due to its high collagen content, was assumed to be transversely isotropic and poroelastic. Under instantaneous strain-controlled compression, the FEM indicated that the fluid pressure within the chondrocyte increased nonlinearly as a function of the in-plane Young’s modulus of the collagen network. Under instantaneous force-controlled compression, the chondrocyte experienced the highest fluid pressure when the in-plane Young’s modulus of the collagen network was ~4 MPa. Based on the present results, the mechanical characteristics of the collagen network of articular cartilage can modify fluid flow and stresses in chondrocytes. Therefore, the integrity of the collagen network may be an important determinant in cell stimulation and in the control of the matrix maintenance.
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paper_title: Physical signals and solute transport in human intervertebral disc during compressive stress relaxation: 3D finite element analysis

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A 3D finite element model for charged hydrated soft tissues containing charged/uncharged solutes was developed based on the multi-phasic mechano-electrochemical mixture theory (Lai et al., J. Biomech. Eng. 113 (1991), 245-258; Gu et al., J. Biomech. Eng. 120 (1998), 169-180). This model was applied to analyze the mechanical, chemical and electrical signals within the human intervertebral disc during an unconfined compressive stress relaxation test. The effects of tissue composition (e.g., water content and fixed charge density (FCD)) on the physical signals and the transport rate of fluid, ions and nutrients were investigated. The numerical simulation showed that, during disc compression, the fluid pressurization was more pronounced at the center (nucleus) region of the disc while the effective (von Mises) stress was higher at the outer (annulus) region. Parametric analyses revealed that the decrease in initial tissue water content (0.7-0.8) increased the peak stress and relaxation time due to the reduction of permeability, causing greater fluid pressurization effect. The electrical signals within the disc were more sensitive to FCD than tissue porosity, and mechanical loading affected the large solute (e.g., growth factor) transport significantly, but not for small solute (e.g., glucose). Moreover, this study confirmed that the interstitial fluid pressurization plays an important role in the load support mechanism of IVD by sharing more than 40% of the total load during disc compression. This study is important for understanding disc biomechanics, disc nutrition and disc mechanobiology.
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paper_title: Biomechanical Influence of Disk Properties on the Load Transfer of Healthy and Degenerated Disks Using a Poroelastic Finite Element Model

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Spine degeneration is a pathology that will affect 80% of the population. Since the intervertebral disks play an important role in transmitting loads through the spine, the aim of this study was to evaluate the biomechanical impact of disk properties on the load carried by healthy (Thompson grade I) and degenerated (Thompson grades III and IV) disks. A three-dimensional parametric poroelastic finite element model of the L4/L5 motion segment was developed. Grade I, grade II, and grade IV disks were modeled by altering the biomechanical properties of both the annulus and nucleus. Models were validated using published creep experiments, in which a constant compressive axial stress of 0.35 MPa was applied for 4 h. Pore pressure (PP) and effective stress (SE) were analyzed as a function of time following loading application (1 min, 5 min, 45 min, 125 min, and 245 min) and discal region along the midsagittal profile for each disk grade. A design of experiments was further implemented to analyze the influence of six disk parameters (disk height (H), fiber proportion (%F), drained Young's modulus (Ea,En), and initial permeability (ka,kn) of both the annulus and nucleus) on load-sharing for disk grades I and IV. Simulations of grade I, grade III, and grade IV disks agreed well with the available published experimental data. Disk height (H) had a significant influence (p<0.05) on the PP and SE during the entire loading history for both healthy and degenerated disk models. Young’s modulus of the annulus (Ea) significantly affected not only SE in the annular region for both disk grades in the initial creep response but also SE in the nucleus zone for degenerated disks with further creep response. The nucleus and annulus permeabilities had a significant influence on the PP distribution for both disk grades, but this effect occurred at earlier stages of loading for degenerated than for healthy disk models. This is the first study that investigates the biomechanical influence of both geometrical and material disk properties on the load transfer of healthy and degenerated disks. Disk height is a significant parameter for both healthy and degenerated disks during the entire loading. Changes in the annulus stiffness, as well as in the annulus and nucleus permeability, control load-sharing in different ways for healthy and degenerated disks.
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paper_title: Statistical methods in finite element analysis

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Finite element analysis (FEA) is a commonly used tool within many areas of engineering and can provide useful information in structural analysis of mechanical systems. However, most analyses within the field of biomechanics usually take no account either of the wide variation in material properties and geometry that may occur in natural tissues or manufacturing imperfections in synthetic materials. This paper discusses two different methods of incorporating uncertainty in FE models. The first, Taguchi's robust parameter design, uses orthogonal matrices to determine how to vary the parameters in a series of FE models, and provides information on the sensitivity of a model to input parameters. The second, probabilistic analysis, enables the distribution of a response variable to be determined from the distributions of the input variables. The methods are demonstrated using a simple example of an FE model of a beam that is assigned material properties and geometry over a range similar to an orthopaedic fixation plate. In addition to showing how each method may be used on its own, we also show how computational effort may be minimised by first identifying the most important input variables before determining the effects of imprecision.
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paper_title: Sensitivity of tibio-menisco-femoral joint contact behavior to variations in knee kinematics.

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Use of computational models with kinematic boundary conditions to study the knee joint contact behavior for normal and pathologic knee joints depends on an understanding of the impacts of kinematic uncertainty. We studied the sensitivities of tibio-menisco-femoral joint contact behavior to variations in knee kinematics using a finite element model (FEM) with geometry and kinematic boundary conditions derived from sequences of magnetic resonance (MR) images. The MR images were taken before and after axial compression was applied to the knee joint of a healthy subject. A design of experiments approach was used to study the impact of the variation in knee kinematics on the contact outputs. We also explored the feasibility of using supplementary hip images to improve the accuracy of knee kinematics. Variations in knee kinematics (0.25mm in medial-lateral, 0.1mm in anterior-posterior and superior-inferior translations, and 0.1 degrees in flexion-extension and varus-valgus, 0.25 degrees in external-internal rotations) caused large variations in joint contact behavior. When kinematic boundary conditions resulted in close approximations of the model-predicted joint contact force to the applied force, variations in predictions of contact parameters were also reduced. The combination of inferior-superior and medial-lateral translations accounted for over 70% of variations for all the contact parameters examined. The inclusion of hip images in kinematic calculations improved knee kinematics by matching the femoral head position. Our findings demonstrate the importance of improving the accuracy and precision of knee kinematic measurements, especially when utilized as an input for finite element models.
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paper_title: Sensitivities of Medial Meniscal Motion and Deformation to Material Properties of Articular Cartilage, Meniscus and Meniscal Attachments Using Design of Experiments Methods

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This study investigated the role of the material properties assumed for articular cartilage, meniscus and meniscal attachments on the fit of a finite element model (FEM) to experimental data for meniscal motion and deformation due to an anterior tibial loading of 45 N in the anterior cruciate ligament-deficient knee. Taguchi style L18 orthogonal arrays were used to identify the most significant factors for further examination. A central composite design was then employed to develop a mathematical model for predicting the fit of the FEM to the experimental data as a function of the material properties and to identify the material property selections that optimize the fit. The cartilage was modeled as isotropic elastic material, the meniscus was modeled as transversely isotropic elastic material, and meniscal horn and the peripheral attachments were modeled as noncompressive and nonlinear in tension spring elements. The ability of the FEM to reproduce the experimentally measured meniscal motion and deformation was most strongly dependent on the initial strain of the meniscal horn attachments (E 1H ), the linear modulus of the meniscal peripheral attachments (Ep) and the ratio of meniscal moduli in the circumferential and transverse directions (E θ /E R ). Our study also successfully identified values for these critical material properties (e 1H =-5%, Ep=5.6 MPa, E θ /E R =20) to minimize the error in the FEM analysis of experimental results. This study illustrates the most important material properties for future experimental studies, and suggests that modeling work of meniscus, while retaining transverse isotropy, should also focus on the potential influence of nonlinear properties and inhomogeneity.
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paper_title: A finite element model of an idealized diarthrodial joint to investigate the effects of variation in the mechanical properties of the tissues

paper_content:

AbstractThe stiffness of articular cartilage increases dramatically with increasing rate of loading, and it has been hypothesized that increasing the stiffness of the subchondral bone may result in damaging stresses being generated in the articular cartilage. Despite the interdependence of these tissues in a joint, little is understood of the effect of such changes in one tissue on stresses generated in another. To investigate this, a parametric finite element model of an idealized joint was developed. The model incorporated layers representing articular cartilage, calcified cartilage, the subchondral bone plate and cancellous bone. Taguchi factorial design techniques, employing a two-level full-factorial and a four-level fractional factorial design, were used to vary the material properties and thicknesses of the layers over the wide range of values found in the literature. The effects on the maximum values of von Mises stress in each of the tissues are reported here. The stiffness of the cartilage was t...
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paper_title: Determining the most important cellular characteristics for fracture healing using design of experiments methods.

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Computational models are employed as tools to investigate possible mechanoregulation pathways for tissue differentiation and bone healing. However, current models do not account for the uncertainty in input parameters, and often include assumptions about parameter values that are not yet established. The objective of this study was to determine the most important cellular characteristics of a mechanoregulatory model describing both cell phenotype-specific and mechanobiological processes that are active during bone healing using a statistical approach. The computational model included an adaptive two-dimensional finite element model of a fractured long bone. Three different outcome criteria were quantified: (1) ability to predict sequential healing events, (2) amount of bone formation at early, mid and late stages of healing and (3) the total time until complete healing. For the statistical analysis, first a resolution IV fractional factorial design (L(64)) was used to identify the most significant factors. Thereafter, a three-level Taguchi orthogonal array (L(27)) was employed to study the curvature (non-linearity) of the 10 identified most important parameters. The results show that the ability of the model to predict the sequences of normal fracture healing was predominantly influenced by the rate of matrix production of bone, followed by cartilage degradation (replacement). The amount of bone formation at early stages was solely dependent on matrix production of bone and the proliferation rate of osteoblasts. However, the amount of bone formation at mid and late phases had the rate of matrix production of cartilage as the most influential parameter. The time to complete healing was primarily dependent on the rate of cartilage degradation during endochondral ossification, followed by the rate of cartilage formation. The analyses of the curvature revealed a linear response for parameters related to bone, where higher rates of formation were more beneficial to healing. In contrast, parameters related to fibrous tissue and cartilage showed optimum levels. Some fibrous connective tissue- and cartilage formation was beneficial to bone healing, but too much of either tissue delayed bone formation. The identified significant parameters and processes are further confirmed by in vivo animal experiments in the literature. This study illustrates the potential of design of experiments methods for evaluating computational mechanobiological model parameters and suggests that further experiments should preferably focus at establishing values of parameters related to cartilage formation and degradation.
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paper_title: Uncertainties in indentation testing of articular cartilage: A fibril-reinforced poroviscoelastic study

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Indentation testing provides a quantitative technique to evaluate mechanical characteristics of articular cartilage in situ and in vivo. Traditionally, analytical solutions proposed by Hayes et al. [Hayes WC, Keer LM, Herrmann G, Mockros LF. A mathematical analysis for indentation tests of articular cartilage. J Biomech 1972;5(5):541-51] have been applied for the analysis of indentation measurements, and due to their practicality, they have been used for clinical diagnostics. Using this approach, the elastic modulus is derived based on scaling factors which depend on cartilage thickness, indenter radius and Poisson's ratio, and the cartilage model is assumed isotropic and homogeneous, thereby greatly simplifying the true tissue characteristics. The aim was to investigate the validity of previous model assumptions for indentation testing. Fibril-reinforced poroviscoelastic cartilage (FRPVE) model including realistic tissue characteristics was used to simulate indentation tests. The effects of cartilage inhomogeneity, anisotropy, and indentation velocity on the indentation response were evaluated, and scaling factors from the FRPVE analysis were derived. Subsequently, the validity of scaling factors obtained using the traditional and the FRPVE analyses was studied by calculating indentation moduli for bovine cartilage samples, and comparing these values to those obtained experimentally in unconfined compression testing. Collagen architecture and compression velocity had significant effects on the indentation response. Isotropic elastic analysis gave significantly higher (30-107%) Young's moduli for indentation compared to unconfined compression testing. Modification of Hayes' scaling factors by accounting for cartilage inhomogeneity and anisotropy improved the agreement of Young's moduli obtained for the two test configurations by 14-28%. These results emphasize the importance of realistic cartilage structure and mechanical properties in the indentation analysis. Although it is not possible to fully describe tissue inhomogeneity and anisotropy with just the Young's modulus and Poisson's ratio, accounting for inhomogeneity and anisotropy in these two parameters may help to improve the in vivo characterization of tissue using arthroscopic indentation testing.
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paper_title: Sensitivity of tissue differentiation and bone healing predictions to tissue properties.

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Computational models are employed as tools to investigate possible mechano-regulation pathways for tissue differentiation and bone healing. However, current models do not account for the uncertainty in input parameters, and often include assumptions about parameter values that are not yet established. The aim was to clarify the importance of the assumed tissue material properties in a computational model of tissue differentiation during bone healing. An established mechano-biological model was employed together with a statistical approach. The model included an adaptive 2D finite element model of a fractured long bone. Four outcome criteria were quantified: (1) ability to predict sequential healing events, (2) amount of bone formation at specific time points, (3) total time until healing, and (4) mechanical stability at specific time points. Statistical analysis based on fractional factorial designs first involved a screening experiment to identify the most significant tissue material properties. These seven properties were studied further with response surface methodology in a three-level Box-Behnken design. Generally, the sequential events were not significantly influenced by any properties, whereas rate-dependent outcome criteria and mechanical stability were significantly influenced by Young's modulus and permeability. Poisson's ratio and porosity had minor effects. The amount of bone formation at early, mid and late phases of healing, the time until complete healing and the mechanical stability were all mostly dependent on three material properties; permeability of granulation tissue, Young's modulus of cartilage and permeability of immature bone. The consistency between effects of the most influential parameters was high. To increase accuracy and predictive capacity of computational models of bone healing, the most influential tissue mechanical properties should be accurately quantified.
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paper_title: Contribution of tissue composition and structure to mechanical response of articular cartilage under different loading geometries and strain rates

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Mechanical function of articular cartilage in joints between articulating bones is dependent on the composition and structure of the tissue. The mechanical properties of articular cartilage are traditionally tested in compression using one of the three loading geometries, i.e., confined compression, unconfined compression or indentation. The aim of this study was to utilize a composition-based finite element model in combination with a fractional factorial design to determine the importance of different cartilage constituents in the mechanical response of the tissue, and to compare the importance of the tissue constituents with different loading geometries and loading rates. The evaluated parameters included water and collagen fraction as well as fixed charge density on cartilage surface and their slope over the tissue thickness. The thicknesses of superficial and middle zones, as based on the collagen orientation, were also included in the evaluated parameters. A three-level resolution V fractional factorial design was used. The model results showed that inhomogeneous composition plays only a minor role in indentation, though that role becomes more significant in confined compression and unconfined compression. In contrast, the collagen architecture and content had a more profound role in indentation than with two other loading geometries. These differences in the mechanical role of composition and structure between the loading geometries were emphasized at higher loading rates. These findings highlight how the results from mechanical tests of articular cartilage under different loading conditions are dependent upon tissue composition and structure.
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paper_title: Determination of nonlinear fibre-reinforced biphasic poroviscoelastic constitutive parameters of articular cartilage using stress relaxation indentation testing and an optimizing finite element analysis

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An inverse method was developed to determine the material constitutive parameters of human articular cartilage from stress relaxation indentation tests. The cartilage was modeled as a fibre-reinforced nonlinear biphasic poroviscoelastic material, and a finite element (FE) model was used with a simulated annealing (SA) optimization algorithm to determine the material parameters that minimized the error between the experimental and predicted time dependant indentation loads. The values of the 15 optimized material parameters were found to be insensitive to the initial guesses, and, when friction between the indenter and the cartilage was considered, resulted in good agreement between the measured stress relaxation response and the FE prediction (R^2=0.99). The optimized material parameters determined from experiments that used two different indenter sizes on the same samples were compared. When assuming frictionless contact between the indenter and the cartilage, all of the optimized parameters except for the Poisson's ratio were found to be relatively insensitive to indenter size. A second set of models that included frictional contact greatly reduced the sensitivity of the optimized Poisson's ratio to indenter size, thus confirming the validity of the model and demonstrating the importance of modeling friction. The results also demonstrate the robustness of the SA optimization algorithm to ensure convergence of a large number of material properties to a global minimum regardless of the quality of the initial guesses.
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paper_title: A review of probabilistic analysis in orthopaedic biomechanics

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Probabilistic analysis methods are being increasingly applied in the orthopaedics and biomechanics literature to account for uncertainty and variability in subject geometries, properties of various structures, kinematics and joint loading, as well as uncertainty in implant alignment. As a complement to experiments, finite element modelling, and statistical analysis, probabilistic analysis provides a method of characterizing the potential impact of variability in parameters on performance. This paper presents an overview of probabilistic analysis and a review of biomechanics literature utilizing probabilistic methods in structural reliability, kinematics, joint mechanics, musculoskeletal modelling, and patient-specific representations. The aim of this review paper is to demonstrate the wide range of applications of probabilistic methods and to aid researchers and clinicians in better understanding probabilistic analyses.
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paper_title: An Axisymmetric Boundary Element Model for Determination of Articular Cartilage Pericellular Matrix Properties In Situ via Inverse Analysis of Chondron Deformation

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The pericellular matrix (PCM) is the narrow tissue region surrounding all chondrocytes in articular cartilage and, together, the chondrocyte(s) and surrounding PCM have been termed the chondron. Previous theoretical and experimental studies suggest that the structure and properties of the PCM significantly influence the biomechanical environment at the microscopic scale of the chondrocytes within cartilage. In the present study, an axisymmetric boundary element method (BEM) was developed for linear elastic domains with internal interfaces. The new BEM was employed in a multiscale continuum model to determine linear elastic properties of the PCM in situ, via inverse analysis of previously reported experimental data for the three-dimensional morphological changes of chondrons within a cartilage explant in equilibrium unconfined compression (Choi, et al., 2007, "Zonal Changes in the Three-Dimensional Morphology of the Chondron Under Compression: The Relationship Among Cellular, Pericellular, and Extracellular Deformation in Articular Cartilage," J. Biomech., 40, pp. 2596-2603). The microscale geometry of the chondron (cell and PCM) within the cartilage extracellular matrix (ECM) was represented as a three-zone equilibrated biphasic region comprised of an ellipsoidal chondrocyte with encapsulating PCM that was embedded within a spherical ECM subjected to boundary conditions for unconfined compression at its outer boundary. Accuracy of the three-zone BEM model was evaluated and compared with analytical finite element solutions. The model was then integrated with a nonlinear optimization technique (Nelder-Mead) to determine PCM elastic properties within the cartilage explant by solving an inverse problem associated with the in situ experimental data for chondron deformation. Depending on the assumed material properties of the ECM and the choice of cost function in the optimization, estimates of the PCM Young's modulus ranged from ~24 kPa to 59 kPa, consistent with previous measurements of PCM properties on extracted chondrons using micropipette aspiration. Taken together with previous experimental and theoretical studies of cell-matrix interactions in cartilage, these findings suggest an important role for the PCM in modulating the mechanical environment of the chondrocyte.
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paper_title: Intraspecies and Interspecies Comparison of the Compressive Properties of the Medial Meniscus

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Quantification of the compressive material properties of the meniscus is of paramount importance, creating a “gold-standard” reference for future research. The purpose of this study was to determine compressive properties in six animal models (baboon, bovine, canine, human, lapine, and porcine) at six topographical locations. It was hypothesized that topographical variation of the compressive properties would be found in each animal model and that interspecies variations would also be exhibited. To test these hypotheses, creep and recovery indentation experiments were performed on the meniscus using a creep indentation apparatus and analyzed via a finite element optimization method to determine the material properties. Results show significant intraspecies and interspecies variation in the compressive properties among the six topographical locations, with the moduli exhibiting the highest values in the anterior portion. For example, the anterior location of the human meniscus has an aggregate modulus of 160 ± 40 kPa, whereas the central and posterior portions exhibit aggregate moduli of 100 ± 30 kPa. Interspecies comparison of the aggregate moduli identifies the lapine anterior location having the highest value (450 ± 120 kPa) and the human posterior location having the lowest (100 ± 30 kPa). These baseline values of compressive properties will be of help in future meniscal repair efforts.
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paper_title: A nonlinear biphasic fiber-reinforced porohyperviscoelastic model of articular cartilage incorporating fiber reorientation and dispersion.

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A nonlinear biphasic fiber-reinforced porohyperviscoelastic (BFPHVE) model of articular cartilage incorporating fiber reorientation effects during applied load was used to predict the response of ovine articular cartilage at relatively high strains (20%). The constitutive material parameters were determined using a coupled finite element-optimization algorithm that utilized stress relaxation indentation tests at relatively high strains. The proposed model incorporates the strain-hardening, tension-compression, permeability, and finite deformation nonlinearities that inherently exist in cartilage, and accounts for effects associated with fiber dispersion and reorientation and intrinsic viscoelasticity at relatively high strains. A new optimization cost function was used to overcome problems associated with large peak-to-peak differences between the predicted finite element and experimental loads that were due to the large strain levels utilized in the experiments. The optimized material parameters were found to be insensitive to the initial guesses. Using experimental data from the literature, the model was also able to predict both the lateral displacement and reaction force in unconfined compression, and the reaction force in an indentation test with a single set of material parameters. Finally, it was demonstrated that neglecting the effects of fiber reorientation and dispersion resulted in poorer agreement with experiments than when they were considered. There was an indication that the proposed BFPHVE model, which includes the intrinsic viscoelasticity of the nonfibrillar matrix (proteoglycan), might be used to model the behavior of cartilage up to relatively high strains (20%). The maximum percentage error between the indentation force predicted by the FE model using the optimized material parameters and that measured experimentally was 3%.
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paper_title: Diffusion coefficients of articular cartilage for different CT and MRI contrast agents.

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In contrast enhanced magnetic resonance imaging (MRI) and computed tomography (CT), the equilibrium distribution of anionic contrast agent is expected to reflect the fixed charged density (FCD) of articular cartilage. Diffusion is mainly responsible for the transport of contrast agents into cartilage. In osteoarthritis, cartilage composition changes at early stages of disease, and solute diffusion is most likely affected. Thus, investigation of contrast agent diffusion could enable new methods for imaging of cartilage composition. The aim of this study was to determine the diffusion coefficient of four contrast agents (ioxaglate, gadopentetate, iodide, gadodiamide) in bovine articular cartilage. The contrast agents were different in molecular size and charge. In peripheral quantitative CT experiments, penetration of contrast agent into the tissue was allowed either through the articular surface or through deep cartilage. To determine diffusion coefficients, a finite element model based on Fick's law was fitted to experimental data. Diffusion through articular surface was faster than through deep cartilage with every contrast agent. Iodide, being of atomic size, diffused into the cartilage significantly faster (q<0.05) than the other three contrast agents, for either transport direction. The diffusion coefficients of all clinical contrast agents (ioxaglate, gadopentetate and gadodiamide) were relatively low (142.8-253.7 μm(2)/s). In clinical diagnostics, such slow diffusion may not reach equilibrium and this jeopardizes the determination of FCD by standard methods. However, differences between diffusion through articular surface and deep cartilage, that are characterized by different tissue composition, suggest that diffusion coefficients may correlate with cartilage composition. Present method could therefore enable image-based assessment of cartilage composition by determination of diffusion coefficients within cartilage tissue.
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paper_title: Evaluating knee replacement mechanics during ADL with PID-controlled dynamic finite element analysis.

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Validated computational knee simulations are valuable tools for design phase development of knee replacement devices. Recently, a dynamic finite element (FE) model of the Kansas knee simulator was kinematically validated during gait and deep flexion cycles. In order to operate the computational simulator in the same manner as the experiment, a proportional-integral-derivative (PID) controller was interfaced with the FE model to control the quadriceps actuator excursion and produce a target flexion profile regardless of implant geometry or alignment conditions. The controller was also expanded to operate multiple actuators simultaneously in order to produce in vivo loading conditions at the joint during dynamic activities. Subsequently, the fidelity of the computational model was improved through additional muscle representation and inclusion of relative hip-ankle anterior-posterior (A-P) motion. The PID-controlled model was able to successfully recreate in vivo loading conditions (flexion angle, compressive joint load, medial-lateral load distribution or varus-valgus torque, internal-external torque, A-P force) for deep knee bend, chair rise, stance-phase gait and step-down activities.
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paper_title: Dynamic finite element knee simulation for evaluation of knee replacement mechanics.

paper_content:

In vitro pre-clinical testing of total knee replacement (TKR) devices is a necessary step in the evaluation of new implant designs. Whole joint knee simulators, like the Kansas knee simulator (KKS), provide a controlled and repeatable loading environment for comparative evaluation of component designs or surgical alignment under dynamic conditions. Experimental testing, however, is time and cost prohibitive for design-phase evaluation of tens or hundreds of design variations. Experimentally-verified computational models provide an efficient platform for analysis of multiple components, sizes, and alignment conditions. The purpose of the current study was to develop and verify a computational model of a dynamic, whole joint knee simulator. Experimental internal-external and valgus-varus laxity tests, followed by dynamic deep knee bend and gait simulations in the KKS were performed on three cadaveric specimens. Specimen-specific finite element (FE) models of posterior-stabilized TKR were created from magnetic resonance images and CAD geometry. The laxity data was used to optimize mechanical properties of tibiofemoral soft-tissue structures on a specimen-specific basis. Each specimen was subsequently analyzed in a computational model of the experimental KKS, simulating both dynamic activities. The computational model represented all joints and actuators in the experimental setup, including a proportional-integral-derivative (PID) controller to drive quadriceps actuation. The computational model was verified against six degree-of-freedom patellofemoral (PF) and tibiofemoral (TF) kinematics and actuator loading during both deep knee bend and gait activities, with good agreement in trends and magnitudes between model predictions and experimental kinematics; differences were less than 1.8 mm and 2.2° for PF and TF translations and rotations. The whole joint FE simulator described in this study can be applied to investigate a wide range of clinical and research questions.
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paper_title: Stresses in the local collagen network of articular cartilage: a poroviscoelastic fibril-reinforced finite element study.

paper_content:

Osteoarthritis (OA) is a multifactorial disease, resulting in diarthrodial joint wear and eventually destruction. Swelling of cartilage, which is proportional to the amount of collagen damage, is an initial event of cartilage degeneration, so damage to the collagen fibril network is likely to be one of the earliest signs of OA cartilage degeneration. We propose that the local stresses and strains in the collagen fibrils, which cause the damage, cannot be determined dependably without taking the local arcade-like collagen-fibril structure into account. We investigate this using a poroviscoelastic fibril-reinforced FEA model. The constitutive fibril properties were determined by fitting numerical data to experimental results of unconfined compression and indentation tests on samples of bovine patellar articular cartilage. It was demonstrated that with this model the stresses and strains in the collagen fibrils can be calculated. It was also exhibited that fibrils with different orientations at the same location can be loaded differently, depending on the local architecture of the collagen network. To the best of our knowledge, the present model is the first that can account for these features. We conclude that the local stresses and strains in the articular cartilage are highly influenced by the local morphology of the collagen-fibril network.
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paper_title: Characterization of articular cartilage by combining microscopic analysis with a fibril-reinforced finite-element model.

paper_content:

Load-bearing characteristics of articular cartilage are impaired during tissue degeneration. Quantitative microscopy enables in vitro investigation of cartilage structure but determination of tissue functional properties necessitates experimental mechanical testing. The fibril-reinforced poroviscoelastic (FRPVE) model has been used successfully for estimation of cartilage mechanical properties. The model includes realistic collagen network architecture, as shown by microscopic imaging techniques. The aim of the present study was to investigate the relationships between the cartilage proteoglycan (PG) and collagen content as assessed by quantitative microscopic findings, and model-based mechanical parameters of the tissue. Site-specific variation of the collagen network moduli, PG matrix modulus and permeability was analyzed. Cylindrical cartilage samples (n=22) were harvested from various sites of the bovine knee and shoulder joints. Collagen orientation, as quantitated by polarized light microscopy, was incorporated into the finite-element model. Stepwise stress-relaxation experiments in unconfined compression were conducted for the samples, and sample-specific models were fitted to the experimental data in order to determine values of the model parameters. For comparison, Fourier transform infrared imaging and digital densitometry were used for the determination of collagen and PG content in the same samples, respectively. The initial and strain-dependent fibril network moduli as well as the initial permeability correlated significantly with the tissue collagen content. The equilibrium Young's modulus of the nonfibrillar matrix and the strain dependency of permeability were significantly associated with the tissue PG content. The present study demonstrates that modern quantitative microscopic methods in combination with the FRPVE model are feasible methods to characterize the structure-function relationships of articular cartilage.
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paper_title: A subject specific multibody model of the knee with menisci.

paper_content:

The menisci of the knee play an important role in joint function and our understanding of knee mechanics and tissue interactions can be enhanced through computational models of the tibio-menisco-femoral structure. Several finite element models of the knee that include meniscus-cartilage contact exist, but these models are typically limited to simplified boundary conditions. Movement simulation and musculoskeletal modeling can predict muscle forces, but are typically performed using the multibody method with simplified representation of joint structures. This study develops a subject specific computational model of the knee with menisci that can be incorporated into neuromusculoskeletal models within a multibody framework. Meniscus geometries from a 78-year-old female right cadaver knee were divided into 61 discrete elements (29 medial and 32 lateral) that were connected through 6x6 stiffness matrices. An optimization and design of experiments approach was used to determine parameters for the 6x6 stiffness matrices such that the force-displacement relationship of the meniscus matched that of a linearly elastic transversely isotropic finite element model for the same cadaver knee. Similarly, parameters for compliant contact models of tibio-menisco-femoral articulations were derived from finite element solutions. As a final step, a multibody knee model was developed and placed within a dynamic knee simulator model and the tibio-femoral and patello-femoral kinematics compared to an identically loaded cadaver knee. RMS errors between finite element displacement and multibody displacement after parameter optimization were 0.017 mm for the lateral meniscus and 0.051 mm for the medial meniscus. RMS errors between model predicted and experimental cadaver kinematics during a walk cycle were less than 11 mm translation and less than 7 degrees orientation. A small improvement in kinematics, compared to experimental measurements, was seen when the menisci were included versus a model without the menisci. With the menisci the predicted tibio-femoral contact force was significantly reduced on the lateral side (937 N peak force versus 633 N peak force), but no significant reduction was seen on the medial side.
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paper_title: Inverse analysis of constitutive models: biological soft tissues.

paper_content:

The paper describes a procedure for estimating the material parameters of biological soft tissue by fitting model prediction to experimental load-deformation data. This procedure minimizes the error between data and theoretical model prediction through systematically adjusting the parameters in the latter. The procedure uses commercially available software and is not specific to any particular model; nevertheless, for illustration purposes, we employ a six parameter fibril-reinforced poroelastic cartilage model. We are able to estimate any and all of these parameters by the procedure. Convergence of the parameters and convergence of the arbitrary initial stress relaxation to the data was demonstrated in all cases. Though we illustrate the optimization procedure here for unconfined compression only, it can be adapted easily to other experimental configurations such as confined compression, indentation and tensile test. Furthermore, the procedure can be applied in other areas of biomechanics where material parameters need to be extracted from experimental data.
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paper_title: A finite element formulation and program to study transient swelling and load-carriage in healthy and degenerate articular cartilage

paper_content:

The theory of poroelasticity is extended to include physico-chemical swelling and used to predict the transient responses of normal and degenerate articular cartilage to both chemical and mechanical loading; with emphasis on isolating the influence of the major parameters which govern its deformation. Using a new hybrid element, our mathematical relationships were implemented in a purpose-built poroelastic finite element analysis algorithm (u-pi-c program) which was used to resolve the nature of the coupling between the mechanical and chemical responses of cartilage when subjected to ionic transport across its membranous skeleton. Our results demonstrate that one of the roles of the strain-dependent matrix permeability is to limit the rate of transmission of stresses from the fluid to the collagen-proteoglycan solid skeleton in the incipient stages of loading, and that the major contribution of the swelling pressure is that of preventing any excessive deformation of the matrix.
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paper_title: A biphasic viscohyperelastic fibril-reinforced model for articular cartilage: formulation and comparison with experimental data.

paper_content:

Experiments in articular cartilage have shown highly nonlinear stress-strain curves under finite deformations, nonlinear tension-compression response as well as intrinsic viscous effects of the proteoglycan matrix and the collagen fibers. A biphasic viscohyperelastic fibril-reinforced model is proposed here, which is able to describe the intrinsic viscoelasticity of the fibrillar and nonfibrillar components of the solid phase, the nonlinear tension-compression response and the nonlinear stress-strain curves under tension and compression. A viscohyperelastic constitutive equation was used for the matrix and the fibers encompassing, respectively, a hyperelastic function used previously for the matrix and a hyperelastic law used before to represent biological connective tissues. This model, implemented in an updated Lagrangian finite element code, displayed good ability to follow experimental stress-strain equilibrium curves under tension and compression for human humeral cartilage. In addition, curve fitting of experimental reaction force and lateral displacement unconfined compression curves showed that the inclusion of viscous effects in the matrix allows the description of experimental data with material properties for the fibers consistent with experimental tensile tests, suggesting that intrinsic viscous effects in the matrix of articular cartilage plays an important role in the mechanical response of the tissue.
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paper_title: Stress–relaxation of human patellar articular cartilage in unconfined compression: Prediction of mechanical response by tissue composition and structure

paper_content:

Abstract Mechanical properties of articular cartilage are controlled by tissue composition and structure. Cartilage function is sensitively altered during tissue degeneration, in osteoarthritis (OA). However, mechanical properties of the tissue cannot be determined non-invasively. In the present study, we evaluate the feasibility to predict, without mechanical testing, the stress–relaxation response of human articular cartilage under unconfined compression. This is carried out by combining microscopic and biochemical analyses with composition-based mathematical modeling. Cartilage samples from five cadaver patellae were mechanically tested under unconfined compression. Depth-dependent collagen content and fibril orientation, as well as proteoglycan and water content were derived by combining Fourier transform infrared imaging, biochemical analyses and polarized light microscopy. Finite element models were constructed for each sample in unconfined compression geometry. First, composition-based fibril-reinforced poroviscoelastic swelling models, including composition and structure obtained from microscopical and biochemical analyses were fitted to experimental stress–relaxation responses of three samples. Subsequently, optimized values of model constants, as well as compositional and structural parameters were implemented in the models of two additional samples to validate the optimization. Theoretical stress–relaxation curves agreed with the experimental tests ( R =0.95–0.99). Using the optimized values of mechanical parameters, as well as composition and structure of additional samples, we were able to predict their mechanical behavior in unconfined compression, without mechanical testing ( R =0.98). Our results suggest that specific information on tissue composition and structure might enable assessment of cartilage mechanics without mechanical testing.
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paper_title: A composition-based cartilage model for the assessment of compositional changes during cartilage damage and adaptation

paper_content:

Summary Objective The composition of articular cartilage changes with progression of osteoarthritis. Since compositional changes are associated with changes in the mechanical properties of the tissue, they are relevant for understanding how mechanical loading induces progression. The objective of this study is to present a computational model of articular cartilage which enables to study the interaction between composition and mechanics. Methods Our previously developed fibril-reinforced poroviscoelastic swelling model for articular cartilage was combined with our tissue composition-based model. In the combined model both the depth- and strain-dependencies of the permeability are governed by tissue composition. All local mechanical properties in the combined model are directly related to the local composition of the tissue, i.e., to the local amounts of proteoglycans and collagens and to tissue anisotropy. Results Solely based on the composition of the cartilage, we were able to predict the equilibrium and transient response of articular cartilage during confined compression, unconfined compression, indentation and two different 1D-swelling tests, simultaneously. Conclusion Since both the static and the time-dependent mechanical properties have now become fully dependent on tissue composition, the model allows assessing the mechanical consequences of compositional changes seen during osteoarthritis without further assumptions. This is a major step forward in quantitative evaluations of osteoarthritis progression.
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paper_title: A Conewise Linear Elasticity Mixture Model for the Analysis of Tension-Compression Nonlinearity in Articular Cartilage

paper_content:

A biphasic mixture model is developed which can account for the observed tension-compression nonlinearity of cartilage by employing the continuum-based Conewise Linear Elasticity (CLE) model of Curnier et al. (J Elasticity 37:1–38, 1995) to describe the solid phase of the mixture. In this first investigation, the orthotropic octantwise linear elasticity model was reduced to the more specialized case of cubic symmetry, to reduce the number of elastic constants from twelve to four. Confined and unconfined compression stress-relaxation, and torsional shear testing were performed on each of nine bovine humeral head articular cartilage cylindrical plugs from 6 month old calves. Using the CLE model with cubic symmetry, the aggregate modulus in compression and axial permeability were obtained from confined compression (H−A =0.64±0.22 MPa, kz = 3.62 ± .97 × 10−16 m4/N.s, r2 =0.95±0.03), the tensile modulus, compressive Poisson ratio and radial permeability were obtained from unconfined compression (E+Y = 12.75 ± 1.56 MPa, ν− =0.03±0.01, kr =6.06±2.10×10−16 m4/N.s, r2 =0.99±0.00), and the shear modulus was obtained from torsional shear (µ=0.17±0.06 MPa). The model was also employed to successfully predict the interstitial fluid pressure at the center of the cartilage plug in unconfined compression (r2 =0.98±0.01). The results of this study demonstrate that the integration of the CLE model with the biphasic mixture theory can provide a model of cartilage which can successfully curvefit three distinct testing configurations while producing material parameters consistent with previous reports in the literature.
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paper_title: Experimental Verification and Theoretical Prediction of Cartilage Interstitial Fluid Pressurization At an Impermeable Contact Interface in Confined Compression

paper_content:

Interstitial fluid pressurization has long been hypothesized to play a fundamental role in the load support mechanism and frictional response of articular cartilage. However, to date, few experimental studies have been performed to verify this hypothesis from direct measurements. The first objective of this study was to investigate experimentally the hypothesis that cartilage interstitial fluid pressurization does support the great majority of the applied load, in the testing configurations of confined compression creep and stress relaxation. The second objective was to investigate the hypothesis that the experimentally observed interstitial fluid pressurization could also be predicted using the linear biphasic theory of Mow et al. (J. Biomech. Engng ASME, 102, 73-84, 1980). Fourteen bovine cartilage samples were tested in a confined compression chamber fitted with a microchip piezoresistive transducer to measure interstitial fluid pressure, while simultaneously measuring (during stress relaxation) or prescribing (during creep) the total stress. It was found that interstitial fluid pressure supported more than 90% of the total stress for durations as long as 725 +/- 248 s during stress relaxation (mean +/- S.D., n = 7), and 404 +/- 229 s during creep (n = 7). When comparing experimental measurements of the time-varying interstitial fluid pressure against predictions from the linear biphasic theory, nonlinear coefficients of determination r2 = 0.871 +/- 0.086 (stress relaxation) and r2 = 0.941 +/- 0.061 (creep) were found. The results of this study provide some of the most direct evidence to date that interstitial fluid pressurization plays a fundamental role in cartilage mechanics; they also indicate that the mechanism of fluid load support in cartilage can be properly predicted from theory.
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paper_title: Mechanics of chondrocyte hypertrophy

paper_content:

Chondrocyte hypertrophy is a characteristic of osteoarthritis and dominates bone growth. Intra- and extracellular changes that are known to be induced by metabolically active hypertrophic chondrocytes are known to contribute to hypertrophy. However, it is unknown to which extent these mechanical conditions together can be held responsible for the total magnitude of hypertrophy. The present paper aims to provide a quantitative, mechanically sound answer to that question. To address this aim requires a quantitative tool that captures the mechanical effects of collagen and proteoglycans, allows temporal changes in tissue composition, and can compute cell and tissue deformations. These requirements are met in our numerical model that is validated for articular cartilage mechanics, which we apply to quantitatively explain a range of experimental observations related to hypertrophy. After validating the numerical approach for studying hypertrophy, the model is applied to evaluate the direct mechanical effects of axial tension and compression on hypertrophy (Hueter-Volkmann principle) and to explore why hypertrophy is reduced in case of partially or fully compromised proteoglycan expression. Finally, a mechanical explanation is provided for the observation that chondrocytes do not hypertrophy when enzymatical collagen degradation is prohibited (S1Pcko knock-out mouse model). This paper shows that matrix turnover by metabolically active chondrocytes, together with externally applied mechanical conditions, can explain quantitatively the volumetric change of chondrocytes during hypertrophy. It provides a mechanistic explanation for the observation that collagen degradation results in chondrocyte hypertrophy, both under physiological and pathological conditions.
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paper_title: Stresses in the local collagen network of articular cartilage: a poroviscoelastic fibril-reinforced finite element study.

paper_content:

Osteoarthritis (OA) is a multifactorial disease, resulting in diarthrodial joint wear and eventually destruction. Swelling of cartilage, which is proportional to the amount of collagen damage, is an initial event of cartilage degeneration, so damage to the collagen fibril network is likely to be one of the earliest signs of OA cartilage degeneration. We propose that the local stresses and strains in the collagen fibrils, which cause the damage, cannot be determined dependably without taking the local arcade-like collagen-fibril structure into account. We investigate this using a poroviscoelastic fibril-reinforced FEA model. The constitutive fibril properties were determined by fitting numerical data to experimental results of unconfined compression and indentation tests on samples of bovine patellar articular cartilage. It was demonstrated that with this model the stresses and strains in the collagen fibrils can be calculated. It was also exhibited that fibrils with different orientations at the same location can be loaded differently, depending on the local architecture of the collagen network. To the best of our knowledge, the present model is the first that can account for these features. We conclude that the local stresses and strains in the articular cartilage are highly influenced by the local morphology of the collagen-fibril network.
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paper_title: A fibril-reinforced poroviscoelastic swelling model for articular cartilage.

paper_content:

From a mechanical point of view, the most relevant components of articular cartilage are the tight and highly organized collagen network together with the charged proteoglycans. Due to the fixed charges of the proteoglycans, the cation concentration inside the tissue is higher than in the surrounding synovial fluid. This excess of ion particles leads to an osmotic pressure difference, which causes swelling of the tissue. The fibrillar collagen network resists straining and swelling pressures. This combination makes cartilage a unique, highly hydrated and pressurized tissue, enforced with a strained collagen network. Many theories to explain articular cartilage behavior under loading, expressed in computational models that either include the swelling behavior or the properties of the anisotropic collagen structure, can be found in the literature. The most common tests used to determine the mechanical quality of articular cartilage are those of confined compression, unconfined compression, indentation and swelling. All theories currently available in the literature can explain the cartilage response occurring in some of the above tests, but none of them can explain these for all of the tests. We hypothesized that a model including simultaneous mathematical descriptions of (1) the swelling properties due to the fixed-change densities of the proteoglycans and (2) the anisotropic viscoelastic collagen structure, can explain all these test simultaneously. To study this hypothesis we extended our fibril-reinforced poroviscoelastic finite element model with our biphasic swelling model. We have shown that the newly developed fibril-reinforced poroviscoelastic swelling (FPVES) model for articular cartilage can simultaneously account for the reaction force during swelling, confined compression, indentation and unconfined compression as well as the lateral deformation during unconfined compression. Using this theory it is possible to analyze the link between the collagen network and the swelling properties of articular cartilage.
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paper_title: A composition-based cartilage model for the assessment of compositional changes during cartilage damage and adaptation

paper_content:

Summary Objective The composition of articular cartilage changes with progression of osteoarthritis. Since compositional changes are associated with changes in the mechanical properties of the tissue, they are relevant for understanding how mechanical loading induces progression. The objective of this study is to present a computational model of articular cartilage which enables to study the interaction between composition and mechanics. Methods Our previously developed fibril-reinforced poroviscoelastic swelling model for articular cartilage was combined with our tissue composition-based model. In the combined model both the depth- and strain-dependencies of the permeability are governed by tissue composition. All local mechanical properties in the combined model are directly related to the local composition of the tissue, i.e., to the local amounts of proteoglycans and collagens and to tissue anisotropy. Results Solely based on the composition of the cartilage, we were able to predict the equilibrium and transient response of articular cartilage during confined compression, unconfined compression, indentation and two different 1D-swelling tests, simultaneously. Conclusion Since both the static and the time-dependent mechanical properties have now become fully dependent on tissue composition, the model allows assessing the mechanical consequences of compositional changes seen during osteoarthritis without further assumptions. This is a major step forward in quantitative evaluations of osteoarthritis progression.
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paper_title: Swelling of articular cartilage and other connective tissues: electromechanochemical forces.

paper_content:

We have measured the relationship between tissue swelling stress and consolidation for bovine articular cartilage and corneal stroma in uniaxial confined compression as a function of bath ionic strength. Our experimental protocol and results clearly demonstrate that two concentration-dependent material properties are necessary to describe the chemical dependence of tissue swelling stress in uniaxial compression over the range of deformations and concentrations explored. A general electromechanochemical model for the swelling stress of charged connective tissues is developed. The model focuses on the role of charged matrix macromolecules in determining the mechanical behavior of the tissue. A constitutive relation for the swelling stress in uniaxial confined compression is formulated and the concentration dependence of the material properties of articular cartilage and corneal stroma is determined. The associated free swelling behavior of cartilage and cornea specimens is computed from these results and is found to compare favorably with data from the literature.
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paper_title: A cross-validation of the biphasic poroviscoelastic model of articular cartilage in unconfined compression, indentation, and confined compression.

paper_content:

The biphasic poroviscoelastic (BPVE) model was curve fit to the simultaneous relaxation of reaction force and lateral displacement exhibited by articular cartilage in unconfined compression (n=18). Model predictions were also made for the relaxation observed in reaction force during indentation with a porous plane-ended metal indenter (n=4), indentation with a nonporous plane ended metal indenter (n=4), and during confined compression (n=4). Each prediction was made using material parameters resulting from curve fits of the unconfined compression response of the same tissue. The BPVE model was able to account for both the reaction force and the lateral displacement during unconfined compression very well. Furthermore, model predictions for both indentation and confined compression also followed the experimental data well. These results provide substantial evidence for the efficacy of the biphasic poroviscoelastic model for articular cartilage, as no successful cross-validation of a model simulation has been demonstrated using other mathematical models.
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paper_title: Compressive and tensile properties of articular cartilage in axial loading are modulated differently by osmotic environment.

paper_content:

Aims of the present study were to test the hypotheses that (1) the compressive properties of articular cartilage are affected more by changes in the medium ionic concentration than the tensile properties, (2) collagen network controls the compression-tension nonlinearity of articular cartilage, and (3) proteoglycan (PG) and collagen contents are primary determinants of the compressive and tensile properties of cartilage, respectively. These hypotheses were experimentally tested by axial compressive and tensile tests (perpendicular to the cartilage surface) of bovine articular cartilage samples immersed in 0.005 M (n=6), 0.15M (n=12) and 1.0M (n=6) saline solutions. Compressive and tensile behaviour was analyzed by a nonlinear fibril-reinforced poroelastic model. Tissue PG and collagen contents were measured using Fourier transform infrared imaging spectroscopy (FT-IRIS). The compressive modulus of cartilage varied significantly (n=6, p<0.05) as the medium concentration changed. The tensile modulus changed significantly only as the medium concentration was reduced from 0.15 to 0.005 M (n=6, p<0.05). The fibril-reinforced poroelastic model with stiff, nonlinear collagen fibrils predicted the experimentally measured compression-tension nonlinearity of cartilage. Tissue PG and collagen contents accounted for the compressive and tensile properties of cartilage.
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paper_title: A fibril-reinforced poroviscoelastic swelling model for articular cartilage.

paper_content:

From a mechanical point of view, the most relevant components of articular cartilage are the tight and highly organized collagen network together with the charged proteoglycans. Due to the fixed charges of the proteoglycans, the cation concentration inside the tissue is higher than in the surrounding synovial fluid. This excess of ion particles leads to an osmotic pressure difference, which causes swelling of the tissue. The fibrillar collagen network resists straining and swelling pressures. This combination makes cartilage a unique, highly hydrated and pressurized tissue, enforced with a strained collagen network. Many theories to explain articular cartilage behavior under loading, expressed in computational models that either include the swelling behavior or the properties of the anisotropic collagen structure, can be found in the literature. The most common tests used to determine the mechanical quality of articular cartilage are those of confined compression, unconfined compression, indentation and swelling. All theories currently available in the literature can explain the cartilage response occurring in some of the above tests, but none of them can explain these for all of the tests. We hypothesized that a model including simultaneous mathematical descriptions of (1) the swelling properties due to the fixed-change densities of the proteoglycans and (2) the anisotropic viscoelastic collagen structure, can explain all these test simultaneously. To study this hypothesis we extended our fibril-reinforced poroviscoelastic finite element model with our biphasic swelling model. We have shown that the newly developed fibril-reinforced poroviscoelastic swelling (FPVES) model for articular cartilage can simultaneously account for the reaction force during swelling, confined compression, indentation and unconfined compression as well as the lateral deformation during unconfined compression. Using this theory it is possible to analyze the link between the collagen network and the swelling properties of articular cartilage.
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paper_title: Cell deformation behavior in mechanically loaded rabbit articular cartilage 4 weeks after anterior cruciate ligament transection

paper_content:

OBJECTIVE ::: Chondrocyte stresses and strains in articular cartilage are known to modulate tissue mechanobiology. Cell deformation behavior in cartilage under mechanical loading is not known at the earliest stages of osteoarthritis. Thus, the aim of this study was to investigate the effect of mechanical loading on volume and morphology of chondrocytes in the superficial tissue of osteoarthritic cartilage obtained from anterior cruciate ligament transected (ACLT) rabbit knee joints, 4 weeks after intervention. ::: ::: ::: METHODS ::: A unique custom-made microscopy indentation system with dual-photon microscope was used to apply controlled 2 MPa force-relaxation loading on patellar cartilage surfaces. Volume and morphology of chondrocytes were analyzed before and after loading. Also global and local tissue strains were calculated. Collagen content, collagen orientation and proteoglycan content were quantified with Fourier transform infrared microspectroscopy, polarized light microscopy and digital densitometry, respectively. ::: ::: ::: RESULTS ::: Following the mechanical loading, the volume of chondrocytes in the superficial tissue increased significantly in ACLT cartilage by 24% (95% confidence interval (CI) 17.2-31.5, P < 0.001), while it reduced significantly in contralateral group tissue by -5.3% (95% CI -8.1 to -2.5, P = 0.003). Collagen content in ACLT and contralateral cartilage were similar. PG content was reduced and collagen orientation angle was increased in the superficial tissue of ACLT cartilage compared to the contralateral cartilage. ::: ::: ::: CONCLUSIONS ::: We found the novel result that chondrocyte deformation behavior in the superficial tissue of rabbit articular cartilage is altered already at 4 weeks after ACLT, likely because of changes in collagen fibril orientation and a reduction in PG content.
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paper_title: Regulatory volume decrease (RVD) by isolated and in situ bovine articular chondrocytes

paper_content:

Articular chondrocytes in vivo are exposed to a changing osmotic environment under both physiological (static load) and pathological (osteoarthritis) conditions. Such changes to matrix hydration could alter cell volume in situ and influence matrix metabolism. However the ability of chondrocytes to regulate their volume in the face of osmotic perturbations have not been studied in detail. We have investigated the regulatory volume decrease (RVD) capacity of bovine articular chondrocytes within, and isolated from the matrix, before and following acute hypotonic challenge. Cell volumes were determined by visualising fluorescently-labelled chondrocytes using confocal laser scanning microscopy (CLSM) at 21°C. Chondrocytes in situ were grouped into superficial (SZ), mid (MZ), and deep zones (DZ). When exposed to 180mOsm or 250mOsm hypotonic challenge, cells in situ swelled rapidly (within ∼90 sec). Chondrocytes then exhibited rapid RVD (t1/2 ∼ 8 min), with cells from all zones returning to ∼3% of their initial volume after 20 min. There was no significant difference in the rates of RVD between chondrocytes in the three zones. Similarly, no difference in the rate of RVD was observed for an osmotic shock from 280 to 250 or 180mOsm. Chondrocytes isolated from the matrix into medium of 380mOsm and then exposed to 280mOsm showed an identical RVD response to that of in situ cells. The RVD response of in situ cells was inhibited by REV 5901. The results suggested that the signalling pathways involved in RVD remained intact after chondrocyte isolation from cartilage and thus it was likely that there was no role for cell-matrix interactions in mediating RVD. © 2001 Wiley-Liss, Inc.
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paper_title: Nanomechanical properties of individual chondrocytes and their developing growth factor-stimulated pericellular matrix

paper_content:

Abstract The nanomechanical properties of individual cartilage cells (chondrocytes) and their aggrecan and collagen-rich pericellular matrix (PCM) were measured via atomic force microscope nanoindentation using probe tips of two length scales (nanosized and micron-sized). The properties of cells freshly isolated from cartilage tissue (devoid of PCM) were compared to cells that were cultured for selected times (up to 28 days) in 3-D alginate gels which enabled PCM assembly and accumulation. Cells were immobilized and kept viable in pyramidal wells microfabricated into an array on silicon chips. Hertzian contact mechanics and finite element analyses were employed to estimate apparent moduli from the force versus depth curves. The effects of culture conditions on the resulting PCM properties were studied by comparing 10% fetal bovine serum to medium containing a combination of insulin growth factor-1 (IGF-1)+osteogenic protein-1 (OP-1). While both systems showed increases in stiffness with time in culture between days 7 and 28, the IGF-1+OP-1 combination resulted in a higher stiffness for the cell-PCM composite by day 28 and a higher apparent modulus of the PCM which is compared to the FBS cultured cells. These studies give insight into the temporal evolution of the nanomechanical properties of the pericellar matrix relevant to the biomechanics and mechanobiology of tissue-engineered constructs for cartilage repair.
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paper_title: The effect of collagen degradation on chondrocyte volume and morphology in bovine articular cartilage following a hypotonic challenge

paper_content:

Collagen degradation is one of the early signs of osteoarthritis. It is not known how collagen degradation affects chondrocyte volume and morphology. Thus, the aim of this study was to investigate the effect of enzymatically induced collagen degradation on cell volume and shape changes in articular cartilage after a hypotonic challenge. Confocal laser scanning microscopy was used for imaging superficial zone chondrocytes in intact and degraded cartilage exposed to a hypotonic challenge. Fourier transform infrared microspectroscopy, polarized light microscopy, and mechanical testing were used to quantify differences in proteoglycan and collagen content, collagen orientation, and biomechanical properties, respectively, between the intact and degraded cartilage. Collagen content decreased and collagen orientation angle increased significantly (p < 0.05) in the superficial zone cartilage after collagenase treatment, and the instantaneous modulus of the samples was reduced significantly (p < 0.05). Normalized cell volume and height 20 min after the osmotic challenge (with respect to the original volume and height) were significantly (p < 0.001 and p < 0.01, respectively) larger in the intact compared to the degraded cartilage. These findings suggest that the mechanical environment of chondrocytes, specifically collagen content and orientation, affects cell volume and shape changes in the superficial zone articular cartilage when exposed to osmotic loading. This emphasizes the role of collagen in modulating cartilage mechanobiology in diseased tissue.
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paper_title: Alterations in the Mechanical Properties of the Human Chondrocyte Pericellular Matrix With Osteoarthritis

paper_content:

In articular cartilage, chondrocytes are surrounded by a pericellular matrix (PCM), which together with the chondrocyte have been termed the "chondron." While the precise function of the PCM is not know there has been considerable speculation that it plays a role in regulating the biomechanical environment of the chondrocyte. In this study, we measured the Young's modulus of the PCM from normal and osteoarthritic cartilage using the micropipette aspiration technique, coupled with a newly developed axisymmetric elastic layered half-space model of the experimental configuration. Viable, intact chondrons were extracted from human articular cartilage using a new microaspiration-based isolation technique. In normal cartilage, the Young's modulus of the PCM was similar in chondrons isolated from the surface zone (68.9 +/- 18.9 kPa) as compared to the middle and deep layers (62.0 +/- 30.5 kPa). However, the mean Young's modulus of the PCM (pooled for the two zones) was significantly decreased in osteoarthritic cartilage (66.5 +/- 23.3 kPa versus 41.3 +/- 21.1 kPa, p < 0.001). In combination with previous theoretical models of cell-matrix interactions in cartilage, these findings suggest that the PCM has an important influence on the stress-strain environment of the chondrocyte that potentially varies with depth from the cartilage surface. Furthermore, the significant loss of PCM stiffness that was observed in osteoarthritic cartilage may affect the magnitude and distribution of biomechanical signals perceived by the chondrocytes.
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paper_title: Chondrocyte deformation and local tissue strain in articular cartilage: A confocal microscopy study

paper_content:

It is well accepted that mechanical forces can modulate the metabolic activity of chondrocytes, although the specific mechanisms of mechanical signal transduction in articular cartilage are still unknown. One proposed pathway through which chondrocytes may perceive changes in their mechanical environment is directly through cellular deformation. An important step toward understanding the role of chondrocyte deformation in signal transduction is to determine the changes in the shape and volume of chondrocytes during applied compression of the tissue. Recently, a technique was developed for quantitative morphometry of viable chondrocytes within the extracellular matrix using three-dimensional confocal scanning laser microscopy. In the present study, this method was used to quantify changes in chondrocyte morphology and local tissue deformation in the surface, middle, and deep zones in explants of canine articular cartilage subjected to physiological levels of matrix deformation. The results indicated that at 15% surface-to-surface equilibrium strain in the tissue, a similar magnitude of local tissue strain occurs in the middle and deep zones. In the surface zone, local strains of 19% were observed, indicating that the compressive stiffness of the surface zone is significantly less than that of the middle and deep zones. With this degree of tissue deformation, significant decreases in cellular height of 26, 19, and 20% and in cell volume of 22, 16, and 17% were observed in the surface, middle, and deep zones, respectively. The deformation of chondrocytes in the surface zone was anisotropic, with significant lateral expansion occurring in the direction perpendicular to the local split-line pattern. When compression was removed, there was complete recovery of cellular morphology in all cases. These observations support the hypothesis that deformation of chondrocytes or a change in their volume may occur during in vivo joint loading and may have a role in the mechanical signal transduction pathway of articular cartilage.
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paper_title: Osmotic loading of articular cartilage modulates cell deformations along primary collagen fibril directions.

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Osmotic loading is known to modulate chondrocyte (cell) height, width and volume in articular cartilage. It is not known how cartilage architecture, especially the collagen fibril orientation, affects cell shape changes as a result of an osmotic challenge. Intact patellae of New Zealand white rabbits (n=6) were prepared for fluorescence imaging. Patellae were exposed to a hypotonic osmotic shock and cells were imaged before loading and 5-60 min after the osmotic challenge. Cell volumes and aspect ratios (height/width) were analyzed. A fibril-reinforced poroelastic swelling model with realistic primary collagen fibril orientations, i.e. horizontal, random and vertical orientation in the superficial, middle and deep zones, respectively and cells in different zones was used to estimate cell aspect ratios theoretically. As the medium osmolarity was reduced, cell aspect ratios decreased and volumes increased in the superficial zone of cartilage both experimentally (p<0.05) and theoretically. Theoretically determined aspect ratios of middle zone cells remained virtually constant, while they increased for deep zone cells as osmolarity was reduced. Findings of this study suggest that osmotic loading modulates chondrocyte shapes in accordance with the primary collagen fibril directions in articular cartilage.
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paper_title: Mechanical loading of in situ chondrocytes in lapine retropatellar cartilage after anterior cruciate ligament transection

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The aims of this study were (i) to quantify chondrocyte mechanics in fully intact articular cartilage attached to its native bone and (ii) to compare the chondrocyte mechanics for cells in healthy and early osteoarthritis (OA) tissue. We hypothesized that cells in the healthy tissue would deform less for given articular surface pressures than cells in the early OA tissue because of a loss of matrix integrity in early OA and the associated loss of structural integrity that is thought to protect chondrocytes. Chondrocyte dynamics were quantified by measuring the deformation response of the cells to controlled loading of fully intact cartilage using a custom-designed confocal indentation system. Early OA was achieved nine weeks following transection of the anterior cruciate ligament (ACL) in rabbit knees. Experiments were performed on the retropatellar cartilage of early OA rabbit knees (four joints and 48 cells), the corresponding intact contralateral control knees (four joints and 48 cells) and knees from normal control rabbits (four joints and 48 cells). Nine weeks following ACL transection, articular cartilage of the experimental joints showed substantial increases in thickness, and progression towards OA as assessed using histological grading. Local matrix strains in the superficial zone were greater for the experimental (38 ± 4%) compared with the contralateral (27 ± 5%) and normal (28 ± 4%) joints (p = 0.04). Chondrocyte deformations in the axial and depth directions were similar during indentation loading for all experimental groups. However, cell width increased more for the experimental cartilage chondrocytes (12 ± 1%) than the contralateral (6 ± 1%) and normal control chondrocytes (6 ± 1%; p < 0.001). On average, chondrocyte volume increased with indentation loading in the early OA cartilage (8 ± 3%, p = 0.001), while it decreased for the two control groups (−8 ± 2%, p = 0.002 for contralateral and −8 ± 1%, p = 0.004 for normal controls). We conclude from these results that our hypothesis of cell deformations in the early OA tissue was only partially supported: specifically, changes in chondrocyte mechanics in early OA were direction-specific with the primary axial deformations remaining unaffected despite vastly increased average axial matrix deformations. Surprisingly, chondrocyte deformations increased in early OA in specific transverse directions which have received little attention to date but might be crucial to chondrocyte signalling in early OA.
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paper_title: Hypotonic challenge modulates cell volumes differently in the superficial zone of intact articular cartilage and cartilage explant

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The objective of this study was to evaluate the effect of sample preparation on the biomechanical behaviour of chondrocytes. We compared the volumetric and dimensional changes of chondrocytes in the superficial zone (SZ) of intact articular cartilage and cartilage explant before and after a hypotonic challenge. Calcein-AM labelled SZ chondrocytes were imaged with confocal laser scanning microscopy through intact cartilage surfaces and through cut surfaces of cartilage explants. In order to clarify the effect of tissue composition on cell volume changes, Fourier Transform Infrared microspectroscopy was used for estimating the proteoglycan and collagen contents of the samples. In the isotonic medium (300 mOsm), there was a significant difference (p < 0.05) in the SZ cell volumes and aspect ratios between intact cartilage samples and cartilage explants. Changes in cell volumes at both short-term (2 min) and long-term (2 h) time points after the hypotonic challenge (180 mOsm) were significantly different (p < 0.05) between the groups. Further, proteoglycan content was found to correlate significantly (r 2 = 0.63, p < 0.05) with the cell volume changes in cartilage samples with intact surfaces. Collagen content did not correlate with cell volume changes. The results suggest that the biomechanical behaviour of chondrocytes following osmotic challenge is different in intact cartilage and in cartilage explant. This indicates that the mechanobiological responses of cartilage and cell signalling may be significantly dependent on the integrity of the mechanical environment of chondrocytes.
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paper_title: Mechanics of chondrocyte hypertrophy

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Chondrocyte hypertrophy is a characteristic of osteoarthritis and dominates bone growth. Intra- and extracellular changes that are known to be induced by metabolically active hypertrophic chondrocytes are known to contribute to hypertrophy. However, it is unknown to which extent these mechanical conditions together can be held responsible for the total magnitude of hypertrophy. The present paper aims to provide a quantitative, mechanically sound answer to that question. To address this aim requires a quantitative tool that captures the mechanical effects of collagen and proteoglycans, allows temporal changes in tissue composition, and can compute cell and tissue deformations. These requirements are met in our numerical model that is validated for articular cartilage mechanics, which we apply to quantitatively explain a range of experimental observations related to hypertrophy. After validating the numerical approach for studying hypertrophy, the model is applied to evaluate the direct mechanical effects of axial tension and compression on hypertrophy (Hueter-Volkmann principle) and to explore why hypertrophy is reduced in case of partially or fully compromised proteoglycan expression. Finally, a mechanical explanation is provided for the observation that chondrocytes do not hypertrophy when enzymatical collagen degradation is prohibited (S1Pcko knock-out mouse model). This paper shows that matrix turnover by metabolically active chondrocytes, together with externally applied mechanical conditions, can explain quantitatively the volumetric change of chondrocytes during hypertrophy. It provides a mechanistic explanation for the observation that collagen degradation results in chondrocyte hypertrophy, both under physiological and pathological conditions.
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paper_title: Implementation of subject‐specific collagen architecture of cartilage into a 2D computational model of a knee joint—data from the osteoarthritis initiative (OAI)

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A subject-specific collagen architecture of cartilage, obtained from T2 mapping of 3.0 T magnetic resonance imaging (MRI; data from the Osteoarthritis Initiative), was implemented into a 2D finite element model of a knee joint with fibril-reinforced poroviscoelastic cartilage properties. For comparison, we created two models with alternative collagen architectures, addressing the potential inaccuracies caused by the nonoptimal estimation of the collagen architecture from MRI. Also two models with constant depth-dependent zone thicknesses obtained from literature were created. The mechanical behavior of the models were analyzed and compared under axial impact loading of 846N. Compared to the model with patient-specific collagen architecture, the cartilage model without tangentially oriented collagen fibrils in the superficial zone showed up to 69% decrease in maximum principal stress and fibril strain and 35% and 13% increase in maximum principal strain and pore pressure, respectively, in the superficial layers of the cartilage. The model with increased thickness for the superficial and middle zones, as obtained from the literature, demonstrated at most 73% increase in stress, 143% increase in fibril strain, and 26% and 23% decrease in strain and pore pressure, respectively, in the intermediate cartilage. The present results demonstrate that the computational model of a knee joint with the collagen architecture of cartilage estimated from patient-specific MRI or literature lead to different stress and strain distributions. The findings also suggest that minor errors in the analysis of collagen architecture from MRI, for example due to the analysis method or MRI resolution, can lead to alterations in knee joint stresses and strains. © 2012 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 31:10–22, 2012
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paper_title: Mechanical characterization of articular cartilage by combining magnetic resonance imaging and finite-element analysis—a potential functional imaging technique

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Magnetic resonance imaging (MRI) provides a method for non-invasive characterization of cartilage composition and structure. We aimed to see whether T1 and T2 relaxation times are related to proteoglycan (PG) and collagen-specific mechanical properties of articular cartilage. Specifically, we analyzed whether variations in the depthwise collagen orientation, as assessed by the laminae obtained from T2 profiles, affect the mechanical characteristics of cartilage. After MRI and unconfined compression tests of human and bovine patellar cartilage samples, fibril-reinforced poroviscoelastic finite-element models (FEM), with depthwise collagen orientations implemented from quantitative T2 maps (3 laminae for human, 3–7 laminae for bovine), were constructed to analyze the non-fibrillar matrix modulus (PG specific), fibril modulus (collagen specific) and permeability of the samples. In bovine cartilage, the non-fibrillar matrix modulus (R = −0.64, p < 0.05) as well as the initial permeability (R = 0.70, p < 0.05) correlated with T1. In bovine cartilage, T2 correlated positively with the initial fibril modulus (R = 0.62, p = 0.05). In human cartilage, the initial fibril modulus correlated negatively (R = −0.61, p < 0.05) with T2. Based on the simulations, cartilage with a complex collagen architecture (5 or 7 laminae), leading to high bulk T2 due to magic angle effects, provided higher compressive stiffness than tissue with a simple collagen architecture (3 laminae). Our results suggest that T1 reflects PG-specific mechanical properties of cartilage. High T2 is characteristic to soft cartilage with a classical collagen architecture. Contradictorily, high bulk T2 can also be found in stiff cartilage with a multilaminar collagen fibril network. By emerging MRI and FEM, the present study establishes a step toward functional imaging of articular cartilage.
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paper_title: Proteoglycan and collagen sensitive MRI evaluation of normal and degenerated articular cartilage

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Quantitative magnetic resonance imaging (MRI) techniques have earlier been developed to characterize the structure and composition of articular cartilage. Particularly, Gd-DTPA(2-)-enhanced T1 imaging is sensitive to cartilage proteoglycan content, while T2 relaxation time mapping is indicative of the integrity and arrangement of the collagen network. However, the ability of these techniques to detect early osteoarthrotic changes in cartilage has not been demonstrated. In this study, normal and spontaneously degenerated bovine patellar cartilage samples (n=32) were investigated in vitro using the aforementioned techniques. For reference, mechanical, histological and biochemical properties of the adjacent tissue were determined, and a grading system, the cartilage quality index (CQI), was used to score the structural and functional integrity of each sample. As cartilage degeneration progressed, a statistically significant increase in the superficial T2 (r=0.494, p<0.05) and a decrease in superficial and bulk T1 in the presence of Gd-DTPA(2-) (r=-0.681 and -0.688 (p<0.05), respectively) were observed. Gd-DTPA(2-)-enhanced T1 imaging served as the best predictor of tissue integrity and accounted for about 50% of the variation in CQI. The present results reveal that changes in the quantitative MRI parameters studied are indicative of structural and compositional alterations as well as the mechanical impairment of spontaneously degenerated articular cartilage.
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paper_title: Relaxation anisotropy in cartilage by NMR microscopy (μMRI) at 14‐μm resolution

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To study the structural anisotropy and the magic-angle effect in articular cartilage, T 1 and T 2 images were constructed at a series of orientations of cartilage specimens in the magnetic field by using NMR microscopy (μMRI). An isotropic T 1 and a strong anisotropic T 2 were observed across the cartilage tissue thickness. Three distinct regions in the microscopic MR images corresponded approximately to the superficial, transitional, and radial histological zones in the cartilage. The percentage decrease of T 2 follows the pattern of the curve of (3cos 2 θ - 1) 2 at the radial zone, where the collagen fibrils are perpendicular to the articular surface. In contrast, little orientational dependence of T 2 was observed at the transitional zone, where the collagen fibrils are more randomly oriented. The result suggests that the interactions between water molecules and proteoglycans have a directional nature, which is somehow influenced by collagen fibril orientation. Hence, T 2 anisotropy could serve as a sensitive and noninvasive marker for molecular-level orientations in articular cartilage.
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paper_title: Contrast agent-enhanced computed tomography of articular cartilage: Association with tissue composition and properties

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BACKGROUND ::: Contrast agent-enhanced computed tomography may enable the noninvasive quantification of glycosaminoglycan (GAG) content of articular cartilage. It has been reported that penetration of the negatively charged contrast agent ioxaglate (Hexabrix) increases significantly after enzymatic degradation of GAGs. However, it is not known whether spontaneous degradation of articular cartilage can be quantitatively detected with this technique. ::: ::: ::: PURPOSE ::: To investigate the diagnostic potential of contrast agent-enhanced cartilage tomography (CECT) in quantification of GAG concentration in normal and spontaneously degenerated articular cartilage by means of clinical peripheral quantitative computed tomography (pQCT). ::: ::: ::: MATERIAL AND METHODS ::: In this in vitro study, normal and spontaneously degenerated adult bovine cartilage (n=32) was used. Bovine patellar cartilage samples were immersed in 21 mM contrast agent (Hexabrix) solution for 24 hours at room temperature. After immersion, the samples were scanned with a clinical pQCT instrument. From pQCT images, the contrast agent concentration in superficial as well as in full-thickness cartilage was calculated. Histological and functional integrity of the samples was quantified with histochemical and mechanical reference measurements extracted from our earlier study. ::: ::: ::: RESULTS ::: Full diffusion of contrast agent into the deep cartilage was found to take over 8 hours. As compared to normal cartilage, a significant increase (11%, P<0.05) in contrast agent concentration was seen in the superficial layer of spontaneously degenerated samples. Significant negative correlations were revealed between the contrast agent concentration and the superficial or full-thickness GAG content of tissue (|R| > 0.5, P<0.01). Further, pQCT could be used to measure the thickness of patellar cartilage. ::: ::: ::: CONCLUSION ::: The present results suggest that CECT can be used to diagnose proteoglycan depletion in spontaneously degenerated articular cartilage with a clinical pQCT scanner. Possibly, the in vivo use of clinical pQCT for CECT arthrography of human joints is feasible.
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paper_title: T2relaxation reveals spatial collagen architecture in articular cartilage: A comparative quantitative MRI and polarized light microscopic study

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It has been suggested that orientational changes in the collagen network of articular cartilage account for the depthwise T2 anisotropy of MRI through the magic angle effect. To investigate the relationship between laminar T2 appearance and collagen organization (anisotropy), bovine osteochondral plugs (N = 9) were T2 mapped at 9.4T with cartilage surface normal to the static magnetic field. Collagen fibril arrangement of the same samples was studied with polarized light microscopy, a quantitative technique for probing collagen organization by analyzing its ability to rotate plane polarized light, i.e., birefringence (BF). Depthwise variation of safranin O-stained proteoglycans was monitored with digital densitometry. The spatially varying cartilage T2 followed the architectural arrangement of the collagen fibril network: a linear positive correlation between T2 and the reciprocal of BF was established in each sample, with r = 0.91 +/- 0.02 (mean +/- SEM, N = 9). The current results reveal the close connection between the laminar T2 structure and the collagen architecture in histologic zones.
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paper_title: Prediction of biomechanical properties of articular cartilage with quantitative magnetic resonance imaging.

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Quantitative magnetic resonance imaging (MRI) is the most potential non-invasive means for revealing the structure, composition and pathology of articular cartilage. Here we hypothesize that cartilage mechanical properties as determined by the macromolecular framework and their interactions can be accessed by quantitative MRI. To test this, adjacent cartilage disk pairs (n=32) were prepared from bovine proximal humerus and patellofemoral surfaces. For one sample, the tissue Young's modulus, aggregate modulus, dynamic modulus and Poisson's ratio were determined in unconfined compression. The adjacent disk was studied at 9.4T to determine the tissue T(2) relaxation time, sensitive to the integrity of the collagen network, and T(1) relaxation time in the presence of Gd-DTPA, a technique developed for the estimation of cartilage proteoglycan (PG) content. Quantitative MRI parameters were able to explain up to 87% of the variations in certain biomechanical parameters. Correlations were further improved when data from the proximal humerus was assessed separately. MRI parameters revealed a topographical variation similar to that of mechanical parameters. Linear regression analysis revealed that Young's modulus of cartilage may be characterized more completely by combining both collagen- and PG-sensitive MRI parameters. The present results suggest that quantitative MRI can provide important information on the mechanical properties of articular cartilage. The results are encouraging with respect to functional imaging of cartilage, although in vivo applicability may be limited by the inferior resolution of clinical MRI instruments.
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paper_title: Partial Meniscectomy Changes Fluid Pressurization in Articular Cartilage in Human Knees

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Partial meniscectomy is believed to change the biomechanics of the knee joint through alterations in the contact of articular cartilages and menisci. Although fluid pressure plays an important role in the load support mechanism of the knee, the fluid pressurization in the cartilages and menisci has been ignored in the finite element studies of the mechanics of meniscectomy. In the present study, a 3D fibril-reinforced poromechanical model of the knee joint was used to explore the fluid flow dependent changes in articular cartilage following partial medial and lateral meniscectomies. Six partial longitudinal meniscectomies were considered under relaxation, simple creep, and combined creep loading conditions. In comparison to the intact knee, partial meniscectomy not only caused a substantial increase in the maximum fluid pressure but also shifted the location of this pressure in the femoral cartilage. Furthermore, these changes were positively correlated to the size of meniscal resection. While in the intact joint, the location of the maximum fluid pressure was dependent on the loading conditions, in the meniscectomized joint the location was predominantly determined by the site of meniscal resection. The partial meniscectomy also reduced the rate of the pressure dissipation, resulting in even larger difference between creep and relaxation times as compared to the case of the intact knee. The knee joint became stiffer after meniscectomy because of higher fluid pressure at knee compression followed by slower pressure dissipation. The present study indicated the role of fluid pressurization in the altered mechanics of meniscectomized knees.
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paper_title: Tissue engineering of functional articular cartilage: the current status

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Osteoarthritis is a degenerative joint disease characterized by pain and disability. It involves all ages and 70% of people aged >65 have some degree of osteoarthritis. Natural cartilage repair is limited because chondrocyte density and metabolism are low and cartilage has no blood supply. The results of joint-preserving treatment protocols such as debridement, mosaicplasty, perichondrium transplantation and autologous chondrocyte implantation vary largely and the average long-term result is unsatisfactory. One reason for limited clinical success is that most treatments require new cartilage to be formed at the site of a defect. However, the mechanical conditions at such sites are unfavorable for repair of the original damaged cartilage. Therefore, it is unlikely that healthy cartilage would form at these locations. The most promising method to circumvent this problem is to engineer mechanically stable cartilage ex vivo and to implant that into the damaged tissue area. This review outlines the issues related to the composition and functionality of tissue-engineered cartilage. In particular, the focus will be on the parameters cell source, signaling molecules, scaffolds and mechanical stimulation. In addition, the current status of tissue engineering of cartilage will be discussed, with the focus on extracellular matrix content, structure and its functionality.
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paper_title: Finite element modeling following partial meniscectomy: Effect of various size of resection

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Introduction: Meniscal tears are a common occurrence in the human knee joint. Orthopaedic surgeons routinely perform surgery to remove a portion of the torn meniscus. This surgery is referred to as a partial meniscectomy. It has been shown that individuals who have decreased amount of meniscus are likely to develop knee osteoarthritis. This research presents the analysis of the stresses in the knee joint upon various amounts of partial meniscectomy. Methods: To analyse the stresses in the knee joint using finite element method an axisymmetric model was developed. Articular cartilage was considered as three layers, which were modelled as a poroelastic transversely isotropic superficial layer, a poroelastic isotropic middle and deep layers and an elastic isotropic calcified cartilage layer. Eight cases were modelled including a knee joint with an intact meniscus, 10%, 20%, 30%, 40%, 50%, 60% and 65% medial meniscotomy. Findings: Under the axial load of human weight on the femoral articular cartilage with 40% removal of meniscus high contact stresses took place on cartilage surface. Further, with 30%, 40%, 50% of meniscectomy significant amount of contact area noticed between femoral and tibial articular cartilage. After 65% of meniscectomy the maximal shear stress in the cartilage increased up to 225% compared to knee with intact meniscus. It appears that meniscectomies greater than 20% drastically increases the stresses in the knee joint. I. BACKGROUND
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paper_title: Analysis of partial meniscectomy and ACL reconstruction in knee joint biomechanics under a combined loading

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Abstract Background Despite partial meniscectomies and ligament reconstructions as treatments of choice for meniscal and ligament injuries, respectively, the knee joint osteoarthritis persists. Methods A detailed nonlinear finite element model of the knee joint was developed to evaluate biomechanics of the tibiofemoral joint under 200 N drawer load with and without 1500 N compression preload. The model incorporated composite structure of cartilage and meniscus. The effects on joint response and articular contact pressure of unilateral partial meniscectomy, of changes in prestrain or material properties of the anterior cruciate ligament and of their combination were investigated. Findings Compressive preload further increases anterior cruciate ligament strains/forces in drawer loading. Partial meniscectomy and perturbations in anterior cruciate ligament prestrain/material properties, alone or combined, substantially alter the load transfer via covered and uncovered areas of cartilage as well as contact pressure distribution on cartilage. Partial meniscectomy especially when combined with a slacker anterior cruciate ligament diminish the load via affected meniscus generating unloaded regions on the cartilage. Interpretation Partial meniscectomy concurrent with a slack anterior cruciate ligament substantially alter cartilage contact pressures. These alterations further intensify in the event of greater external forces, larger meniscal resections and total anterior cruciate ligament rupture, thus suggesting a higher risk of joint degeneration.
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paper_title: Prediction of collagen orientation in articular cartilage by a collagen remodeling algorithm

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Summary Objective Tissue engineering is a promising method to treat damaged cartilage. So far it has not been possible to create tissue-engineered cartilage with an appropriate structural organization. It is envisaged that cartilage tissue engineering will significantly benefit from knowledge of how the collagen fiber orientation is directed by mechanical conditions. The goal of the present study is to evaluate whether a collagen remodeling algorithm based on mechanical loading can be corroborated by the collagen orientation in healthy cartilage. Methods According to the remodeling algorithm, collagen fibrils align with a preferred fibril direction, situated between the positive principal strain directions. The remodeling algorithm was implemented in an axisymmetric finite element model of the knee joint. Loading as a result of typical daily activities was represented in three different phases: rest, standing and gait. Results In the center of the tibial plateau the collagen fibrils run perpendicular to the subchondral bone. Just below the articular surface they bend over to merge with the articular surface. Halfway between the center and the periphery, the collagen fibrils bend over earlier, resulting in a thicker superficial and transitional zones. Near the periphery fibrils in the deep zone run perpendicular to the articular surface and slowly bend over to angles of −45° and +45° with the articular surface. Conclusion The collagen structure as predicted with the collagen remodeling algorithm corresponds very well with the collagen structure in healthy knee joints. This remodeling algorithm is therefore considered to be a valuable tool for developing loading protocols for tissue engineering of articular cartilage.
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paper_title: Mechanical stimulation to stimulate formation of a physiological collagen architecture in tissue-engineered cartilage: a numerical study.

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The load-bearing capacity of today's tissue-engineered (TE) cartilage is insufficient. The arcade-like collagen network in native cartilage plays an important role in its load-bearing properties. Inducing the formation of such collagen architecture in engineered cartilage can, therefore, enhance mechanical properties of TE cartilage. Considering the well-defined relationship between tensile strains and collagen alignment in the literature, we assume that cues for inducing this orientation should come from mechanical loading. In this study, strain fields prescribed by loading conditions of unconfined compression, sliding indentation and a novel loading regime of compression-sliding indentation are numerically evaluated to assess the probability that these would trigger a physiological collagen architecture. Results suggest that sliding indentation is likely to stimulate the formation of an appropriate superficial zone with parallel fibres. Adding lateral compression may stimulate the formation of a deep zone with perpendicularly aligned fibres. These insights may be used to improve loading conditions for cartilage tissue engineering.
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paper_title: Effect of superficial collagen patterns and fibrillation of femoral articular cartilage on knee joint mechanics-a 3D finite element analysis.

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Collagen fibrils of articular cartilage have specific depth-dependent orientations and the fibrils bend in the cartilage surface to exhibit split-lines. Fibrillation of superficial collagen takes place in osteoarthritis. We aimed to investigate the effect of superficial collagen fibril patterns and collagen fibrillation of cartilage on stresses and strains within a knee joint. A 3D finite element model of a knee joint with cartilage and menisci was constructed based on magnetic resonance imaging. The fibril-reinforced poroviscoelastic material properties with depth-dependent collagen orientations and split-line patterns were included in the model. The effects of joint loading on stresses and strains in cartilage with various split-line patterns and medial collagen fibrillation were simulated under axial impact loading of 1000 N. In the model, the collagen fibrils resisted strains along the split-line directions. This increased also stresses along the split-lines. On the contrary, contact and pore pressures were not affected by split-line patterns. Simulated medial osteoarthritis increased tissue strains in both medial and lateral femoral condyles, and contact and pore pressures in the lateral femoral condyle. This study highlights the importance of the collagen fibril organization, especially that indicated by split-line patterns, for the weight-bearing properties of articular cartilage. Osteoarthritic changes of cartilage in the medial femoral condyle created a possible failure point in the lateral femoral condyle. This study provides further evidence on the importance of the collagen fibril organization for the optimal function of articular cartilage.
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paper_title: Structure–function relationships in osteoarthritic human hip joint articular cartilage

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Summary Objectives It is currently poorly known how different structural and compositional components in human articular cartilage are related to their specific functional properties at different stages of osteoarthritis (OA). The objective of this study was to characterize the structure–function relationships of articular cartilage obtained from osteoarthritic human hip joints. Methods Articular cartilage samples with their subchondral bone ( n = 15) were harvested during hip replacement surgeries from human femoral necks. Stress–relaxation tests, Mankin scoring, spectroscopic and microscopic methods were used to determine the biomechanical properties, OA grade, and the composition and structure of the samples. In order to obtain the mechanical material parameters for the samples, a fibril-reinforced poroviscoelastic model was fitted to the experimental data obtained from the stress–relaxation experiments. Results The strain-dependent collagen network modulus ( E fe ) and the collagen orientation angle exhibited a negative linear correlation ( r = −0.65, P M ) and the collagen content exhibited a positive linear correlation ( r = 0.56, P E nf ) also exhibited a positive linear correlation with the proteoglycan content ( r = 0.54, P Conclusion The study suggests that increased collagen orientation angle during OA primarily impairs the collagen network and the tensile stiffness of cartilage in a strain-dependent manner, while the decreased collagen content in OA facilitates fluid flow out of the tissue especially at high compressive strains. Thus, the results provide interesting and important information of the structure–function relationships of human hip joint cartilage and mechanisms during the progression of OA.
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paper_title: Computational biomechanics of articular cartilage of human knee joint: effect of osteochondral defects.

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Articular cartilage and its supporting bone functional conditions are tightly coupled as injuries of either adversely affects joint mechanical environment. The objective of this study was set to quantitatively investigate the extent of alterations in the mechanical environment of cartilage and knee joint in presence of commonly observed osteochondral defects. An existing validated finite element model of a knee joint was used to construct a refined model of the tibial lateral compartment including proximal tibial bony structures. The response was computed under compression forces up to 2000 N while simulating localized bone damage, cartilage-bone horizontal split, bone overgrowth and absence of deep vertical collagen fibrils. Localized tibial bone damage increased overall joint compliance and substantially altered pattern and magnitude of contact pressures and cartilage strains in both tibia and femur. These alterations were further exacerbated when bone damage was combined with base cartilage split and absence of deep vertical collagen fibrils. Local bone boss markedly changed contact pressures and strain patterns in neighbouring cartilage. Bone bruise/fracture and overgrowth adversely perturbed the homeostatic balance in the mechanical environment of articulate cartilage surrounding and opposing the lesion as well as the joint compliance. As such, they potentially contribute to the initiation and development of post-traumatic osteoarthritis.
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paper_title: Indentation Stiffness of Repair Tissue after Autologous Chondrocyte Transplantation

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Our main hypothesis was that indentation stiffness of the repair tissue approaches the values of adjacent cartilage 1 year after autologous chondrocyte transplantation. We also wanted to investigate the differences between osteochondritic lesions and full-thickness lesions. Thirty patients with cartilage lesions were operated on with autologous chondrocyte transplantation. The repair was evaluated arthroscopically, indentation stiffness was measured, and clinical evaluations were done. The stiffness of the repair tissue improved to 62% (mean 2.04 +/- 0.83 N, mean +/- SD) of adjacent cartilage (3.58 +/- 1.04 N). Fifty-three percent of the patients graded their knee as excellent or good and 47% of the patients graded their knee as fair at the followup. In six patients the normalized stiffness was at least 80%, suggesting hyaline-like repair. The indentation stiffness of the osteochondritis dissecans lesion repairs (1.45 +/- 0.46 N; n = 7) was less than that of the nonosteochondritis dissecans lesion repair sites (2.37 +/- 0.72 N; n = 19). Gadolinium-enhanced magnetic resonance imaging of the cartilage (dGEMRIC) during followup of four patients suggested proteoglycan replenishment, although all grafts showed low indentation values. Low stiffness values may indicate incomplete maturation or predominantly fibrous repair. The indentation analysis showed that the repair tissue stiffness could, in some cases, reach the same level as the adjacent cartilage, but there was a large variation among the grafts.
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paper_title: Creep behavior of the intact and meniscectomy knee joints

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Abstract The mechanical functions of the menisci may be partially performed through the fluid pressurization in articular cartilages and menisci. This creep behavior has not been investigated in whole knee joint modeling. A three-dimensional finite element knee model was employed in the present study to explore the fluid-flow dependent creep behaviors of normal and meniscectomy knees. The model included distal femur, tibia, fibula, articular cartilages, menisci and four major ligaments. Articular cartilage or meniscus was modeled as a fluid-saturated solid matrix reinforced by a nonlinear orthotropic and site-specific collagen network. A 300 N compressive force, equal to half of body weight, was applied to the knee in full extension followed by creep. The results showed that the fluid pressurization played a substantial role in joint contact mechanics. Menisci bore more loading as creep developed, leading to decreased stresses in cartilages. The removal of menisci not only changed the stresses in the cartilages, which was in agreement with published studies, but also altered the distribution and the rate of dissipation of fluid pressure in the cartilages. The high fluid pressures in the femoral cartilage moved from anterior to more central regions of the condyles after total meniscectomy. For both intact and meniscectomy joints, the fluid pressure level remained considerably high for thousands of seconds during creep, which lasted even longer after meniscectomy. For the femoral cartilage, the maximum principal stress was generally in agreement with the fiber direction, which indicated the essential role of fibers in load support of the tissue.
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Title: A Review of the Combination of Experimental Measurements and Fibril-Reinforced Modeling for Investigation of Articular Cartilage and Chondrocyte Response to Loading

Section 1: Introduction
Description 1: Describe the structure and mechanical function of articular cartilage, including its composition and cellular components.

Section 2: Review of Fibril Reinforced Computational Models of Articular Cartilage
Description 2: Discuss the application and justification of fibril reinforced mixture models, detailing the components and mechanical characteristics of these models.

Section 3: Tissue-Level Fibril Reinforced Models
Description 3: Explain the implementation and development of fibril reinforced models at the tissue level, including details of the nonfibrillar matrix and collagen fibril network.

Section 4: Extensions to Fibrillar and Nonfibrillar Matrices
Description 4: Discuss additional features and complexities in modeling fibril and nonfibrillar matrices, such as tissue swelling and chemical expansion.

Section 5: Controversies and Limitations Related to Tissue-Level Fibril Reinforced Models
Description 5: Highlight the challenges and unresolved issues in applying fibril reinforced models to simulate cartilage mechanics.

Section 6: Cell-Level Models and Cell-Tissue Interactions
Description 6: Discuss the development and application of biphasic multiscale models to evaluate chondrocyte behavior and cell-tissue interactions under mechanical loading.

Section 7: Adaptation Models
Description 7: Explore models that investigate the biological responses of cells to physical loading and how these responses influence tissue adaptation over time.

Section 8: Practical Considerations in Modeling Applications
Description 8: Provide guidance on parametric analysis, model optimization, and convergence testing necessary for reliable and accurate simulations.

Section 9: Model Validation
Description 9: Explain the importance and methods of validating computational models using experimental data.

Section 10: Experimental Tests
Description 10: Describe the design and implementation of mechanical tests at the tissue and cell levels used to determine material properties through optimization.

Section 11: New Challenges
Description 11: Highlight future challenges and directions for research, including the development of patient-specific models and prediction of cartilage degeneration.

Section 12: Combining In Vivo Imaging with Modeling
Description 12: Discuss the integration of imaging techniques and modeling to obtain realistic evaluations of tissue and joint forces.

Section 13: Toward Patient-Specific Estimation of Disease Progression and Treatment
Description 13: Outline how advanced fibril reinforced models could lead to predictions of cartilage degeneration and inform clinical decision-making for individual patients.