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Modeling adaptive processes: vascular remodeling

Presented by: 
A Pries [Freie, Berlin]
Tuesday 21st July 2009 - 10:15 to 10:30
INI Seminar Room 1
Session Title: 
Vascular Fluid - Structure Interaction
Session Chair: 
Sarah Waters

Dynamic biological systems adapt to changes in internal or external conditions. A typical example is the response of the vascular system to changes in body size or local tissue function. Also during development, adaptive responses are used widely to determine the design of body systems. Such reactions entail functional or structural feedback signals which are typical for the system considered. In the case of the vascular system, the most relevant signals are generated by hemodynamics (local blood pressure and wall shear stress) and the metabolic situation determined by the relation between supply and demand (e.g. of oxygen).

According to the usual approach, reactions to such signals are established in experimental conditions aiming at a single stimulus at a time and interrupting the involved feedback loop. Such experiments showed an increase of vessel diameter with increasing flow or metabolic demand and a decrease with increasing pressure. Such reactions seem to be reasonable and the described reactions may be congruent with observed system responses under certain conditions (e.g. lower resistance for higher perfusion). Thus they are frequently used as the basis for concepts of vascular adaptation or design. However, the isolated appreciation of individual reaction patterns can not support an ‘understanding’ of system properties in several aspects: The quantitative relation of the different reactions is not addressed, it is not possible to determine whether the observed reactions are necessary and sufficient to explain system behavior and the stability of the assumed feedback regulation can not be assessed.

To answer such questions, a mathematical description or modeling of the assumed responses in a functional context is needed. Obviously, the prerequisite for such modeling is a gross simplification of the biological situation raising questions as to the validity of the obtained results. However, by not pertaining to specific biological properties lost in the simplification, the modeling analysis should represent general characteristics of systems which fit into the assumptions made in the model. With respect to vascular adaptation, mathematical models were, e.g., able to demonstrate that a directed information transfer along the vessel wall is necessary to prevent maldistribution of the blood flow within the tissue and the generation of functional shunting. Such a finding should be independent of the biological implementation of the information transfer but should stimulate respective experimental investigations. Based on the respective findings intuitive assumptions on systems behavior can then be tested by more detailed and more realistic models.

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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons