extfieldsofstudy: Chemistry Medicine

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Extracellular hydrogen peroxide measurements using a flow injection system in combination with microdialysis probes – Potential and challenges

ABSTRACT There is a strong need for techniques that can quantify the important reactive oxygen species hydrogen peroxide (H2O2) in complex media and in vivo. We combined chemiluminescence‐based H2O2 measurements on a commercially available flow injection analysis (FIA) system with sampling of the analyte using microdialysis probes (MDPs), typically used for measurements in tissue. This allows minimally invasive, quantitative measurements of extracellular H2O2 concentration and dynamics utilizing the chemiluminescent reaction of H2O2 with acridinium ester. By coupling MDPs to the FIA system, measurements are no longer limited to filtered, liquid samples with low viscosity, as sampling via a MDP is based on a dynamic exchange through a permeable membrane with a specific cut‐off. This allows continuous monitoring of dynamic changes in H2O2 concentrations, alleviates potential pH effects on the measurements, and allows for flexible application in different media and systems. We give a detailed description of the novel experimental setup and its measuring characteristics along with examples of application in different media and organisms to highlight its broad applicability, but also to discuss current limitations and challenges. The combined FIA‐MDP approach for H2O2 quantification was used in different biological systems ranging from marine biology, using the model organism Exaiptasia pallida (light stress induced H2O2 release up to ˜ 2.7 &mgr;M), over biomedical applications quantifying enzyme dynamics (glucose oxidase in a glucose solution producing up to ˜ 60 &mgr;M H2O2 and the subsequent addition of catalase to monitor the H2O2 degradation process) and the ability of bacteria to modify their direct environment by regulating H2O2 concentrations in their surrounding media. This was shown by the bacteria Pseudomonas aeruginosa degrading ˜ 18 &mgr;M background H2O2 in LB‐broth. We also discuss advantages and current limitations of the FIA‐MDP system, including a discussion of potential cross‐sensitivity and interfering chemical species. HighlightsSuccessful combination of a FIA system with microdialysis probes for H2O2 detection.Near real time, chemiluminescence detection of H2O2 dynamics in different media.Extracellular H2O2 dynamics in liquid and semisolid, untreated samples.System tunable to different calibration ranges (0–1000 nM; 0–10 &mgr;M; 1–100 &mgr;M).Cross‐sensitivity study of potentially interfering species and the chemiluminescent reaction. Graphical abstract Figure. No Caption available.

Introduction
Hydrogen peroxide (H2O2) is a reactive oxygen species (ROS) [1] and a strong oxidant, but due to its high activation energy H2O2 is relatively unreactive in comparison to other ROS [2]. The peroxide bond is nonetheless prone to cleaving due to heating, photolysis or contact with redox metals [2,3]. These cleaving reactions can form the highly reactive hydroxyl radical (OH • ), which has a very low activation energy and is one of the strongest known oxidants [2,4]; thus it is very important to understand the production and degradation processes of H2O2 as one of the main sources of OH • . Furthermore, H2O2 is of great importance in cell biology, where it plays a key role in important biochemical processes such as oxidative stress and as a transmitter of redox signals [2,5]. However, the exact role of H2O2 is often not fully understood due to uncertainties in the determination of real concentrations in vivo [6].
Quantification of H2O2 is frequently attempted with optical techniques based on irreversible luminescent probes. Such approaches can be used to detect H2O2 via the luminescence intensity upon probe exposure giving valuable insights into hotspots and the presence of a species. However, correlating such changes in luminescence intensity to real H2O2 concentrations is difficult and often impossible [6]. A frequently used and well established technique for the determination of H2O2 in liquid samples is based on flow injection analysis (FIA) in combination with a H2O2-specific chemiluminescent reaction (Figure 1) [6,19]. This approach enables dynamic H2O2 concentration measurements in retrieved samples in near real time, where FIA overcomes the issue of the irreversibility of the underlying reaction scheme. Typically, such FIA-based systems consist of a valve system, which can switch between two modes (load and injection), a peristaltic pump ensuring a continuous flow of sample and reagents, and a photomultiplier tube coupled to a mixing cell for sensitive detection of the chemiluminescence intensity caused by the reaction of a chemiluminescent reagent (CL reagent) with the analyte of interest. Different chemistries such as luminol with a Co(II) catalyst [17,29,[45][46][47] or the acridinium ester (10-methyl-9-(p-formylphenyl)-acridinium carboxylate trifluoromethanesulfonate) [19,[48][49][50][51] have been used for H2O2 detection. Both chemiluminescence reaction schemes are pH dependent and show crosssensitivities to Fe(II), which can however be overcome by working with buffered solutions and addition of FerroZine TM to complex freely available Fe(II) [45,48]. Temperature effects have to be taken into consideration as well, as chemiluminescent reactions are temperature dependent [52]. Luminol-based measurements are also influenced by other analytes [45], while acridinium ester (AE) based measurements (employed in this the present study) show high specificity towards H2O2 [19]. Other FIA-based H2O2 detection approaches are reviewed elsewhere [6].
A major shortcoming of the overall FIA technique is its restriction to aggregate-free, liquid samples of low viscosity, as connectors and tubes are very narrow and block easily. Thus, the sample often needs a pretreatment step, such as filtering. Additionally, a relatively large sample volume (up to a few mL) is typically required, which can impose dramatic changes and artefacts in systems with a restricted volume and limits the spatio-temporal resolution. To overcome these limitations, we combined the FIA system with sampling via so-called microdialysis probes (MDPs) ( Figure 2). Such probes are minimally invasive as analytes are retrieved from the sample via diffusion across a microdialysis membrane with a defined molecular cut-off into a perfusion solution. MDPs consist of a semipermeable membrane, which can be used to dialyze liquid, semisolid or solid media [53]; they were first developed for minimally invasive in vivo measurements of drug concentrations in tissue and organs of animals or humans [54]. MDPs can be applied in vivo as well as in vitro; they have been frequently coupled to different analytical systems, such as liquid chromatography, flow-through biosensors and capillary and microchip electrophoresis [55] and also allow measurements beyond liquid samples [53]. The analyte recovery by the MDPs is dependent on various factors, such as MDP membrane length, perfusion speed of the internal carrier solution or temperature, making it a tunable system for specific applications with a variety of sampling schemes [54]. In combination with a dynamic measurement technique such as the FIA system, MPDs can Figure 1: Schematic representation of a flow injection analysis (FIA) system used to quantify H2O2 in the load mode. The sample is acquired with a sample tube and filled in the sample loop. When switching to injection mode, the sample is mixed with the chemiluminescent reagent (CL) and flushed by the carrier solution into a mixing chamber, where it is mixed with a buffer solution to adjust the pH and facilitate the reaction with the chemiluminescent reagent. The mixing chamber is optically coupled to a photomultiplier tube (PMT) detector that monitors the analyte-dependent chemiluminescence signal. Even flow of sample and reagents is facilitated with a peristaltic pump. thus facilitate flexible measurements in a range of media and systems. In this study, we give a detailed presentation of a MDP-based FIA system for minimally invasive quantification of H2O2 concentration and dynamics. We give a detailed description of the novel experimental setup and its measuring characteristics along with different medical and biological applications to highlight its broad applicability, but also to discuss current limitations and challenges.

Instrumentation
We used a flow injection analysis system (FeLume; Waterville Analytical) with the dedicated analysis software. The FIA system was coupled to a peristaltic pump (Dynamax, Rainin Instrument Company; shoprainin.com) and a syringe pump (Aladdin, World Precision Instruments; wpiinc.com) using PVC pump tubes (Tygon R3607, red/red) obtained from Glass Expansion (geicp.com). The tubing in-between valves in the FIA system consisted of fluoropolymer tubing (Upchurch Scientific® FEP; idex-hs.com). Microdialysis probes (CMA 7 Metal Free, 2 mm membrane length, with a cut-off of 6 kDa) were purchased from CMA (microdialysis.se, reference number: 8010772) and handled according to the manufacturer's guidelines, flushing it with ethanol prior to the first usage. Measurements of O2 concentration were done with a FireStingGO2 meter in combination with an OXR430 fiber-optic O2 sensor or a respiration vial equipped with an O2 sensor spot (OXVIAL20) that was monitored via the transparent glass wall of the vial with a bare fiber connected to the meter; all items were obtained from Pyroscience (pyro-science.com). Electrochemical measurements of H2O2 were done with a H2O2 microsensor (ISO-HPO-100) coupled to a free radical analysis system (both obtained from World Precision Instruments; wpiinc.com). Solutions were filtered through syringe filters (Whatman, 0.02 µm, 10 mm; Anatop TM 10, gelifesciences.com; catalog number: 6809-1102). Samples were illuminated with a fiber-optic tungsten-halogen lamp equipped with a branched flexible light guide (KL1500, Schott.com), and incident light levels (400-700 nm) for different lamp settings were quantified in the samples with a submersible, spherical mini quantum sensor (US-SQS/L) coupled to a calibrated quantum irradiance meter (ULM-500) both purchased from Walz (walz.com).

Flow Injection Analysis (FIA) System Combined MDPs
The commercially available FIA system has a 10-port valve, which can be switched between load mode and injection mode (Figure 2) via the PC-controlled software. The system can be set up to also include a washing loop (e.g. diluted HCl) in order to clean the system tubings; this is e.g. relevant when using seawater in order to dissolve precipitates formed during the measurement [57]. The chemistry and chemiluminescent reaction for H2O2 measurements was described by King et al. [58]. Briefly, the chemiluminescent acridinium ester reagent (AE) reacts irreversibly with H2O2 forming an instable dioxetane complex, which releases energy in the form of light upon degradation to N-methylacridone under alkaline conditions. The chemiluminescence is detected by the PMT as a signal peak for a particular sample. In order to not over-saturate the PMT, signal intensities above ~1 million counts were avoided by adjusting the concentration of the chemiluminescent reagent. The peak integral can then be correlatedafter prior calibrationto a specific H2O2 concentration. The MDPs allow the diffusive exchange of the analyte between the external sample medium and the inner, analyte-free probe perfusion medium, which are separated by a microdialysis membrane, with a specific molecular cut-off. A perfusion fluid (untreated DI water) is pumped through the dialysis probe at a certain speed, and is then transported into the 20 cm long sample loop of the flow injection system. The inner diameter (ID) of the FEP tubing used for the sample loop is 0.75 mm, which means the minimal sample volume is 88.4 µL (a small excess is however recommended to make sure the loop as well as the connectors are filled with bubble free sample solution). The sample loop is then flushed out by a catalase treated carrier solution, mixed with the AE reagent and transported into the reaction chamber in front of the PMT, where the pH is adjusted by a buffer solution (0.1 M Na2CO3, pH ~11.3). Switching back to 'sample mode' flushes the system with HCl (0.01 M) to keep the system from clogging due to precipitates (Figure 2.2).

Calibration With and Without MDPs
Calibration of the FIA system without the MDP connected ( Figure 3A and Figure 4A) were done by adding defined volumes of the H2O2 stock solution (made in DI water) to the measurement medium. The same medium was used as carrier solution but treated with 3 mg L -1 catalase and filtered if necessary. For calibrations with the MDP connected to the FIA system ( Figure 3A and Figure 4B), the perfusion-fluid pumped from the syringe through the MDP was untreated DI water, while DI water treated with 3 mg L -1 catalase was used as a reagent carrier solution and calibration solutions were stirred. As H2O2 has to enter the MDP via diffusion, a diffusion boundary layer establishes H2O2 is sampled via the microdialysis probe and guided into the sample loop. Excess solution will be flushed into the waste. Once the sample loop is filled, the 10-port valve can be switched to 2) injection mode. The sample solution containing H2O2 is flushed out of the sample loop, is mixed with the acridinium ester (AE) reagent and then transported into the detector mixing chamber by the carrier solution (such as catalase treated MilliQ water or seawater), where it is mixed with a buffer solution adjusting the pH. The microdialysis probe is operated by a syringe pump, where different speeds can be set. All other solutions (carrier solution, HCl solution / acid wash, chemiluminescent reagent (acridinium ester) and the Na2CO3 buffer are pumped through the system using a peristaltic pump.
around the probe making it sensitive to stirring. The H2O2 stock solution was made in DI water and added to the stirred sample medium. For calibrations at elevated temperatures, vials containing the medium were heated to the required temperature, and H2O2 was only added right before measurement to avoid loss due to degradation. Real zero values were determined by adding catalase to a medium blank. The limit of detection (LOD) and limit of quantification (LOQ) were determined according to literature [59,60] by taking 3.3 times the standard deviation of the catalase treated blank divided by the slope of the calibration curve (LOD; equation 1) or 10 times the standard deviation of the catalase treated blank divided by the slope of the calibration curve (LOQ; equation 2).
Where σ is the standard deviation of the catalase treated blank (n = 3) and k is the slope of the calibration curve.

Enzymatic Reaction Measurements
The experiment was conducted at room temperature in 200 mL of a stirred PBS buffered, glucose solution (1 mM), wherein H2O2 and O2 were measured simultaneously ( Figure 5) using a similar protocol of enzyme addition as in Koren et al. [61]. The sample solution was kept in a container sealed with a rubber stopper, to avoid O2 leakage. The rubber stopper had three holes, one for the O2 sensor, one for the MDP mounted on a glass rod, and one for the addition of the chemicals, which was sealed in-between reagent additions. Glucose oxidase (GOX) and catalase stock solutions were prepared in DI water (5 mg mL -1 ). After baseline measurements, 0.125 mg GOX was added. The reaction was followed for 30 minutes. Then 0.125 mg catalase was added and the reaction was followed for 20 minutes. 0.250 mg GOX was added and the reaction monitored for 15 minutes. 0.500 mg catalase was added and the reaction followed for 15 minutes. Finally, 0.250 mg GOX was added together with additional 1mM glucose, and the reaction was followed until O2 was consumed completely and no more H2O2 was produced. O2 input via the MDP membrane was tested for in Figure S3.

H2O2 Dynamics in Light Stressed Sea Anemones
The sea anemone Exaiptasia pallida (strain H2) was transferred to a beaker containing aerated artificial seawater heated to 32°C. The organism was first kept in the dark for 60 minutes, while monitoring H2O2 ( Figure 6) and O2 levels. Subsequently, the sea anemone was exposed to high light (~1500 µmol photons m -2 s -1 ; 400-700 nm) by irradiation from the side and top with a 2-branch flexible light guide connected to a fiber-optic tungsten-halogen lamp (KL1500, Schott). After ~80 minutes, the MDP was positioned in closer proximity to the animal than in the first position. The H2O2 build up due to light stress was followed for approximately 1 hour.

H2O2 Levels in LB Medium
The bacterium Pseudomonas aeruginosa was grown overnight at 37°C in an Erlenmeyer flask shaken at 170 rpm. Three falcon tubes were filled with 20 mL autoclaved and diluted LB medium (4mL LB + 16 mL DI) heated to 37°C and stirred within a heating block to ensure constant temperature. One tube was used to monitor H2O2 dynamics using the MDP -FIA system. The second tube was used to measure O2 dynamics using a FireStingGO2. Every 10 minutes during the experiment, 1 mL samples were taken from this second tube, filtered via a 0.02 µm syringe filters (Whatman) into Eppendorf tubes and stored at 4°C over-night before measuring their H2O2 content via direct injection (FIA without a MDP) the following day. The third falcon tube was used to measure O2 and H2O2 dynamics simultaneously using an electrochemical microsensor (ISO-HPO-100) coupled to a free radical analysis system (World Precision Instruments; wpiinc.com). Results are shown in the SI ( Figure S2)). 2 mL of bacterial overnight culture were added to each of the stirred diluted LB media (37°C) resulting in a final density of approx. 2 x 10 8 CFU mL -1 . H2O2 and O2 concentrations were monitored for 2 hours.

Results
We present the measuring characteristics of the combined MDP-based FIA measurement of H2O2, and illustrate various measurements optimization steps regarding reagent concentrations, syringe pump speeds and choice of sample media. The design of the set-up allows minimally invasive sampling without removing sample volume, which enables a wide variety of application in environmental and biomedical science. We demonstrate the application of the combined MDP-FIA system for minimally invasive measurements of H2O2 dynamics in almost real time.

Calibration
In the commercially available FIA system, the aggregate-free sample is sampled via a tube and then guided through a FEP tube alongside the carrier, the buffer, the HCl wash and the AE solution. They are transported via the peristaltic pump with the same pump speed through the valve systemto avoid differences in pressure (e.g. buildup of backpressure) within the system and to secure even flow speeds. A calibration curve of the 'direct injection' method (DI) is depicted in Figure 3A (black), using a 1 nM AE solution, a 0.1 M Na2CO3 buffer at pH 11.3, a 0.01 M HCl wash and MilliQ as carrier. All reagents were pre-treated with catalase according to literature [58] as described in the methods section. H2O2 standard solutions were prepared in untreated DI water and diluted in the measurement medium.
In comparison, 2 calibration curves are depicted for the measurement with a MDP coupled to the FIA system ( Figure  3A, blue and green). Sampling via a MDP connected to the FIA system (MDP-FIA) decreased the signal intensities, as the analyte recovery is diffusion limited and strongly dependent on external factors such as the syringe pump speed and MDP membrane characteristics ( Figure 3A and B).
The measurement time was mainly influenced by the syringe pump speed, which is responsible for filling the 20 cm long sample loop, with a volume of ~88.4 µL (Table S1). The time needed for the sample solution to reach the sample loop also needs to be taken into consideration and this depends on the used tubes, their IDs and lengths. In our setup, the volume before the sample loop was ~50 µL. Thus the system response time -the time needed between sampling and signal out-put -comprises the time required to fill the sample loop plus the tubes connecting the MDP with the sample loop. However, once a continuous reaction is monitored only the time required for flushing the sample into the detector and refilling the sample loop needs to be taken into account in between measurements. The time necessary for flushing the sample out of the sample loop and through the detector can be monitored by observing the signal peak in the analysis software. The time depends on the pump speed of the peristaltic pump (here 1.8 mL min -1 ), the length of tubing in between the sample loop and the detector as well as the geometry and volume of the flow cell. In our set-up the operational flushing time of the system was ~30 -35 seconds.

A B
It is well known [54] that the analyte recovery with MDPs depends on the syringe pump speed. Figure 3B shows the difference in analyte recovery over different pump speeds for a 100 µM and a 50 µM H2O2 solution for the MDP-FIA system. However, the slope of the linear calibration curves cannot only be modified by changing the syringe pump speeds, but also by changing the concentration of the AE reagent or the measurement medium ( Figure 4A and B). We performed calibrations in DI water, MilliQ water, filtered seawater (FSW), artificial seawater (ASW), F2 medium, PBS and LB broth. The AE reagent concentration was gradually increased until signal intensities in comparable ranges could be achieved, in order to compensate for medium effects and the reduced analyte recovery caused by the MDP. The DI water used for preparing the H2O2 stock solution was untreated to avoid degradation of the calibration solutions prior to measurement and each measurement was repeated 3 times (n=3). H2O2 background values were determined by measuring in untreated blank medium and catalase treated medium samples.
Measurements of H2O2 using direct injection into the FIA or using the combined MDP-FIA set-up exhibited highly reproducible and linear calibrations curves with small error bars for each particular setting of the various system parameters. If the system is switched off, it is however recommendable to recalibrate before measurement. Characteristics of the calibration curves in the different investigated media (shown in Figure 4) are given in Table 1 for the direct injection (DI) method as well as the MDP-FIA system, together with the used AE reagent concentrations aiming for an operational measuring range of 1 -100 µM. The slope, R 2 value as well as the determined LOD and LOQ are given. LOD (Equation 1) and LOQ (Equation 2) were determined according to literature [59,60]. The slopes allow a comparison between the different calibrations and chosen chemiluminescent reagent (AE) concentrations. It can be used to estimate the AE reagent concentration necessary to get a calibration curve of a certain steepness, which however does not oversaturate the PMT at higher H2O2 concentrations. Here we aimed for a slope of ~ 1.2*10 4 -3*10 4 counts · s per µM H2O2 for a calibration range between 1 -100 µM.  Table 1: Overview of calibration curve characteristics in different media at room temperature using direct injection (DI) or MDP-FIA (the same membrane was used for all measurements) based measurements at a range of acridinium ester (AE) reagent concentrations enabling a measurement range of 1-100 µM H2O2. k denotes the slope of the calibration curve, while σ is the standard deviation of the baseline, i.e. the signal measured in the catalase treated blank.

Medium
Injection Mode

Applications
We tested the combined MDP-FIA system in a range of different samples in order to demonstrate its broad applicability and to discuss some of the current limitations of this new H2O2 measurement approach. The microdialysis probe was successfully applied to monitor the enzymatic reactions of glucose oxidase and catalase in a PBS buffered glucose solution ( Figure 5). The MDP-FIA system was also applied for measurements of H2O2 production due to lightinduced, photo-oxidative stress within an important model organism in symbiosis research; the sea anemone Exaiptasia pallida that harbors photosynthetic microalgae as symbionts in its tissue [62] (Figure 6). The MDP-FIA approach has the advantage here, that it allows the positioning in close proximity to the animal / in the bulk water close to the animal, without the danger of accidentally attaching the tube to the moving animal due to the suction of the tube or blocking the tube by aggregates in the water. Figure 6 shows the difference the positioning of the MDP in relation to the animal makes concerning a stable signal output; especially in a bubbled system. Finally, we looked at H2O2 dynamics in a bacterial culture (Figure 7). Calibration measurements in several media show high background levels of H2O2 in the blank; especially the commonly used bacterial culture medium LB showed elevated levels of H2O2 after autoclaving. Therefore, we investigated how bacteria (in this case Pseudomonas aeruginosa) deal with the external H2O2.

Enzyme reactions.
Glucose oxidase (GOX) was added to 200 mL stirred, PBS buffered glucose solution (1mM) at room temperature, resulting in a decrease in O2 concentration approximately correlating with the stoichiometrically expected increase in H2O2 concentration ( Figure 5). The observed decrease in O2 concentration (taking a ~ 6 minute delay due to loading times in account) was ~63 µM O2 while the H2O2 concentration increased by ~57 µM H2O2. When adding catalase, the H2O2 concentration decreased again, while the decrease in O2 concentration was slowed down due to the O2 produced by the reaction of catalase and H2O2. When reaching anoxia, the H2O2 production stopped and a decrease towards 0 µM could be observed due to continuous catalase activity.

H2O2 dynamics in the sea anemone Exaiptasia pallida.
The sea anemone was kept for one hour in darkness ( Figure 6; grey) where there was a visible decrease in the background H2O2 concentration from ~ 1.3 µM to 0.6 µM. When switching to high light, an immediate increase in H2O2 concentration was observed. In one approach the MDP was placed in proximity to the moving anemone (>1 cm distance). In a second approach, the MDP was in close proximity to the tissue of one of the sea anemone's tentacles (<0.5 cm). H2O2 increased up to similar apparent steadystate concentration in light of ~2.7 µM in both positions. Measurements closer to the sea anemone tissue surface were

H2O2 levels in LB medium.
A solution of the bacterium Pseudomonas aeruginosa was pipetted into stirred, heated (37°C) LB medium (indicated at ~10 minutes in Figure 7), which was monitored by an optical O2 sensor, while H2O2 was measured either via direct injection into the FIA or via a MDP inserted in the solution. Both H2O2 measurements via direct injection and via the MDP-FIA set-up showed a similar behavior, however, the direct injection measurement did not include blank values measured prior to bacteria addition. Therefore, the blank value of the calibration curve, which is LB medium without the addition of bacteria measured right before the experiment, is displayed to visualize the determined background concentration. The O2 was depleted within 60 min, while the H2O2 concentration was depleted within 2-3 hours due to an apparent catalase activity in the bacterial solution. We note that the apparent blank value in the medium contained a significant amount of H2O2, which was then consumed by the bacteria.

Figure 7:
Monitoring of bacterial H2O2 and O2 depletion in diluted, stirred LB growth medium at 37°C. The O2 concentration (blue) was monitored by an optode, while H2O2 was measured with the combined MDP-FIA system (light blue) and with FIA system using direct sample injection (dark green). For the direct injection, the solution needed to be filtered (0.02 µm syringe filter) and was stored at 4°C in the fridge overnight before measurement. For the direct injection (dark green), no sample was taken and filtered for the blank before the addition of the bacteria, the blank from the calibration is depicted instead.

Discussion
We developed a flexible measuring setup for quantifying the important reactive oxygen species H2O2 by combining sampling via microdialysis probes (MDPs) with sensitive chemiluminescence-based detection of H2O2 on a flow injection analysis (FIA) system. In its current configuration, the combined MDP-FIA based systems enables quantification of H2O2 in a variety of aquatic samples with high sensitivity (LODs and LOQs are shown in Table 1), linear calibration characteristics and a time resolution of ~4 min between measurements and ~6 minutes between samples. However, these system parameters can easily be modified e.g. by optimizing parameters such as the chemiluminescent reagent concentration, pumping speed of the system, tubing lengths and diameter, or choice of MDPs with different geometries and membrane characteristics. This system can now be used in a variety of environmental and biomedical samples.
As mentioned in the introduction, H2O2 can be found in natural waters. The formation of H2O2 in natural waters can be due to e.g. photochemical reactions of dissolved organic substances in the water [20]. However, background concentrations of H2O2 in other media, have to the best of our knowledge, not been studied in detail, especially when it comes to media used in the laboratory, such as DI water, MilliQ water, different seawater samples (ASW, FSW, F2 medium) or growth media used in microbiology such as LB-broth. To our knowledge, effects of water treatments such as autoclaving on the potential formation of background levels of H2O2 in liquid media have also not been studied. In order to determine such potential effects of media treatment and composition on H2O2 concentration a sensor system is required, which ideally allows continuous measurements in a broad variety of media. In liquid samples, the FIA system is well established as it allows continuous monitoring and can overcome pH interferences, which are often problematic for irreversible luminescent probes [6]. By combining the FIA system with a MDP we alleviated a major limitation of the FIA system, which is the need of pure samples. Small particulates such as cell or mineral aggregations or biofilms in the sample can block the narrow tubes of the FIA system, posing a need for sample cleaning or filtration steps. This extra treatment can be avoided by the MDP-FIA system, as the MDP functions as a filter to substances larger than the specific molecular cut-off of the microdialysis membrane. Thus no aggregates can get into the sampling tube, while H2O2 enters the perfusion solution in the MDP via diffusion across the microdialysis membrane. This can also reduce the recovery of other potentially interfering species.
Due to its high activation energy, H2O2 is relatively stable and does not readily react with most biological molecules [2]. The basic mechanisms described in literature to be responsible for H2O2 decay in natural waters are enzymatic removal (biological) and abiotic chemical reduction [28]. The O-O bond itself is relatively weak and prone to homolysis caused by heating, radiolysis, photolysis or the presence of redox metals, such as iron or copper [2]. Both of these redox metals are for example present in seawater and are even enriched in F2 medium. Higher temperatures are also frequently employed, especially in medical applications. This can lead to an accelerated degradation of the H2O2 calibration solutions over time and needs to be taken into consideration as well when calibrating and measuring in different media.

4.1.
Calibration. As long as the PMT in the FIA system is not saturated, the system sensitivity can be tuned by modifying the chemiluminescent reagent (AE) concentration, pump speed and MDP membrane length enabling a broad calibration range (here tested for concentrations between 1-10 µM and 1-100 µM). Lower AE concentrations allow a broader operational working range (Figure 4), whereas the use of higher AE concentrations can be used to measure H2O2 in the nM to µM ranges ( Figure S1, Table 1). However, the increase is AE concentration increases the baseline as well. In theory, if the used solutions were completely H2O2 free, the baseline value should stay the same, but the FIA system is able to detect very low concentrations (in the pM range [19]) and thus the signal output can be influenced by residual amounts of H2O2. When catalase was added to the MilliQ or DI water (3 mg L -1 ) used for the preparation of all solutions, the H2O2 background levels should be close to zero. This is however not true for the MDP perfusion-fluid which did not contain catalase to avoid degradation of the H2O2 diffusing into the perfusion fluid from the sample across the microdialysis membrane. It is also not true for the calibration standards, which contain the baseline H2O2 concentration of the specific medium. Such effects can be compensated for in the calibration procedure, by measuring in apparent zero H2O2 solutions before and after addition of catalase. This is necessary, as many real life systems can degrade H2O2 by releasing e.g. catalase, which then reacts with the background H2O2 as well as shown in our measurements in growth medium with bacteria ( Figure 7). Therefore, it is important to know both the blank value and the real zero value in many applications when measuring H2O2.

Salt precipitation.
Another issue, which needs to be considered is salt precipitation within the measuring system. At the working pH of ~11.3, seawater as well as F2 medium showed a white precipitate, most likely Mg(OH)2 that is known to precipitate in seawater [49]. According to literature [1], the washing loop is sufficient to avoid excessive formation of the precipitate when working with seawater. However, as the combination with the MDP increased the loading time interval more precipitate formed, and the wash loop proved to be insufficient. Therefore, the pH buffer tube, as well as the AE tube were flushed with HCl instead during the loading step. 2-4 minutes prior to switching to the inject mode, the system was flushed again with the buffer and the AE solution to allow the baseline value to stabilize. This also has the benefit of less consumption of the AE solution.

Syringe pump speed.
Different syringe pump speeds were tested with a 2 mm long microdialysis probe membrane. However, the analyte recovery rate also depends on the MDP membrane length [54] and can thus be modulated by choosing MDPs with different dialysis membrane characteristics. With the MDPs having a 2 mm long membrane, pump speeds <50 µL min -1 gave sufficient measuring signals for H2O2 without introducing excessive loading times of the FIA sample loop (Table S1). For this experiment ( Figure 3B), relatively high H2O2 concentrations were chosen (100 µM and 50 µM), but it is apparent that highest signal differences could be detected at the lowest syringe pump speed, thus resulting in a lower H2O2 detection limit. Overall, for our applications we chose a pump speed of 25 µL min -1 , which correlates to an initial ~6 minute cycle to fill all tubes (this however, strongly depends on the tube length and diameter). After initial sampling, the following measuring cycles only depend on the time required to fill the sample loop, which for our set-up involved a loading time of ~4 minutes (20 cm long tubes, ID: 0.75 mm). This means there is a slight delay in the system, but the values can be correlated to the specific sampling interval if all the tube lengths and IDs are known, or experimentally tested.

4.2.
Medium effects. We observed that the chemiluminescent signal and thus the apparent H2O2 level in different media can vary widely (Table 1, Figure 4). These effects were weak when comparing e.g. DI water to tap water, while e.g. a strong decrease in the detected signal was observed when switching from DI water to F2 medium or LB medium (Figure 4). These effects were strongest when using direct sample injection in the FIA system, where lower signals could e.g. be compensated for by increasing the AE reagent concentration. When using the combined MDP-FIA approach much less media effects on the chemiluminescent signal were observed and the same AE concentration could be used for all tested media in the MDP-FIA set-up. In the direct injection method, catalase treated medium was used as the carrier solution, which was directly mixed with the AE reagent and the buffer solution, and this resulted in more exposure to potentially interfering species. With the MDP-FIA set-up, the probe perfusion fluid is DI water (not the catalase treated medium), and the membrane of the MDP together with the chosen perfusion speed reduces the recovery of not only H2O2 but also of potentially interfering species. In addition, the external carrier in the MDP-FIA set-up is catalase treated DI water, which means that no raw sample medium is injected into the system. This also alleviates precipitation from seawater, which is no longer injected into the system.
Depending on the sample medium, the observed changes in chemiluminescent intensity can have different reasons such as higher baseline concentrations of H2O2 in the medium, a slight change in pH or salinity, or the presence of transition metals reacting with the H2O2 added to the medium during calibration. The effect of changing from DI water to other media is shown in Figure 4A (DI) and Figure 4B (MDP-FIA) using identical settings and concentrations. Overall, some of the media effects can be attributed to precipitating salts from the artificial seawater and F2 medium, which affect the signal and can cause back pressure to build up in the system [49]. F2 medium also has a very high metal content. Cross-sensitivities of the AE reagent to other species (apart from Fe(II)) have not been reported to the best of our knowledge. However, testing for interferences by individual redox or transition metals and vitamins could give more insight into understanding the apparent drop in signal intensity. Higher baselines can be an indication for H2O2 present in the blank (e.g. LB broth; Figure 7), which can be compensated for by the addition of catalase. If the baseline decreases below the initial blank value after addition of catalase, the difference can be assumed to be due to the background H2O2 concentration for the given medium/solution. The cross sensitivity to Fe(II) was compensated for by the addition of FerroZine TM to the AE reagent. The FerroZine TM binds the Fe(II) before it can react with the AE solution. Ideally, the FerroZine TM would be directly added to the MDP perfusion -fluid reservoir in the syringe pump. However, we wanted to avoid FerroZine TM diffusion out of the MDP membrane into the sample. The addition of FerroZine TM to the carbonate buffer solution would be too late, as by then the reaction with the AE reagent would have already taken place. Therefore, adding FerroZine TM to the AE solution was the best choice. We conclude that irrespective of the various mechanisms causing such media effects, careful calibration and optimization for a given application alleviated the effects and resulted in highly linear calibration curves for H2O2.

Enzyme Reaction.
The MDP was used in combination with an optical O2 sensor to follow the reaction dynamics of glucose oxidase (GOX) and catalase in a PBS buffered glucose solution ( Figure 5). Upon addition of GOX, glucose and O2 reacted producing H2O2, as quantified by the combined MDP-FIA system. Upon addition of catalase the formed H2O2 was degraded according to the reaction Scheme 1.

Scheme 1:
Enzymatic reaction of GOX with glucose in the presence of O2 producing H2O2, which is subsequently degraded into O2 and water upon addition of catalase.
This resulted in a temporary increase in O2 concentration. However, as more O2 was degraded than produced O2 depletion was observed. The addition of GOX as well as catalase was repeated to demonstrate the capability of the MDP-FIA system to monitor dynamic H2O2 concentration changes. In the first addition step, the decrease in O2 was higher than the increase in H2O2 probably due to the time delay between the FIA system response (6 minute cycle time) and the immediate response of the O2 sensor. When looking at the O2 signal 6 minutes prior to the addition of catalase the overall decrease in O2 concentration was 63 µM, while the corresponding increase in H2O2 concentration was 57 µM, which was approximately in accordance with the reaction scheme stoichiometry. The combined MDP-FIA system is thus well suited to monitor dynamic H2O2 changes in solutions due to enzymatic reactions or other (bio)chemical processes. Such measurements are highly relevant in both environmental and biomedical sciences.

H2O2 Dynamics in the Sea Anemone Exaiptasia pallida.
In a second application, we assessed the H2O2 production of the anemone Exaiptasia pallida (strain H2) under a global change relevant stress scenario [63], i.e., increased seawater temperature (32°C) and high irradiance (1500 mol photons m -2 s -1 ). Exaiptaisa pallida is commonly used in ecophysiological and biomolecular research as a model organism for cnidarian-coral symbioses [64], and technical advances in the assessment of quantitative H2O2 production of such organisms under oxidative stress are in strong demand. Besides the very first successful detection of light-stress induced H2O2 formation in Exaiptasia, we could also show that the positioning of the MDP has a direct effect on the signal quality. When the MDP was positioned >1 cm from the animal, significant fluctuation in the signal was observed and could be explained by the distance of the MDP to the anemone in connection to the weak mixing of the seawater via an air stone, which hampers an even buildup of H2O2 in the seawater surrounding the sea anemone. Additionally, bubbles could get trapped on the MDP membrane affecting H2O2 diffusion through the membrane. When positioning the MDP in closer contact with the anemone tissue (within the more stagnant water, i.e., the diffusive boundary layer surrounding the animal) more stable measuring signals were observed with a quasi-linear increase in signal over time once the MDP was poditioned. The combined MDP-FIA system thus enables spatially resolved measurements of H2O2 in open or closed systems containing living organisms, and this opens for a wide range of applications in the biological sciences, where O2 respirometry is a core technique, which can now be easily combined with quantitative measurements of H2O2. 4.5. H2O2 Levels in LB medium. In a third application, the bacterium Pseudomonas aeruginosa was grown in diluted LB-broth medium. The autoclaved medium exhibited a high H2O2 background level (~17-18 µM in the diluted sample) causing a high baseline signal in the FIA. After addition of the bacteria, a drop in the signal intensity was observed due to catalase activity of the bacteria leading to H2O2 consumption. Such signal behavior was observed with direct FIA measurements of H2O2 as well as with FIA-MDP based measurements and measurements with an electrochemical H2O2 sensor ( Figure S2). Such high H2O2 background levels were also confirmed by adding catalase to the reaction mixture (MDP-FIA) or to a LB medium blank, which was measured subsequently to finishing the experiment (DI). This illustrates the importance of careful assessment of background H2O2 levels in sample media, typically assumed to contain no H2O2. The autoclaved LB medium contained almost 20 µM H2O2, while non-autoclaved LB medium at room temperature showed a lower background concentration of ~ 4.9 µM H2O2 (Figure 4). This shows that the treatment of the sample medium can have an influence on background H2O2 concentrations and this needs to be evaluated before setting up an experiment. In addition, it indicates that media used e.g. for isolation and cultivation of bacteria may impose some oxidative stress if they contain such high H2O2 background levels. This result was rather unexpected and should be analyzed in more detail in the future. With proper calibration and quantification of background levels of H2O2 in apparent blank controls, the combined MDP-FIA system is an ideal instrument for such studies.

Conclusion
Coupling MDPs to a FIA system bypasses laborious sample cleaning and pre-treatment steps as well as consumption of the sample. It is possible to measure dynamic changes in H2O2 directly in complex sample solutions for extended time periods and without special sample treatment. It was possible to determine concentrations down to the sub µM range with good linear calibration curves. The set-up is highly tunable as the measurement range can be modified to enable broad calibration ranges (e.g. 1 -100 µM) or highly sensitive measurements over a smaller operational range depending on the used MDP, the syringe pump speed, chemiluminescent reagent concentrations, or measurement temperature. Variation of the chemiluminescent (AE) reagent concentration allows a tuning of sensitivity and dynamic range of the H2O2 measurements that can compensate e.g. for a lower recovery when sampling H2O2 via the MDP membrane and/or at increased perfusion velocities of the carrier solution through the MDP. This tunability makes the MDP-FIA method a potent technique for H2O2 determination in many different samples and settings.
In this study we calibrated the combined MDP-FIA system within 1-10 µM and 1 -100 µM (higher and lower was not tested; LODs depend on the measurement medium and the chosen settings) and optimize the syringe pump speed as well as reagent concentrations for different media and thus different applications. We successfully applied it to quantify the dynamics of H2O2 in solutions subject to enzyme reactions; we monitored H2O2 development in the sea anemone Exaiptasia under light stress, and quantified high background levels of H2O2 in autoclaved growth medium, which was consumed by the addition of bacteria. The combined MDP-FIA based system thus has a broad applicability for extracellular, near-real time H2O2 concentration measurements in both natural and defined samples. The method is minimally invasive, adjustable to different media and concentration ranges, and significantly reduces media effects in comparison to direct FIA-based measurements. While we have focused on H2O2 measurements in this study, the system can also be used for chemiluminescent reaction-based quantification of other chemical species [65][66][67] including ROS such as superoxide [68][69][70], where suitable chemiluminescent detection schemes have been described.


extfieldsofstudy:
Biology
Medicine
Computer Science

text:
In Vivo Measurement of Blood Clot Mechanics from Computational Fluid Dynamics based on Intravital Microscopy Images

Ischemia leading to heart attacks and strokes is the major cause of deaths in the world. Whether an occlusion occurs or not, depends on the ability of a growing thrombus to resist forces exerted on its structure. This manuscript provides the first known in vivo measurement of the stresses that clots can withstand, before yielding to the surrounding blood flow. Namely, Lattice-Boltzmann Method flow simulations are performed based on 3D clot geometries. The latter are estimated from intravital microscopy images of laser-induced injuries in cremaster microvasculature of live mice. In addition to reporting the blood clot yield stresses, we also show that the thrombus 'core' does not experience significant deformation, while its 'shell' does. This indicates that the latter is more prone to embolization. Hence, drugs should be designed to target the shell selectively, while leaving the core intact (to minimize excessive bleeding). Finally, we laid down a foundation for a nondimensionalization procedure, which unraveled a relationship between clot mechanics and biology. Hence, the proposed framework could ultimately lead to a unified theory of thrombogenesis, capable of explaining all clotting events. Thus, the findings presented herein will be beneficial to the understanding and treatment of heart attacks, strokes and hemophilia.

Introduction
Achieving hemostasis following penetrating injuries is essential for the survival of organisms that possess a closed high-pressure circulatory system. However, pathological manifestation of thrombosis and embolism can potentially lead to life-threatening complications when occurring in the heart (i.e., a heart attack), brain (i.e., a stroke), or lungs (i.e., DVT/PE). Among these, thromboembolic infarction is the leading cause of mortality and morbidity in the United States, while stroke is the 5 th . [1] Conversely, deficiencies in the clotting mechanisms (hemophilia or due to drug interactions) can result in bleeding risks that confront surgeons on a regular basis. Yet, despite tremendous efforts by the medical research community (e.g., ~$3 billion of annual expenditure on heart attack and brain stroke research alone [2]), the problem that essentially amounts to a clogged "pipe" remains largely unsolved to this day. Moreover, what makes one thrombus benign, while another one dangerous, is also not well understood. Therefore, gaining insight into the thrombi's tendency to occlude blood vessels would be beneficial for public health, since it could pave the way towards a better understanding of the risk factors involved; and subsequently to better disease treatments and thromboectomy devices. [3]

Observed Structural Heterogeneity of Thrombi Imply Mechanical Differences
Whether an occlusion occurs or not, depends on the ability of the growing thrombus to resist the blood flow forces exerted on its structure. With development of advanced intravital microscopy experiments, the thrombi structures have been shown to be heterogeneous: consisting of a densely packed "core" nearest the injury site, and a loose "shell" overlaying the core (see Figure 1). [4,5]. It is also reported that the core is composed of highly "activated" platelets (as is measured by P-selectin expression), while the shell consists of loosely-packed P-selectin -negative cells. The biological purpose, as well as the cause of this heterogeneity, are unknown. One thing that is apparent, however, is that the core and the shell contribute differently to key parts of the thrombus formation and hemostasis: The shell is observed to shed the most mass (leading to the conclusion that embolism is mostly caused by this part of the clot); while the core can be seen to anchor the thrombus to the injury, and stop the escape of blood to the extravascular space by "sealing" the damage. This leads to an important conclusion that there are potentially significant material and functional differences between these two regions of blood clots.

Figure 1
LEFT -"Core-and-Shell" model schematic showing that the clot is comprised of two regions differing in degree of platelet activation and packing density; Image reprinted with permission, from Ref. [6] RIGHT -Confocal fluorescent microscopy image of a clot (Blue = Pselectin exposure marking the activated core; Red = anti-CD41 platelet marker). Scale bar is 10µm.

Hypothesis: Bingham-like Viscoplastic Behavior of Blood Clots
At the same time, the viscoplastic behavior exhibited by the thrombi resembles that of a Bingham plastic -a material, like toothpaste, that behaves as a rigid body at low stresses, but flows as a viscous fluid when its critical yield stress c is exceeded (see . Namely, like a Bingham plastic, the clot consists of discrete particles (in this case platelets) trapped in a liquid gel. The platelets interact with each other creating a weak solid structure known as a "false body". A certain amount of stress corresponding to c is required to break this structure and allow the platelets to rearrange within the gel under viscous forces. After the stress is reduced however, the platelets associate again, solidifying the structure. Figure 2 illustrates the Bingham plastic-like behavior of a blood clot as observed from intravital microscopy.

Figure 2
Red -Platelets (Anti-CD41 platelet marker); Blue -Core (anti-P-selectin thrombus "core" marker); Green -Injury (Uncaged Fluorescent Albumin). White Arrowindicates the direction of flow; Yellow Arrow -Upstream portion of the clot; Cyan Arrow -Downstream portion of the clot. A -Initial attachment at injury; B -Uniform growth prior to transition; C -Final stable steady-state core-and-shell thrombus structure, after the thrombus' yielding to the blood flow.
The figure shows three major progression stages of a typical thrombus formation: 1) initial platelet attachment to the injury site (see Figure 2-A); 2) clot growth radially outward from the injury site (see Figure 2-B); and 3) steady state stability (see Figure 2-C). The transition from the second to the third stage ( Figure 2, panels BC) is the Bingham-like "yielding" of the thrombus. During this critical event, platelet mass from the upstream portion of the thrombus is forced to its downstream side. As a result, the thrombus changes shape from a "ball"-like structure, to the characteristic "comet-tail" shape typically seen in blood clots. This transition occurs because the obstructing thrombus experiences stronger forces from the surrounding fluid, which is trying to squeeze through the little remaining openings left in the lumen. Consequently, if there is no full occlusion of the blood vessel, the thrombus' structure eventually yields to the flow forces, and rearranges its shape to minimize the fluid drag imposed on its surface.
Interestingly, despite the underlying complexity of the thrombo-genesis mechanism, the discrete regimes shown in Figure 2 appear to be common to all thrombi. Therefore, it is hypothesized here that the critical yield stress c is a parameter that is key to understanding the extent to which the clot's structure can resist deformation and breakage. In other words, it is an important measure of stiffness that can provide information on when the thrombus is likely to become pathogenic. Yet, c remains unmeasured to this day. This is because insight into thrombogenesis is made difficult by the fact that it is a fast, small scale process that involves a combination of coupled biochemical reaction cascades, intra-and inter-cell signaling, cell and tissue biomechanics, and non-Newtonian fluid flow. [7,8]

State-of-the-Art: Limitations of Stand-alone Experiments and Simulations
Among the experimental techniques, compression testing, [9,10] tensile testing, [11][12][13] shear rheometry, [14,15] nano-indentation[16] and ultrasound elastography [17][18][19] are commonly used to estimate mechanical properties of the thrombi (e.g., elastic modulus, shear modulus and stiffness). [9-12, 14, 16-18] However, most of these works use in vitro flow loops to generate thrombi, which may not be representative of the real physiological conditions in vivo. For example, there are some discrepancies between the ex vivo and the in vivo measurements. One such discrepancy is the platelet attachment, which happens so fast in vivo, that even the high speed cameras have trouble resolving it. [20] In contrast, the time scales of platelet activation observed ex-vivo are on the order of minutes, which is several orders of magnitude longer than that of invivo. [21][22][23][24] Alternatively, a preformed thrombus could be explanted from the body for an ex vivo measurement. However, this type of experiment corresponds to just a single time point, and only at a late stage of the thrombus formation. Hence, it would not capture the full thrombo-genesis dynamics; knowledge of which is necessary to measure the critical yield stress of the clot. Unfortunately, only a few studies among the above works measure thrombi biomechanical properties directly in vivo. A typical example is Mfoumou et al., [19] who used shear wave ultrasound imaging to measure thrombus stiffness in rabbits' veins. However, a) the temporal resolution of the measurements in such studies is on the order of t = 10 mins, which is again too slow to capture thrombus growth dynamics (lasts on the order of seconds), and b) the measurement occurs through tissue, which could reduce its accuracy. Therefore, better approaches are needed to deduce the ability of blood clots to resist deformation in vivo.
Computational models offer an attractive alternative, because they can resolve the time scale limitation by recreating thrombo-genesis in silico. [25][26][27][28][29][30][31][32] However, the clot structures generated by the simulations are not guaranteed to have realistic geometries, or to follow a realistic deformation trajectory over time. The reasons behind these limitations are the numerous unknowns in biology: for example, simulated clot structures are typically represented using either continuum models, [25,27,30,[32][33][34][35] discrete particle-based [26,36,37] or hybrid continuum/discrete particle-based [28,29,31,[38][39][40] dynamics. All these approaches rely on defining the clot biomechanics via parameters such as platelet-platelet, platelet-vessel wall/injury, platelet-proteins and fibrin-fibrin bond strengths (typically modeled using simple spring constants). However, since most of these parameters are obtained from in vitro experimental measurements, it is difficult to verify whether they are truly representative of the in vivo values. Moreover, some of the biological processes are simply too complex, and consequently require numerous simplifications / assumptions for achieving bottom-up modeling. For example, platelet activationa process central to clotting, is typically modeled using top-down neural networks pretrained on an individual's unique platelet phenotypes; [41] while bottom-up approaches to modeling the same phenomenon require unknown-parameter estimation. [42] Therefore, the purely computational methods, ultimately do not guarantee a realistic trajectory of thrombus evolution over time.

Proposed Hybrid Image-based Modeling Approach, and 3D Clot Structure Estimation
Thus, this seemingly "simple" phenomenon that is responsible for a wide range of lifethreatening pathologies is not easily accessible to either experimental or computational inquiries alone. Consequently, semi-empirical approaches offer a reasonable compromise for overcoming these limitations: they bypass the need for generating the clot structure mathematically, by obtaining it from experimental imaging instead. This ensures that a realistic geometry is used for solving the physics involved in the process. For example, in refs. [24,30,43,44] such models were used to calculate the time-dependent effects of surface shear stresses on thrombi developed in vitro. However, as mentioned previously, in vitro experiments may not depict realistic physiological conditions observed in vivo. Hence, in ref. [45] intravital imaging was used as the basis for calculating shear stresses in the near-thrombus region in vivo. However, these simulations were 2D, which may not provide quantitatively accurate descriptions of the 3D thrombus behavior. Moreover, no yield point or time-dependent stress data were reported.
The reason why the latter study was done in 2D is because the thrombus structure changes faster than a 3D confocal microscopy scan can be completed. [30] Moreover, considerable fluorophore bleaching is experienced during 3D image acquisition, even if the scanned thrombus is static. To overcome this problem, here we instead estimate the 3D geometry of the clots from the high-speed imaging of their cross-sections. In this manner, our image-driven simulation approach avoids the pitfalls of using either just experiments or just computation alone. To the best of our knowledge, this combination of advanced time lapse imaging and high-fidelity computation provides the first estimate of the thrombi's yield stress in vivo.

Methods
The overall semi-empirical approach used in this work is summarized in Figure 3. Namely, the evolution of the clot structures over time is obtained from 2D intravital microscopy of laser-induced injuries in microvasculature of live mice. Then, the 3D shape of the thrombi is estimated by casting assumptions about the relationship between the 2D and the 3D structures (based on our previous observations). [30] Finally, Lattice-Boltzmann Method (LBM) is used to calculate the fluid forces causing the thrombi to deform (i.e. the critical yield stress c).

Figure 3
Process flow diagram for the image-based modeling methodology used in this work. Injury was first induced in the artery of mice to initiate thrombus formation (Blueindicates activated thrombus core; Redindicates thrombus shell; Greenrepresents lumen and interstitial space within the thrombus). Then high-resolution confocal microscopy was used for 2D visualization of the process. Afterwards, a reconstructed 3D thrombus geometry was estimated from the 2D images and imported into the LBM fluid flow solver. Finally, LBM simulation results were used to compute the shear stresses on thrombus surface.

In-Vivo Laser Injury Model and Intravital Microscopy
All of the experiments in this manuscript were performed by the Skip Brass laboratory at the University of Pennsylvania (see Acknowledgements), as described in refs. [20,46] Briefly, thrombus formation was visualized in the microcirculation of live mice, following procedures previously developed in Ref. [47] In order to image the thrombus structure, intravital microscopy experiments were performed in male C57Bl/6J mice 8-12 weeks of age (Jackson Laboratories, Bar Harbor, ME). Thrombus formation in the mice was induced via laser injury of their cremaster muscle, according to procedures originally developed by Falati et al. [47] Alexa-Fluor® monoclonal antibody labeling kits from Invitrogen (Carlsbad, CA) were used to label antibodies. Anti-CD41 F(ab)2 fragments (clone MWReg30, BD Biosciences, San Diego, CA) were used to visualize platelet surfaces, anti-P-selectin (clone RB40.34, BD Bioscience) was used to visualize degranulated platelets, and caged fluorescein conjugated to albumin [46] was used for lumen and laser injury site visualization. The 2D structure of the thrombus formed due to the laser injury was imaged using confocal microscopy.
The center line maximum velocity through the mouse blood vessels was measured using optical Doppler velocimetry and divided by a factor of 1.6. The latter was done to account for a known artifact of the measuring technique: velocity profiles to appear slightly blunted and nonparabolic due to out-of-focus cells modulating the light intensity signals. [48][49][50] This procedure yielded an average blood vessel velocity of 4.78 mm/s. The velocimetry measurement was taken in a region away from the thrombus, to ensure that the velocity field was unaffected by the thrombi' presence. More details of the experimental procedures can be found in prior publications [4,46]. All procedures and protocols were approved by the Institutional Animal Care and Use Committee (IACUC) of the University of Pennsylvania.

2D Image Acquisition, Post-Processing and 3D thrombus Shape Estimation
Since 3D imaging is too slow to capture clot shape changes, 2D images from the confocal microscope were acquired using SlideBook 5 software (Intelligent Imaging Innovations) with a time interval of 0.619 seconds and a spatial resolution of 0.22 µm/pixel. A total of 300 time images were collected for every experiment. The obtained images were deblurred using a technique reported in Ref. [20] Next, Fiji [51] plug-ins were used to compensate for vibrations due to muscle contractions in the mouse, and air currents surrounding the sample. Specifically, to achieve video stabilization, all intensity channels were superimposed together, and stabilized collectively using either StackReg [52] or Image Stabilizer ImageJ plug-ins; [53] where the choice of plug-in is based on which gave better results for each particular capture. Finally, a custom Matlab code (MathWorks Inc., Natick, MA) was used to further enhance the signal-to-noise ratio of the 2D images and subsequently segment 2D thrombus shapes using standard image processing techniques.
Once the 2D images were post-processed, an in-house Matlab code (MathWorks Inc., Natick, MA) was used to generate estimated 3D clot geometries based on the 2D confocal images, at each time point. Specifically, the code assumed that each time-point image represented longitudinal (i.e., parallel to the blood flow axis) 2D cross-sections through the center of the actual 3D thrombi, at that same instant. This is a good assumption, since the microscope's operator particularly chose an imaging plane such that the thrombi' cross-sections were maximized. A representative grayscale thrombus cross-section from microscopy is shown in Figure 4-LEFT. Subsequently, cross-wise (i.e., perpendicular to the blood flow axis) parabolic cross-sections were stacked along the "spine" of each clot artificially, to estimate the thrombi's 3D shapes (see Figure 4-MIDDLE). The resulting parabolic shape, chosen to represent the outer thrombus perimeter, was selected based on experimentally-observed 3D reconstructions of a static clot. [20] Specifically, the height of each parabola was dictated by the height of thrombus' "spine" at every position along the longitudinal direction; while the widths of the parabolas were assumed to be in a constant 2:3 ratio with the parabola heights throughout the thrombus. This ratio was again consistent with experimental observations from static 3D in vivo imaging shown in Ref. [20].

Figure 4 3D Thrombus Shape Estimation
Proceedure: LEFTa 2D grayscale image of a thrombus crossection obtained via confocal fluorescent microscopy (yellow lines mark the blood vessel edges); MIDDLE -illustration of how parabola are fit on the edges to generate 3D geometry (red is the 2D cross-section, blue are the parabolas fitted to its "spine"); RIGHT -resulting 3D reconstruction (blue is a pipe fitted around thrombus depicting the blood vessel; red is the estimated thrombus). Pipe diameter and lengths are 0.03685mm and 0.2275mm for this experiment, respectively. White arrow indicates the direction of blood flow.
Finally, the blood vessel walls were manually segmented from the 2D images to measure the lumen diameter. Subsequently, a 3D pipe of the same size was created around the estimated 3D blood clot (see Figure 4-RIGHT). The length of the pipe was chosen to be three times the maximum clot length, to avoid entrance effects in fluid flow simulations.

Fluid Flow Modeling: Lattice-Boltzmann Method (LBM)
Convection within the blood vessels and around the 3D thrombi was modeled via LBM. LBM is a numerical technique for simulating mesoscopic fluid flows, which consists of solving the discrete Boltzmann equation. [54][55][56] In addition to computational advantages e.g., LBM is inherently parallelizable, [57,58] LBM techniques have been used in a wide spectrum of applications [turbulence, [59] non-Newtonian flows [60][61][62], and multiphase flows [63]]. Moreover, it has recently gained popularity for modeling biological flows. [64][65][66][67][68][69][70][71] It was chosen for this work because of the ease with which it handles complex boundary conditions, and due to its efficient parallelizability on supercomputers. [72] Both of these aspects make the method especially attractive for dealing with high-resolution images, such as the ones used in our study. A previously developed custom-written, parallelized, in-house code was used in this work. [20,64,[66][67][68][69][73][74][75] The D3Q15 lattice [76] in conjunction with the single-relaxation time Bhatnagar, Gross and Krook [77] collision term approximation was used to perform the simulations in this study. The no-slip boundary condition was applied at wall faces using the "bounce-back" technique. [55] To take advantage of inherent LBM parallelizability, domains were decomposed using message passing interface. [64,69] The code has been validated for several flow cases for which analytical solutions are available: forced flow in a slit, flow in a pipe and flow through an infinite array of spheres. [64,68] The LBM simulations were performed for a total of ten different laser-injury experiments (see ). For each one, a pseudo-steady state approach was taken, to update the clot shape based on the successive microscopy images. Namely, flows through geometries representing each individual time step were solved separately from each other, as steady state simulations. Ultimately, the individual time step results were then concatenated to form a continuous timeseries. The pseudo-steady state approach is a good assumption, given than the fluid velocity field changes much faster than do the clot geometries. While the fluid dynamic viscosity of blood is known to be shear-dependent, [78,79] here it is assumed to exhibit Newtonian behavior with a viscosity of µ ≈ 0.03 gr/cm-s. [80,81] This is considered to be a good assumption due to the low hematocrit typically observed in microvasculature. [82] Given that the reality is likely to be something in-between, two different boundary conditions commonly encountered in literature were modeled: constant pressure drop [25,44,83] and constant flow rate. [44,84] For the latter, the flow is continuously adjusted to ensure that input flow rate is maintained consistently throughout thrombus development. In both cases, the initial average lumen blood velocity in LBM was matched to the in vivo value of 4.78mm/s, obtained by optical Doppler velocimetry for a comparable diameter blood vessel (as discussed in the experimental methodology Section 2.1). The simulations were considered converged when smallest, average, and highest flow velocities in the whole simulation domain varied by less than 0.01% per LBM 1000 steps. Approximately 60,000 steps were needed for full conversion of each experimental time step. The image-based LBM simulation results were validated against an idealized homogeneous porous media model of a thrombus using a commercial computational fluid dynamics package COMSOL®.

Stress Calculations
Since the thrombi deformation was obtained from imaging, their geometry in the model was assumed to be solid. The fluid-induced shear stresses acting on thrombi surfaces were estimated following a scheme suggested by Porter et al. [65] using the equation (3): Where   is the shear stress tensor and U is local velocity vector.
Derivatives of the velocity field given in equation (3) were approximated numerically using centered finite difference method (Equations (4) -(6)). The same was done for the partials of Uy and Uz. Following this, the symmetric strain matrices were found by adding the 3 × 3 partials matrix for each field location to its own transpose.
Where lu is the length of one side of an element in the LBM model.
The 3×3 partials matrix for each point in the field was added to its transpose to produce a symmetric strain matrix. The eigenvalues of the symmetric matrix are found using the Jacobi method, and largest absolute-value eigenvalue are used to determine shear stress. It is important to note that only stresses due to fluid shear are reported in this study. The upstream wall stress value obtained from stimulation was ~31 dyn/cm 2 , which is comparable with experimental value of 40 dyn/cm 2 from literature. [85] 3D reconstructions generated using Tecplot 360 EX 2017 (Tecplot Inc., Bellevue, WA USA) were used for visualizing velocity and stress distributions acting on and around the thrombi.

Results
The material properties of thrombi provide a measure of when the clots can potentially become pathological. The goal of this paper is to estimate the mechanical strength of the thrombi formed in the microcirculation of live mice. This is done by calculating the stresses induced on the clot by the surrounding blood flow, from LBM simulations based on intravital microscopy images. The hybrid semi-empirical approach helps to overcome limitations of conventional experimental and simulation tools: such as, the inability to do fast 3D fluorescent imaging in case of the former, and the uncertainty in generating the thrombi structures mathematically, in case of the latter.

Nondimensionalization via Data Normalization
Firstly, it was found that although each clot has unique properties (size, formation kinetics, etc.), the thrombo-genesis dynamics look similar for different clots when compared on a nondimensional scale. Therefore, to normalize all clots to the same scale, we nondimensionalized the experiment time by dividing it by a "characteristic" one, as shown in Equation 7 * = / ℎ (7) where t  is the dimensionless time, 't' is the experiment time, tchar is some characteristic time.
To define the latter, we hypothesized that time of the "yielding" could be used for this purpose, given that it appears to be a transition that is characteristic to all blood clots. We have also noticed that the yielding coincides with the peak in the blood clot size, as measured by the anti-CD41 marker area in the microscopy images. Hence, we chose the time of the peak clot size as the 'tchar', for simplicity (since it doesn't require performing simulations). The normalization results are shown in Figure 5.
Here, the thrombus size (quantified via the anti-CD41 platelet marker area in the fluorescence images) and aspect ratio (a measure of morphology, defined as the clot height divided by clot length, also measured via anti-CD41) are plotted versus the dimensionless time, t  . The ordinate values are also normalized by their respective maxima, as follows A * = A / Amax (8) where, A * is the dimensionless clot area, A is the clot area as measured from the anti-CD41 marker's fluorescence, and Amax is the peak value of A. AR * = AR / ARmax (9) where, AR * is the dimensionless aspect ratio of the clot, AR is the aspect ratio of the clot as measured from the anti-CD41 marker's fluorescence, and ARmax is the peak value of AR.
Several observations can be made from Figure 5. Firstly, Amax occurs at t  = 1, as is expected from the normalization procedure. Secondly, ARmax occurs at t  = 0.5, which we define as the beginning of the clot's deformation region, because at this point the AR * (i.e., the clots morphology) begins to experience a significant elongation. The yielding is not instantaneous however, as the clot continues to gain mass beyond t  = 0.5. This is evident from the red curve in Figure 5. Finally, the clot growth and deformation settle down at approximately t  = 1. Hence, the two mentioned time points appear to be physiologically characteristic of the thrombo-genesis process.

Figure 5
Data nondimensionalization strategy: Red graph shows the clot's cross-sectional size, quantified based on the anti-CD41 marker area in the microscopy images. Blue graph shows the clot's aspect ratio = height / length. Abscissa is the dimensionless time; whose unity corresponds to the peak CD41 area in the red color curve. Both curves are moving averages with a window of 0.5 and the error bars represent the moving variance for the 10 experiments in .

Clots Experience Heterogeneous Deformation During Thrombogenesis
Interestingly, the thrombus' inner region (i.e., the "core") does not show a similar trend of deformation. Figure 6 shows an analysis of the cores' morphology analogous to Figure 5. Namely, this figure plots the core's P-selectin area and aspect ratio on the same dimensionless time scale, t   Similar to the overall thrombus growth shown in Figure 5, the core increases in size up until t  = 1, after which it stays about the same size. Physiologically, the core's growth corresponds to the activation of the platelet mass nearest the injury, similarly to what was shown in Figure 1. However, unlike the overall thrombus shape, the core's aspect ratio remains unchanged throughout the whole formation of the clot. From this, it can be concluded that most the clots' deformation occurs in the only thrombus' outer region (i.e., the "shell"), where loosely bound platelets are rearranged in response to fluid flow stresses.

Figure 6
Changes in nondimensionalized thrombus' core size and morphology, plotted as function of normalized time. Red graph shows the core's cross-sectional size, quantified based on the anti-P-selectin marker area in the microscopy images. Blue graph shows the core's aspect ratio = height / length. Abscissa is the dimensionless time; whose unity corresponds to the peak CD41 area in the red color curve in Figure 5. Both curves are moving averages with a window of 0.5 and the error bars represent the moving variance for the 10 experiments in .

Image-based Modeling of the Fluid-induced Stresses Imposed on the Clots
Since the thrombus partially obstructs blood flow within the vasculature, the thrombus structure experiences forces exerted onto it by the passing fluid. These forces can drive thrombus break-up and embolism. Additionally, platelet adhesion and aggregation [86] and activation [87,88] are influenced by local shear rate. Hence, we wanted to correlate how the fluid-induced stresses that the thrombi experience due to the flow in the blood vessels correlate to their deformation. To do this, we reconstructed the 3D thrombus shapes, estimated from the intravital microscopy images, in a virtual blood vessel (procedure in Section 2.2). Once the clot geometry was obtained, an in-house LBM code was used to calculate the blood velocity field established around the thrombi versus dimensionless time (see Supplemental Figure 1 and Video 1).

Supplemental Figure 1
"Heatmap" of the LBM velocity field established in the lumen, calculated using the constant pressure boundary condition. The results are shown at different key time points: t  = 0.023 is an earlier time in the thrombus formation process; t  = 0.5 is the time marking the beginning of deformation/yielding; t  = 1 is the time marking the end of deformation/yielding; t  = 2.67 is a later time, after the thrombus yielding, during which it has assumed its final shape. Black arrow indicates direction of flow.
This figure shows how the velocity changes for a typical thrombus, under the constant pressure drop boundary conditions. In this case, the blood flow around the clot decreases, as the growing thrombus creates a larger and larger resistance to the flow. This is because at a constant pressure drop, it is more difficult to overcome the growing resistance of the thrombus protruding into the center of the lumen.
Conversely, in the case of the constant flow rate boundary condition (not shown), the velocity would increase to push the same amount of fluid through a narrower opening in the lumen. As discussed previously in Section 2.3, we performed both types of the simulations, to obtain the upper and lower bounds of the stress experienced by the thrombi. This is because the physiological reality is likely to be something in between the two boundary conditions: namely, a) an injured blood vessel tends to relax in order to avoid occlusion (similar to the constant pressure drop case), b) blood may get re-routed through other pathways in the vasculature (similar to the constant pressure drop case), and c) the heart may compensate in order to clear the obstruction by pushing the blood harder (similar to the constant flowrate case).
Ultimately, the LBM velocity fields for both boundary condition types were used to calculate the fluid-induced stresses experienced in the lumen, using the procedure described in Section 2.4. A representative result for the constant pressure drop boundary condition is shown in Figure 7 and Video 2. As expected, the stress distributions change with time, due to the effects that the evolving thrombus structure has on the surrounding blood flow in the lumen. As validation, the thrombus base (nearest the blood vessel wall) experienced stresses comparable to the value of ~31 dynes/cm 2 , which is expected for an empty blood vessel of a similar diameter (calculated using Hagen-Poiseuille equation). [89] Moreover, these values are also comparable to the experimentally measured values of ~47 dynes/cm 2 for similar size arterioles of cat mesentery. [85] Finally, the top part of the thrombus protrudes into the center of the blood vessel, and experiences stresses that are several fold higher than are imposed on its base. Hence, the highest flow forces are acting on the shell of the thrombus, rather than on the core. This is consistent with the shell being the part of the thrombus that experiences the most deformation. formation process; t * = 0.5 is the time marking the beginning of deformation/yielding; t * = 1 is the time marking the end of deformation/yielding, when significant mass is transferred to the back of the clot; t * = 2.67 is a later time after thrombus yielding during which thrombus has assumed its final shape. Black arrow indicates direction of blood flow.
Next, the stresses were plotted as a function of the dimensionless time t   and normalized as follows: where,  * is the dimensionless fluid-induced shear stress,  is dimensional fluid-induced shear stress, and max is the peak value of . Furthermore, since the simulations are computationally expensive, only every 10 th time step out of the total 300 was modeled for each experiment. However, we did solve one of the experiments fully, confirming that the obtained trends would be similar. This confirmation is shown in Supplemental Figure 2. From this figure, it is apparent that solving every 10 th time step is sufficient to capture the stress trends displayed by the thrombi. Hence, the time-coarsed stress results are shown in Figure 8.
In Figure 8, the normalized stresses are averaged over the thrombi surfaces, and plotted versus the normalized time, for both the constant pressure drop and constant flow rate scenarios. In both cases, as the thrombi grow in the blood vessel, the shear stresses imposed on their surfaces initially increase with time. However, the locations of the peaks do not coincide. Instead, they are located approximately at the beginning (t  = 0.5) and the end (t  = 1) of the clot's "deformation region", for the constant pressure drop and constant flow rate cases, respectively. This again, supports the notion that the two boundary conditions represent extreme cases, while the reality is likely to be something in-between them. Furthermore, it is worthy of noting that in the limit of long time, the stresses decrease roughly to their initial values, while the clot sizes remain nearly constant after peaking. This supports the notion that the thrombi shape rearrangements are driven by drag minimization.

Figure 8
Normalized stress data, averaged over the thrombus surface, and plotted as a function of normalized time. Blue curve represents constant flow rate simulation results. Red curve represents constant pressure drop simulation. Abscissa is the dimensionless time; whose unity corresponds to the peak CD41 area in the red color curve in Figure 5. Both curves are moving averages with a window of 0.5 and the error bars represent the moving variance for the 10 experiments in . Finally, Table 1 catalogues the max values for the 10 thrombi modeled in this study. These can be used to recover the actual (i.e., dimensional) stresses from the dimensionless curves in Figure 8. Additionally, the max results can be extrapolated to other blood vessel sizes. For example, we have observed a strong dependence of the yield stresses on the blood vessel diameter (see Figure 9). Although, this may seem surprising at first, it appears that geometric attributes of the blood vessel dictate the peak size of the thrombi. Specifically, the maximum clot volume was found to vary with the blood vessel diameter and injury length (see Figure 10). Consequently, it makes sense that the clots found in different blood vessels can withstand varying amounts of stresses, depending on how big or small their structures are.

Discussion
The yield stress is a critical property representing mechanical strength of the thrombi' material; and as such, it provides a measure of when a blood clot can potentially become pathological. Therefore, quantitative characterization of this parameter is important to public health. However, it is difficult to measure in vivo by using either purely experimental or purely computational tools alone. Hence, we applied a semi-empirical framework that combined intravital imaging and flow dynamics simulations, to overcome the technological challenges of the conventional approaches. To the best of our knowledge, this is the first measurement of the thrombi' critical yield stress made in vivo. Expectedly, our stress results compare well with both the 2D in vivo stress calculations (see Figure 4 in Ref. [45]) and, the 40 dyn/cm 2 in vitro value for "dynamic" elastic modulus of less activated platelet aggregate (see Table 1 in [33]).
Moreover, we have reported that the thrombogenesis mechanism appears to consist of several discrete regimes common to all clots, despite the underlying uniqueness and complexity of their formation. Consequently, we identified the time of the clot yielding to be a characteristic nondimensionalization parameter, which appears to coincide with both mechanics (e.g., the clots stop growing after the deformation at t* = 1) and biology (e.g. P-selectin expression in the core plateaus at t* = 1) of thrombi formation. Hence, we showed that it can be used to collapse data from multiple injury events onto a single master curve. Furthermore, the consistency of the nondimensionalized trends across the multiple blood vessel injuries gives hope that a uniform theory of thrombo-genesis can be developed, which would be able to describe all clotting events using a single analytical expression.
Finally, we showed that the thrombus core does not change shape appreciably. In contrast, the shell experiences significantly higher fluid-induced stresses, which result in its deformation. This raises the likelihood that the shell is an inherently compromised part of the clot (the high shear stresses may facilitate shell fragmentation due to mechanical disturbance); and that as such, it is responsible for most of the embolism. Hence, it can be concluded that the core is structurally stronger, and that it tethers the overall body of the thrombus to the injury. Consequently, the biological differences between these thrombi regions could mean that it is possible to dissolve just the dangerous part of the blood clot (i.e., the embolizing shell), while leaving the useful one (i.e., the core which seals the injury) intact. In this manner, a new generation of drugs could be developed that would selectively target just the shell; thereby avoiding the dangerous bleeding complications of the medications currently available on the market.
Although our study provides important information regarding the thrombus biomechanics, it is necessary to keep in mind that it is only an estimate; and that several assumptions and simplifications had to be made to obtain it. Specifically, the limitations of this study are as follows: 1) The clots' 3D shapes were extrapolated from their 2D longitudinal cross-sections, by assuming that thrombi crosswise profiles are parabolic in shape and have a constant width-to-height ratio (see Figure 4-MIDDLE). Although this was measured experimentally, [20] a late-stage static thrombus was used. Hence, this assumption may not work well for the very early stages (i.e., t  < 0.5) of the thrombus formation (when the clot has a less elongated shape). However, this only concerns the 3D LBM simulations, while the 2D experimental results would not be affected; 2) The pseudo-steady state approach to the simulation necessitated the assumption that the velocity field of the blood flow establishes faster than the clots change their shape; 3) The thrombi are assumed to be impermeable to the fluid flow, since the true nature of their porous structure could not be approximated using our minimalistic approach; 4) We did not model blood escape from the injury site, which could cause the simulated flow field to deviate from the real one; 5) The shape of the blood vessel was assumed to be a straight solid pipe, while in reality it may bend and deform, (especially near the injury site); 6) Finally, the blood was assumed to be a Newtonian fluid for simplicity. However, this is commonly done in similar thrombo-genesis modeling studies. [20,24,43,90] Moreover, inaccuracies incurred due to this assumption are believed to be small, since blood behaves close to a Newtonian fluid when the shear stress is larger than 1 Pa (which is our case). [45] The future directions for this work include performing similar measurements of the blood flow forces experienced by occlusive and embolizing thrombi (both of which are harder to induce and capture experimentally). Furthermore, we plan to continue working towards developing a universal model of thrombo-genesis. This will be done by correlating other physiological phenomena, such as the dynamics of the blood's escape to the extravascular space, to the dimensionless time scale, t  . Additionally, the "plastic viscosity" (in the second term on the righthand side of Equation 2) will be measured via image-based modeling). Finally, superior imaging methods will be used to capture the real-time 3D thrombi shape changes, instead of relying on extrapolations based on the 2D cross-sections from conventional confocal microscopy.

Conclusions
In this study, we have performed an in-depth analysis of intravital microscopy images, showing thrombi development in response to laser-induced injuries in live mouse microvasculature. Based on these results, we were able to conclude that the thrombus core does not change shape appreciably during thrombo-genesis, but its shell does. This implies that there are inherent differences in the material properties of these two regions of the clots. Furthermore, we performed image-based LBM modeling, which allowed us to calculate the fluid-induced shear stresses imposed on the thrombi's surfaces by the blood flow. From these results, we observed that it is the thrombus shell that experiences the highest fluid-induced shear stresses on its surface. A combination of the two results, namely that the shell is both weaker and experiences more deformation, leads to the conclusion that it is the most prone to embolism. The implications of this finding are that a new class of anti-embolic drugs could be developed, which would target the dissolution of the shell selectively, while preventing the risk of severe bleeding (typically associated with the existing antithrombotic medications) by leaving the core of the clots intact. Finally, we have laid down a foundation for a nondimensionalization approach to interpreting thrombogenesis data, with the hope that a uniform theory could be developed through an extension of this procedure. Overall, the findings herein are expected to be beneficial to understanding the process of thrombo-genesis, which is central to heart attacks and strokes that are plaguing the public health today.

Codes and Data Sharing
The codes used for this work can be found at https://git.njit.edu/rvoronov/lbm. The raw data is too large (> 1 TB) for web repository storage. Instead, it is hosted on supercomputing tape storage at https://portal.tacc.utexas.edu/user-guides/ranch, and is provided upon request. Figure 9 Yield Stress as a function of Blood Vessel Diameter: solid markers indicate LBM calculations, while dashed lines are linear least squares fits through the data.

Figure 10
Dependence of clot size on blood vessel diameter and injury length. Red "stems" represent the 10 experimental measurements from this study, while the colored mesh is a fit through these points (meant to serve as a guide for the eye).

Video 1
Animation of 3D LBM results showing how blood clot formation affects the velocity field in the lumen of a representative blood vessel. The calculation was carried out using the pressure boundary condition. Blood vessel diameter is 34.18µm.

Video 2
Animation of 3D LBM results showing how blood clot formation affects the fluidinduced stress field in the lumen of a representative blood vessel. The calculation was carried out using the pressure boundary condition. Blood vessel diameter is 34.18µm.