Decoding thrombosis through code: a review of computational models

Figures

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  FIGURE 1. Multiple scales involved in thrombus growth. At the largest scale, blocked flow can change flow and pressure waveforms in the circulation, while potentially preventing blood flow to vital organs. On the scale of a blood vessel, blood is often considered a continuum (fluid). On the scale of a thrombus, platelet aggregation and fibrin formation are sometimes modeled as a continuum for large-scale models or as particle-based models when the length scale of the simulation and thrombus approaches the size of platelets. Within the thrombus are platelets bind to plasma proteins and the sub-endothelium. On the platelet membrane, there are individual receptors, and a sufficient number of receptors require ligation in order to slow a platelet after transient interactions with a surface. Furthermore, granule secretion leads to release of proteins and platelet activation agonists. With outside-in and inside-out signaling, platelet activation can proceed with cytoskeletal rearrangement causing platelet shape change and contraction. Models of thrombus formation usually involve a continuum and/or a particle-based modeling method. In the bottom panel, a continuum method is used to discretize a…

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  FIGURE 2. Macroscale modeling of hemodynamic descriptors of thrombosis. (A) Spatial distribution of time averaged wall shear stress and activated platelet concentration in Kawasaki disease aneurysms [33,34]. (B) Spatial distributions of endothelial cell activation potential, platelet activation potential and thrombus formation potential in an abdominal aortic aneurysm having a thin thrombus on the central anterior surface [35]. (C) Aortic dissection volume rendering of scalar shear rate at peak systole for two lesions at the initial (left) and final (right) stages of thrombus formation upon dissection (blood flow direction is from top to bottom in all cases) [36]. (D) Type B aortic dissection velocity magnitude contours at peak systole just above second tear showing the effects of thrombus growth on the flow field at different time points, compared with follow-up CT scans. The velocity in the thrombosed region is gradually reduced as thrombus is formed. In the model S4 (left), in red, thrombus [37].

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  FIGURE 3. Examples of transport modeling. (A) Continuum model to predict transport of erythrocytes and platelets [6]. (B) Modeling and simulation of platelet transport in a blood suspension with flow through a constriction using particle based methods [12].

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  FIGURE 4. Examples of platelet aggregation simulations using continuum models. (A) Depicts thrombus growth in an axial flow ventricular assist device relative to clinical observations [7]; and (B) shows thrombus growth modeling over a stenosis to investigate growth on an ex vivo stenosis [6]. Mesoscale models of individual cells can be used to (C) quantitate platelet aggregation behavior when individual cellular biomechanics are altered [52]. (D) Model of von Willebrand factor extension and interaction with platelet transport near a reactive surface using glycoprotein Ibα-von Willebrand factor A1 kinetics using particle based methods for a shear rate of 10,000 s−1 [55].

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  FIGURE 5. A coupled model of thrombin production with platelet aggregation compared with in vitro microfluidic results [48]. (A) Images of the experimental platelet aggregation (red) relative to simulated platelet aggregation (gray) with (B) corresponding thrombus height measurements from experiments compared with predicted heights from simulations.

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  FIGURE 6. Computational modeling of thrombus mechanics. (A) Impact of the flow shear rate on blood clot stability. (A–D) Spatial distributions of clot volume fraction at different shear rates: (a) 250 s−1, (b) 500 s−1, (c) 1000 s−1, and (d) 2000 s−1 [79]. (B) Illustration of a hybrid particle–continuum fictitious domain modeling framework to incorporate clot shape and morphological heterogeneities in computational models [22].