Integrating Multiscale Modeling and in vivo Experiments for Studying Blood Clot Development

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To prevent the loss of blood following a break in blood vessels, components in blood and vessel wall interact rapidly to form a blood clot (thrombus) to limit hemorrhage. This hemostatic response is rapid and regulated, since excessive and inappropriate clotting reduces the patency of blood flow. While knockout mice provide qualitative results about the role of particular hemostatic components, the mathematical and computational models can suggest threshold values of particular elements critical for hemostasis. Determining such thresholds will help identify hemostatic risk factors in human population. This has significant biomedical implications. For instance, deep vein thrombosis affects 250,000 Americans each year and leads to 20,000 deaths mainly from clot fragments that break off from the thrombus and cause pulmonary embolisms. The incidence will increase as the population ages. Developing accurate, quantitative models of thrombus formation that help us understand the physical and biochemical processes involved in clot structure and stability will contribute to the development of new diagnostic approaches and therapeutic strategies. The overall goal of this proposal is to develop three-dimensional multiscale mathematical models and a computational toolkit for simulating thrombus formation. These models will be validated with specifically designed experiments to test predictions of thrombus development, structure and stability. Moreover, the development of reasonable models will serve as a generator of new hypotheses that can be tested in experiments in vivo. To achieve this goal, a new collaboration has been formed between Dr. Alber and Dr. Xu (Notre Dame), Dr. Rosen (Indiana University Medical School) and Dr. Jiang (Los Alamos National Lab). To bring different scale levels of thrombus model together, new mathematical techniques and computational schemes will be developed and these will include elements of stochastic analysis, nonlinear analysis and kinetic theory. New methods will include coarsening methods, new numerical schemes, error estimates of numerical solutions as well as parallelization algorithms for the coupled discrete and continuous models needed for the long time simulations. The mathematical and computational models will incorporate many biological processes (platelet interactions, coagulation pathways, hemodynamic effects) into the simulation thus integrating biological fields that have traditionally been studied separately.