My main research interest is in using mathematics and computation to understand how the complex biochemical and biophysical components, especially the fluid dynamics, of platelet aggregation and coagulation interact in hemostasis (normal blood clotting) and thrombosis (pathological blood clotting within blood vessels). This is a fascinating area with tremendous practical importance because thrombosis is the proximal cause of most heart attacks and strokes. My efforts on this problem involve formulating mathematical models that are sufficiently realistic to give insights into the real biological processes and yet are not so complex as to make intractable even computational study of their behavior. Because the models are very complex (they involve fluid dynamics, fluid-structure interactions, chemical kinetics, chemical and mass transport), they pose substantial computational challenges and another major part of my research concerns development of numerical methods to meet these challenges. Because the platelet aggregation and coagulation problems have many features in common with other biological problems, these numerical methods have more general use, and another part of my research concerns applying the numerical methods to other biological or engineering problems and developing software to facilitate others using the methods to solve such problems.
Movie 1: 2d platelet thrombosis -- adhesion and aggregation of pre-activated platelets.(11m)
Movie 2: 3d platelet adhesion, ADP release, and aggregation along a sticky flow-chamber wall. (4.8m)
Movie 3: 2d platelet thrombosis in stenotic coronary artery. (3.9m)
Movie 4: 2d platelet thrombosis in stenotic coronary artery. Downstream plaque rupture. (2.7m)
Movie 5: 2d platelet thrombosis in stenotic coronary artery. Upstream plaque rupture. (2.7m)
IBIS: Immersed Boundary Software Package
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