An overview of mathematical modeling of thrombus formation under flow.

In the last decade numerous mathematical models have been formulated to investigate specific components of the clotting system such as the tissue factor pathway of coagulation. Sophisticated, multiscale models were developed to better understand the interplay of flow-mediated transport, platelet deposition, and coagulation kinetics, and their overall effect on thrombus formation. Promotion of thrombus growth is partially due to the well-known pro-coagulant roles of platelets like the surface-dependent coagulation reactions. Iterations of theoretical model predictions and experiment have helped to elucidate anticoagulant roles of platelets as well. These roles include paving over the subendothelium and hindering transport of substrates to and from enzyme complexes which can strongly affect thrombus formation. In this review, we give a brief overview of theoretical models of thrombus formation under flow and some of the experiments that motivated them and were motivated by them.