David Aristoff's homepage Title: Mathematical modeling of blood clot formation under flow

Abstract: Many biological fluid environments are inherently heterogeneous, comprised of macromolecules, polymers networks, and/or cells. These environments can be thought of, in some sense, as fluids interacting with biological porous materials. In this talk I will describe a mathematical model of dynamic formation of blood clots under flow. The model of clot formation was developed to better understand the interplay between flow-mediated transport of clotting proteins and cells, blood cell deposition at an injury site, complex clotting biochemistry, and the overall effect of these on clot formation. A derivation of hindrance coefficients for the advection and diffusion of clotting proteins will be presented. Results show that the effects of such hindrance are profound and suggest a possible physical mechanism for limiting clot growth. Next I will describe more recent work that extends this model to look at the bleeding in complex geometries with comparisons to in vitro experiments.