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Mathematical modeling of hemostasisÌý

Hemostasis is the process by which a blood clot forms to prevent bleedingÌýat a site of injury. The formation time, size, and structure of a bloodÌýclotÌýdepends on the local hemodynamics and the nature of the injury. OurÌýgroup has previously developed computational models to study intravascularÌýclotÌýformation, a process confined to the interior of a single vessel.ÌýHere we present the first stage of an experimentally-validated,Ìýcomputational model ofÌýextravascular clot formation (hemostasis) in whichÌýblood through a single vessel initially escapes through a hole in theÌývessel wall and out a separateÌýinjury channel. This stage of the modelÌýconsists of a system of partial differential equations that describeÌýplatelet aggregation and hemodynamics,Ìýsolved via the finite element method.ÌýWe also present results from the analogous, in vitro, microfluidic model.ÌýIn both models, formation of a blood clotÌýoccludes the injury channel andÌýstops flow from escaping while blood in the main vessel retains itsÌýfluidity. We discuss the different biochemical andÌýhemodynamic effects onÌýclot formation using distinct geometries representing intra- andÌýextravascular injuries. If time permits, there will also be aÌýdiscussion of recentÌýmodeling efforts to explain how blood clots sequester large quantities ofÌýenzymes by utilizing a bivalent binding mechanism.