Anna C. Nelson, Duke University
Authors: Anna C. Nelson, Aaron L. Fogelson
2022 AWM Research Symposium
Recent Advances in Mathematical Biology

The formation of a blood clot involves complex biophysical and biochemical processes that occur under flow. In the event of an injury, platelets become active and weakly aggregate to form a plug at the injury site. Activated platelets express binding sites for procoagulant species, and platelet surface-bound complexes convert zymogen prothrombin into enzyme thrombin; thrombin further activates platelets and converts soluble fibrinogen molecules in the blood plasma to fibrin monomers. These monomers then polymerize to form a gel that is a major structural component of a blood clot. Fibrin(ogen) interacts with activated platelets through surface integrins that allow platelets to adhere and cohere through bonds mediated by fibrin(ogen). Experimental evidence suggests platelet integrins interact differently with fibrinogen, fibrin, and fibrin oligomer. We propose a mean field mathematical model of fibrin branch formation which tracks fibrinogen, fibrin, and platelet species in either a bound or unbound state. Fibrin oligomers form in both the bulk and on the surface of platelets, and flow-mediated transport will affect fluid-phase species. A kinetic fibrin polymerization model is used to model fibrin gel formation; this model is studied up until gelation, which is defined as the emergence of an oligomer of infinite size. In this presentation, we show how the gel time depends on model parameters and how platelet-fibrin(ogen) interactions affect the gel structure.

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