Anna C. Nelson, Duke University
Authors: Anna C. Nelson, Aaron L. Fogelson
2023 AWM Research Symposium
Early Career Researchers in Mathematical Biology and Differential Equations [Organized by Rayanne Luke, Sarah Strikwerda, and Prajakta Bedekar]

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 platelet allow for surface-bound complexes to convert zymogen prothrombin into enzyme thrombin. Thrombin further activates platelets and converts fibrinogen molecules in the blood to fibrin monomers, which polymerize and form a gel that is a major structural component of a blood clot. Fibrin(ogen) interacts with activated platelets and facilitates platelet adhesion and cohesion through bonds mediated by fibrin(ogen). In this work, 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. Finally, we discuss on going work of incorporating biological parameters into our modeling framework.

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