Mathematical Modeling of Blood Clotting Dynamics
Formation of a blood clot involves complex interplay between numerous biochemical, biophysical, and fluid dynamic processes. Broadly speaking, clotting consists of three intertwined processes: platelet accumulation at the site of a vascular injury, enzyme reactions triggered by the injury that result in production of the enzyme thrombin, and fibrin polymerization around and between the accumulated platelets. Over the years, my group has used mathematics to model several aspects of clotting accounting to various degrees for this interplay. In today’s talk, I plan to tell you about two of our projects. The first project models the tissue factor pathway of coagulation (the enzyme reactions mentioned above) triggered by vascular injury. Uniquely at the time the model was first developed, it considers that essential ones of these reactions occur on the surfaces of activated platelets and that the gradual accumulation of activated platelets on the injury is procoagulant by providing surfaces for these reactions and anticoagulant by covering the vascular wall and inhibiting the reactions there that initiate coagulation. The model also considers that blood flow transports coagulation proteins and platelets to and from the vicinity of the injury and thus also has a strong regulatory impact. The second project involves a model of fibrin polymerization following conversion of plasma fibrinogen to fibrin monomers by thrombin. The model allows for both linear extension of fibrin protofibrils and the formation of branches in the growing protofibrils. The mechanisms of branching in real fibrin polymerization remain mysterious. The mechanism we propose in the model has the consequence that the structure of the resulting fibrin gel is sensitive to the concentration of thrombin in the way observed experimentally.