Modeling and Simulation of Pathological Blood Coagulation Under the Consideration of Distinct Pathways for Prothrombin Activation
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The blood coagulation mechanism prevents blood loss in case of vascular injury, but excessive thrombosis may impede blood flow to vital organs or tissues. As an essential stage of the coagulation mechanism, prothrombin is activated to thrombin. Thrombin is then involved in the activation of blood platelets, the production of fibrin, and an amplification mechanism of coagulation. As recently shown, in equilibrium prothrombin exists in two forms: “closed” (~80%) and “open” (~20%). In this work, we present a mathematical model for the prediction of localized thrombus formation which covers the mechanisms of the human blood coagulation process as well as the impact of the changes in prothrombin open/close ratio on blood clotting upon prothrombin mutations and ligand binding. In particular, we discuss the incorporation of distinct pathways for thrombin activation. Hereby, a set of convection-diffusion-reaction (CDR) equations is coupled to the incompressible Navier-Stokes equations which are solved by using a stabilized space-time finite element method.
