Modeling the Coagulation Dynamics in Human Blood

Blood coagulation is an extremely complex biological process in which blood forms clots to prevent bleeding, following by their dissolution and the subsequent repair of the injured tissue. The process involves different interactions between the plasma, the vessel wall and platelets having a huge impact of the flowing blood on the thrombus growth regularization. The blood coagulation model we are working on consists of a system of reaction-advection-diffusion equations, describing the cascade of biochemical reactions, coupled with rheological models for the blood flow (Newtonian, shear-thinning and viscoelastic models). We introduce the effect of blood slip at the vessel wall emphasizing an extra supply of activated platelets to the clotting site. We expect that such contribution could be dominant, resulting in the acceleration of thrombin production and eventually of the whole clot progression. Such model will have the capacity to predict effects of specific perturbations in the hemostatic system that can’t be done by laboratory tests, and will assist in clinical diagnosis and therapies of blood coagulation diseases. A mathematical model and numerical results for thrombus development will be presented. The chain of biochemical reactions interacting with the platelets, resulting in a fibrin-platelets clot formation and the additional blood flow influence on thrombus development will be discussed.