A Model for Blood Coagulation and Lysis Utilizing the Intrinsic and Extrinsic Pathways



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Blood is a complex mixture of formed cellular elements, proteins, and ions dissolved in a solution. It is a difficult fluid to model because it is a shear-thinning, viscoelastic fluid that stress- relaxes. In this study, a new mathematical model for whole blood is developed from a general equation for a fluid with a shear dependent viscosity. The model is then used as a backdrop for 28 different biochemical factors interacting to form a clot. The full intrinsic and extrinsic pathways are both used in the simulation; the inclusion of the full intrinsic pathway is something that had not been done prior to this work. The model is executed in one spatial direction in an infinite domain as well as within a rigid walled cylinder using a finite volume scheme. The rigid wall, similar to the new mathematical equation for blood, is an oversimplification of actual in-vitro conditions. The results of both simulations show the formation and dissolution of the clot. Sensitivity analysis is then performed in the finite domain model by adjusting the initial levels of factors Va and Xa. The results show that by increasing the initial level of one or both of these factors leads to the quicker formation of a clot.