Mathematical Modeling of Human Blood Clotting Formation

Abstract

Over the last two decades, mathematical modeling has become a popular tool in study of blood coagulation. This paper describes the coagulation pathway and presents a mathematical model for the generation of blood clot in human vasculature. Parameters of interest in this study include procoagulants and anticoagulants whose activity may be enhanced by various activator enzymes. The process of human blood clotting involves a complex interaction between these parameters and continuous time and state processes. In this work, we propose to model these highly inter-relational processes by a set of nonlinear chemical rate equations. We have modeled this process as a dynamical system, as chemical reaction of blood clot is similar to the Michaclis-Mcntcn kinetics. Simulation result reveals that for zero concentration of certain activators, blood clot can't embark and for positive concentration of those activators, the clot is formed. In our analytical model some particular anticoagulants are studied and their role in the clotting process is evaluated. Furthermore simulation results for low concentrations of APC, the active protein C, which acts as a anticoagulant, states formation of blood clot.