Analysis of point mathematical models of blood coagulation by numerical methods

Mathematical modeling of blood coagulation is important for medical biophysics. We considered two mathematical models of the blood coagulation system (BCS). This models are ODE systems. The first model takes into account the role of activation reactions of blood coagulation factors on membranes and fibrin polymerization. The second model is reduced. The model describes a cascade of activation of blood coagulation factors, but does not take into account the process of fibrin polymerization. We used the one-step Rosenbrock’s method with complex coefficients (CROS) to solve the stiff ODE system. The method was realized on programming language C. In our work we considered the influence of factor XI and the release of factor V from platelets during their activation. Many parameters of mathematical models of blood coagulation are known with low accuracy (some of them - with an accuracy of several magnitude). Therefore, the task of analyzing the sensitivity of the BCS model to parameters occures. The analysis can be carried out in a variety of ways. 1) The system equations in variations is built and solved. Based on its solution, a dimensionless sensitivity function of concentrations to parameters was built. Based on this method, the sensitivity of the tenase complex to the numbers of sites and constants associated with the V factor were investigated. We tested the hypothesis that the composition of the lipid membrane has little effect on blood coagulation. A unified approach to the study of sensitivity by parameters and solving problems selection of the coefficients of the model on experimental data based on the solution of the system in variations was formulated. 2) We changed parameters one by one and monitor change in model calculations. The dependence of the lag period and endogenous thrombin potential on parameters, as well as on the initial concentrations of blood coagulation factors were investigated. The principal possibility of its research for the design of selective drugs is shown. There is a lack of factor VIII when a person has hemophilia A. Accordingly, the blood coagulates slowly or does not coagulates at all. A study of BCS for the post-infart state was carried out (at the same time, the concentration of factor XIa changes). Calculations are carried out at normal concentration of factor VIII and in case of its deficiency.