A mathematical model for the spatio-temporal dynamics of intrinsic pathway of blood coagulation. I. The model description.

We developed and analyzed the mathematical model of the intrinsic pathway based on the current biochemical data on the kinetics of blood coagulation individual stages. The model includes eight differential equations describing the spatio-temporal dynamics of activation of factors XI, IX, X, II, I, VIII, V, and protein C. The assembly of tenase and prothrombinase complexes is considered as a function of calcium concentration. The spatial dynamics of coagulation was analyzed for the one-dimensional case. We examined the formation of active factors, their spreading, and growth of the clot from the site of injury in the direction perpendicular to the vessel wall, into the blood thickness. We assumed that the site of injury (in the model one boundary of the space segment under examination) becomes a source of the continuous influx of factor XIa. In the first part, we described the model, selected the parameters, etc. In the second part, we compared the model with experimental data obtained in the homogeneous system and analyzed the spatial dynamics of the clot growth.