A MATHEMATICAL-MODEL FOR THE SPATIOTEMPORAL DYNAMICS OF INTRINSIC PATHWAY OF BLOOD-COAGULATION .1. THE MODEL DESCRIPTION

We developed and analyzed the mathematical model of the intrinsic path way based on the current biochemical data on the kinetics of blood coa gulation individual stages. The model includes eight differential equa tions 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 concen tration. The spatial dynamics of coagulation was analyzed for the one- dimensional case. We examined the formation of active factors, their s preading, and growth of the clot from the site of injury in the direct ion perpendicular to the vessel wall, into the blood thickness. We ass umed that the site of injury (in the model one boundary of the space s egment under examination) becomes a source of the continuous influx of factor XIa. In the first part, we described the model, selected the p arameters, etc. In the second part, we compared the model with experim ental data obtained in the homogeneous system and analyzed the spatial dynamics of the clot growth. Copyright (C) 1996 Elsevier Science Ltd