A mathematical model of thrombin production in blood coagulation, Part I: The sparsely covered membrane case

This paper presents the first attempt to model the blood coagulation reactions in flowing blood. The model focuses on the common pathway and includes activation of factor X and prothrombin, including feedback activation of cofactors VIII and V by thrombin, and plasma inhibition of factor Xa and thrombin. In this paper, the first of two, the sparsely covered membrane (SCM) case is presented. This considers the limiting situation where platelet membrane binding sites are in excess, such that no membrane saturation or binding competition occurs. Under these conditions, the model predicts that the two positive feedback loops lead to multiple steady-state behavior in the range of intermediate mass transfer rates. It will be shown that this results in three parameter regions exhibiting very different thrombin production patterns. The model predicts the effect of flow on steady-state and dynamic thrombin production and attempts to explain the difference between venous and arterial thrombi. The reliance of thrombin production on precursor procoagulant protein concentrations is also assessed.