The quick machine--a mathematical model for the extrinsic activation of coagulation

The present paper describes a mathematical model of the kinetics of the extrinsic coagulation cascade in vitro. The coagulation factors FI, FII, FV, FVII, FX, heparin and antithrombin III (ATIII) as well as soluble fibrin polymers are considered. The effect of single-factor deficiencies of the factors II, V, VII and X, diseases like hypo- and dysfibrinogenaemia, hepatic insufficiency, inhibited polymerisation by degradation products, heparin therapy with and without ATIII deficiency and coumarin therapy on prothrombin time can be portrayed. Physiology of coagulation is represented in a dynamic mathematical model as a differential equation system. The model is based on three reaction types: enzymatic cleavage, complex formation and polymerisation. The model was implemented in a continuous simulation program on a personal computer using the Pascal programming language. Unknown rate constants were estimated by chi 2 fit. Prothrombin time calculated by the model was compared to the training set of 20 plasma samples. In most but not all cases the model harmonized quite well with the coagulometric data.