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Thromb Res. 1996 Dec 1;84(5):333-44.

A mathematical model for the spatio-temporal dynamics of intrinsic pathway of blood coagulation. II. Results.

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National Scientific Center for Hematology, Russian Academy of Medical Sciences, Moscow, Russia.


This paper continues our study (see Part I) where we modeled the spatio-temporal dynamics of the intrinsic pathway of blood coagulation. Here, we analyzed this model and showed that it describes the threshold behavior of coagulation. When activation is subthreshold (which produces not more than 0.07 nM factor XIa at saturating free calcium concentrations of 2 mM or higher), the concentration of generated thrombin remains below 0.01 nM. At the abovethreshold activation corresponding to factor XIa exceeding 0.07 nM, the concentration of thrombin explosively increases and then abruptly decreases. The peak concentration of thrombin reaches hundreds nM. With respect to free calcium concentration, the system also behaves in a threshold manner. For activation corresponding to 0.3 nM factor XIa, the threshold concentration of free calcium where the outburst of explosive thrombin generation occur is equal to 0.21 mM. The model simulations are in a good agreement with the experimentally recorded kinetics of thrombin generation at different concentrations of free calcium (1). Analysis of the spatial dynamics of coagulation showed that if activation exceeded the threshold level at a certain point, the concentration wave of thrombin arises and propagates at a high speed from the activation zone. The parameters of this wave depends mainly on the efficiency of the feedback loops. The feedback loops through the backbone factors of the intrinsic pathway (autoactivation of factor X or activation of factor XI by thrombin) has a potential for the unlimited propagation of the thrombin wave. With increasing activity of activated protein C (the effect equivalent to that of thrombomodulin), oscillating regimes arise in the model. The first thrombin wave is followed by several secondary running waves. The amplitudes of secondary waves increases to the periphery of the clot consolidating its surface layer.

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