Spatio-Temporal Dynamics of Blood coagulation and Pattern Formation: a Theoretical Approach

We have previously examined spatio-temporal dynamics of clot formation in vitro [Ataullakhanov et al., 2002]. Here we describe a mathematical model developed to analyze the obtained experimental results. This model is based on a modern view of the molecular pathways of blood coagulation. Most of the results, which led to this view, were obtained in the in vitro stirred systems and provided the main contribution to our knowledge of the molecular mechanisms of biochemical reactions of clotting [Walz et al., 1986; Fenton, 1988; Davie et al., 1991]. Such approach, however, cannot directly address the spatio-temporal aspects of clot growth and, as we will show below, the existing concept of blood clotting is therefore incomplete. We will also consider several hypothetical reactions, which when added to the coagulation pathways, allow to develop a more complete and balanced concept of blood clotting. Inclusion of these reactions into the model leads to accurate description of all spatio-temporal aspects of clotting, as well as of data obtained in the homogeneous systems. Clotting occurs when fibrinogen, an abundant plasma protein, is converted to fibrin in a proteolytic reaction catalyzed by thrombin. Fibrin polymerizes rapidly to form fabrics of the clot. The kinetics of clotting is largely defined by the kinetics of thrombin production and inactivation [Walz et al., 1986; Berliner, 1992; Colman et al., 1993]. Thrombin is the last enzyme in the cascade of proteolytic reactions, initiated in blood by the appearance of activators of clotting. The nature of these activators (tissue factor or a foreign surface) define the initial set of reactions — extrinsic or intrinsic pathway, both of which eventually lead to the generation of thrombin (Fig. 1) [Walz et al., 1986; Willems et al., 1991; Berliner, 1992; Colman et al., 1993; Lawson et al., 1994]. In the in vitro stirred systems the clotting is activated more strongly by the extrinsic pathway than the