A Model for the Formation and Lysis of Blood Clots
Pathophysiology of Haemostasis and Thrombosis
characterized nearly 150 years ago by Virchow  as: (1) local fl ow stasis/stagnation, (2) blood vessel injury/endothelial dysfunction, and (3) hypercoagulability, an augmented intrinsic tendency for blood to clot. Clearly, the fi rst cause, local stasis or stagnation, is a consequence of hemodynamic conditions, while the latter two are primarily biochemically driven. However, these factors are interrelated. Clots form when a certain threshold dictated by hemodynamic and biochemical factors
... ochemical factors is reached, including the fl ow characteristics (stresses in the fl uid), concentrations of various ions, particularly Ca 2+ , availability of membrane binding sites, and local concentrations of platelets and coagulation factors. Under subthreshold conditions, blood fl ows in a normal manner, and when the threshold is reached, the balance is shifted towards promotion of coagulation, and in net, a cascade of reactions are set into motion, resulting in the initiation of coagulation. At the end of the hemostatic process, the normal subthreshold conditions are restored. However, pathological conditions may result in either impairment of clotting, thereby leading to bleeding disorders, or hypercoagulability, leading to thrombotic/thromboembolic disorders. These pathological conditions have their origins in both hemodynamic and biochemical factors associated with fl owing blood. Pro-and antithrombotic factors are simultaneously active. These balancing mechanisms serve to maintain blood in the fl uid, much less viscous than clot, phase under nomal conditions. Hemodynamic factors play a critical role in modulating biochemical reactions and have to Abstract Both biochemical and mechanical factors have to be taken into account if a meaningful model for the formation, growth, and lysis of clots in fl owing blood is to be developed. Most models that are currently in use neglect one or the other of these factors. We have previously reported a model [J Theoret Med 2003;5:183-218] that we believe is a step in this direction, incorporating many of the crucial biochemical and rheological factors that play a role in the formation, growth, and lysis of clots. While this model takes into account the extrinsic pathway of coagulation, it largely ignores the intrinsic pathway. Here, we discuss some of the general issues with respect to mathematical modeling of thrombus formation and lysis, as well as specifi c aspects of the model that we have developed.