Mathematical modeling of thrombus growth in mesenteric vessels

Richardson's phenomenological mathematical model of the thrombi growth in microvessels is extended to describe the realistic features of the phenomenon. The main directions of the generalization of Richardson's model are: (1) the dependence of platelet activation time on the distance from the injured vessel wall; (2) the non-homogeneity of the platelet distribution in blood flow in the vicinity of the vessel wall; (3) the adequate choice of the phenomenological function describing the dependence of blood velocity on the thrombus size. The generalization of the model corresponds to the main experimental results and theoretical considerations concerning thrombus formation obtained in recent years. The extended model permits to achieve qualitative agreement between model and experimental data.