Russ. J. Numer. Anal. Math. Modelling, Vol. 27, No. 2, pp. 191–212 (2012) DOI 10.1515/ rnam-2012-0011 c  de Gruyter 2012 Continuous mathematical model of platelet thrombus formation in blood flow A. TOKAREV ∗ , I. SIRAKOV † , G. PANASENKO † , V. VOLPERT ‡ , E. SHNOL § , A. BUTYLIN ∗¶ , and F. ATAULLAKHANOV ∗ ¶ ‖ Abstract — An injury of a blood vessel requires quick repairing of the wound in order to prevent a loss of blood. This is done by the hemostatic system. The key point of its work is the formation of an aggregate from special blood elements, namely, platelets. The construction of a mathematical model of the formation of a thrombocyte aggregate with an adequate representation of its physical, chemical, and biological processes is an extremely complicated problem. A large size of platelets compared to that of molecules, strong inhomogeneity of their distribution across the blood flow, high shear velocities, the moving boundary of the aggregate, the interdependence of its growth and the blood flux hamper the construction of closed mathematical models convenient for biologists. We propose a new PDE-based model of a thrombocyte aggregate formation. In this model, the movement of its boundary due to the adhesion and detachment of platelets is determined by the level set method. The model takes into account the distribution inhomogeneity of erythrocytes and platelets across the blood flow, the invertible adhesion of platelets, their activation, secretion, and aggregation. The calculation results are in accordance with the experimental data concerning the kinetics of the ADP-evoked growth of a thrombus in vivo for different flow velocities. The model constructed here can be easily extended to the case of other hemostatic mechanisms and can be integrated into different continuous blood flow models. The hemostasis is an evolutionary developed protection system minimizing blood loss in a rupture of the vascular system, i.e., in an injury of the wall of some blood vessel of an organism [12]. The central participants of the hemostasis system are platelets, which are the smallest form elements of the blood having the size about 1 μ m. These elements are comparatively few in number, but possess unique prop- erties. Platelets are instantly activated near the injured vascular wall and become capable of strong adhesion to the wall and to each other [31, 45, 52]. Due to this fact, the injured place quickly becomes pasted up with an aggregate of activated platelets, which prevents the loss of blood. The activated platelets produce solu- ∗ National Research Center for Hematology, Ministry of Health and Social Development of Russian Federation, Moscow 125167, Russia. Corresponding author (e-mail: alexey.tokarev@mail.ru). † University Jean Monnet, Saint-Etienne 42023, France ‡ Institute of Mathematics, University Lyon 1, Villeurbanne 69622, France § Institute of Mathematical Problems of Biology RAS, Pushchino 142290, Moscow Region, Russia ¶ Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow, Russia ‖ Center for Theoretical Problems of Physicochemical Pharmacology RAS, Moscow 119991, Rus- sia Brought to you by | University of Guelph (University of Guelph) Authenticated | 172.16.1.226 Download Date | 4/13/12 5:39 PM