ISSN 2070-0482, Mathematical Models and Computer Simulations, 2016, Vol. 8, No. 1, pp. 54–62. © Pleiades Publishing, Ltd., 2016. Original Russian Text © E.A. Pogorelova, A.I. Lobanov, 2015, published in Matematicheskoe Modelirovanie, 2015, Vol. 27, No. 6, pp. 54–66. 54 1. INTRODUCTION The system of haemostasis keeps blood in a liquid state inside the vessels and stops blood flow in the event of damage. Haemostasis has two pathways has two links. The plasma pathway starts a cascade of fer- mentative reactions of blood plasma proteins [1]. The platelet pathway of homeostasis ensures that the platelets stick with each other and their adhesion to the damaged part of the vascular wall. The primary haemostatic closure is formed of an aggregated platelets. In this work, a model taking into account only the thrombocytic mechanism of blood clot formation is considered. The concentration of platelets is small—2–4 × 10 11 L –1 [2]—so the hypothesis of solidness is not sup- ported. The motion of platelets can be described by means of equations of the solid medium in case the analog of the Knudsen number is Kn < 10 –3 . In the considered statement of the problem Kn = 10 –2 (the estimation is given below). In [3, 4] the models of the platelet clot formation using a solid medium equa- tion are described. In order to use the equation of the diffusion type for describing platelets’ transport, it is necessary to introduce the diffusion matrix estimating the frequency of particle collisions [5]. In [3, 4] mathematical models are described of the formation of platelet clots, including the motion of viscous noncompressed fluid, the interaction of subpopulations of active and passive platelets among themselves and with an acti- vator (ADP or thrombin), as well as platelet adhesion to the vascular wall. In [4] the mechanical interac- tion of separate platelets and the occurrence of relations among platelets are described. 2. PROBLEM STATEMENT We consider a model of the formation of a platelet clot in the flow in an axisymmetric vessel, where the area of flow changes its shape because of the growing clot. In this work the mathematical model [6] is modified. Unlike [6], in this work the matrix of the shear-induced diffusion is filled, which agrees with the experimental valuations [7, 8]. The blood plasma is thought of as viscous incompressible fluid and its motion is described by Navier–Stokes equations. 2.1. Mathematical model of platelet transport in a shear flow. The platelet has the shape of an ellipsoid and the proportion of its semiaxes is ordinarily from 1 : 2 to 3 : 4; thus, for simplifying the mathematical model, it is possible for the platelet with the attached fluid to approach a spherical particle. We have con- sidered the transport of nondeformable spherical particles of radius a in the shear flow of viscous fluid. The particles are moving due to transport by the fluid flow and the shear-induced diffusion [5]. The shear- induced diffusion is a consequence of the hydrodynamic interaction of particles moving along different streamlines at different rates. In the absence of shear flow, the shear-induced diffusion is not observed [9]. Particle aggregation is not taken into account. Multiple collisions are ignored. Calculation of Platelet Clot Growth Based on Advection-Diffusion Equations E. A. Pogorelova and A. I. Lobanov Moscow Institute of Physics and Technology (State University), Moscow, Russia e-mail: pogorelova_lena@mail.ru, alexey@crec.mipt.ru Received June 5, 2014 Abstract—A numerical method for solving equations of a model for platelet transport in blood plasma flow and platelet clot formation is modified. The full matrix for shear-induced diffusion of the platelets is used. A comparison of a blood clot’s shapes corresponding to various lengths of vessel-wall damage is given. Keywords: shear-induced diffusion, platelets, blood clot, viscous fluid, advection-diffusion DOI: 10.1134/S2070048216010075