Two mathematical models of clot growth in the fluid flows have been considered. The first one is the model of embolus growth in a wall-adjacent flow. The effect of hydrodynamic flows on proceeding chemical reactions and the backward effect of the growing clot on the flow are taken into account. The growing thrombus is assumed to be porous and having low permeability, that is in good agreement with experimental data. The exact solutions determining the distribution of a fluid velocity close to the embolus have been used. Numerical analysis of these solutions have demonstrated that hydrodynamic flows can essentially affect the processes of blood coagulation, and consequently on the clot structure. Their presence might lead to the destruction of chemical fronts having a cylindrical symmetry and formation of the so-called chemical spots. The second model describes the initial stage of thrombus growing in the hemorrhage into a natural internal space. It permits accounting for vessel geometry and provides studying the effects of geometric parameters on fluid flows and coagulation processes. The process of thrombus growth is shown to depend on the ratio of typical values of blood velocity in the vessel and rate of chemical reactions.

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