E.V. Yatchenko
Post-graduate Student, A. Blagonravov’s Institute of Machines Science of the Russian Academy of Sciences (IMASH RAS) (Moscow)
E-mail: elenablv@yandex.ru
T.A. Rakcheeva
Ph.D. (Eng.), Associate Professor, Senior Research Scientist, A.Blagonravov’s Institute of Machines Science

In this paper we consider the problem of determining the main parameters of hemodynamics and visualizing the blood flow through the vessel in places of pathological changes using mathematical modeling. The calculations were performed on a real carotid vessel with pathological changes (aneurysm) obtained with images of magnetic resonance imaging. A two-way interaction method was implemented that connects the problems of solving the equations of hydrodynamics and the equations of an elastic continuous medium into one system of equations. The influence of blood flows on the wall shear stress was studied with the possible spasm of the leading vessel. The analysis of data showed that in the case of the narrowing of the lumen of the leading vessel the blood flow rate increases in the spasmodic area and in the aneurysm. Consequently in the area of the hit wave the wall shear stress increases, that increases the risk of rupture of the aneurysm. Also the geometry of the vessel without aneurysm was simulated to compare the effect of the pathological state on the blood flow and the distribution of pressure on the vessel walls. The obtained results demonstrate that a remote aneurysm promotes more even redistribution of blood pressure in the vessel and shear stress on the vessel wall. Modeling of geometry vessel makes it possible to imagine the processes occurring when blood passes through the vessels. Also the emerging changes that occur in the system of blood vessels in various anatomical pathologies. That makes possible to apply mathematical models based on the data of specific patients to assess the risks and choose the optimal treatment tactics. The issues while analyzing medical images are poor quality, noisy image, low resolution and low contrast. The main aim is to improve the visual quality of images using new algorithms. It is necessary to continue work on modeling processes in vessels and aneurysms, which is more approximate to the real conditions of hemodynamics. The connection of anatomical models and the possibilities of mathematical modeling will help in the study of changes in hemodynamics in a particular patient and can be used to develop various therapeutic measures.

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