# Mathematical modelling of blood flow in vascular system of the brain with pathological changes

### Abstract

The paper presents numerical study of blood flow in vascular system without stenosis and with pathological changes. The Navier – Stokes system of equation is used for modeling of liquid flow inblood vessels. The numerical algorithm was based on projection method. At first stage, it is assumed that the transfer of the movement of amount occurred is due to convection and diffusion. The intermediate regions of velocity are determined by using the 5-step Runge – Kutta method algorithm. At second stage the intermediate velocity field is used to define the pressure field. The Poisson equation for pressure field is solved by Jacobi method. The numerical results are checked by comparing analytical solutions for the Poiseuille flow with numerical results. The influence of the blood velocity flow on behavior of the liquid in vascular system of brain was investigated. One of the characteristic features of blood flow in blood vessels affected by stenosis is an appearance of vortex currents, which manifests as a pathology, as

opposite to normal blood circulation. The results of this work can be used in mathematical modeling

investigations of blood circulation in brain and solving problems in practical medicine.

Published

Jun 27, 2016

How to Cite

ISSAKHOV, A.; SHUBAY, A..
Mathematical modelling of blood flow in vascular system of the brain with pathological changes.

**International Journal of Mathematics and Physics**, [S.l.], v. 7, n. 1, p. 33-39, june 2016. ISSN 2409-5508. Available at: <http://ijmph.kaznu.kz/index.php/kaznu/article/view/157>. Date accessed: 24 oct. 2018.
Section

Informatics and Mathematical Modeling

### Keywords

Navier-Stokes equation, Poiseuille flow, atherosclerotic plaque, stenosis, pathological changes in the blood vessels