Model of blood circulation in the cerebral cortex on the theory of fluid flow in heterogeneous medium

N. Korsakova, V. Penkovskij, A. Shilova, V. Shevchenko

Abstract: The mathematical model of the circulatory system in the cerebral cortex is formulated. The model is founded on the law of viscous fluid motion in the heterogeneous medium composed of two interpenetrating continua. The continua include the distribution network of vessels – two-scale system of relatively large blood-vessels (arteriolae) connected with the system of small capillaries – and similar in structure the collector network as system of small capillaries which change to system of venulae.
The system of differential equations of parabolic type is written, for which the problem without initial data is formulated. After simplifying the system, a periodic in time solution is determined. This solution is consistent with sinusoidal vibrations that the cardiac rate specifies. Some analytical solutions and numerical results of calculation are obtained for the domain of near-brain shape.

Series on Biomechanics, Vol.30, No.2 (2016), 24-31

Keywords: Arteries; blood pressure; capillaries; circulation; heterogeneous medium; mathematical modeling; veins

Date published: 2016-12-21