Model of Blood Circulation in Human Lower Limbs
V. I. Penkovskii, N. K. Korsakova
Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia, 630090
Keywords: математическая модель, циркуляция крови, нижние конечности, гетерогенная среда, фильтрация, артерии, вены, капилляры, метод конечных элементов, mathematical model, blood circulation, lower limbs, heterogeneous medium, filtration, arteries, veins, capillaries, finite element method
Abstract
A mathematical model of blood circulation in human lower limbs is proposed. The model is based on the laws of motion (filtration) of a viscous fluid in a heterogeneous medium consisting of two or more interpenetrating continua. It is assumed that the blood system consists of a distribution network of comparatively large vessels (arterioles) connected to small capillaries and a similarly structured collection network of small capillaries united into larger veins. A system of parabolic differential equations is derived, for which a problem with no initial data is posed. A periodic (in time) solution of the system corresponding to harmonic oscillations defined by the cardiac rhythm is found. Analytical solutions for particular cases of problems following from the general model of blood circulation are obtained. Numerical calculations are performed, and a numerical solution is found for a one-dimensional problem with parameters similar to those corresponding to real conditions of blood circulation with allowance for the cross-sectional area of the muscular tissue of the lower limb.
|
