Erythrocyte in the Capillary — The Mathematical Model

Abstract

A mathematical model consisting in a system of partial differential equations solved by the method of finite differences has been developed to describe the motion of red blood cells through microvessels less than 8 micrometers in a diameter. The model implies simulation of a three-dimensional asymmetrical elastic red cell with a tanktreading flexible but inextensible membrane and lubrication theory is used to describe the flow of plasma between them and vessel walls. The computations allow the estimation of the shape of the red blood cells, their positions in the capillary tube, the frequency of the cell membrane rotation and the pressure gradient over an individual red cell. It is shown that the final result of the interplay of the assumed basic conditions is a reduction in hydrodynamic resistance.