Mathematical model of erythrocyte in the capillary motion

Abstract

Practical medicine requires new research to better understand the processes of blood flow through the vascular system. In particular, the processes of blood movement in capillaries, when their diameter is smaller than the diameter of erythrocytes, are of interest. It is believed that the center of mass of the erythrocyte lies on the midline of the capillary. While in the arterioles, the erythrocyte releases nutrients, so its mass decreases. When moving in the venule, the mass of the erythrocyte increases because it receives spent substances from the tissue space. The vascular wall of the capillary and its midline are modeled using the equation of the parabola, which makes it possible to calculate within the specified limits the length of the wall and the midline. The movement of an erythrocyte is described by the Meshchersky equation for bodies with variable mass. The proposed article is devoted to the construction of static models of capillaries in the norm and a dynamic model of movement in the capillary of an erythrocyte with variable mass.