Mathematical modeling of the magnetic field of red blood cells in narrow capillaries

Abstract

The red blood cell (RBC) moves in a narrow capillary and asymmetric of its shape lead to tank-treading motion of the membrane. Electric charges on the RBC membrane generate a magnetic field in the surrounding space. A mathematical model imitating the motion of RBC through capillaries with a diameter less than 8 μm is developed in order to estimate the distribution of plasma pressure, plasma velocity and magnetic field strength in the vicinity of RBC. It is assumed that plasma flow between erythrocytes in the capillary satisfies the Poiseuille law, and in the gap between the capillary wall and the RBC membrane satisfies the Reynolds system of equations for the lubricating layer. Calculations made on a computer allow us to estimate the shape of the RBC, the speed of rotation of the RBC membrane, the plasma pressure, the plasma velocity and the magnetic field strength in the vicinity of the RBC. It is shown that the distribution of the magnetic field strength in the vicinity of the erythrocyte is non-uniform and depends on the capillary diameter, RBC speed, RBC charge, volume and surface area of RBC.