Mathematical modeling of the magnetic field near a narrow capillary at various hematocrit values
Abstract
Mathematical modeling of the magnetic field near a narrow capillary at various hematocrit values
Incoming article date: 10.06.2023When erythrocytes move along a narrow capillary, they take an asymmetric shape and roll along the capillary like a tractor caterpillar (tank - treading motion). The shape of the erythrocyte is approximated by a truncated cylinder and is uniquely determined by the diameter of the erythrocyte in the capillary, the volume and surface area of the erythrocyte. Other input parameters are the speed of the erythrocyte in the capillary, the frequency of rotation of the erythrocyte membrane, the charge of the erythrocyte, and the number of closed trajectories along which the charges move. It is assumed that the negative charges located on the membrane are equal in magnitude and distributed evenly over the membrane and move along closed trajectories together with the membrane. From the last parameters, you can find the number of charges on the erythrocyte membrane. According to the Biot-Savart-Laplace law, mobile charges generate a magnetic field in the surrounding space. Using computer calculations, the distributions of the magnetic field strength were obtained both near a single erythrocyte rolling along a narrow capillary, and near a capillary along which several erythrocytes move, at various values of hematocrit. The dependence of the maximum value of the magnetic field strength near the capillary on the hematocrit is found. In particular, it was shown that at a distance from the capillary equal to 8 capillary diameters, the maximum value of the magnetic field strength increases by a factor of 1.29–1.36 (depending on direction) with increasing hematocrit from 12.27% to 18.25%.
Keywords: mathematical model, magnetic field, charge, membrane, erythrocyte, capillary, hematocrit