Mathematical modeling of the magnetic field distribution in the vicinity of the erythrocyte
Abstract
Mathematical modeling of the magnetic field distribution in the vicinity of the erythrocyte
Incoming article date: 06.04.2018Erythrocyte, when moving through a narrow capillary, stretches out and rolls like a tractor's caterpillar. Charges located on the surface of the erythrocyte, move together with the membrane and generate a magnetic field in the vicinity of the erythrocyte membrane, which can affect both elements of blood flow outside the erythrocyte, and its contents, in particular, the iron atoms that make up the hemoglobin. A three-dimensional model of the erythrocyte is constructed. The shape of the erythrocyte is approximated by a truncated cylinder of radius r with generators L1 and L2. It is assumed that all charges on the surface of the erythrocyte are the same and evenly distributed over the surface of the erythrocyte. Charges move along with the membrane along closed curves (trapezoids). Moving charge creates a magnetic field, the strength of which depends on the magnitude and speed of the charge. On the erythrocyte membrane there are several charges and each of them at some selected point creates a magnetic field. The total strength of the magnetic field is defined as the vector sum of the strains created by each of the charges. The following parameter values were used in the calculations. The charge of the erythrocyte is 20 million elementary charges. The number of charges on the erythrocyte membrane is 38594. The rotation frequency of the erythrocyte membrane is 20 revolutions per second. The erythrocyte radius is 2 μm. The erythrocyte volume is 94 μm3. The erythrocyte surface area is 135 μm2, the lengths of the truncated cylinder forming are 3.4 μm and 11.5 μm. The erythrocyte speed is 100 μm / sec. The step along the space is 0.1 μm. The performed calculations of the magnetic field strength H have shown that the rotation of the erythrocyte membrane with the charges placed on it leads to a significant redistribution of the magnetic field in the vicinity of the erythrocyte. And with an increase in the frequency of rotation of the erythrocyte membrane, the heterogeneity of H increases significantly and can lead to a change in hemodynamics in the microcirculation system.
Keywords: mathematical model, erythrocyte, narrow capillary, magnetic field, microcirculation