Numerical Analysis for Elucidation of Nonlinear Frictional Characteristics of a Deformed Erythrocyte Moving on a Plate in Medium Subject to Inclined Centrifugal Force

Complex interactions between blood cells, plasma proteins, and glycocalyx in the endothelial surface layer are crucial in microcirculation. To obtain measurement data of such interactions, we have previously performed experiments using an inclined centrifuge microscope, which revealed that the nonlinear velocity-friction characteristics of erythrocytes moving on an endothelia-cultured glass plate in medium under inclined centrifugal force are much larger than those on plain or material-coated glass plates. The purpose of this study was to elucidate the nonlinear frictional characteristics of an erythrocyte on plain or material-coated glass plates as the basis to clarify the interaction between the erythrocyte and the endothelial cells. We propose a model in which steady motion of the cell is realized as an equilibrium state of the force and moment due to inclined centrifugal force and hydrodynamic flow force acting on the cell. Other electrochemical effects on the surfaces of the erythrocyte and the plate are ignored for the sake of simplicity. Numerical analysis was performed for a three-dimensional flow of a mixture of plasma and saline around a rigid erythrocyte model of an undeformed biconcave shape and a deformed shape with a concave top surface and a flat bottom surface. A variety of conditions for the concentration of plasma in a medium, the velocity of the cell, and the minimum gap width and the angle of attack of the cell from the plate, were examined to obtain the equilibrium states. A simple flat plate model based on the lubrication theory was also examined to elucidate the physical meaning of the model. The equilibrium angle of attack was obtained only for the deformed cell model and was represented as a power function of the minimum gap width. A simple flat plate model qualitatively explains the power function relation of the frictional characteristics, but it cannot explain the equilibrium relation, confirming the computational result that the deformation of the cell is necessary for the equilibrium. The frictional characteristics obtained from the present computation qualitatively agree with those of former experiments, showing the validity of the proposed model.