The biological vesicle elastohydrodynamic model of deformation of red blood cells in permeable microvessels

The purpose of this paper is to investigate the deformation of red blood cells (RBCs) in permeable microvessels by establishing the biological vesicle elastohydrodynamic model. Unlike the current deformation models of red blood cells (such as elastic shell model and liquid-drop model), a red blood cell is regarded as an axisymmetric biological vesicle in the liquid crystal state in this study. Elastohydrodynamic theory and the Starling assumptions are applied to explain the flow of suspending plasma in gaps between red blood cells and vessel walls and the coupling effect between plasma pressure and tissue fluid pressure in permeable microvessels. In addition, the calculation dealing with deformation shapes derives from the shooting method, in which the deformation shape of red blood cells is approximately a vesicle of stomatocyte in microvessels. Furthermore, the deformation quantity of red blood cells increases with increasing velocity of red blood cells or decreasing diameter of vessels. As for the comparisons, the biomembrane model possesses a smaller hematocrit ratio and a greater relative apparent viscosity calculated than the thin shell model at the same velocity of red blood cells; Fahraeus-Lindqvist effect predicted in the biomembrane model is more obvious than the thin shell model in a range of (0-8μm) vessel diameters.