An approximation to red blood cells with a model of three-center-combined shells

Red blood cells present a biconcave shape and bear an inner pressure (osmotic pressure) when they are in the static state. In this paper, a model of “three-center-combined shells”, which consists of two spherical shells and a toroidal shell, is employed to describe the geometric shape of red blood cells. Surface area and volume of the combined shells model are very close to those measured from experiment. The stress distribution in the cell membrane is formulized as a closed form according to the Novozhilov's theory of the three-center-combined shells. Calculating results in terms of Novozhilov's formula give a good agreement with the numerical results given by ABAQUS when using actual measurements. It is concluded that the combined shells model can well approximate to the biconcave structure of red blood cells. In addition, stress calculation shows that the membrane of biconcave red blood cells can carry bending moments, and the moments reach a maximum value in the vicinity of joint line of the spherical shell and the toroidal shell in the combined shells model.