The red cell shape from discocyte to hypotonic spherocyte—A mathematical delineation based on a uniform shell hypothesis

Mathematical modeling was used to test two assumptions regarding red cell shape. The assumptions are that the elastic moduli of the red cell membrane are uniformly distributed throughout the membrane shell and that the biconcave shape results primarily from minimization of strain energy when this uniform shell is partially deflated. This strain energy is assumed to arise from bending (involving surface area strain) and shear (involving superficial tensile strain). The mathematical delineation demonstrated that it was impossible to produce a smooth symmetrical biconcave shape by minimizing shear energy in a partially deflated shell. It was possible to generate a symmetrical biconcave shape by minimizing bending energy; the shape was, however, thicker along the axis of symmetry than the measured red cell shape. A combination of bending and shear in the ratio of 6 to 1 produced a shape which matched the measured shape of a red cell to better than 1%, a deviation of the order of the thickness of the red cell membrane. The success of the mathematical model provides very strong evidence for the uniform shell-minimum bending energy hypothesis as the primary determinant of the discoid red cell shape.