Stability of the thin elastic shell model of the red blood cell

Fung and Tong have recently explained the sphering of red blood cells in hypotonic solution by showing that a thin-walled elastic membrane with the right extensional stiffness and surface tension distribution will swell into a sphere under internal pressure. In this report we investigate the stability of the spherical state of Fung and Tong's model by applying the static energy criterion, which requires a determination of the sign of the quadratic terms in the potential energy functional. It turns out that a spherical cell model with radius less than that of the equatorial radius of the original undeformed cell is indeed stable, if and only if the supposedly arbitrary elastic parameters in the model are restricted in their possble range of values.