Cellular forms: The tri-axial cell. I

Abstract

Without assuming a spheroidal shape for the cell, more general approximate deformation equations are derived which allow for non-uniformities in the external diffusion field and within the cell itself. It is found that in the absence of such non-uniformities, however, the only stable shapes are those in which the cell is spheroidal. Moreover, in conformity with previous results derived by somewhat different approximations, it is found that the spherical equilibrium is always stable and the approach monotonic unless, for a sufficiently large volume or a sufficiently high metabolic rate, there exist two non-spherical equilibria, one of prolate type and one of oblate type.