On the analytical description of transmembrane voltage induced on spheroidal cells with zero membrane conductance

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Abstract
We present analytical equations for the transmembrane voltage (ΔΦ) induced by a homogeneous field on oriented cells of spheroidal shape in spherical coordinates. For simplicity, a nonconductive membrane and a highly polarizable cytoplasm were assumed. Under these conditions, the cell's polarizability is determined by the nonconductive membrane. For symmetry reasons the surface of the highly polarizable cytoplasm can be assumed to be at 0 V. Since the cell is of ellipsoidal shape its effective local field, i.e. the field of its Maxwellian equivalent body, must be constant. This allows for a simple description of the potential at the external membrane side, directly leading to ΔΦ. The dependence of ΔΦ on cell size and shape as well as on the location of the considered membrane site is described for both possible orientations of the symmetry axis, parallel and perpendicular to the external field, respectively.

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