Analytical description of the transmembrane voltage induced on arbitrarilyoriented ellipsoidal and cylindrical cells

We present an analytical equation for the transmembrane voltage (Delta phi) induced by a homogeneous AC field on arbitrarily oriented cells of the gen eral ellipsoidal shape. The equation generalizes the Schwan equation for sp herical cells and describes the dependence of Delta phi on field frequency, cell size and shape, membrane capacitance, conductivities of cytoplasm, me mbrane and external medium, the location of the membrane site under conside ration, and on the orientation of the cell with respect to the field. The d erivation is based on the fact that the cytoplasm and the Maxwellian equiva lent body of the whole cell are both of a general ellipsoidal shape and mus t thus exhibit constant local fields. The constant fields allow for a relat ively simple description of the potentials on the internal and external mem brane sides, leading to Delta phi. For this, the properties of cytoplasm, m embrane, and external medium have been introduced into a special, finite el ement model. We found that AO can be unambiguously defined for non-spherica l cells, provided that the membrane thickness is thin in comparison to the cell dimensions.