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Biophys J, October 2001, p. 1888-1896, Vol. 81, No. 4

Analytical Description of the Transmembrane Voltage Induced on Arbitrarily Oriented Ellipsoidal and Cylindrical Cells

Jan Gimsa* and Derk Wachnerdagger

 *Fachbereich Biologie, Biophysik, Universität Rostock, D-18051 Rostock, and  dagger Institut für Biologie, Humboldt-Universität Berlin, D-10115 Berlin, Germany

We present an analytical equation for the transmembrane voltage (Delta phi ) induced by a homogeneous AC field on arbitrarily oriented cells of the general ellipsoidal shape. The equation generalizes the Schwan equation for spherical cells and describes the dependence of Delta phi on field frequency, cell size and shape, membrane capacitance, conductivities of cytoplasm, membrane and external medium, the location of the membrane site under consideration, and on the orientation of the cell with respect to the field. The derivation is based on the fact that the cytoplasm and the Maxwellian equivalent body of the whole cell are both of a general ellipsoidal shape and must thus exhibit constant local fields. The constant fields allow for a relatively simple description of the potentials on the internal and external membrane sides, leading to Delta phi . For this, the properties of cytoplasm, membrane, and external medium have been introduced into a special, finite element model. We found that Delta phi can be unambiguously defined for non-spherical cells, provided that the membrane thickness is thin in comparison to the cell dimensions.

Biophys J, October 2001, p. 1888-1896, Vol. 81, No. 4
© 2001 by the Biophysical Society   0006-3495/01/10/1888/09  $2.00


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