Numerical analysis of DC-field-induced transmembrane potential of spheroidal cells in axisymmetric orientations

This paper presents the electrostatic analysis of direct-current and steady-state transmembrane potential of non-spherical biological cells. The purpose of this analysis is to clarify the influences of different cell geometries and conductivity of the extracellular medium on transmembrane potential. The cells are modeled as spherical or spheroidal and as having different ratios between the radii in different axial directions. The boundary element method, a numerical method, is applied to the calculation of the transmembrane potential. The calculations show that a decrease in the conductivity affects both magnitude and distribution of transmembrane potential. The cell membrane can be approximated as a perfect dielectric, provided that the conductivity of the extracellular medium is sufficiently high. For the same cell geometries, transmembrane potential is smaller for pairs of cells than for isolated cells, and this potential is more reduced at the contact poles than at the opposite poles. Either different axial lengths or different radii between the cells results in this disparity in transmembrane potential of the cell pair. However, the maximum potential of both cells approaches the same value and is located at the contact poles if the conductivity in the extracellular medium is very low.