Theoretical analyses of cellular transmembrane voltage in suspensions induced by high-frequency fields

A change of the transmembrane voltage is considered to cause biophysical and biochemical responses in cells. The present study focuses on the cellular transmembrane voltage (Δφ) induced by external fields. We detail analytical equations for the transmembrane voltage induced by external high-frequency (above the relaxation frequency of the cell membrane) fields on cells of a spherical shape in suspensions and layers. At direct current (DC) and low frequencies, the cell membrane was assumed to be non-conductive under physiologic conditions. However, with increasing frequency, the permittivity of the cytoplasm/extracellular medium and conductivity of the membrane must be accounted for. Our main work is to extend application of the analytical solution of Δφ to the high-frequency range. We first introduce the transmembrane voltage generated by DC and low-frequency exposures on a single cell. Then, we focus on cell suspensions exposed to high-frequency fields. Using the effective medium theory and the reasonable assumption, the approximate analytical solution of Δφ on cells in suspensions and layers can be derived. Phenomenological effective medium theory equations cannot be used to calculate the local electric field of cell suspensions, so we raised a possible solution based on the Bergman theory.