Potentials induced by applied electrical fields in and around particles comprised of four dielectric layers

Knowledge of the electrical potentials within different compartments of a biological cell induced by applied alternating fields is needed for assessing the effects of electromagnetic radiation on cells, understanding electroporation and other electric field-induced effects, and deriving expressions for the complex permittivity of suspensions of cells. In the work presented in this paper, closed-form analytical expressions have been derived for the electrical potentials within different layers of an inhomogeneous particle consisting of four different dielectric layers and suspended in a homogeneous medium. Those expressions have been used to derive, for the case of a realistic model of a cell containing a large concentric organelle, expressions for the transmembrane potentials (at cell and organelle level) and electric fields within the cell compartments induced by applied fields. The results of the present theoretical model indicate points of departure between the present and previous theoretical models. The present theory also confirms the validity of the equivalence approach introduced by Irimajiri and co-workers for computing the complex permittivity for suspensions of multi-shelled particles. In addition, it shows that the electric field is amplified at the level of the cell and organelle membranes, but not within other cell compartments.