Lumped Element Model of Spherical Cells Exposed to an External Electric Field

Abstract

A lumped element model for cells is proposed, giving an overview of the general electrical behavior (e.g., in terms of current distribution within different cell layers) of a cell exposed to an external electric field. The aim is to provide a model which is easily adaptable to different cell types and cell sizes such that it can be used in the frame of different studies where cells are exposed to electric fields, e.g., <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Tumor Treating Fields</i> , operating at frequencies around 200 kHz. Originating from the usual model of a spherical cell, an electric lumped element model is derived under consideration of the electric field distribution within a cell. Possible simplifications of the model are suggested, which are justified by consideration of electrical material properties. Lumped element parameters of the model are approximated with formulas containing only cell dimensional parameters and electrical material parameters. The lumped element model is validated on the basis of a glioblastoma cell model with two different nuclei sizes. The proposed lumped element model with the according formulas for the lumped element parameters is easily adaptable to different cell types and cell sizes. It leads to a sufficient approximation of the general electrical behavior of cells in terms of current distribution and general frequency behavior in frequency ranges up to several hundreds of megahertz. The model is an easy to handle electrical description of a biological cell.