Nonlinear cable models for cells exposed to electric fields I. General theory and space-clamped solutions

Abstract

We develop a generalized cable model to study the response of cylindrical cells to external electric fields. A class of nonlinear cable models is then introduced by assuming quasielectrostatic conditions and modelling current flow through the membrane in terms of a voltage dependent conductivity and a Fitzhugh-Nagumo type recovery variable. For active cell membranes, we study a model based on cubic membrane nonlinearity, while in the case of passive membranes, a simple diode form is used for the conductivity and the recovery variable is taken to be zero. Space-clamped solutions to these models are then investigated in detail. For the diode model, modulated sinusoidal external fields are cons..