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

We develop a generalized cable model to study the response of cylindrical c ells to external electric fields. A class of nonlinear cable models is then introduced by assuming quasielectroslatic 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 st udy a model based on cubic membrane nonlinearity, while in the case of pass ive membranes, a simple diode form is used for the conductivity and the rec overy 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 considered in order to study nonlinear phenomena such as harmonic generation and demodulation. For the cubic Fitzhugh-Nagumo type model, a variety of complex dynamical behaviour including phase locked lim it cycles, quasiperiodicity, intermittancy and chaos are observed for sinus oidal external fields. (C) 1999 Elsevier Science Ltd. All rights reserved.