Nonlinear cable models for cells exposed to electric fields. I: General theory and space-clamped solutions. (English) Zbl 0967.35139
From the summary: 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.
MSC:
35Q60 | PDEs in connection with optics and electromagnetic theory |
78A70 | Biological applications of optics and electromagnetic theory |
92C20 | Neural biology |