Passive models of excitable cells

Excitable cells show a strongly nonlinear relationship between the transmembrane potential and the membrane current. In particular, after the membrane potential reaches threshold, the membrane potential follows a stereotyped wave shape called the action potential. Nevertheless, up to about 80% of the threshold level, the membrane potential and current can be described accurately using linear, or passive, models. In this chapter, we focus on the description of biological tissue as a target for electrical stimulation based on the passive properties of excitable cells. We first look at the relevant structure of the excitable cell with regard to electrical activation: the cell membrane, and the presence of ion channels. Then the resting potential is described and, finally, linear models for the response of excitable cells to intracellular and extracellular electrical stimuli are given for various kinds of cells.