Modeling the effects of electric fields on nerve fibers: Determination of excitation thresholds

A method for predicting excitation of axons based on the response of passive models is proposed. An expression describing the transmembrane potential induced in passive models to an applied electric field is presented. Two terms drive the polarization of each node: a source term described by the activating function at the node, and an ohmic term resulting from redistribution of current from sources at other nodes. It is shown that a total equivalent driving function including both terms can be used to provide predictions of excitation thresholds for any applied field. The method requires only knowledge of the intracellular strength-duration relationship of the axon, the passive step response of the axon to an intracellular current, and the values of the extracellular potentials. Excitation thresholds for any given applied field can then be calculated using a simple algebraic expression. This method eliminates the errors associated with use of the activating function alone, and greatly reduces the computation required.