Analysis of Models for External Stimulation of Axons

Abstract

Extracellular electrodes produce electrical fields at the outside of nerve fibers. Discretization of the axon's length coordinate allows simulation of the excitation by a system of differential equations in time, and difference equations in space. For myelinated fibers this segmentation is naturally given by the nodes of Ranvier, whereas unmyelinated axons can be segmented arbitrarily. In both cases the equations are similar and can be treated in parallel. The activity of the axon depends on the second space derivative of the extracellular medium. The activating function is discussed for monopolar electrodes but the principle can be extended to arbitrary configurations of electrodes.