Modelling the effect of ephaptic coupling on spike propagation in peripheral nerve fibres

Abstract

Experimental and theoretical studies have shown that ephaptic coupling leads to the synchronisation and slowing down of spikes propagating along the axons within peripheral nerve bundles. However, the main focus thus far has been on a small number of identical axons, whereas realistic peripheral nerve bundles contain numerous axons with different diameters. Here, we present a computationally efficient spike propagation model, which captures the essential features of propagating spikes and their ephaptic interaction, and facilitates the theoretical investigation of spike volleys in large, heterogeneous fibre bundles. The spike propagation model describes an action potential, or spike, by its position on the axon, and its velocity. The velocity is primarily defined by intrinsic features of the axons, such as diameter and myelination status, but it is also modulated by changes in the extracellular potential. These changes are due to transmembrane currents that occur during the generation of action potentials. The resulting change in the velocity is appropriately described by a linearised coupling function, which is calibrated with a biophysical model. We first lay out the theoretical basis to describe how the spike in an active axon changes the membrane potential of a passive axon. These insights are then incorporated into the spike propagation model, which is calibrated with a biophysically realistic model based on Hodgkin-Huxley dynamics. The fully calibrated model is then applied to fibre bundles with a large number of axons and different types of axon diameter distributions. One key insight of this study is that the heterogeneity of the axonal diameters has a dispersive effect, and that with increasing level of heterogeneity the ephaptic coupling strength has to increase to achieve full synchronisation between spikes. Another result of this study is that in the absence of full synchronisation, a subset of spikes on axons with similar diameter can form synchronised clusters. These findings may help interpret the results of noninvasive experiments on the electrophysiology of peripheral nerves.