A space-fractional cable equation for the propagation of action potentials in myelinated neurons

TL;DR

This paper introduces a space-fractional cable equation to model the propagation of action potentials in myelinated neurons, accounting for non-local effects influencing neural signal transmission.

Contribution

It proposes a novel space-fractional mathematical model for action potential propagation in myelinated neurons, incorporating non-local effects.

Findings

Non-local effects significantly influence membrane potential distribution.

Numerical simulations demonstrate the impact of fractional derivatives on signal propagation.

The model provides new insights into the complex biophysical processes in myelinated neurons.

Abstract

Myelinated neurons are characterized by the presence of myelin, a multilaminated wrapping around the axons formed by specialized neuroglial cells. Myelin acts as an electrical insulator and therefore, in myelinated neurons, the action potentials do not propagate within the axons but happen only at the nodes of Ranvier which are gaps in the axonal myelination. Recent advancements in brain science have shown that the shapes, timings, and propagation speeds of these so-called saltatory action potentials are controlled by various biochemical interactions among neurons, glial cells, and the extracellular space. Given the complexity of brain's structure and processes, the work hypothesis made in this paper is that non-local effects are involved in the optimal propagation of action potentials. A space-fractional cable equation for the action potentials propagation in myelinated neurons is proposed that involves spatial derivatives of fractional order. The effects of non-locality on the distribution of the membrane potential are investigated using numerical simulations.