From modelling to understanding: the signals in nerves

TL;DR

This paper reviews interdisciplinary studies on nerve signal propagation, proposing a mathematical model that integrates electrical, mechanical, and thermal effects, validated through simulations and aligned with experimental data.

Contribution

It introduces a comprehensive mathematical model for nerve signals that couples multiple physical phenomena, emphasizing interdisciplinary approaches and physical principles.

Findings

Model qualitatively matches experimental observations.

Generalization to myelinated axons improves measurement alignment.

Guidelines for complex electrophysiological modelling are proposed.

Abstract

This paper attempts to review our studies on the propagation of signals in nerves over the past decade. The need for interdisciplinary studies is stressed that helps to understand the physical mechanisms of coupling the electrical, mechanical, and thermal effects in nerves. Based on the analysis of structural properties of axons and possible mechanisms of interaction between different physical phenomena, a set of assumptions and hypotheses is formulated. As a proof of concept, a rather general mathematical model is presented for describing a wave ensemble in unmyelinated axons. This model is composed of several governing equations ("building blocks") which are coupled by forces describing the interaction between the effects. The numerical simulation using the dimensionless variables demonstrated a rather good qualitative match with experiments. The further generalisation of this model in physical units for the processes in myelinated axons permits a closer match to measurements. Based on modelling and in silico experiments, the guidelines for modelling such a complex electrophysiological process are formulated. These guidelines reflect the importance of following the physical principles in modelling together with interdisciplinary knowledge from continuum mechanics and mathematics.