On phenomenology of physical effects in axons

TL;DR

This paper explores phenomenological mathematical models of nerve signal propagation, integrating electrical, mechanical, and thermal effects to better reflect the complex reality of axonal activity.

Contribution

It introduces a phenomenological approach to modeling ion currents, temperature effects, and inductance in nerve fibers, enhancing the realism of existing models.

Findings

Incorporating phenomenological variables improves model accuracy.

Phenomenological inductance aids understanding of action potential propagation.

Models now better account for coupled electrical, mechanical, and thermal effects.

Abstract

This paper deals with the mathematical modelling of signal propagation in nerve fibres. Due to the complexity of the processes where electrical, mechanical, and thermal effects are coupled, a phenomenological approach helps to build mathematical models. The ideas of phenomenology are briefly presented, and their application is described. These applications cover the modelling of ion currents (the Hodgkin-Huxley model), temperature effects, and inductance. This means that the ion currents through the biomembrane, the influence of endo- and exothermic reactions on temperature, and the influence of energy in a non-electrical form are taken into account using phenomenological variables, i.e., observables. Such an approach brings the mathematical models closer to reality. Using the concept of phenomenological inductance helps us better understand the propagation of an action potential in myelinated axons. In principle, contemporary mathematical models describing the process in axons are hybrid in nature, combining physical laws with phenomenology, i.e., with observables.