Mechanical waves in myelinated axon wall

TL;DR

This paper develops a mathematical model to analyze mechanical wave propagation in myelinated axon walls, incorporating microstructured material mechanics, dispersion, and dissipation effects, supported by numerical simulations.

Contribution

It introduces a novel combined model for myelinated axon wall deformation, extending previous unmyelinated models with new wave equations and dispersion analysis.

Findings

Dispersion analysis explains group and phase velocities.

Dissipative effects influence wave behavior.

Numerical results show velocity and wave profile changes.

Abstract

The propagation of an action potential is accompanied by mechanical and thermal effects. Several mathematical models explain the deformation of the unmyelinated axon wall. In this paper, the deformation of the myelinated axon wall is studied. The mathematical model is inspired by the mechanics of microstructured materials. The model involves the improved Heimburg-Jackson equation together with another equation of wave motion that describes the process in the myelin sheath. The dispersion analysis of such a model explains the behaviour of group and phase velocities. In addition, it is shown how dissipative effects may influence the process. Numerical calculations demonstrate the changes in velocities and wave profiles in the myelinated axon wall.