Electromechanical coupling of waves in nerve fibres

TL;DR

This paper develops a mathematical model coupling electrical, mechanical, and thermal waves in nerve fibers, demonstrating how action potentials can generate associated pressure and membrane waves through simplified differential equations.

Contribution

It introduces a coupled wave model in nerve fibers, linking electrical signals with mechanical and pressure waves, advancing understanding of electromechanical interactions in neural propagation.

Findings

Coupled waves (AP, PW, LW, TW) emerge from the model.

Coupling forces influence mechanical wave generation.

Simulation results support the feasibility of wave interactions.

Abstract

The propagation of an action potential (AP) in a nerve fibre is accompanied by mechanical and thermal effects. In this paper an attempt is made to build up a mathematical model which couples the AP with a possible pressure wave (PW) in the axoplasm and waves in the nerve fibre wall (longitudinal - LW and transverse - TW) made of a lipid bilayer (biomembrane). A system of differential equations includes the governing equations of single waves with coupling forces between them. The single equations are kept as simple as possible in order to carry out the proof of concept. An assumption based on earlier studies is made that the coupling forces depend on changes (the gradient, time derivative) of the voltage. In addition it is assumed that the transverse displacement of the biomembrane can be calculated from the gradient of the LW in the biomembrane. The computational simulation is focused to determining the influence of possible coupling forces on the emergence of mechanical waves from the AP. As a result, an ensemble of waves (AP, PW, LW, TW) emerges. The further experiments should verify assumptions about coupling forces. In the Appendix, the numerical scheme used for simulations, is presented.