Electromechanical coupling of waves in nerve fibres

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.

Temperature changes accompanying signal propagation in axons

“…The coupled system of model equations has been previously proposed by the authors for describing the nerve pulse (action potential (AP)) propagation including the accompanying mechanical effects (pressure wave (PW) and longitudinal density change in the lipide bi-layer (LW)) [4][5][6][7]14]. In this paper, the temperature effects which accompany the propagation of an AP in the axoplasm, are also described.…”

“…It is of great interest to formulate the mathematical basis for calculating the heat production or temperature changes given these experimental assumptions. In our earlier studies [4][5][6][7]14] a system of differential equations is derived in order to model the action potential (AP) and accompanying mechanical effects -pressure wave (PW) in axoplasm, longitudinal (LW) and transverse (TW) waves in the surrounding biomembrane. This system will here be enlarged by including the temperature (Θ) effects.…”

Thinking About the Nerve Impulse: The Prospects for the Development of a Comprehensive Account of Nerve Impulse Propagation

“…The idea behind the latter proposal, although not stated explicitly by the authors, seems to be that incorporating all relevant details about these manifestations and the processes underlying them enables the representation of the nerve impulse and its propagation in a complete and accurate way (something that could not be achieved by Hodgkin and Huxley (1952a) with their model). In this section, as an illustration , we will discuss a recently introduced general unifying model that is still in the process of development and refinement, the Engelbrecht model (Engelbrecht et al, 2016, 2018a,b). More specifically, we will answer the question whether this model can represent the nerve impulse and its propagation completely and accurately (without assuming that this is in fact the aim of the model).…”

“…The electrical pulse and the pressure wave together generate a mechanical wave in the neural membrane, which has a longitudinal and a transverse component. In its turn, the mechanical wave can influence the electrical pulse via mechanical activation; e.g., the opening of ion channels via mechanical input (Engelbrecht et al, 2016, 2018a,b).…”

On solutions of a Boussinesq-type equation with displacement-dependent nonlinearity: A soliton doublet

“…Most prominent nonelectrical effects are a mechanical wave (swelling) [16][17][18][19] and a pressure wave [20] that propagate along the nerve fibre together with the action potential. It is clear that for a complete understanding of nerve function, a model describing all processes in a joint framework is needed [21,22]. However, the models describing single waves should be well understood.…”