Temperature changes accompanying signal propagation in axons

Abstract

In this paper mathematical models are formulated in order to simulate heat production and corresponding temperature changes which accompany the propagation of an axon potential. Based on earlier experimental results, several models are proposed. Together with the earlier system of coupled differential equations derived by the authors for describing the electrical and mechanical components of signalling in nerve fibres, the novel results permit to cast the whole process of signalling into one system. The emphasis is on the mathematical description of coupling forces. The numerical results are qualitatively similar to experiments.

Modelling of processes in nerve fibres at the interface of physiology and mathematics

“…The derivation of a suitable model for temperature Θ generation is more complicated because there is no widely accepted consensus about the mechanism of the heat generation. The simulations show [40] that there are several mathematical models that could match various experimental results. It seems, however, that a diffusion equation with a source term based on the conservation of energy, is best suited for modelling the temperature change accompanying the AP.…”

“…In addition it is assumed that the TW is derived from the LW like in mechanics of rods [37] the transverse displacement is a space derivative of the longitudinal displacement. Concerning the posssible temperature changes, there are several possibilities to build up a mathematical model [40].…”

“…The mathematical model in the dimensionless setting presented below has been elaborated and used for numerical simulations in earlier publications [16][17][18][19][20]40]. Here and further subindex X denotes partial derivative with respect to space and T denotes partial derivative with respect to time.…”

Shock and detonation waves at an interface and the collision of action potentials

“…In contrast, the debate around the acoustic nature of action potentials has predominantly relied on the reversibility of temperature pulse. While a valid argument, it leaves scope for ambiguity as critics have provided irreversible mechanisms to explain the observation (El Hady and Machta, 2015;Tamm et al, 2019). We can learn from how the acoustic foundation of the detonation phenomenon was historically established, and rephrase the present debate in terms of efficiency, or the ratio of irreversible/reversible heat observed during action potentials.…”

“…However, it is widely acknowledged that such a model doesn't explain a variety of observations made during an action potential, for example, the mechanical and thermal changes (Tasaki, 1982). There are two ways to address these inconsistencies, first is to try to refine the Hodgkin and Huxley model through additional equation to couple the mechanical and thermal changes with the electrical ones (El Hady and Machta, 2015;Tamm et al, 2019). The second is to come up with an entirely new description based on the first principles, i.e.…”