P237 Modelling of ensemble of signals in single axons
Tanel Peets*1, Kert Tamm1, Jüri Engelbrecht1,2
1Department of Cybernetics, Tallinn University of Technology, Tallinn, Estonia 2Estonian Academy of Sciences, Tallinn, Estonia
*Email: tanel.peets@taltech.ee
Introduction Since Hodgkin and Huxley’s classical works, it has become clear that nerve function is a richer phenomenon than just electrical action potentials (AP). Experimental observations demonstrate that electrical signals in nerve fibres are accompanied by mechanical and thermal effects[1,2,3]. These include the pressure wave (PW) in axoplasm, the longitudinal wave (LW) in biomembrane, the transverse displacement (TW) of a biomembrane and temperature changes (θ). The whole nerve signal is, therefore, an ensemble of primary waves accompanied by the secondary components. The primary components (AP, LW, PW) are characterised by corresponding velocities and the secondary components (TW, θ) are derived from the primary components and have no independent velocities on their own. Methods We present a coupled mathematical model [2] which unites the governing equations for the action potential, the pressure wave in the axoplasm and the longitudinal and the transverse waves in the surrounding biomembrane and corresponding temperature change into one system of equations. The electrical AP is the carrier of information and triggers all other processes. The main attention is on modelling effects accompanying the AP, therefore the AP itself is modelled by the simple FitzHugh-Nagumo model. Coupling effects are modelled by contact forces. The system of nonlinear partial differential equations is solved numerically making use of the pseudospectral method. Results As a proof of concept, a simple dimensionless model based on the description of physical effects is described involving all the components of the signal. The results obtained by the numerical simulation match qualitatively well with experimentally measured ones. Discussion
The model described in this contribution is an attempt to couple all the measurable effects of the signal propagation in nerves (axons) into a system. The attention is not on the detailed description of the AP but on possible accompanying mechanical and thermal effects and their coupling with each other. The governing equations for the elements of the ensemble stem from the laws of physics and form a consistent system. This is an interdisciplinary approach at the interface of physiology, physics, and mathematics[2].
Acknowledgements This research was supported by the Estonian Research Council (PRG 1227). Jüri Engelbrecht acknowledges the support from the Estonian Academy of Sciences. References [1]https://doi.org/10.1016/S0006-3495(89)82902-9 [2]https://doi.org/10.1007/978-3-030-75039-8 [3]https://doi.org/10.1073/pnas.192003911
