P296 The modelling of the action potentials in myelinated nerve fibres K. Tamm 1*, T. Peets 1, J. Engelbrecht 1,2
1Tallinn University of Technology, Department of Cybernetics, Tallinn, Estonia 2Estonian Academy of Sciences, Tallinn, Estonia *kert.tamm@taltech.ee
Introduction. The classical Hodgkin-Huxley (HH) model [1] describes the propagation of an axon potential (AP) in unmyelinated axons. In many cases, the axons have a myelin sheath. A theoretical model is proposed describing the AP propagation in myelinated axons drawing inspiration from the studies of Lieberstein [2], who included the possible effect of inductance. The Lieberstein-inspired model (in the form of coupled partial differential equations (PDEs)) can describe all the essential effects characteristic to the formation and propagation of an AP in an unmyelinated axon. Then a phenomenological model for a myelinated axon is described including the influence of the structural properties of the myelin sheath and the radius of an axon.
Methods. The model equations are solved numerically by making use of the pseudospectral method (PSM) [3]. Briefly, the main point of PSM is that the discrete Fourier transform (DFT) can be used to approximate space derivatives reducing, therefore, the PDE to an ordinary differential equation (ODE) and then to use standard ODE solvers for integration in time. Here the ODE solver is used through its NumPy (a Python package) implementation. The parameters for the model are collected from experiments (most of them from the classical HH paper [1]) or estimated separately based on experimental observations.
Results. Using the parameters from the experiments we investigated the numerical solutions of the noted model for the unmyelinated axon and demonstrated that the behaviour of the solutions is in the physiologically plausible range and the key characteristics of the nervous signalling are fulfilled (annihilation of counter-propagating signals, threshold, refractory period). The model includes the structural properties of the myelin sheath: the μ-ratio (longitudinal geometry) and g-ratio (perpendicular geometry). The key difference between the classical HH model and the Lieberstein-inspired model used here is that the mechanism for signal propagation along the axon emerges like a wave as a consequence of opting to keep the inductivity.
Discussion. The goal of constructing yet another equation for describing the AP propagation along the axon is clearer physical interpretation as we start from the elementary form of Maxwell equations which is modified to include the influence of myelination on the signal propagating along the axon. It is important to stress that the proposed continuum-based model is philosophically similar to how the transmission line equations are composed. The ‘unit-cell’ in the context of the myelinated axon in the model is composed of the node of Ranvier and the myelinated section next to it. Having a pair of PDEs with a straightforward connection to underlying physics could be useful for investigating causal connections in the context of nerve signalling.
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/10.1113/jphysiol.1952.sp004764 [2] https://doi.org/10.1016/0025-5564(67)90026-0 [3] https://doi.org/10.1007/978-3-030-75039-8
