Simulations of nerve signal propagation in axons

Abstract

PurposeIn the literature, soliton solutions of the Heimburg–Jackson model have been proposed by Drab et al. (2022), but for the considered models, i.e. Eq.(1) and Eq.(2), the existence of solitons, the dispersion analysis and the pseudospectral method have been studied (Engelbrecht et al., 2006, 2018, 2020; Tamm et al., 2017, 2022; Peets et al., 2013). Therefore, the gap should be filled by this work.Design/methodology/approachWhen nonlinear terms, dissipative terms and forcing terms are ignored, the system (Eq.(2)) reduces to a single, sixth-order partial differential equation (Tamm et al., 2022). In this work, our aim is to propose analytical solutions in the explicit form via ansatz-based method. Therefore, the parameter effects in wave profile will be proposed clearly in figures.FindingsWhile progress has been made in signal propagation in nerves, thanks to many experimental studies and theoretical predictions over the last two centuries, the results obtained in this study may answer new questions that arise.Originality/valueIn the literature, the existence of solitons, dispersion analysis and pseudospectral method have been investigated for the Heimburg-Jackson model (Engelbrecht et al., 2006, 2018, 2020; Tamm et al., 2017, 2022; Peets et al., 2013), and this study fills the gap in soliton solutions. Additionally, when nonlinear terms, dissipative term and forcing terms are ignored, the system (Eq.(2)) reduced to a single equation that is sixth-order partial differential equation (Tamm et al., 2022). In this work, our aim is to propose analytical solutions in the explicit form via ansatz-based method. Therefore, the parameter effects in wave profile will be proposed clearly in figures.