Dynamics of Nerve Pulse Propagation in a Weakly Dissipative Myelinated Axon

Abstract

We analytically derived the complex Ginzburg-Landau equation from the Liénard form of the discrete FitzHugh Nagumo model by employing the multiple scale expansions in the semidiscrete approximation. The complex Ginzburg-Landau equation now governs the dynamics of a pulse propagation along a myelinated nerve fiber where the wave dispersion relation is used to explain the famous phenomena of propagation failure and saltatory conduction. Stability analysis of the pulse soliton solution that mimics the action potential fulfills the Benjamin-Feir criteria for plane wave solutions. Finally, results from our numerical simulations show that as the dissipation along the myelinated axon increases, the nerve impulse broadens and finally degenerates to front solutions.

Localized nonlinear waves in a myelinated nerve fiber with self-excitable membrane

“…In fact, this work is an extension of the one carried out in Ref. [4], with the exception that the membrane capacitance of the myelinated axon is now a polynomial function of transmembrane voltage. Hence this membrane is considered as a self-excitable organ with capacitive feedback parameter, α, used to modify the dynamics of the propagating modulated nerve impulses.…”

“…There is a growing interest in recent years to investigate the nonlinear processing of information in reaction-diffusion systems, with sharp focus on neural networks. [1][2][3][4][5][6] From a biophysical perspective, the knowledge of neural information propagation mechanism constitutes one of the most interesting scientific challenges in excitable media. Generally speaking, an excitable system is one in which an initial stimulus of sufficient amplitude initiates a traveling wave propagating through the medium.…”

“…The phenomenon of modulational instability, which is triggered by competitive effects of nonlinearity and dispersion in nonlinear systems, [17][18][19][20] is inextricably linked to the observation of soliton-like modes in neural networks. [1,4,5] Ever since the discovery of solitons by Fermi, Pasta, and Ulam, [17] enormous efforts have been made to elucidate on many complex phenomena in a plethora of nonlinear physical systems. This ranges from the propagation of femtosecond pulses in erbium doped fibers, [21] observation of first-order bright solitary waves in non-autonomous generalized AB system, [22,23] classification of solutions to the defocusing complex modified Korteweg-de Vries equation with the step-like initial condition, [24] among many others.…”

Investigation of bright and dark solitons in α, β-Fermi Pasta Ulam lattice

“…MI is responsible for many physically interesting effects such as the break-up of deep water-gravity waves in the ocean, the formation of bright solitons in optical fibers and nonlinear electrical transmission lines, [4,5] as well as the observation of localized nonlinear excitations in neural networks. [1][2][3] The plane-wave solution to the NLS Eq. ( 24) can be written in the general form…”

“…Nature provides many examples of coherent nonlinear structures and wave patterns. Among these beautiful nonlinear phenomena are localized large amplitude solitary waves called solitons, which have been observed in neural networks, [1][2][3] optical fiber systems, [4][5][6] and many other physical regimes. Solitons can propagate along one direction over long distances without spreading, and maintaining their form after collision.…”