Effect of high-frequency stimulation on nerve pulse propagation in the FitzHugh–Nagumo model

Abstract

We consider the FitzHugh-Nagumo model axon under action of a homogeneous high-frequency stimulation (HFS) current. Using a multiple scale method and a geometrical singular perturbation theory, we derive analytically the main characteristics of the traveling pulse. We show that the effect of HFS on the axon is determined by a parameter proportional to the ratio of the amplitude to the frequency of the stimulation current. When this parameter is increased, the pulse slows down and shrinks. At some threshold value, the pulse stops and its width becomes zero. The HFS prevents the pulse propagation when the parameter exceeds the threshold value. The analytical results are confirmed by numerical experiments performed with the original system of partial differential equations.

Pulse propagation and failure in the discrete FitzHugh-Nagumo model subject to high-frequency stimulation

“…In this case, the high-frequency term in Eq. (1a) can be eliminated via a two-scale expansion method [29] in a way similar to what has been done in our recent paper [10] for the continuous version of FHN equations. In the Appendix, however, we present an alternative approach based on the method of averaging [28].…”

“…(3a) and changes the excitability properties of the neuron (see Ref. [10] for details). We emphasize that the approximate solution (2) is valid only for large frequencies ω 1 since terms of accuracy of O(ω −1 ) are neglected.…”

“…Studding an excitable system under the action of external time-dependent perturbations is an actual problem of physics, neuroscience, physiology and medicine. Various periodic perturbations with periods comparable to the characteristic time scales of an excitable system [1][2][3][4][5][6], high-frequency (HF) perturbations [7][8][9][10], and a combination of low-and high-frequency perturbations [11,12] have been considered in the literature. In this paper we deal with the HF perturbations, which are of particular interest for the problems of neural control.…”

“…Recently, we exploited the FHN model to analyze the effect of a homogeneous HFS on nerve pulse propagation in a nonmyelinated axon [10]. We derived analytically the main characteristics of the traveling pulse and showed that with an increase of the amplitude of the HFS current the pulse slows down, shrinks, and disappears when the amplitude exceeds some threshold value.…”

Suppressing Activity of an Array of Coupled Fitzhugh-Nagumo Oscillators

“…In the recent papers [14,15] detailed investigations, both analytical and numerical, have been carried out towards understanding of the mechanism of the existing DBS therapy technique. We hope that search for alternative methods, in particular using experimental approach, can contribute to the problem of the treatment of the Parkinson disease.…”