Mechanism of suppression of sustained neuronal spiking under high-frequency stimulation

Abstract

Using Hodgkin–Huxley and isolated subthalamic nucleus (STN) model neurons as examples, we show that electrical high-frequency stimulation (HFS) suppresses sustained neuronal spiking. The mechanism of suppression is explained on the basis of averaged equations derived from the original neuron equations in the limit of high frequencies. We show that for frequencies considerably greater than the reciprocal of the neuron’s characteristic time scale, the result of action of HFS is defined by the ratio between the amplitude and the frequency of the stimulating signal. The effect of suppression emerges due to a stabilization of the neuron’s resting state or due to a stabilization of a low-amplitude subthreshold oscillation of its membrane potential. Intriguingly, although we neglect synaptic dynamics, neural circuity as well as contribution of glial cells, the results obtained with the isolated high-frequency stimulated STN model neuron resemble the clinically observed relations between stimulation amplitude and stimulation frequency required to suppress Parkinsonian tremor.

Suppression of spontaneous oscillations in high-frequency stimulated neuron models

“…7. gumo and Morris-Lecar neurons as well as the fourdimensional Hodgkin-Huxley model. The generic nature of this effect is further substantiated by our previous findings in isolated subthalamic nucleus model neurons [27]. This phenomenon is common not only for neuronal systems, but it is typical for any self-sustained oscillator.…”

“…Based on the results obtained in our simple model presented here and in our previous study [27] we may expect high-frequency stimulation to effectively suppress low-frequency oscillations, such as theta and beta band LFP oscillations, and to induce high-frequency oscillations (in the range of the stimulation frequency) of the membrane potential. The functional role of these high-frequency, stimulus-induced oscillations in a neuronal network still remains to be investigated.…”

“…The effect is common for different neuron models and can be explained in terms of the stabilization of the neuron resting state, similar to the stabilization of the upsidedown position of a rigid pendulum with a vibrating pivot. In a previous study we have applied a similar vibrational mechanics based approach to investigate the high-frequency stimulation-induced suppression of sustained neuronal spiking in Hodgkin-Huxley and isolated subthalamic nucleus model neurons [27].…”

Stabilization of a Network of the FitzHugh–Nagumo Oscillators by Means of a Single Capacitor Based RC Filter Feedback Technique

“…Unfortunately, the DBS treatment is often accompanied with undesirable side effects. In recent papers [41][42][43], it has been demonstrated that the high frequency forcing eventually stabilizes the UFP of the neuronal oscillators in case of HH, FHN, and other neuronal models. Two shortcomings of the DBS have been emphasized [43].…”

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.…”