Suppression of spontaneous oscillations in high-frequency stimulated neuron models

Abstract

We analyze the influence of high-frequency current stimulation on spontaneous neuronal activity and show that it may cause a death of spontaneous low-frequency oscillations. We demonstrate the universality of this effect for typical neuron models such as FitzHugh–Nagumo, Morris–Lecar, and Hodgkin–Huxley neurons as well as for the  normal form of the  supercritical Hopf bifurcation. Using a multiple scale method we separate the solutions of the neuron equations into slow and fast components and derive averaged equations for the slow components. The mechanism of suppression of neuronal activity is explained by an analysis of the bifurcations in the averaged equations governing the dynamics of the slow motion. Our results may contribute to the understanding of therapeutic effects of high-frequency deep brain stimulation, the golden standard for the treatment of medically refractory patients suffering from Parkinson’s disease. Furthermore, our study enables hypotheses concerning possible improvements of high-frequency deep brain stimulation.