Analysis of Neural Clusters due to Deep Brain Stimulation Pulses

TL;DR

This paper investigates how deep brain stimulation influences neural clustering behavior, using simplified dynamical models to understand the effects of stimulation parameters and pulse variations on neural synchronization patterns.

Contribution

It introduces a novel approach to analyze neural clustering under DBS using one-dimensional circle maps and extends the analysis to complex pulse stimuli.

Findings

Clustering behavior depends on stimulation frequency and amplitude.

Simplified models effectively capture complex neural dynamics.

Alternating pulse stimuli offer new control over neural synchronization.

Abstract

Deep brain stimulation (DBS) is an established method for treating pathological conditions such as Parkinson's disease, dystonia, Tourette syndrome, and essential tremor. While the precise mechanisms which underly the effectiveness of DBS are not fully understood, theoretical studies of populations of neural oscillators stimulated by periodic pulses suggest that this may be related to clustering, in which subpopulations of the neurons are synchronized, but the subpopulations are desynchronized with respect to each other. The details of the clustering behavior depend on the frequency and amplitude of the stimulation in a complicated way. In the present study, we investigate how the number of clusters, their stability properties, and their basins of attraction can be understood in terms of one-dimensional maps defined on the circle. Moreover, we generalize this analysis to stimuli that consist of pulses with alternating properties, which provide additional degrees of freedom in the design of DBS stimuli. Our results illustrate how the complicated properties of clustering behavior for periodically forced neural oscillator populations can be understood in terms of a much simpler dynamical system.