Clustered Desynchronization from High-Frequency Deep Brain Stimulation

While high-frequency deep brain stimulation is a well established treatment for Parkinson’s disease, its underlying mechanisms remain elusive. Here, we show that two competing hypotheses, desynchronization and entrainment in a population of model neurons, may not be mutually exclusive. We find that in a noisy group of phase oscillators, high frequency perturbations can separate the population into multiple clusters, each with a nearly identical proportion of the overall population. This phenomenon can be understood by studying maps of the underlying deterministic system and is guaranteed to be observed for small noise strengths. When we apply this framework to populations of Type I and Type II neurons, we observe clustered desynchronization at many pulsing frequencies.Author Summary: While high-frequency deep brain stimulation (DBS) is a decades old treatment for alleviating the motor symptoms Parkinsons disease, the way in which it alleviates these symptoms is not well understood. Making matters more complicated, some experimental results suggest that DBS works by making neurons fire more regularly, while other seemingly contradictory results suggest that DBS works by making neural firing patterns less synchronized. Here we present theoretical and numerical results with the potential to merge these competing hypotheses. For predictable DBS pulsing rates, in the presence of a small amount of noise, a population of neurons will split into distinct clusters, each containing a nearly identical proportion of the overall population. When we observe this clustering phenomenon, on a short time scale, neurons are entrained to high-frequency DBS pulsing, but on a long time scale, they desynchronize predictably.