Abstract / Summary
Objective: Oscillations in field potentials are associated with a large spectrum of brain function. These oscillations are altered by deep brain stimulation (DBS), but the mechanistic understanding of interactions between brain oscillations and DBS is incomplete. In people living with Parkinson's disease, DBS can alter pre-existing gamma oscillations or induce gamma oscillations, with a frequency at half the stimulation frequency in both cases. However, these half-harmonic responses, vary between patients. The objective of this work is to provide a dynamical-systems explanation for the heterogeneity in response to DBS. Approach: A Wilson-Cowan model of neuronal populations was used to provide a broad theoretical framework that explains the heterogeneity of observed responses. Main result: In the absence of stimulation and noise, the model exhibited either damped oscillations or self-sustained oscillations, depending on parameter values. Off-stimulation behaviour determined observed stimulation response. When oscillations in the gamma range were strongly-damped off-stimulation, the only observed stimulation response was a driven oscillation at the stimulation frequency. When oscillations were weakly-damped off-stimulation, stimulation resulted in either harmonic or half-harmonic responses. Half-harmonic responses only occurred for a band of frequencies around half the stimulation frequency and only for sufficiently large amplitude stimulation. When self-sustained oscillations were present off-stimulation, the self-sustained oscillations were entrained by the stimulation frequency and harmonic, half-harmonic and many other subharmonic responses emerged. Ramping stimulation amplitude up and down revealed hysteresis with the onset and offset of half-harmonic responses appearing at different amplitude thresholds. Addition of noise blurred distinctions between different states but the underlying dynamical structure was preserved. Significance: This framework captures the heterogeneity of DBS responses seen in patients and explains subharmonic phenomena which may otherwise be discarded as device artefacts. The observed hysteresis highlights challenges for adaptive control systems which rely on a one-to-one relationship between stimulation settings and stimulation outcome.