Heterogeneity in deep brain stimulation gamma enhancement explained by bifurcations in neural dynamics

BackgroundOscillations underpin a large spectrum of brain function. Brain oscillations are altered by neuromodulation approaches including deep brain stimulation (DBS), but a mechanistic understanding of the brain oscillation - DBS interaction is missing. DBS is predominantly used in the treatment of Parkinsons disease. DBS can induce or alter pre-existing narrow frequency band gamma oscillations at half the stimulation frequency. Such half-harmonic responses have been interpreted as entrainment of endogenous oscillations by an exogenous oscillator with an associated Arnold tongue structure. However, half-harmonic responses are not exhibited by all patients. MethodsHere, a Wilson-Cowan model of subcortical neuronal populations is used to set out a broad theoretical framework explaining the heterogeneity of observed responses. ResultsIn the absence of stimulation, the model exhibited either damped oscillations or self-sustained oscillations, depending on parameter values. Off-stimulation behaviour determined observed stimulation response. When oscillations were strongly damped, the only observed response was a driven oscillation at the stimulation frequency. When off-stimulation oscillations were weakly damped, additional half-harmonic responses occurred for sufficiently large amplitude stimulation. When self-sustained oscillations were present they were entrained by the stimulation frequency leading to harmonic, half-harmonic and many other subharmonic responses. Varying stimulation amplitude highlighted hysteresis with the onset and offset of half-harmonic responses appearing at different thresholds. Such two-threshold systems present challenges for adaptive control systems. ConclusionsThis framework captures observed heterogeneity and will help guide future therapeutic practices and the development of adaptive neuromodulation techniques for more effective promotion of physiological rhythms and suppression of abnormal rhythms.