Dynamics of Parkinsonian tremor during deep brain stimulation

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Abstract
The mechanism by which chronic, high frequency, electrical deep brain stimulation (HF-DBS) suppresses tremor in Parkinson’s disease is unknown. Rest tremor in subjects with Parkinson’s disease receiving HF-DBS was recorded continuously throughout switching the deep brain stimulator on (at an effective frequency) and off. These data suggest that the stimulation induces a qualitative change in the dynamics, called a Hopf bifurcation, so that the stable oscillations are destabilized. We hypothesize that the periodic stimulation modifies a parameter affecting the oscillation in a time dependent way and thereby induces a Hopf bifurcation. We explore this hypothesis using a schematic network model of an oscillator interacting with periodic stimulation. The mechanism of time-dependent change of a control parameter in the model captures two aspects of the dynamics observed in the data: (1) a gradual increase in tremor amplitude when the stimulation is switched off and a gradual decrease in tremor amplitude when the stimulation is switched on and (2) a time delay in the onset and offset of the oscillations. This mechanism is consistent with these rest tremor transition data and with the idea that HF–DBS acts via the gradual change of a network property.