Theory of feedback controlled brain stimulations for Parkinson’s disease

Limb tremor and other debilitating symptoms caused by the neurodegenerative Parkin- son’s disease are currently treated by administering drugs and by fixed-frequency deep brain stimulation. The latter interferes directly with the brain dynamics by delivering elec- trical impulses to neurons in the subthalamic nucleus. While deep brain stimulation has shown therapeutic benefits in many instances, its mechanism is still unclear. Since its un- derstanding could lead to improved protocols of stimulation and feedback control, we have studied a mathematical model of the many-body neural network dynamics controlling the dynamics of the basal ganglia. On the basis of the results obtained from the model, we pro- pose a new procedure of active stimulation, that depends on the feedback of the network and that respects the constraints imposed by existing technology. We show by numerical simulations that the new protocol outperforms the standard ones for deep brain stimula- tion and we suggest future experiments that could further improve the feedback procedure.