Theory of feedback controlled brain stimulations for Parkinson’s disease

• We derive an effective model for the dynamics of the subthalamic nucleus.
• The phase diagram of the neural network activity is analysed.
• Tremor-related activity is ascribed to an instability in the network.
• We propose a stimulation protocol to avoid the unstable region, and hence tremor.

Limb tremor and other debilitating symptoms caused by the neurodegenerative Parkinson’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 electrical 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 understanding 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 propose 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 stimulation and we suggest future experiments that could further improve the feedback procedure.