Model Predictive Control for Closed-Loop Deep Brain Stimulation

This paper describes a model predictive control (MPC) algorithm for Deep Brain Stimulation (DBS) implants that are used to treat common movement disorders. DBS is currently used in clinical practice in open-loop with constant stimulation, which shortens the effective lifespan of the treatment and can lead to unpleasant side-effects. The goal of closed-loop control is to alleviate symptoms with minimal stimulation. The controller is based on a model of the amplitude of beta-band ($13-30 \mathrm{~Hz}$) oscillations of population-level neural activity at the site of the implant, which is a bio-marker related to the presence of symptoms of Parkinson’s Disease. We present a two-stage approach in which a dynamic model for bio-marker activity is identified from data after applying a linearizing transformation, followed by a regulation stage using the identified model together with a model of response to stimulation based on average patient data. A Kalman filter is used to estimate the state of both the stimulation response and the nominal beta activity. The controller is compared to thresholded on/off (bang-bang) and proportional-integral (PI) feedback controllers, which are the most advanced form of control tested in vivo to date. Simulations demonstrate reductions in control input for similar levels of tracking error.