Model-Based Evaluation of Closed-Loop Deep Brain Stimulation Controller to Adapt to Dynamic Changes in Reference Signal

Abstract

High-frequency deep brain stimulation (DBS) of the subthalamic nucleus (STN) is effective in suppressing the motor symptoms of Parkinson's disease (PD). Current clinically-deployed DBS technology operates in an open-loop fashion, i.e., fixed parameter high-frequency stimulation is delivered continuously, invariant to the needs or status of the patient. This poses two major challenges: (1) depletion of the stimulator battery due to the energy demands of continuous high-frequency stimulation, (2) high-frequency stimulation-induced side-effects. Closed-loop deep brain stimulation (CL DBS) may be effective in suppressing parkinsonian symptoms with stimulation parameters that require less energy and evoke fewer side effects than open loop DBS. However, the design of CL DBS comes with several challenges including the selection of an appropriate biomarker reflecting the symptoms of PD, setting a suitable reference signal, and implementing a controller to adapt to dynamic changes in the reference signal. Dynamic changes in beta oscillatory activity occur during the course of voluntary movement, and thus there may be a performance advantage to tracking such dynamic activity. We addressed these challenges by studying the performance of a closed-loop controller using a biophysically-based network model of the basal ganglia. The model-based evaluation consisted of two parts: (1) we implemented a Proportional-Integral (PI) controller to compute optimal DBS frequencies based on the magnitude of a dynamic reference signal, the oscillatory power in the beta band (13–35 Hz) recorded from model globus pallidus internus (GPi) neurons. (2) We coupled a linear auto-regressive model based mapping function with the Routh-Hurwitz stability analysis method to compute the parameters of the PI controller to track dynamic changes in the reference signal. The simulation results demonstrated successful tracking of both constant and dynamic beta oscillatory activity by the PI controller, and the PI controller followed dynamic changes in the reference signal, something that cannot be accomplished by constant open-loop DBS.

Simulation of Closed-Loop Deep Brain Stimulation Control Schemes for Suppression of Pathological Beta Oscillations in Parkinson’s Disease

“…This approach, however, would require sampling multiple points in the parameter space which may not be practical clinically. An alternative controller design approach is to linearize the inputoutput relationship of the system using a model and subsequently design a controller which meets the required closed-loop system response (Santaniello et al, 2011;Liu et al, 2017a;Yang et al, 2018;Su et al, 2019). This approach was used by Santaniello et al (2011), Liu et al (2017a), and Su et al (2019) where autoregressive models were derived from spiking neuron models.…”

“…An alternative controller design approach is to linearize the inputoutput relationship of the system using a model and subsequently design a controller which meets the required closed-loop system response (Santaniello et al, 2011;Liu et al, 2017a;Yang et al, 2018;Su et al, 2019). This approach was used by Santaniello et al (2011), Liu et al (2017a), and Su et al (2019) where autoregressive models were derived from spiking neuron models. To normalize aberrant neural activity during parkinsonian tremor, Santaniello et al (2011) designed a minimum variance controller, while Liu et al (2017a) implemented a generalized predictive control algorithm.…”

“…To normalize aberrant neural activity during parkinsonian tremor, Santaniello et al (2011) designed a minimum variance controller, while Liu et al (2017a) implemented a generalized predictive control algorithm. In contrast, Su et al (2019) optimized the parameters of a discrete PI controller to track a dynamic target of betaband power which may be associated with fluctuations of the oscillatory activity during voluntary movement. Haddock et al (2017) illustrated the potential of the approach by deriving an autoregressive model of the relationship between DBS amplitude and parkinsonian tremor from patient data, using the identified model as part of a model predictive controller for parkinsonian tremor (Haddock et al, 2017).…”

“…However, only a small number of models have simulated the coupled DBS electric field and network model during stimulation (Santaniello et al, 2011;Grant and Lowery, 2013). In the absence of a description of the electric field in the surrounding tissue during DBS, modeling studies are limited to simulating frequency modulation where the DBS waveform is injected as an intracellular current (Kang and Lowery, 2013;Holt et al, 2016;Popovych and Tass, 2019;Su et al, 2019). To develop clinically relevant closed-loop algorithms requires a model which captures modulation of the targeted networks behavior due to variations in both stimulation amplitude and frequency.…”

“…Computational modeling provides an alternative approach for designing and testing more complex forms of closed-loop DBS control. Although computational models have been previously used to investigate closed-loop control strategies for DBS (Santaniello et al, 2011;Carron et al, 2013;Gorzelic et al, 2013;Grant and Lowery, 2013;Pasillas-Lepine et al, 2013;Haidar et al, 2016;Liu et al, 2017a;Popovych and Tass, 2019;Su et al, 2019), they typically do not relate well to clinically relevant parameters and, in particular, rarely incorporate both simulation of the LFP and extracellular application of DBS. Simulation of the LFP is desirable for developing computational models that can be readily translated to patients as LFP derived features, such as frequency and time domain features, are currently the most accessible biomarkers for closed-loop DBS in PD (Priori et al, 2013).…”