Adaptive Parameter Modulation of Deep Brain Stimulation Based on Improved Supervisory Algorithm

Abstract

Clinically deployed deep brain stimulation (DBS) for the treatment of Parkinson's disease operates in an open loop with fixed stimulation parameters, and this may result in high energy consumption and suboptimal therapy. The objective of this manuscript is to establish, through simulation in a computational model, a closed-loop control system that can automatically adjust the stimulation parameters to recover normal activity in model neurons. Exaggerated beta band activity is recognized as a hallmark of Parkinson's disease and beta band activity in model neurons of the globus pallidus internus (GPi) was used as the feedback signal to control DBS of the GPi. Traditional proportional controller and proportional-integral controller were not effective in eliminating the error between the target level of beta power and the beta power under Parkinsonian conditions. To overcome the difficulties in tuning the controller parameters and improve tracking performance in the case of changes in the plant, a supervisory control algorithm was implemented by introducing a Radial Basis Function (RBF) network to build the inverse model of the plant. Simulation results show the successful tracking of target beta power in the presence of changes in Parkinsonian state as well as during dynamic changes in the target level of beta power. Our computational study suggests the feasibility of the RBF network-driven supervisory control algorithm for real-time modulation of DBS parameters for the treatment of Parkinson's disease.

Keywords: Parkinson’s disease; RBF neural network; beta power; feedback signal; supervisory control algorithm.

FIGURE 1

Cortical-basal ganglia-thalamus network model. Gray blocks represent the collections of cortical (CTX) neurons and basal ganglia (BG) neurons, respectively. Model schematic shows connections within the network, where black lines denote inhibitory connections and orange lines denote excitatory connections. Here, the direct pathway (eCTX → dSTR → GPi → TH → eCTX), the indirect pathway (eCTX → idSTR → GPe → GPi → TH → eCTX) and the hyper-direct pathway (eCTX → STN → GPi → TH → eCTX) are depicted. As well, excitatory-inhibitory coupling exists between STN and GPe. Excitatory eCTX and inhibitory iCTX neurons also receive synaptic connections from each other. The numbers in parentheses on the arrows indicate the synaptic conductance (mS/cm²) and transmission delay (ms), respectively.

FIGURE 2

Block diagram of improved supervisory algorithm under the guidance of radial basis function (RBF) network. Stimulation signal u(t) is applied to GPi model neurons and the simulated beta power y(t) is obtained from LFP of the GPi. The stimulation signal u(t) is determined by the joint action of the P controller output u_p(t) and RBF network controller output u_rbf(t).

FIGURE 3

Transmembrane potential as a function of time of model neurons in STN, GPe, and GPi. The blue traces depict model neuron activity in the healthy condition while orange traces depict model neuron activity in the Parkinsonian condition.

FIGURE 4

Characterization of model neuron activity in healthy and Parkinsonian conditions. (A) Firing rates (mean ± standard error) for model STN, GPe, and GPi neurons in healthy (blue) and Parkinsonian (orange) conditions. Values are averaged across three runs for each nucleus. (B) Spike synchrony (mean ± standard error) for model STN, GPe, and GPi neurons under healthy (blue) and Parkinsonian (orange) conditions. All model neurons exhibit increases in spike synchrony in the Parkinsonian state as compared to the healthy state. (*** represented a significant difference, p < 0.001).

FIGURE 5

Local field potential (LFP) activity from model neurons in the GPi. In panels (A,B), blue trace depicts the LFP in the healthy state while the orange trace depicts the LFP in the Parkinsonian state. Panel (C) illustrates the power spectral density of the GPi LFP across 10 trails to quantify the corresponding oscillatory activity, where shaded error region represents standard errors. Panels (D,E) depict the band-pass filtered (13–30 Hz) LFP activity in the GPi.

FIGURE 6

Relationship between the deep brain stimulation pulse repetition frequency and the beta power in the LFP from the GPi (mean ± standard error for 50 trials).

FIGURE 7

Control effect of P controller with beta power as the feedback signal. Blue dotted lines represent the desired GPi beta power that recorded from healthy state, and orange traces represent feedback GPi beta power from the controlled state. Black solid lines denote the beginning of stimulation. (A) k_p = 0.01, (B) k_p = 0.1, (C) k_p = 1, (D) k_p = 10.

FIGURE 8

Control effect of PI controller with beta power as the feedback signal. Blue dotted lines represent the desired GPi beta power that recorded from healthy state, and orange traces represent feedback GPi beta power from the controlled state. Black solid lines denote the beginning of stimulation. (A) k_p = 0.1,k_i = 0.01, (B) k_p = 0.1,k_i = 0.5, (C) k_p = 0.1,k_i = 2, (D) k_p = 0.5,k_i = 0.01, (E) k_p = 0.5,k_i = 0.5, (F) k_p = 0.5,k_i = 2.

FIGURE 9

Feedback control using the RBF controller with beta power as the control signal (k_p = 0.1). Panel (A) depicts the dynamic process of the controller reducing beta power in the GPi, panel (B) shows the evolution of real-time updated weights of the RBF network, (C) plots the trend of P controller and RBF controller, respectively, (D) generates the DBS pulse repetition frequency. Panel (E) is the stimulation signal, a series of 0.3 ms duration 300μA/cm² amplitude pulses with the instantaneous frequency determined by the controller.

FIGURE 10

Robustness analysis of the RBF controller in the presence of dynamic changes in the Parkinsonian state (k_p = 0.1). (A) Dynamic change of Parkinsonian state is characterized by the parameter, pd. The RBF-controller modulated beta power during dynamic changes is depicted in the bottom panel. Panel (B) shows the evolution of real-time updated weights of the RBF network, (C) plots the trend of P controller and RBF controller, and (D) generates the DBS pulse repetition frequency. Here, the stimulation amplitude is set to 300μA/cm² and the pulse duration is set to 0.3 ms.

FIGURE 11

Robustness analysis of the RBF controller during dynamic changes in the reference beta power (k_p = 0.1). (A) Dynamic change of the reference beta power is characterized by the blue dotted line. The RBF-controller modulated beta power is depicted in the bottom panel. Panel (B) shows the evolution of real-time updated weights of the RBF network, (C) plots the trend of P controller and RBF controller, and (D) generates the DBS pulse repetition frequency. Here, the stimulation amplitude is set to 300μA/cm² and the pulse duration is set to 0.3 ms.