Multi-timescale neuromodulation strategy for closed-loop deep brain stimulation in Parkinson’s disease

Abstract Objective. Beta triggered closed–loop deep brain stimulation (DBS) shows great potential for improving the efficacy while reducing side effect for Parkinson’s disease. However, there remain great challenges due to the dynamics and stochasticity of neural activities. In this study, we aimed to tune the amplitude of beta oscillations with different time scales taking into account influence of inherent variations in the basal ganglia–thalamus–cortical circuit. 
Approach. A dynamic basal ganglia–thalamus–cortical mean–field model was established to emulate the medication rhythm. Then, a dynamic target model was designed to embody the multi-timescale dynamic of beta power with milliseconds, seconds and minutes. Moreover, we proposed a closed-loop DBS strategy based on a proportional–integral–differential (PID) controller with the dynamic control target. In addition, the bounds of stimulation amplitude increments and different parameters of the dynamic target were considered to meet the clinical constraints. The performance of the proposed closed-loop strategy, including beta power modulation accuracy, mean stimulation amplitude, and stimulation variation were calculated to determine the PID parameters and evaluate neuromodulation performance in the computational dynamic mean–field model. 
Main results. The Results show that the dynamic basal ganglia–thalamus–cortical mean–field model simulated the medication rhythm with the fasted and the slowest rate. The dynamic control target reflected the temporal variation in beta power from milliseconds to minutes. With the proposed closed-loop strategy, the beta power tracked the dynamic target with a smoother stimulation sequence compared with closed-loop DBS with the constant target. Furthermore, the beta power could be modulated to track the control target under different long-term targets, modulation strengths, and bounds of the stimulation increment.
Significance. This work provides a new method of closed–loop DBS for multi-timescale beta power modulation with clinical constraints.