Modulation of Parkinsonian State With Uncertain Disturbance Based on Sliding Mode Control

Abstract

Parkinson's disease (PD) is a degenerative disorder of central nervous system that endangers the olds' health seriously. The motor symptoms of PD can be attributed to the distorted relay reliability of thalamus to cortical sensorimotor input that results from the increase of inhibitory input from internal segment of the globus pallidum (GPi). Based on this, we construct the GPi-thalamocortical computational model to generate the normal and pathological firing patterns by varying GPi spike train input. A kind of closed-loop deep brain stimulation (DBS) strategy is proposed here. Our control objective is to make the controlled membrane potential of the thalamic neuron return to the normal firing pattern. The control input that directly acts on the thalamus is the DBS waveform, which is adjusted in real time according to the feedback signal. Aimed at a certain system without the change of object parameters or stochastic disturbance, the input-output feedback linearization method is able to eliminate the error between the system output and the desired output. When uncertain elements taken into consideration in the system, the simulation results indicate that sliding mode control scheme provides better effectiveness and higher robustness.

Robust multi-input multi-output adaptive fuzzy terminal sliding mode control of deep brain stimulation in Parkinson’s disease: a simulation study

“…In the current paper, a class of fast and robust MIMO control scheme based on AFTSMC has been presented for control of membrane potential of thalamic neuron populations in the BG–thalamic network model through continuous adaptive DBS pulses. In the previous work 6 , a robust SMC was proposed for modulation of Parkinsonian state with uncertain disturbance. A property of the classical SMC is the convergence of the tracking error to the origin in an infinite time.…”

“…A property of the classical SMC is the convergence of the tracking error to the origin in an infinite time. Moreover, in the previous work 6 , to design the control input the membrane potential of the thalamic neuron being controlled should be assumed known. In the current study, to resolve the limitation of globally asymptotic stabilization of classical SMC and speed up the convergence time in both reaching and sliding phases of the motion, an AFTSMC control has been proposed to guarantee the global stability of the closed-loop system with the fast speed.…”

“…Sliding mode control (SMC) is a robust and powerful control technique to handle the nonlinear uncertain system in the presence of bounded external disturbances 22 – 24 . Zhu et al proposed a robust control technique based on SMC for control of membrane potential of a thalamic neuron in a thalamocortical computational model of BG network consisting of STN, GPe, internal segment of the globus pallidum (GPi), and TH 6 . The control objective was to design a DBS waveform to force the membrane potential of the thalamic neuron to track the normal firing pattern in real-time in a closed-loop manner using the feedback signal.…”

“…The proposed controller generates an adaptive control signal (stimulation current applied to the TH) automatically to force the firing patterns of the Parkinsonian state to track the normal firing patterns. The main innovations of the work are as follows: In 6 , the problem of robust control of a single thalamic neuron with uncertain external disturbance has been addressed. In contrast, in the current study, by modeling the interaction between the neurons in populations of the thalamic, the network-level modulation of thalamic is represented in a standard canonical form as the multi-input multi-output (MIMO) nonlinear first-order system with uncertainty and external disturbances.…”

“…In 6 , the problem of robust control of a single thalamic neuron with uncertain external disturbance has been addressed. In contrast, in the current study, by modeling the interaction between the neurons in populations of the thalamic, the network-level modulation of thalamic is represented in a standard canonical form as the multi-input multi-output (MIMO) nonlinear first-order system with uncertainty and external disturbances.…”