Model-based optimized phase-deviation deep brain stimulation for Parkinson 's disease

Suppression of beta oscillations by delayed feedback in a cortex-basal ganglia-thalamus-pedunculopontine nucleus neural loop model

Excessive neural synchronization of neural populations in the beta (β) frequency range (12-35 Hz) is intimately related to the symptoms of hypokinesia in Parkinson's disease (PD). Studies have shown that delayed feedback stimulation strategies can interrupt excessive neural synchronization and effectively alleviate symptoms associated with PD dyskinesia. Work on optimizing delayed feedback algorithms continues to progress, yet it remains challenging to further improve the inhibitory effect with reduced energy expenditure. Therefore, we first established a neural mass model of the cortex-basal ganglia-thalamus-pedunculopontine nucleus (CBGTh-PPN) closed-loop system, which can reflect the internal properties of cortical and basal ganglia neurons and their intrinsic connections with thalamic and pedunculopontine nucleus neurons. Second, the inhibitory effects of three delayed feedback schemes based on the external globus pallidum (GPe) on β oscillations were investigated separately and compared with those based on the subthalamic nucleus (STN) only. Our results show that all four delayed feedback schemes achieve effective suppression of pathological β oscillations when using the linear delayed feedback algorithm. The comparison revealed that the three GPe-based delayed feedback stimulation strategies were able to have a greater range of oscillation suppression with reduced energy consumption, thus improving control performance effectively, suggesting that they may be more effective for the relief of Parkinson's motor symptoms in practical applications.

Stability and synchronization for complex-valued neural networks with stochastic parameters and mixed time delays

In this paper, a class of complex-valued neural networks (CVNNs) with stochastic parameters and mixed time delays are proposed. The random fluctuation of system parameters is considered in order to describe the implementation of CVNNs more practically. Mixed time delays including distributed delays and time-varying delays are also taken into account in order to reflect the influence of network loads and communication constraints. Firstly, the stability problem is investigated for the CVNNs. In virtue of Lyapunov stability theory, a sufficient condition is deduced to ensure that CVNNs are asymptotically stable in the mean square. Then, for an array of coupled identical CVNNs with stochastic parameters and mixed time delays, synchronization issue is investigated. A set of matrix inequalities are obtained by using Lyapunov stability theory and Kronecker product and if these matrix inequalities are feasible, the addressed CVNNs are synchronized. Finally, the effectiveness of the obtained theoretical results is demonstrated by two numerical examples.

Model-based quantitative optimization of deep brain stimulation and prediction of parkinson's states

Although the exact etiology of Parkinson's disease (PD) is still unknown, there are a variety of treatments available to alleviate its symptoms according to the development stage of PD. Deep brain stimulation (DBS), the most common surgical treatment for advanced PD, accurately locates and implants stimulating electrodes at specific targets in the brain to deliver high-frequency electrical stimulation that alters the excitability of the corresponding nuclei. However, for different patients and stages of PD development, there exists a choice of the optimal DBS protocol. In this paper, we propose a quantitative method (multi-dimensional feature indexes) to determine the stimulation pattern, stimulation parameters, and target of DBS from the perspective of the network model. On the other hand, based on this method, the development of PD can be predicted so that timely treatment can be given to patients. Simulation results show that, first, different network states can be distinguished by extracting features of the firing activity of neuronal populations within the basal ganglia network system. Secondly, the optimal DBS treatment can be selected by comparing the feature indexes vectors of the pre- and post-state of the network after the action of different modes of DBS. Lastly, the evolution of the network state from normal to pathological is simulated. The critical point of network state transitions is determined. These results provide a quantitative and qualitative method for determining the optimal regimen for DBS for PD, which is helpful for clinical practice.

Closing the loop of DBS using the beta oscillations in cortex

Cortical information has great importance to reflect the deep brain stimulation (DBS) effects for Parkinson's disease patients. Using cortical activities to feedback is an available closed-loop idea for DBS. Previous studies have demonstrated the pathological beta (12-35 Hz) cortical oscillations can be suppressed by appropriate DBS settings. Thus, here we propose to close the loop of DBS based on the beta oscillations in cortex. By modify the cortico-basal ganglia-thalamic neural loop model, more biologically realistic underlying the Parkinsonian phenomenon is approached. Stimulation results show the proposed closed-loop DBS strategy using cortical beta oscillation as feedback information has more profound roles in alleviating the pathological neural abnormality than the traditional open-loop DBS. Additionally, we compare the stimulation effects with subthalamic nucleus feedback strategy. It is shown that using cortical beta information as the feedback signals can further enlarge the control parameter space based on proportional-integral control structure with a lower energy expenditure. This work may pave the way to optimizing the DBS effects in a closed-loop arrangement.

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

Deep brain stimulation (DBS) has become an effective therapeutic solution for Parkinson’s disease (PD). Adaptive closed-loop DBS can be used to minimize stimulation-induced side effects by automatically determining the stimulation parameters based on the PD dynamics. In this paper, 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 a multi-input multi-output (MIMO) nonlinear first-order system with uncertainty and external disturbances. A class of fast and robust MIMO adaptive fuzzy terminal sliding mode control (AFTSMC) has been presented for control of membrane potential of thalamic neuron populations through continuous adaptive DBS current applied to the thalamus. A fuzzy logic system (FLS) is used to estimate the unknown nonlinear dynamics of the model, and the weights of FLS are adjusted online to guarantee the convergence of FLS parameters to optimal values. The simulation results show that the proposed AFTSMC not only significantly produces lower tracking errors in comparison with the classical adaptive fuzzy sliding mode control (AFSMC), but also makes more robust and reliable outputs. The results suggest that the proposed AFTSMC provides a more robust and smooth control input which is highly desirable for hardware design and implementation.

A review of computational modeling and deep brain stimulation: applications to Parkinson's disease

Biophysical computational models are complementary to experiments and theories, providing powerful tools for the study of neurological diseases. The focus of this review is the dynamic modeling and control strategies of Parkinson's disease (PD). In previous studies, the development of parkinsonian network dynamics modeling has made great progress. Modeling mainly focuses on the cortex-thalamus-basal ganglia (CTBG) circuit and its sub-circuits, which helps to explore the dynamic behavior of the parkinsonian network, such as synchronization. Deep brain stimulation (DBS) is an effective strategy for the treatment of PD. At present, many studies are based on the side effects of the DBS. However, the translation from modeling results to clinical disease mitigation therapy still faces huge challenges. Here, we introduce the progress of DBS improvement. Its specific purpose is to develop novel DBS treatment methods, optimize the treatment effect of DBS for each patient, and focus on the study in closed-loop DBS. Our goal is to review the inspiration and insights gained by combining the system theory with these computational models to analyze neurodynamics and optimize DBS treatment.