Closed-Loop Modulation of the Pathological Disorders of the Basal Ganglia Network

Deep brain stimulation and lag synchronization in a memristive two-neuron network

In the pursuit of potential treatments for neurological disorders and the alleviation of patient suffering, deep brain stimulation (DBS) has been utilized to intervene or investigate pathological neural activities. To explore the exact mechanism of how DBS works, a memristive two-neuron network considering DBS is newly proposed in this work. This network is implemented by coupling two-dimensional Morris-Lecar neuron models and using a memristor synaptic synapse to mimic synaptic plasticity. The complex bursting activities and dynamical effects are revealed numerically through dynamical analysis. By examining the synchronous behavior, the desynchronization mechanism of the memristor synapse is uncovered. The study demonstrates that synaptic connections lead to the appearance of time-lagged or asynchrony in completely synchronized firing activities. Additionally, the memristive two-neuron network is implemented in hardware based on FPGA, and experimental results confirm the abundant neuronal electrical activities and chaotic dynamical behaviors. This work offers insights into the potential mechanisms of DBS intervention in neural networks.

Predictive modeling of evoked intracranial EEG response to medial temporal lobe stimulation in patients with epilepsy

Despite promising advancements, closed-loop neurostimulation for drug-resistant epilepsy (DRE) still relies on manual tuning and produces variable outcomes, while automated predictable algorithms remain an aspiration. As a fundamental step towards addressing this gap, here we study predictive dynamical models of human intracranial EEG (iEEG) response under parametrically rich neurostimulation. Using data from n = 13 DRE patients, we find that stimulation-triggered switched-linear models with ~300 ms of causal historical dependence best explain evoked iEEG dynamics. These models are highly consistent across different stimulation amplitudes and frequencies, allowing for learning a generalizable model from abundant STIM OFF and limited STIM ON data. Further, evoked iEEG in nearly all subjects exhibited a distance-dependent pattern, whereby stimulation directly impacts the actuation site and nearby regions (≲ 20 mm), affects medium-distance regions (20 ~ 100 mm) through network interactions, and hardly reaches more distal areas (≳ 100 mm). Peak network interaction occurs at 60 ~ 80 mm from the stimulation site. Due to their predictive accuracy and mechanistic interpretability, these models hold significant potential for model-based seizure forecasting and closed-loop neurostimulation design.

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

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.

Nonlinear dynamical modeling of neural activity using volterra series with GA-enhanced particle swarm optimization algorithm

In order to improve the modeling performance of Volterra sequence for nonlinear neural activity, in this paper, a new optimization algorithm is proposed to identify Volterra sequence parameters. Algorithm combines the advantages of particle swarm optimization (PSO) and genetic algorithm (GA) improve the performance of the identification of nonlinear model parameters from rapidity and accuracy. In the modeling experiments of neural signal data generated by the neural computing model and clinical neural data set in this paper, the proposed algorithm shows its excellent potential in nonlinear neural activity modeling. Compared with PSO and GA, the algorithm can achieve less identification error, and better balance the convergence speed and identification error. Further, we explore the influence of algorithm parameters on identification efficiency, which provides possible guiding significance for parameter setting in practical application of the algorithm.

Closed-loop Modulation of the Self-regulating Brain: A Review on Approaches, Emerging Paradigms, and Experimental Designs

Closed-loop approaches, setups, and experimental designs have been applied within the field of neuroscience to enhance the understanding of basic neurophysiology principles (closed-loop neuroscience; CLNS) and to develop improved procedures for modulating brain circuits and networks for clinical purposes (closed-loop neuromodulation; CLNM). The contents of this review are thus arranged into the following sections. First, we describe basic research findings that have been made using CLNS. Next, we provide an overview of the application, rationale, and therapeutic aspects of CLNM for clinical purposes. Finally, we summarize methodological concerns and critics in clinical practice of neurofeedback and novel applications of closed-loop perspective and techniques to improve and optimize its experiments. Moreover, we outline the theoretical explanations and experimental ideas to test animal models of neurofeedback and discuss technical issues and challenges associated with implementing closed-loop systems. We hope this review is helpful for both basic neuroscientists and clinical/ translationally-oriented scientists interested in applying closed-loop methods to improve mental health and well-being.

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.

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

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.

Subspace-based predictive control of Parkinson's disease: A model-based study

Deep brain stimulation (DBS) of the Basal Ganglia (BG) is an effective treatment to suppress the symptoms of Parkinson's disease (PD). Using a closed-loop scheme in DBS can not only improve its therapeutic effects but it can also reduce its energy consumption and possible side effects. In this paper, a predictive closed loop control strategy is employed to suppress the PD in real-time. A linear multi-input multi-output (MIMO) state-delayed system is considered as a simplified model of the BG neuronal network relating the stimulation signals as inputs to the beta power of local field potentials as PD biomarkers. The effect of time delay in different areas of the BG is incorporated into this model and a real-time subspace-based identification is implemented to continuously model the state of the BG neuronal network and drive the predictive control strategy. Simulation results show that the proposed MIMO subspace based predictive controller can suppress PD symptoms more effectively and with less power consumption compared to the conventional open-loop DBS and a recently proposed single-input single-output closed loop controller.

Optimizing deep brain stimulation based on isostable amplitude in essential tremor patient models

OBJECTIVE

Deep brain stimulation is a treatment for medically refractory essential tremor. To improve the therapy, closed-loop approaches are designed to deliver stimulation according to the system's state, which is constantly monitored by recording a pathological signal associated with symptoms (e.g. brain signal or limb tremor). Since the space of possible closed-loop stimulation strategies is vast and cannot be fully explored experimentally, how to stimulate according to the state should be informed by modeling. A typical modeling goal is to design a stimulation strategy that aims to maximally reduce the Hilbert amplitude of the pathological signal in order to minimize symptoms. Isostables provide a notion of amplitude related to convergence time to the attractor, which can be beneficial in model-based control problems. However, how isostable and Hilbert amplitudes compare when optimizing the amplitude response to stimulation in models constrained by data is unknown.

APPROACH

We formulate a simple closed-loop stimulation strategy based on models previously fitted to phase-locked deep brain stimulation data from essential tremor patients. We compare the performance of this strategy in suppressing oscillatory power when based on Hilbert amplitude and when based on isostable amplitude. We also compare performance to phase-locked stimulation and open-loop high-frequency stimulation.

MAIN RESULTS

For our closed-loop phase space stimulation strategy, stimulation based on isostable amplitude is significantly more effective than stimulation based on Hilbert amplitude when amplitude field computation time is limited to minutes. Performance is similar when there are no constraints, however constraints on computation time are expected in clinical applications. Even when computation time is limited to minutes, closed-loop phase space stimulation based on isostable amplitude is advantageous compared to phase-locked stimulation, and is more efficient than high-frequency stimulation.

SIGNIFICANCE

Our results suggest a potential benefit to using isostable amplitude more broadly for model-based optimization of stimulation in neurological disorders.

Fractional order controllers increase the robustness of closed-loop deep brain stimulation systems

We studied the effects of using fractional order proportional, integral, and derivative (PID) controllers in a closed-loop mathematical model of deep brain stimulation. The objective of the controller was to dampen oscillations from a neural network model of Parkinson's disease. We varied intrinsic parameters, such as the gain of the controller, and extrinsic variables, such as the excitability of the network. We found that in most cases, fractional order components increased the robustness of the model multi-fold to changes in the gains of the controller. Similarly, the controller could be set to a fixed set of gains and remain stable to a much larger range, than for the classical PID case, of changes in synaptic weights that otherwise would cause oscillatory activity. The increase in robustness is a consequence of the properties of fractional order derivatives that provide an intrinsic memory trace of past activity, which works as a negative feedback system. Fractional order PID controllers could provide a platform to develop stand-alone closed-loop deep brain stimulation systems.

Model Predictive Control for Seizure Suppression Based on Nonlinear Auto-Regressive Moving-Average Volterra Model

This article investigates a closed-loop brain stimulation method based on model predictive control strategy to suppress epileptic seizures. A neural mass model (NMM), exhibiting the normal and various epileptic seizures by changing physiologically meaningful parameters, is used as a black-box model of the brain. Based on system identification, an auto-regressive moving-average Volterra model is established to reveal the relationship between stimulation and neuronal responses. Then, the model predictive control strategy is implemented based the Volterra model, which can generate an optimal stimulation waveform to eliminate epileptiform waves. The computational simulation results indicate the proposed closed-loop control strategy can optimize the stimulation waveform without particular knowledge of the physiological properties of the system. The robustness of the proposed control strategy to system disturbances makes it more appropriate for future clinical application.

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

This study presents a computational model of closed-loop control of deep brain stimulation (DBS) for Parkinson's disease (PD) to investigate clinically viable control schemes for suppressing pathological beta-band activity. Closed-loop DBS for PD has shown promising results in preliminary clinical studies and offers the potential to achieve better control of patient symptoms and side effects with lower power consumption than conventional open-loop DBS. However, extensive testing of algorithms in patients is difficult. The model presented provides a means to explore a range of control algorithms in silico and optimize control parameters before preclinical testing. The model incorporates (i) the extracellular DBS electric field, (ii) antidromic and orthodromic activation of STN afferent fibers, (iii) the LFP detected at non-stimulating contacts on the DBS electrode and (iv) temporal variation of network beta-band activity within the thalamo-cortico-basal ganglia loop. The performance of on-off and dual-threshold controllers for suppressing beta-band activity by modulating the DBS amplitude were first verified, showing levels of beta suppression and reductions in power consumption comparable with previous clinical studies. Proportional (P) and proportional-integral (PI) closed-loop controllers for amplitude and frequency modulation were then investigated. A simple tuning rule was derived for selecting effective PI controller parameters to target long duration beta bursts while respecting clinical constraints that limit the rate of change of stimulation parameters. Of the controllers tested, PI controllers displayed superior performance for regulating network beta-band activity whilst accounting for clinical considerations. Proportional controllers resulted in undesirable rapid fluctuations of the DBS parameters which may exceed clinically tolerable rate limits. Overall, the PI controller for modulating DBS frequency performed best, reducing the mean error by 83% compared to DBS off and the mean power consumed to 25% of that utilized by open-loop DBS. The network model presented captures sufficient physiological detail to act as a surrogate for preclinical testing of closed-loop DBS algorithms using a clinically accessible biomarker, providing a first step for deriving and testing novel, clinically suitable closed-loop DBS controllers.

Application of Reinforcement Learning to Deep Brain Stimulation in a Computational Model of Parkinson's Disease

Deep brain stimulation (DBS) has been proven to be an effective treatment to deal with the symptoms of Parkinson's disease (PD). Currently, the DBS is in an open-loop pattern with which the stimulation parameters remain constant regardless of fluctuations in the disease state, and adjustments of parameters rely mostly on trial and error of experienced clinicians. This could bring adverse effects to patients due to possible overstimulation. Thus closed-loop DBS of which stimulation parameters are automatically adjusted based on variations in the ongoing neurophysiological signals is desired. In this paper, we present a closed-loop DBS method based on reinforcement learning (RL) to regulate stimulation parameters based on a computational model. The network model consists of interconnected biophysically-based spiking neurons, and the PD state is described as distorted relay reliability of thalamus (TH). Results show that the RL-based closed-loop control strategy can effectively restore the distorted relay reliability of the TH but with less DBS energy expenditure.

Systems approaches to optimizing deep brain stimulation therapies in Parkinson's disease

Over the last 30 years, deep brain stimulation (DBS) has been used to treat chronic neurological diseases like dystonia, obsessive-compulsive disorders, essential tremor, Parkinson's disease, and more recently, dementias, depression, cognitive disorders, and epilepsy. Despite its wide use, DBS presents numerous challenges for both clinicians and engineers. One challenge is the design of novel, more efficient DBS therapies, which are hampered by the lack of complete understanding about the cellular mechanisms of therapeutic DBS. Another challenge is the existence of redundancy in clinical outcomes, that is, different DBS programs can result in similar clinical benefits but very little information (e.g., predictive models, longitudinal data, metrics, etc.) is available to select one program over another. Finally, there is high variability in patients' responses to DBS, which forces clinicians to carefully adjust the stimulation settings to each patient via lengthy programming sessions. Researchers in neural engineering and systems biology have been tackling these challenges over the past few years with the specific goal of developing novel DBS therapies, design methodologies, and computational tools that optimize the therapeutic effects of DBS in each patient. Furthermore, efforts are being made to automatically adapt the DBS treatment to the fluctuations of disease symptoms. A review of the quantitative approaches currently available for the treatment of Parkinson's disease is presented here with an emphasis on the contributions that systems theoretical approaches have provided to understand the global dynamics of complex neuronal circuits in the brain under DBS. This article is categorized under: Translational, Genomic, and Systems Medicine > Therapeutic Methods Analytical and Computational Methods > Computational Methods Analytical and Computational Methods > Dynamical Methods Physiology > Mammalian Physiology in Health and Disease.

Model and Analysis for the Onset of Parkinsonian Firing Patterns in a Simplified Basal Ganglia

Parkinson's disease (PD) is a degenerative neurological disease that disrupts the movement cycle in the basal ganglia. As the disease progresses, dopamine depletion leads to changes to how the basal ganglia functions as well as the appearance of abnormal beta oscillations. There is much debate on just exactly how these connection strengths change and just how the oscillations emerge. One leading hypothesis claims that the oscillations develop in the globus pallidus external, subthalamic nucleus, and globus pallidus internal loop. We introduce a mathematical model that calculates the average firing rates of this loop while still accounting for the larger closed loop of the entire basal ganglia system. This model is constructed such that physiologically realistic results can be obtained while not sacrificing the use of analytic methods. Because of this, it is possible to determine how the change in the connection strengths can drive the necessary changes in firing rates seen in recordings and account for the generation of trademark beta oscillations of PD without relying on highly specific time delays, stochastic approaches, or numerical approximations. Additionally, we find that the entire cortico-basal ganglia-thalamo-cortical loop is essential for abnormal oscillations to originate.

Modeling and Analysis of Beta Oscillations in the Basal Ganglia

Enhanced beta (12-30 Hz) oscillatory activity in the basal ganglia (BG) is a prominent feature of the Parkinsonian state in animal models and in patients with Parkinson's disease. Increased beta oscillations are associated with severe dopaminergic striatal depletion. However, the mechanisms underlying these pathological beta oscillations remain elusive. Inspired by the experimental observation that only subsets of neurons within each nucleus in the BG exhibit oscillatory activities, a computational model of the BG-thalamus neuronal network is proposed, which is characterized by subdivided nuclei within the BG. Using different currents externally applied to the neurons within a given nucleus, neurons behave according to one of the two subgroups, named "-N" and "-P," where "-N" and "-P" denote the normal and the Parkinsonian states, respectively. The ratio of "-P" to "-N" neurons indicates the degree of the Parkinsonian state. Simulation results show that if "-P" neurons have a high degree of connectivity in the subthalamic nucleus (STN), they will have a significant downstream effect on the generation of beta oscillations in the globus pallidus. Interestingly, however, the generation of beta oscillations in the STN is independent of the selection of the "-P" neurons in the external segment of the globus pallidus (GPe), despite the reciprocal structure between STN and GPe. This computational model may pave the way to revealing the mechanism of such pathological behaviors in a realistic way that can replicate experimental observations. The simulation results suggest that the STN is more suitable than GPe as a deep brain stimulation target.

Toward adaptive deep brain stimulation in Parkinson's disease: a review

Clinical deep brain stimulation (DBS) is now regarded as the therapeutic intervention of choice at the advanced stages of Parkinson's disease. However, some major challenges of DBS are stimulation induced side effects and limited pacemaker battery life. Side effects and shortening of pacemaker battery life are mainly as a result of continuous stimulation and poor stimulation focus. These drawbacks can be mitigated using adaptive DBS (aDBS) schemes. Side effects resulting from continuous stimulation can be reduced through adaptive control using closed-loop feedback, while those due to poor stimulation focus can be mitigated through spatial adaptation. Other advantages of aDBS include automatic, rather than manual, initial adjustment and programming, and long-term adjustments to maintain stimulation parameters with changes in patient's condition. Both result in improved efficacy. This review focuses on the major areas that are essential in driving technological advances for the various aDBS schemes. Their challenges, prospects and progress so far are analyzed. In addition, important advances and milestones in state-of-the-art aDBS schemes are highlighted – both for closed-loop adaption and spatial adaption. With perspectives and future potentials of DBS provided at the end.

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

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.