Model-Based Evaluation of Closed-Loop Deep Brain Stimulation Controller to Adapt to Dynamic Changes in Reference Signal

Robust adaptive deep brain stimulation control of in-silico non-stationary Parkinsonian neural oscillatory dynamics

Objective. Closed-loop deep brain stimulation (DBS) is a promising therapy for Parkinson's disease (PD) that works by adjusting DBS patterns in real time from the guidance of feedback neural activity. Current closed-loop DBS mainly uses threshold-crossing on-off controllers or linear time-invariant (LTI) controllers to regulate the basal ganglia (BG) Parkinsonian beta band oscillation power. However, the critical cortex-BG-thalamus network dynamics underlying PD are nonlinear, non-stationary, and noisy, hindering accurate and robust control of Parkinsonian neural oscillatory dynamics.Approach. Here, we develop a new robust adaptive closed-loop DBS method for regulating the Parkinsonian beta oscillatory dynamics of the cortex-BG-thalamus network. We first build an adaptive state-space model to quantify the dynamic, nonlinear, and non-stationary neural activity. We then construct an adaptive estimator to track the nonlinearity and non-stationarity in real time. We next design a robust controller to automatically determine the DBS frequency based on the estimated Parkinsonian neural state while reducing the system's sensitivity to high-frequency noise. We adopt and tune a biophysical cortex-BG-thalamus network model as an in-silico simulation testbed to generate nonlinear and non-stationary Parkinsonian neural dynamics for evaluating DBS methods.Main results. We find that under different nonlinear and non-stationary neural dynamics, our robust adaptive DBS method achieved accurate regulation of the BG Parkinsonian beta band oscillation power with small control error, bias, and deviation. Moreover, the accurate regulation generalizes across different therapeutic targets and consistently outperforms current on-off and LTI DBS methods.Significance. These results have implications for future designs of closed-loop DBS systems to treat PD.

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.

Biophysical Principles and Computational Modeling of Deep Brain Stimulation

BACKGROUND

Deep brain stimulation (DBS) has revolutionized the treatment of neurological disorders, yet the mechanisms of DBS are still under investigation. Computational models are important in silico tools for elucidating these underlying principles and potentially for personalizing DBS therapy to individual patients. The basic principles underlying neurostimulation computational models, however, are not well known in the clinical neuromodulation community.

OBJECTIVE

In this study, we present a tutorial on the derivation of computational models of DBS and outline the biophysical contributions of electrodes, stimulation parameters, and tissue substrates to the effects of DBS.

RESULTS

Given that many aspects of DBS are difficult to characterize experimentally, computational models have played an important role in understanding how material, size, shape, and contact segmentation influence device biocompatibility, energy efficiency, the spatial spread of the electric field, and the specificity of neural activation. Neural activation is dictated by stimulation parameters including frequency, current vs voltage control, amplitude, pulse width, polarity configurations, and waveform. These parameters also affect the potential for tissue damage, energy efficiency, the spatial spread of the electric field, and the specificity of neural activation. Activation of the neural substrate also is influenced by the encapsulation layer surrounding the electrode, the conductivity of the surrounding tissue, and the size and orientation of white matter fibers. These properties modulate the effects of the electric field and determine the ultimate therapeutic response.

CONCLUSION

This article describes biophysical principles that are useful for understanding the mechanisms of neurostimulation.

Wireless closed-loop deep brain stimulation using microelectrode array probes

Deep brain stimulation (DBS), including optical stimulation and electrical stimulation, has been demonstrated considerable value in exploring pathological brain activity and developing treatments for neural disorders. Advances in DBS microsystems based on implantable microelectrode array (MEA) probes have opened up new opportunities for closed-loop DBS (CL-DBS) in situ. This technology can be used to detect damaged brain circuits and test the therapeutic potential for modulating the output of these circuits in a variety of diseases simultaneously. Despite the success and rapid utilization of MEA probe-based CL-DBS microsystems, key challenges, including excessive wired communication, need to be urgently resolved. In this review, we considered recent advances in MEA probe-based wireless CL-DBS microsystems and outlined the major issues and promising prospects in this field. This technology has the potential to offer novel therapeutic options for psychiatric disorders in the future.

Bibliometric and visualized analysis of dynamic balance and brain function using web of science and CiteSpace from 1995 to 2022

Purpose

This study aims to explore the dynamic balance of human beings and investigate the relationship between functional structure as well as functional connectivity. Through a comprehensive bibliometric and visual analysis of the research literature from 1995 to 2022, we quantitatively display the development of the dynamic balance and brain structure as well as functional connection. Our objective is to present new trends and frontiers in the study of dynamic balance and brain function through bibliometrics software, providing valuable insights for future research in this domain.

Methods

The literature on dynamic balance, brain structure and functional connectivity between 1995 and 2022 was retrieved from the Web of Science database. We employed CiteSpace software to analyze various aspects, including the year of publication, journal, authors, keywords, institutions, countries, and references. Based on the analysis results, a co-reference map was generated to visually observe research hotspots and knowledge structures.

Results

A total of 1533 records were retrieved during the survey period (1995-2022), with a gradually increase in the number of annual publications. Notably, the data suggests a notable increase in publications between 2020 and 2021. The number of publications increased by 20 % from 2020 to 2021. The journal "Proceedings of the National Academy of Sciences (PNAS)" emerged as the most prolific journal. Among the cited authors, Deco and Gustavo ranked at the top. Key research terms in this field include "neural network", "functional connectivity", "dynamic", "model" and "brain". Particularly, the keyword "neural network" exhibited the strongest growth. The analysis of keywords cluster revealed the top 10 clusters of research themes. Oxford University stood out as the most productive institution, while the United States held the greatest influence with the highest number of publications and centrality. The reference cluster analysis further demonstrated the top 10 clusters in the literature.

Conclusion

Through the use of CiteSpace software, this study performed a comprehensive bibliometric and visual analysis of the Web of Science research literature on human dynamic balance and brain structural as well as functional connectivity over the past few decades. This may help researchers identify new perspectives on potential collaborators as well as collaborating institutions, hot topics, and research frontiers in the research field. The results provided an intuitive displayed overview of research trends, hotspots and frontiers in this field, facilitating a general understanding of its progression. Through unremitting efforts, it provides valuable guidance and reference for future research work.

Towards an optimised deep brain stimulation using a large-scale computational network and realistic volume conductor model

Objective. Constructing a theoretical framework to improve deep brain stimulation (DBS) based on the neuronal spatiotemporal patterns of the stimulation-affected areas constitutes a primary target.Approach. We develop a large-scale biophysical network, paired with a realistic volume conductor model, to estimate theoretically efficacious stimulation protocols. Based on previously published anatomically defined structural connectivity, a biophysical basal ganglia-thalamo-cortical neuronal network is constructed using Hodgkin-Huxley dynamics. We define a new biomarker describing the thalamic spatiotemporal activity as a ratio of spiking vs. burst firing. The per cent activation of the different pathways is adapted in the simulation to minimise the differences of the biomarker with respect to its value under healthy conditions.Main results.This neuronal network reproduces spatiotemporal patterns that emerge in Parkinson's disease. Simulations of the fibre per cent activation for the defined biomarker propose desensitisation of pallido-thalamic synaptic efficacy, induced by high-frequency signals, as one possible crucial mechanism for DBS action. Based on this activation, we define both an optimal electrode position and stimulation protocol using pathway activation modelling.Significance. A key advantage of this research is that it combines different approaches, i.e. the spatiotemporal pattern with the electric field and axonal response modelling, to compute the optimal DBS protocol. By correlating the inherent network dynamics with the activation of white matter fibres, we obtain new insights into the DBS therapeutic action.

Monitoring time domain characteristics of Parkinson's disease using 3D memristive neuromorphic system

Introduction

Parkinson's disease (PD) is a neurodegenerative disorder affecting millions of patients. Closed-Loop Deep Brain Stimulation (CL-DBS) is a therapy that can alleviate the symptoms of PD. The CL-DBS system consists of an electrode sending electrical stimulation signals to a specific region of the brain and a battery-powered stimulator implanted in the chest. The electrical stimuli in CL-DBS systems need to be adjusted in real-time in accordance with the state of PD symptoms. Therefore, fast and precise monitoring of PD symptoms is a critical function for CL-DBS systems. However, the current CL-DBS techniques suffer from high computational demands for real-time PD symptom monitoring, which are not feasible for implanted and wearable medical devices.

Methods

In this paper, we present an energy-efficient neuromorphic PD symptom detector using memristive three-dimensional integrated circuits (3D-ICs). The excessive oscillation at beta frequencies (13-35 Hz) at the subthalamic nucleus (STN) is used as a biomarker of PD symptoms.

Results

Simulation results demonstrate that our neuromorphic PD detector, implemented with an 8-layer spiking Long Short-Term Memory (S-LSTM), excels in recognizing PD symptoms, achieving a training accuracy of 99.74% and a validation accuracy of 99.52% for a 75%-25% data split. Furthermore, we evaluated the improvement of our neuromorphic CL-DBS detector using NeuroSIM. The chip area, latency, energy, and power consumption of our CL-DBS detector were reduced by 47.4%, 66.63%, 65.6%, and 67.5%, respectively, for monolithic 3D-ICs. Similarly, for heterogeneous 3D-ICs, employing memristive synapses to replace traditional Static Random Access Memory (SRAM) resulted in reductions of 44.8%, 64.75%, 65.28%, and 67.7% in chip area, latency, and power usage.

Discussion

This study introduces a novel approach for PD symptom evaluation by directly utilizing spiking signals from neural activities in the time domain. This method significantly reduces the time and energy required for signal conversion compared to traditional frequency domain approaches. The study pioneers the use of neuromorphic computing and memristors in designing CL-DBS systems, surpassing SRAM-based designs in chip design area, latency, and energy efficiency. Lastly, the proposed neuromorphic PD detector demonstrates high resilience to timing variations in brain neural signals, as confirmed by robustness analysis.

Multivariable closed-loop control of deep brain stimulation for Parkinson's disease

Objective. Closed-loop deep brain stimulation (DBS) methods for Parkinson's disease (PD) to-date modulate either stimulation amplitude or frequency to control a single biomarker. While good performance has been demonstrated for symptoms that are correlated with the chosen biomarker, suboptimal regulation can occur for uncorrelated symptoms or when the relationship between biomarker and symptom varies. Control of stimulation-induced side-effects is typically not considered.Approach.A multivariable control architecture is presented to selectively target suppression of either tremor or subthalamic nucleus beta band oscillations. DBS pulse amplitude and duration are modulated to maintain amplitude below a threshold and avoid stimulation of distal large diameter axons associated with stimulation-induced side effects. A supervisor selects between a bank of controllers which modulate DBS pulse amplitude to control rest tremor or beta activity depending on the level of muscle electromyographic (EMG) activity detected. A secondary controller limits pulse amplitude and modulates pulse duration to target smaller diameter axons lying close to the electrode. The control architecture was investigated in a computational model of the PD motor network which simulated the cortico-basal ganglia network, motoneuron pool, EMG and muscle force signals.Main results.Good control of both rest tremor and beta activity was observed with reduced power delivered when compared with conventional open loop stimulation, The supervisor avoided over- or under-stimulation which occurred when using a single controller tuned to one biomarker. When DBS amplitude was constrained, the secondary controller maintained the efficacy of stimulation by increasing pulse duration to compensate for reduced amplitude. Dual parameter control delivered effective control of the target biomarkers, with additional savings in the power delivered.Significance.Non-linear multivariable control can enable targeted suppression of motor symptoms for PD patients. Moreover, dual parameter control facilitates automatic regulation of the stimulation therapeutic dosage to prevent overstimulation, whilst providing additional power savings.

Closed-loop modulation of model parkinsonian beta oscillations based on CAR-fuzzy control algorithm

Closed-loop deep brain stimulation (DBS) can apply on-demand stimulation based on the feedback signal (e.g. beta band oscillation), which is deemed to lower side effects of clinically used open-loop DBS. To facilitate the application of model-based closed-loop DBS in clinical, studies must consider state variations, e.g., variation of desired signal with different movement conditions and variation of model parameters with time. This paper proposes to use the controlled autoregressive (CAR)-fuzzy control algorithm to modulate the pathological beta band (13-35 Hz) oscillation of a basal ganglia-cortex-thalamus model. The CAR model is used to identify the relationship between DBS frequency parameter and beta oscillation power. Then the error between the one-step-ahead predicted beta power of CAR model and the desired value is innovatively used as the input of fuzzy controller to calculate the next step stimulation frequency. Compared with 130 Hz open-loop DBS, the proposed closed-loop DBS method could lower the mean stimulation frequency to 74.04 Hz with similar beta oscillation suppression performance. The Mamdani fuzzy controller is selected because which could establish fuzzy controller rules according to human operation experience. Adding prediction module to closed-loop control improves the accuracy of fuzzy control, compared with proportional-integral control and fuzzy control, the proposed CAR-fuzzy control algorithm has higher tracking reliability, response speed and robustness.

Delayed closed-loop neurostimulation for the treatment of pathological brain rhythms in mental disorders: a computational study

Mental disorders are among the top most demanding challenges in world-wide health. A large number of mental disorders exhibit pathological rhythms, which serve as the disorders characteristic biomarkers. These rhythms are the targets for neurostimulation techniques. Open-loop neurostimulation employs stimulation protocols, which are rather independent of the patients health and brain state in the moment of treatment. Most alternative closed-loop stimulation protocols consider real-time brain activity observations but appear as adaptive open-loop protocols, where e.g., pre-defined stimulation sets in if observations fulfil pre-defined criteria. The present theoretical work proposes a fully-adaptive closed-loop neurostimulation setup, that tunes the brain activities power spectral density (PSD) according to a user-defined PSD. The utilized brain model is non-parametric and estimated from the observations via magnitude fitting in a pre-stimulus setup phase. Moreover, the algorithm takes into account possible conduction delays in the feedback connection between observation and stimulation electrode. All involved features are illustrated on pathological α- and γ-rhythms known from psychosis. To this end, we simulate numerically a linear neural population brain model and a non-linear cortico-thalamic feedback loop model recently derived to explain brain activity in psychosis.

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.

Formal Verification of Deep Brain Stimulation Controllers for Parkinson's Disease Treatment

Deep brain stimulation (DBS) is a widely accepted treatment for the Parkinson's disease (PD). Traditionally, it is done in an open-loop manner, where stimulation is always ON, irrespective of the patient needs. As a consequence, patients can feel some side effects due to the continuous high-frequency stimulation. Closed-loop DBS can address this problem as it allows adjusting stimulation according to the patient need. The selection of open- or closed-loop DBS and an optimal algorithm for closed-loop DBS are some of the main challenges in DBS controller design, and typically the decision is made through sampling based simulations. In this letter, we used model checking, a formal verification technique used to exhaustively explore the complete state space of a system, for analyzing DBS controllers. We analyze the timed automata of the open-loop and closed-loop DBS controllers in response to the basal ganglia (BG) model. Furthermore, we present a formal verification approach for the closed-loop DBS controllers using timed computation tree logic (TCTL) properties, that is, safety, liveness (the property that under certain conditions, some event will eventually occur), and deadlock freeness. We show that the closed-loop DBS significantly outperforms existing open-loop DBS controllers in terms of energy efficiency. Moreover, we formally analyze the closed-loop DBS for energy efficiency and time behavior with two algorithms, the constant update algorithm and the error prediction update algorithm. Our results demonstrate that the closed-loop DBS running the error prediction update algorithm is efficient in terms of time and energy as compared to the constant update algorithm.

Efficient suppression of parkinsonian beta oscillations in a closed-loop model of deep brain stimulation with amplitude modulation

Introduction

Parkinson's disease (PD) is a movement disorder characterized by the pathological beta band (15-30 Hz) neural oscillations within the basal ganglia (BG). It is shown that the suppression of abnormal beta oscillations is correlated with the improvement of PD motor symptoms, which is a goal of standard therapies including deep brain stimulation (DBS). To overcome the stimulation-induced side effects and inefficiencies of conventional DBS (cDBS) and to reduce the administered stimulation current, closed-loop adaptive DBS (aDBS) techniques were developed. In this method, the frequency and/or amplitude of stimulation are modulated based on various disease biomarkers.

Methods

Here, by computational modeling of a cortico-BG-thalamic network in normal and PD conditions, we show that closed-loop aDBS of the subthalamic nucleus (STN) with amplitude modulation leads to a more effective suppression of pathological beta oscillations within the parkinsonian BG.

Results

Our results show that beta band neural oscillations are restored to their normal range and the reliability of the response of the thalamic neurons to motor cortex commands is retained due to aDBS with amplitude modulation. Furthermore, notably less stimulation current is administered during aDBS compared with cDBS due to a closed-loop control of stimulation amplitude based on the STN local field potential (LFP) beta activity.

Discussion

Efficient models of closed-loop stimulation may contribute to the clinical development of optimized aDBS techniques designed to reduce potential stimulation-induced side effects of cDBS in PD patients while leading to a better therapeutic outcome.

Suppression of seizure in childhood absence epilepsy using robust control of deep brain stimulation: a simulation study

Deep brain stimulation (DBS) is a promising technique to relieve the symptoms in patients with intractable seizures. Although the DBS therapy for seizure suppression dates back more than 40 years, determining stimulation parameters is a significant challenge to the success of this technique. One solution to this challenge with application in a real DBS system is to design a closed-loop control system to regulate the stimulation intensity using computational models of epilepsy automatically. The main goal of the current study is to develop a robust control technique based on adaptive fuzzy terminal sliding mode control (AFTSMC) for eliminating the oscillatory spiking behavior in childhood absence epilepsy (CAE) dynamical model consisting of cortical, thalamic relay, and reticular nuclei neurons. To this end, the membrane voltage dynamics of the three coupled neurons are considered as a three-input three-output nonlinear state delay system. A fuzzy logic system is developed to estimate the unknown nonlinear dynamics of the current and delayed states of the model embedded in the control input. Chattering-free control input (continuous DBS pulses) without any singularity problem is the superiority of the proposed control method. To guarantee the bounded stability of the closed-loop system in a finite time, the upper bounds of the external disturbance and minimum estimation errors are updated online with adaptive laws without any offline tuning phase. Simulation results are provided to show the robustness of AFTSMC in the presence of uncertainty and external disturbances.

Predictive neuromodulation of cingulo-frontal neural dynamics in major depressive disorder using a brain-computer interface system: A simulation study

Introduction

Deep brain stimulation (DBS) is a promising therapy for treatment-resistant major depressive disorder (MDD). MDD involves the dysfunction of a brain network that can exhibit complex nonlinear neural dynamics in multiple frequency bands. However, current open-loop and responsive DBS methods cannot track the complex multiband neural dynamics in MDD, leading to imprecise regulation of symptoms, variable treatment effects among patients, and high battery power consumption.

Methods

Here, we develop a closed-loop brain-computer interface (BCI) system of predictive neuromodulation for treating MDD. We first use a biophysically plausible ventral anterior cingulate cortex (vACC)-dorsolateral prefrontal cortex (dlPFC) neural mass model of MDD to simulate nonlinear and multiband neural dynamics in response to DBS. We then use offline system identification to build a dynamic model that predicts the DBS effect on neural activity. We next use the offline identified model to design an online BCI system of predictive neuromodulation. The online BCI system consists of a dynamic brain state estimator and a model predictive controller. The brain state estimator estimates the MDD brain state from the history of neural activity and previously delivered DBS patterns. The predictive controller takes the estimated MDD brain state as the feedback signal and optimally adjusts DBS to regulate the MDD neural dynamics to therapeutic targets. We use the vACC-dlPFC neural mass model as a simulation testbed to test the BCI system and compare it with state-of-the-art open-loop and responsive DBS treatments of MDD.

Results

We demonstrate that our dynamic model accurately predicts nonlinear and multiband neural activity. Consequently, the predictive neuromodulation system accurately regulates the neural dynamics in MDD, resulting in significantly smaller control errors and lower DBS battery power consumption than open-loop and responsive DBS.

Discussion

Our results have implications for developing future precisely-tailored clinical closed-loop DBS treatments for MDD.

Abnormal neural oscillations during gait and dual-task in Parkinson’s disease

Gait dysfunctions are debilitating motor symptoms of Parkinson’s disease (PD) and may result in frequent falling with health complications. The contribution of the motor-cognitive network to gait disturbance can be studied more thoroughly by challenging motor-cognitive dual-task gait performances. Gait is a complex motor task that requires an appropriate contribution from motor and cognitive networks, reflected in frequency modulations among several cortical and subcortical networks. Electrophysiological recordings by scalp electroencephalography and implanted deep brain stimulation (DBS) electrodes have unveiled modulations of specific oscillatory patterns in the cortical-subcortical circuits in PD. In this review, we summarize oscillatory contributions of the cortical, basal ganglia, mesencephalic locomotor, and cerebellar regions during gait and dual-task activities in PD. We detail the involvement of the cognitive network in dual-task settings and compare how abnormal oscillations in the specific frequency bands in the cortical and subcortical regions correlate with gait deficits in PD, particularly freezing of gait (FOG). We suggest that altered neural oscillations in different frequencies can cause derangements in broader brain networks, so neuromodulation and pharmacological therapies should be considered to normalize those network oscillations to improve challenged gait and dual-task motor functions in PD. Specifically, the theta and beta bands in premotor cortical areas, subthalamic nucleus, as well as alpha band activity in the brainstem prepontine nucleus, modulate under clinically effective levodopa and DBS therapies, improving gait and dual-task performance in PD with FOG, compared to PD without FOG and age-matched healthy control groups.

Automated Tuning of Closed-loop Neuromodulation Control Systems using Bayesian Optimization

Tuning the parameters of controllers to attain the best performance is a challenging task in designing effective closed-loop neuromodulation systems. In this paper, we present a distributed architecture for automated tuning and adaptation of closed-loop neuromodulation control systems. We use this approach for the automated parameter tuning of a Proportional-Integral (PI) neuromodulation controller using Bayesian optimization. We use a biophysically-grounded mean-field model of neural populations under electrical stimulation as a simulation environment for testing and prototyping the proposed framework and characterizing its performance. Our results demonstrate the feasibility of using Bayesian optimization for performance-based automated tuning of a PI controller in closed-loop set-point neuromodulation control tasks.

Designing and Validating a Robust Adaptive Neuromodulation Algorithm for Closed-Loop Control of Brain States

OBJECTIVE

Neuromodulation systems that use closed-loop brain stimulation to control brain states can provide new therapies for brain disorders. To date, closed-loop brain stimulation has largely used linear time-invariant controllers. However, nonlinear time-varying brain network dynamics and external disturbances can appear during real-time stimulation, collectively leading to real-time model uncertainty. Real-time model uncertainty can degrade the performance or even cause instability of time-invariant controllers. Three problems need to be resolved to enable accurate and stable control under model uncertainty. First, an adaptive controller is needed to track the model uncertainty. Second, the adaptive controller additionally needs to be robust to noise and disturbances. Third, theoretical analyses of stability and robustness are needed as prerequisites for stable operation of the controller in practical applications.

APPROACH

We develop a robust adaptive neuromodulation algorithm that solves the above three problems. First, we develop a state-space brain network model that explicitly includes nonlinear terms of real-time model uncertainty and design an adaptive controller to track and cancel the model uncertainty. Second, to improve the robustness of the adaptive controller, we design two linear filters to increase steady-state control accuracy and reduce sensitivity to high-frequency noise and disturbances. Third, we conduct theoretical analyses to prove the stability of the neuromodulation algorithm and establish a trade-off between stability and robustness, which we further use to optimize the algorithm design. Finally, we validate the algorithm using comprehensive Monte Carlo simulations that span a broad range of model nonlinearity, uncertainty, and complexity.

MAIN RESULTS

The robust adaptive neuromodulation algorithm accurately tracks various types of target brain state trajectories, enables stable and robust control, and significantly outperforms state-of-the-art neuromodulation algorithms.

SIGNIFICANCE

Our algorithm has implications for future designs of precise, stable, and robust closed-loop brain stimulation systems to treat brain disorders and facilitate brain functions.

Closed-loop controller based on reference signal tracking for absence seizures

Absent epilepsy is a kind of refractory epilepsy, which is characterized by 2–4 Hz spike and wave discharges (SWDs) in electroencephalogram. Open-loop deep brain stimulation (DBS) targeting the thalamic reticular nucleus (TRN) is an effective method to treat absent epilepsy by eliminating SWDs in the brain. Compared with open-loop DBS, closed-loop DBS has been recognized by researchers for its advantages of significantly inhibiting seizures and having fewer side effects. Since traditional trial-and-error methods for adjusting closed-loop controller parameters are too dependent on the experience of doctors, in this paper we designed two proportional integral (PI) controllers based on the basal ganglia-cortical-thalamic model, whose PI parameters are calculated from the stability of the system. The two PI controllers can automatically adjust the frequency and amplitude of DBS respectively according to the change of the firing rate detected by substantia nigra pars reticulata (SNr). The parameters of the PI controller are calculated based on the Routh-Hurwitz stability criterion of a linear system which transformed by the original system using controlled auto-regressive (CAR) model and recursive least squares (RLS) method. Numerical simulation results show that both PI controllers significantly destroy the SWDs of the cerebral cortex and restore it to the other two normal discharge modes according to the different target firing rate, which supplies a promising brain stimulation strategy.

Controlling Clinical States Governed by Different Temporal Dynamics With Closed-Loop Deep Brain Stimulation: A Principled Framework

Closed-loop strategies for deep brain stimulation (DBS) are paving the way for improving the efficacy of existing neuromodulation therapies across neurological disorders. Unlike continuous DBS, closed-loop DBS approaches (cl-DBS) optimize the delivery of stimulation in the temporal domain. However, clinical and neurophysiological manifestations exhibit highly diverse temporal properties and evolve over multiple time-constants. Moreover, throughout the day, patients are engaged in different activities such as walking, talking, or sleeping that may require specific therapeutic adjustments. This broad range of temporal properties, along with inter-dependencies affecting parallel manifestations, need to be integrated in the development of therapies to achieve a sustained, optimized control of multiple symptoms over time. This requires an extended view on future cl-DBS design. Here we propose a conceptual framework to guide the development of multi-objective therapies embedding parallel control loops. Its modular organization allows to optimize the personalization of cl-DBS therapies to heterogeneous patient profiles. We provide an overview of clinical states and symptoms, as well as putative electrophysiological biomarkers that may be integrated within this structure. This integrative framework may guide future developments and become an integral part of next-generation precision medicine instruments.

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.

A Data Driven Experimental System for Individualized Brain Stimulation Design and Validation

Deep brain stimulation (DBS) is an effective clinical treatment for epilepsy. However, the individualized setting and adaptive adjustment of DBS parameters are still facing great challenges. This paper investigates a data-driven hardware-in-the-loop (HIL) experimental system for closed-loop brain stimulation system individualized design and validation. The unscented Kalman filter (UKF) is utilized to estimate critical parameters of neural mass model (NMM) from the electroencephalogram recordings to reconstruct individual neural activity. Based on the reconstructed NMM, we build a digital signal processor (DSP) based virtual brain platform with real time scale and biological signal level scale. Then, the corresponding hardware parts of signal amplification detection and closed-loop controller are designed to form the HIL experimental system. Based on the designed experimental system, the proportional-integral controller for different individual NMM is designed and validated, which proves the effectiveness of the experimental system. This experimental system provides a platform to explore neural activity under brain stimulation and the effects of various closed-loop stimulation paradigms.

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.

Model-Based Closed-Loop Suppression of Parkinsonian Beta Band Oscillations Through Origin Analysis

Excessive beta band (13-30 Hz) oscillations have been observed in the basal ganglia (BG) of patients with Parkinson's disease (PD). Understanding the origin and transmission of beta band oscillations are important to improve treatments of PD, such as closed-loop deep brain stimulation (DBS). This paper proposed a model-based closed-loop GPi stimulation system to suppress pathological beta band oscillations of BG. The feedback nucleus was selected through the analysis of GPi oscillations variation when different synaptic currents were blocked, mainly projections from globus pallidus external (GPe), the subthalamic nucleus (STN) and striatum. Since simulation results proved the important role of synaptic current from GPe in shaping the excessive GPi beta band oscillations, the local field potential (LFP) of GPe was chosen as the feedback signal. That is to say, the feedback nucleus was selected based on the origin analysis of the pathological GPi beta band oscillation. The closed-loop algorithm was the multiplication of linear delayed feedback of the filtered GPe-LFP and modeled synaptic dynamics from GPe to GPi. Thus, the formed stimulation waveform was synaptic current like shape, which was proved to be more energy efficient than open-loop continuous DBS in suppressing GPi beta band oscillation. With the development of DBS devices, the efficiency of this closed-loop stimulation could be testified in animal model and clinical.

FPGA-Based Real-Time Simulation Platform for Large-Scale STN-GPe Network

The real-time simulation of large-scale subthalamic nucleus (STN)-external globus pallidus (GPe) network model is of great significance for the mechanism analysis and performance improvement of deep brain stimulation (DBS) for Parkinson's states. This paper implements the real-time simulation of a large-scale STN-GPe network containing 512 single-compartment Hodgkin-Huxley type neurons on the Altera Stratix IV field programmable gate array (FPGA) hardware platform. At the single neuron level, some resource optimization schemes such as multiplier substitution, fixed-point operation, nonlinear function approximation and function recombination are adopted, which consists the foundation of the large-scale network realization. At the network level, the simulation scale of network is expanded using module reuse method at the cost of simulation time. The correlation coefficient between the neuron firing waveform of the FPGA platform and the MATLAB software simulation waveform is 0.9756. Under the same physiological time, the simulation speed of FPGA platform is 75 times faster than the Intel Core i7-8700K 3.70 GHz CPU 32GB RAM computer simulation speed. In addition, the established platform is used to analyze the effects of temporal pattern DBS on network firing activities. The proposed large-scale STN-GPe network meets the need of real time simulation, which would be rather helpful in designing closed-loop DBS improvement strategies.

Self-Tuning Deep Brain Stimulation Controller for Suppression of Beta Oscillations: Analytical Derivation and Numerical Validation

Closed-loop control strategies for deep brain stimulation (DBS) in Parkinson's disease offer the potential to provide more effective control of patient symptoms and fewer side effects than continuous stimulation, while reducing battery consumption. Most of the closed-loop methods proposed and tested to-date rely on controller parameters, such as controller gains, that remain constant over time. While the controller may operate effectively close to the operating point for which it is set, providing benefits when compared to conventional open-loop DBS, it may perform sub-optimally if the operating conditions evolve. Such changes may result from, for example, diurnal variation in symptoms, disease progression or changes in the properties of the electrode-tissue interface. In contrast, an adaptive or “self-tuning” control mechanism has the potential to accommodate slowly varying changes in system properties over a period of days, months, or years. Such an adaptive mechanism would automatically adjust the controller parameters to maintain the desired performance while limiting side effects, despite changes in the system operating point. In this paper, two neural modeling approaches are utilized to derive and test an adaptive control scheme for closed-loop DBS, whereby the gain of a feedback controller is continuously adjusted to sustain suppression of pathological beta-band oscillatory activity at a desired target level. First, the controller is derived based on a simplified firing-rate model of the reciprocally connected subthalamic nucleus (STN) and globus pallidus (GPe). Its efficacy is shown both when pathological oscillations are generated endogenously within the STN-GPe network and when they arise in response to exogenous cortical STN inputs. To account for more realistic biological features, the control scheme is then tested in a physiologically detailed model of the cortical basal ganglia network, comprised of individual conductance-based spiking neurons, and simulates the coupled DBS electric field and STN local field potential. Compared to proportional feedback methods without gain adaptation, the proposed adaptive controller was able to suppress beta-band oscillations with less power consumption, even as the properties of the controlled system evolve over time due to alterations in the target for beta suppression, beta fluctuations and variations in the electrode impedance.

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.