A control-theoretic system identification framework and a real-time closed-loop clinical simulation testbed for electrical brain stimulation

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.

Event detection and classification from multimodal time series with application to neural data

The detection of events in time-series data is a common signal-processing problem. When the data can be modeled as a known template signal with an unknown delay in Gaussian noise, detection of the template signal can be done with a traditional matched filter. However, in many applications, the event of interest is represented in multimodal data consisting of both Gaussian and point-process time series. Neuroscience experiments, for example, can simultaneously record multimodal neural signals such as local field potentials (LFPs), which can be modeled as Gaussian, and neuronal spikes, which can be modeled as point processes. Currently, no method exists for event detection from such multimodal data, and as such our objective in this work is to develop a method to meet this need. Here we address this challenge by developing the multimodal event detector (MED) algorithm which simultaneously estimates event times and classes. To do this, we write a multimodal likelihood function for Gaussian and point-process observations and derive the associated maximum likelihood estimator of simultaneous event times and classes. We additionally introduce a cross-modal scaling parameter to account for model mismatch in real datasets. We validate this method in extensive simulations as well as in a neural spike-LFP dataset recorded during an eye-movement task, where the events of interest are eye movements with unknown times and directions. We show that the MED can successfully detect eye movement onset and classify eye movement direction. Further, the MED successfully combines information across data modalities, with multimodal performance exceeding unimodal performance. This method can facilitate applications such as the discovery of latent events in multimodal neural population activity and the development of brain-computer interfaces for naturalistic settings without constrained tasks or prior knowledge of event times.

Multimodal subspace identification for modeling discrete-continuous spiking and field potential population activity

Objective.Learning dynamical latent state models for multimodal spiking and field potential activity can reveal their collective low-dimensional dynamics and enable better decoding of behavior through multimodal fusion. Toward this goal, developing unsupervised learning methods that are computationally efficient is important, especially for real-time learning applications such as brain-machine interfaces (BMIs). However, efficient learning remains elusive for multimodal spike-field data due to their heterogeneous discrete-continuous distributions and different timescales.Approach.Here, we develop a multiscale subspace identification (multiscale SID) algorithm that enables computationally efficient learning for modeling and dimensionality reduction for multimodal discrete-continuous spike-field data. We describe the spike-field activity as combined Poisson and Gaussian observations, for which we derive a new analytical SID method. Importantly, we also introduce a novel constrained optimization approach to learn valid noise statistics, which is critical for multimodal statistical inference of the latent state, neural activity, and behavior. We validate the method using numerical simulations and with spiking and local field potential population activity recorded during a naturalistic reach and grasp behavior.Main results.We find that multiscale SID accurately learned dynamical models of spike-field signals and extracted low-dimensional dynamics from these multimodal signals. Further, it fused multimodal information, thus better identifying the dynamical modes and predicting behavior compared to using a single modality. Finally, compared to existing multiscale expectation-maximization learning for Poisson-Gaussian observations, multiscale SID had a much lower training time while being better in identifying the dynamical modes and having a better or similar accuracy in predicting neural activity and behavior.Significance.Overall, multiscale SID is an accurate learning method that is particularly beneficial when efficient learning is of interest, such as for online adaptive BMIs to track non-stationary dynamics or for reducing offline training time in neuroscience investigations.

Modeling and dissociation of intrinsic and input-driven neural population dynamics underlying behavior

Neural dynamics can reflect intrinsic dynamics or dynamic inputs, such as sensory inputs or inputs from other brain regions. To avoid misinterpreting temporally structured inputs as intrinsic dynamics, dynamical models of neural activity should account for measured inputs. However, incorporating measured inputs remains elusive in joint dynamical modeling of neural-behavioral data, which is important for studying neural computations of behavior. We first show how training dynamical models of neural activity while considering behavior but not input or input but not behavior may lead to misinterpretations. We then develop an analytical learning method for linear dynamical models that simultaneously accounts for neural activity, behavior, and measured inputs. The method provides the capability to prioritize the learning of intrinsic behaviorally relevant neural dynamics and dissociate them from both other intrinsic dynamics and measured input dynamics. In data from a simulated brain with fixed intrinsic dynamics that performs different tasks, the method correctly finds the same intrinsic dynamics regardless of the task while other methods can be influenced by the task. In neural datasets from three subjects performing two different motor tasks with task instruction sensory inputs, the method reveals low-dimensional intrinsic neural dynamics that are missed by other methods and are more predictive of behavior and/or neural activity. The method also uniquely finds that the intrinsic behaviorally relevant neural dynamics are largely similar across the different subjects and tasks, whereas the overall neural dynamics are not. These input-driven dynamical models of neural-behavioral data can uncover intrinsic dynamics that may otherwise be missed.

Macroscopic resting-state brain dynamics are best described by linear models

It is typically assumed that large networks of neurons exhibit a large repertoire of nonlinear behaviours. Here we challenge this assumption by leveraging mathematical models derived from measurements of local field potentials via intracranial electroencephalography and of whole-brain blood-oxygen-level-dependent brain activity via functional magnetic resonance imaging. We used state-of-the-art linear and nonlinear families of models to describe spontaneous resting-state activity of 700 participants in the Human Connectome Project and 122 participants in the Restoring Active Memory project. We found that linear autoregressive models provide the best fit across both data types and three performance metrics: predictive power, computational complexity and the extent of the residual dynamics unexplained by the model. To explain this observation, we show that microscopic nonlinear dynamics can be counteracted or masked by four factors associated with macroscopic dynamics: averaging over space and over time, which are inherent to aggregated macroscopic brain activity, and observation noise and limited data samples, which stem from technological limitations. We therefore argue that easier-to-interpret linear models can faithfully describe macroscopic brain dynamics during resting-state conditions.

Unsupervised learning of stationary and switching dynamical system models from Poisson observations

Objective. Investigating neural population dynamics underlying behavior requires learning accurate models of the recorded spiking activity, which can be modeled with a Poisson observation distribution. Switching dynamical system models can offer both explanatory power and interpretability by piecing together successive regimes of simpler dynamics to capture more complex ones. However, in many cases, reliable regime labels are not available, thus demanding accurate unsupervised learning methods for Poisson observations. Existing learning methods, however, rely on inference of latent states in neural activity using the Laplace approximation, which may not capture the broader properties of densities and may lead to inaccurate learning. Thus, there is a need for new inference methods that can enable accurate model learning.Approach. To achieve accurate model learning, we derive a novel inference method based on deterministic sampling for Poisson observations called the Poisson Cubature Filter (PCF) and embed it in an unsupervised learning framework. This method takes a minimum mean squared error approach to estimation. Terms that are difficult to find analytically for Poisson observations are approximated in a novel way with deterministic sampling based on numerical integration and cubature rules.Main results. PCF enabled accurate unsupervised learning in both stationary and switching dynamical systems and largely outperformed prior Laplace approximation-based learning methods in both simulations and motor cortical spiking data recorded during a reaching task. These improvements were larger for smaller data sizes, showing that PCF-based learning was more data efficient and enabled more reliable regime identification. In experimental data and unsupervised with respect to behavior, PCF-based learning uncovered interpretable behavior-relevant regimes unlike prior learning methods.Significance. The developed unsupervised learning methods for switching dynamical systems can accurately uncover latent regimes and states in population spiking activity, with important applications in both basic neuroscience and neurotechnology.

Bayesian target optimisation for high-precision holographic optogenetics

Two-photon optogenetics has transformed our ability to probe the structure and function of neural circuits. However, achieving precise optogenetic control of neural ensemble activity has remained fundamentally constrained by the problem of off-target stimulation (OTS): the inadvertent activation of nearby non-target neurons due to imperfect confinement of light onto target neurons. Here we propose a novel computational approach to this problem called Bayesian target optimisation. Our approach uses nonparametric Bayesian inference to model neural responses to optogenetic stimulation, and then optimises the laser powers and optical target locations needed to achieve a desired activity pattern with minimal OTS. We validate our approach in simulations and using data from in vitro experiments, showing that Bayesian target optimisation considerably reduces OTS across all conditions we test. Together, these results establish our ability to overcome OTS, enabling optogenetic stimulation with substantially improved precision.

Post-stimulus encoding of decision confidence in EEG: toward a brain-computer interface for decision making

Objective.When making decisions, humans can evaluate how likely they are to be correct. If this subjective confidence could be reliably decoded from brain activity, it would be possible to build a brain-computer interface (BCI) that improves decision performance by automatically providing more information to the user if needed based on their confidence. But this possibility depends on whether confidence can be decoded right after stimulus presentation and before the response so that a corrective action can be taken in time. Although prior work has shown that decision confidence is represented in brain signals, it is unclear if the representation is stimulus-locked or response-locked, and whether stimulus-locked pre-response decoding is sufficiently accurate for enabling such a BCI.Approach.We investigate the neural correlates of confidence by collecting high-density electroencephalography (EEG) during a perceptual decision task with realistic stimuli. Importantly, we design our task to include a post-stimulus gap that prevents the confounding of stimulus-locked activity by response-locked activity and vice versa, and then compare with a task without this gap.Main results.We perform event-related potential and source-localization analyses. Our analyses suggest that the neural correlates of confidence are stimulus-locked, and that an absence of a post-stimulus gap could cause these correlates to incorrectly appear as response-locked. By preventing response-locked activity from confounding stimulus-locked activity, we then show that confidence can be reliably decoded from single-trial stimulus-locked pre-response EEG alone. We also identify a high-performance classification algorithm by comparing a battery of algorithms. Lastly, we design a simulated BCI framework to show that the EEG classification is accurate enough to build a BCI and that the decoded confidence could be used to improve decision making performance particularly when the task difficulty and cost of errors are high.Significance.Our results show feasibility of non-invasive EEG-based BCIs to improve human decision making.

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.

Machine learning classifiers for electrode selection in the design of closed-loop neuromodulation devices for episodic memory improvement

Successful neuromodulation approaches to alter episodic memory require closed-loop stimulation predicated on the effective classification of brain states. The practical implementation of such strategies requires prior decisions regarding electrode implantation locations. Using a data-driven approach, we employ support vector machine (SVM) classifiers to identify high-yield brain targets on a large data set of 75 human intracranial electroencephalogram subjects performing the free recall (FR) task. Further, we address whether the conserved brain regions provide effective classification in an alternate (associative) memory paradigm along with FR, as well as testing unsupervised classification methods that may be a useful adjunct to clinical device implementation. Finally, we use random forest models to classify functional brain states, differentiating encoding versus retrieval versus non-memory behavior such as rest and mathematical processing. We then test how regions that exhibit good classification for the likelihood of recall success in the SVM models overlap with regions that differentiate functional brain states in the random forest models. Finally, we lay out how these data may be used in the design of neuromodulation devices.

Multimodal subspace identification for modeling discrete-continuous spiking and field potential population activity

Learning dynamical latent state models for multimodal spiking and field potential activity can reveal their collective low-dimensional dynamics and enable better decoding of behavior through multimodal fusion. Toward this goal, developing unsupervised learning methods that are computationally efficient is important, especially for real-time learning applications such as brain-machine interfaces (BMIs). However, efficient learning remains elusive for multimodal spike-field data due to their heterogeneous discrete-continuous distributions and different timescales. Here, we develop a multiscale subspace identification (multiscale SID) algorithm that enables computationally efficient modeling and dimensionality reduction for multimodal discrete-continuous spike-field data. We describe the spike-field activity as combined Poisson and Gaussian observations, for which we derive a new analytical subspace identification method. Importantly, we also introduce a novel constrained optimization approach to learn valid noise statistics, which is critical for multimodal statistical inference of the latent state, neural activity, and behavior. We validate the method using numerical simulations and spike-LFP population activity recorded during a naturalistic reach and grasp behavior. We find that multiscale SID accurately learned dynamical models of spike-field signals and extracted low-dimensional dynamics from these multimodal signals. Further, it fused multimodal information, thus better identifying the dynamical modes and predicting behavior compared to using a single modality. Finally, compared to existing multiscale expectation-maximization learning for Poisson-Gaussian observations, multiscale SID had a much lower computational cost while being better in identifying the dynamical modes and having a better or similar accuracy in predicting neural activity. Overall, multiscale SID is an accurate learning method that is particularly beneficial when efficient learning is of interest.

Closed-Loop Deep Brain Stimulation for Psychiatric Disorders

ABSTRACT

Deep brain stimulation (DBS) is a well-established approach to treating medication-refractory neurological disorders and holds promise for treating psychiatric disorders. Despite strong open-label results in extremely refractory patients, DBS has struggled to meet endpoints in randomized controlled trials. A major challenge is stimulation "dosing"-DBS systems have many adjustable parameters, and clinicians receive little feedback on whether they have chosen the correct parameters for an individual patient. Multiple groups have proposed closed loop technologies as a solution. These systems sense electrical activity, identify markers of an (un)desired state, then automatically deliver or adjust stimulation to alter that electrical state. Closed loop DBS has been successfully deployed in movement disorders and epilepsy. The availability of that technology, as well as advances in opportunities for invasive research with neurosurgical patients, has yielded multiple pilot demonstrations in psychiatric illness. Those demonstrations split into two schools of thought, one rooted in well-established diagnoses and symptom scales, the other in the more experimental Research Domain Criteria (RDoC) framework. Both are promising, and both are limited by the boundaries of current stimulation technology. They are in turn driving advances in implantable recording hardware, signal processing, and stimulation paradigms. The combination of these advances is likely to change both our understanding of psychiatric neurobiology and our treatment toolbox, though the timeframe may be limited by the realities of implantable device development.

Modeling and dissociation of intrinsic and input-driven neural population dynamics underlying behavior

Neural dynamics can reflect intrinsic dynamics or dynamic inputs, such as sensory inputs or inputs from other regions. To avoid misinterpreting temporally-structured inputs as intrinsic dynamics, dynamical models of neural activity should account for measured inputs. However, incorporating measured inputs remains elusive in joint dynamical modeling of neural-behavioral data, which is important for studying neural computations of a specific behavior. We first show how training dynamical models of neural activity while considering behavior but not input, or input but not behavior may lead to misinterpretations. We then develop a novel analytical learning method that simultaneously accounts for neural activity, behavior, and measured inputs. The method provides the new capability to prioritize the learning of intrinsic behaviorally relevant neural dynamics and dissociate them from both other intrinsic dynamics and measured input dynamics. In data from a simulated brain with fixed intrinsic dynamics that performs different tasks, the method correctly finds the same intrinsic dynamics regardless of task while other methods can be influenced by the change in task. In neural datasets from three subjects performing two different motor tasks with task instruction sensory inputs, the method reveals low-dimensional intrinsic neural dynamics that are missed by other methods and are more predictive of behavior and/or neural activity. The method also uniquely finds that the intrinsic behaviorally relevant neural dynamics are largely similar across the three subjects and two tasks whereas the overall neural dynamics are not. These input-driven dynamical models of neural-behavioral data can uncover intrinsic dynamics that may otherwise be missed.

Genetic, individual, and familial risk correlates of brain network controllability in major depressive disorder

Many therapeutic interventions in psychiatry can be viewed as attempts to influence the brain's large-scale, dynamic network state transitions. Building on connectome-based graph analysis and control theory, Network Control Theory is emerging as a powerful tool to quantify network controllability-i.e., the influence of one brain region over others regarding dynamic network state transitions. If and how network controllability is related to mental health remains elusive. Here, from Diffusion Tensor Imaging data, we inferred structural connectivity and inferred calculated network controllability parameters to investigate their association with genetic and familial risk in patients diagnosed with major depressive disorder (MDD, n = 692) and healthy controls (n = 820). First, we establish that controllability measures differ between healthy controls and MDD patients while not varying with current symptom severity or remission status. Second, we show that controllability in MDD patients is associated with polygenic scores for MDD and psychiatric cross-disorder risk. Finally, we provide evidence that controllability varies with familial risk of MDD and bipolar disorder as well as with body mass index. In summary, we show that network controllability is related to genetic, individual, and familial risk in MDD patients. We discuss how these insights into individual variation of network controllability may inform mechanistic models of treatment response prediction and personalized intervention-design in mental health.

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.

Modeling and inference methods for switching regime-dependent dynamical systems with multiscale neural observations

Objective.Realizing neurotechnologies that enable long-term neural recordings across multiple spatial-temporal scales during naturalistic behaviors requires new modeling and inference methods that can simultaneously address two challenges. First, the methods should aggregate information across all activity scales from multiple recording sources such as spiking and field potentials. Second, the methods should detect changes in the regimes of behavior and/or neural dynamics during naturalistic scenarios and long-term recordings. Prior regime detection methods are developed for a single scale of activity rather than multiscale activity, and prior multiscale methods have not considered regime switching and are for stationary cases.Approach.Here, we address both challenges by developing a switching multiscale dynamical system model and the associated filtering and smoothing methods. This model describes the encoding of an unobserved brain state in multiscale spike-field activity. It also allows for regime-switching dynamics using an unobserved regime state that dictates the dynamical and encoding parameters at every time-step. We also design the associated switching multiscale inference methods that estimate both the unobserved regime and brain states from simultaneous spike-field activity.Main results.We validate the methods in both extensive numerical simulations and prefrontal spike-field data recorded in a monkey performing saccades for fluid rewards. We show that these methods can successfully combine the spiking and field potential observations to simultaneously track the regime and brain states accurately. Doing so, these methods lead to better state estimation compared with single-scale switching methods or stationary multiscale methods. Also, for single-scale linear Gaussian observations, the new switching smoother can better generalize to diverse system settings compared to prior switching smoothers.Significance.These modeling and inference methods effectively incorporate both regime-detection and multiscale observations. As such, they could facilitate investigation of latent switching neural population dynamics and improve future brain-machine interfaces by enabling inference in naturalistic scenarios where regime-dependent multiscale activity and behavior arise.

The expanding horizons of network neuroscience: From description to prediction and control

The field of network neuroscience has emerged as a natural framework for the study of the brain and has been increasingly applied across divergent problems in neuroscience. From a disciplinary perspective, network neuroscience originally emerged as a formal integration of graph theory (from mathematics) and neuroscience (from biology). This early integration afforded marked utility in describing the interconnected nature of neural units, both structurally and functionally, and underscored the relevance of that interconnection for cognition and behavior. But since its inception, the field has not remained static in its methodological composition. Instead, it has grown to use increasingly advanced graph-theoretic tools and to bring in several other disciplinary perspectives-including machine learning and systems engineering-that have proven complementary. In doing so, the problem space amenable to the discipline has expanded markedly. In this review, we discuss three distinct flavors of investigation in state-of-the-art network neuroscience: (i) descriptive network neuroscience, (ii) predictive network neuroscience, and (iii) a perturbative network neuroscience that draws on recent advances in network control theory. In considering each area, we provide a brief summary of the approaches, discuss the nature of the insights obtained, and highlight future directions.

fNIRS-based adaptive visuomotor task improves sensorimotor cortical activation

OBJECTIVE

Investigating how to promote the functional activation of the central sensorimotor system is an important goal in the neurorehabilitation research domain. We aim to validate the effectiveness of facilitating cortical excitability using a closed-loop visuomotor task, in which the task difficulty is adaptively adjusted based on an individual's sensorimotor cortical activation.

APPROACH

We developed a novel visuomotor task, in which subjects moved a handle of a haptic device along a specific path while exerting a constant force against a virtual surface under visual feedback. The difficulty levels of the task were adapted with the aim of increasing the activation of sensorimotor areas, measured non-invasively by functional near-infrared spectroscopy. The changes in brain activation of the bilateral prefrontal cortex, sensorimotor cortex, and the occipital cortex obtained during the adaptive visuomotor task (adaptive group), were compared to the brain activation pattern elicited by the same duration of task with random difficulties in a control group.

MAIN RESULTS

During one intervention session, the adaptive group showed significantly increased activation in the bilateral sensorimotor cortex, also enhanced effective connectivity between the prefrontal and sensorimotor areas compared to the control group.

SIGNIFICANCE

Our findings demonstrated that the fNIRS-based adaptive visuomotor task with high ecological validity can facilitate the neural activity in sensorimotor areas and thus has the potential to improve hand motor functions.

A Control-Theoretical System for Modulating Hippocampal Gamma Oscillations using Stimulation of the Posterior Cingulate Cortex

Closed-loop stimulation for targeted modulation of brain signals has emerged as a promising strategy for episodic memory restoration. In parallel, closed-loop neuromodulation strategies have been applied to treat brain conditions including drug-resistant depression, Parkinson’s Disease, and epilepsy. In this study, we seek to apply control theoretical principles to achieve closed loop modulation of hippocampal oscillatory activity. We focus on hippocampal gamma power, a signal with an established association for episodic memory processing, which may be a promising ‘biomarker’ for the modulation of memory performance. To develop a closed-loop stimulation paradigm that effectively modulates hippocampal gamma power, we use a novel data-set in which open-loop stimulation was applied to the posterior cingulate cortex and hippocampal gamma power was recorded during the encoding of episodic memories. The dataset was used to design and evaluate a linear quadratic integral (LQI) servo-controller in order to determine its viability for in-vivo use. In our simulation framework, we demonstrate that applying an LQI servo controller based on an autoregressive with exogenous input (ARX) plant model achieves effective control of hippocampal gamma power in 15 out of 17 experimental subjects. We demonstrate that we are able to modulate gamma power using stimulation thresholds that are physiologically safe and on time scales that are reasonable for application in a clinical system. We outline further experimentation to test our proposed system and compare our findings to emerging closed-loop neuromodulation strategies.

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 Tracking and Regulation of Emotional Valence State From Facial Electromyogram Measurements

Affective studies provide essential insights to address emotion recognition and tracking. In traditional open-loop structures, a lack of knowledge about the internal emotional state makes the system incapable of adjusting stimuli parameters and automatically responding to changes in the brain. To address this issue, we propose to use facial electromyogram measurements as biomarkers to infer the internal hidden brain state as feedback to close the loop. In this research, we develop a systematic way to track and control emotional valence, which codes emotions as being pleasant or obstructive. Hence, we conduct a simulation study by modeling and tracking the subject's emotional valence dynamics using state-space approaches. We employ Bayesian filtering to estimate the person-specific model parameters along with the hidden valence state, using continuous and binary features extracted from experimental electromyogram measurements. Moreover, we utilize a mixed-filter estimator to infer the secluded brain state in a real-time simulation environment. We close the loop with a fuzzy logic controller in two categories of regulation: inhibition and excitation. By designing a control action, we aim to automatically reflect any required adjustments within the simulation and reach the desired emotional state levels. Final results demonstrate that, by making use of physiological data, the proposed controller could effectively regulate the estimated valence state. Ultimately, we envision future outcomes of this research to support alternative forms of self-therapy by using wearable machine interface architectures capable of mitigating periods of pervasive emotions and maintaining daily well-being and welfare.

Modeling multiscale causal interactions between spiking and field potential signals during behavior

Objective. Brain recordings exhibit dynamics at multiple spatiotemporal scales, which are measured with spike trains and larger-scale field potential signals. To study neural processes, it is important to identify and model causal interactions not only at a single scale of activity, but also across multiple scales, i.e. between spike trains and field potential signals. Standard causality measures are not directly applicable here because spike trains are binary-valued but field potentials are continuous-valued. It is thus important to develop computational tools to recover multiscale neural causality during behavior, assess their performance on neural datasets, and study whether modeling multiscale causalities can improve the prediction of neural signals beyond what is possible with single-scale causality. Approach. We design a multiscale model-based Granger-like causality method based on directed information and evaluate its success both in realistic biophysical spike-field simulations and in motor cortical datasets from two non-human primates (NHP) performing a motor behavior. To compute multiscale causality, we learn point-process generalized linear models that predict the spike events at a given time based on the history of both spike trains and field potential signals. We also learn linear Gaussian models that predict the field potential signals at a given time based on their own history as well as either the history of binary spike events or that of latent firing rates. Main results. We find that our method reveals the true multiscale causality network structure in biophysical simulations despite the presence of model mismatch. Further, models with the identified multiscale causalities in the NHP neural datasets lead to better prediction of both spike trains and field potential signals compared to just modeling single-scale causalities. Finally, we find that latent firing rates are better predictors of field potential signals compared with the binary spike events in the NHP datasets. Significance. This multiscale causality method can reveal the directed functional interactions across spatiotemporal scales of brain activity to inform basic science investigations and neurotechnologies.

Physiologically informed neuromodulation

The rapid evolution of neuromodulation techniques includes an increasing amount of research into stimulation paradigms that are guided by patients' neurophysiology, to increase efficacy and responder rates. Treatment personalisation and target engagement have shown to be effective in fields such as Parkinson's disease, and closed-loop paradigms have been successfully implemented in cardiac defibrillators. Promising avenues are being explored for physiologically informed neuromodulation in psychiatry. Matching the stimulation frequency to individual brain rhythms has shown some promise in transcranial magnetic stimulation (TMS). Matching the phase of those rhythms may further enhance neuroplasticity, for instance when combining TMS with electroencephalographic (EEG) recordings. Resting-state EEG and event-related potentials may be useful to demonstrate connectivity between stimulation sites and connected areas. These techniques are available today to the psychiatrist to diagnose underlying sleep disorders, epilepsy, or lesions as contributing factors to the cause of depression. These technologies may also be useful in assessing the patient's brain network status prior to deciding on treatment options. Ongoing research using invasive recordings may allow for future identification of mood biomarkers and network structure. A core limitation is that biomarker research may currently be limited by the internal heterogeneity of psychiatric disorders according to the current DSM-based classifications. New approaches are being developed and may soon be validated. Finally, care must be taken when incorporating closed-loop capabilities into neuromodulation systems, by ensuring the safe operation of the system and understanding the physiological dynamics. Neurophysiological tools are rapidly evolving and will likely define the next generation of neuromodulation therapies.

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.

A Robust and Adaptive Control Algorithm for Closed-Loop Brain Stimulation

Developing closed-loop brain stimulation systems can benefit the treatment of neurological and neuropsychiatric disorders and facilitate brain functions. Current designs of closed-loop controllers have used time-invariant linear models of brain activity to devise non-adaptive controllers. However, unmodeled nonlinear dynamics can happen during real-time closed-loop control, leading to nonlinear uncertainty in the brain activity model. Current non-adaptive controllers cannot track the nonlinear model uncertainty and are not robust to noise, both of which can compromise their control performance. Here, within an ℒ₁ adaptive control framework, we develop a new discrete-time robust and adaptive closed-loop control algorithm that addresses a general form of nonlinear model uncertainty. We conduct Monte Carlo simulations to validate the robust and adaptive control algorithm and show that it significantly outperforms existing closed-loop control algorithms. Our results can facilitate future designs of precise and safe closed-loop brain stimulation systems to treat neurological and neuropsychiatric disorders and modulate brain functions.

State-space optimal feedback control of optogenetically driven neural activity

Objective.The rapid acceleration of tools for recording neuronal populations and targeted optogenetic manipulation has enabled real-time, feedback control of neuronal circuits in the brain. Continuously-graded control of measured neuronal activity poses a wide range of technical challenges, which we address through a combination of optogenetic stimulation and a state-space optimal control framework implemented in the thalamocortical circuit of the awake mouse.Approach.Closed-loop optogenetic control of neurons was performed in real-time via stimulation of channelrhodopsin-2 expressed in the somatosensory thalamus of the head-fixed mouse. A state-space linear dynamical system model structure was used to approximate the light-to-spiking input-output relationship in both single-neuron as well as multi-neuron scenarios when recording from multielectrode arrays. These models were utilized to design state feedback controller gains by way of linear quadratic optimal control and were also used online for estimation of state feedback, where a parameter-adaptive Kalman filter provided robustness to model-mismatch.Main results.This model-based control scheme proved effective for feedback control of single-neuron firing rate in the thalamus of awake animals. Notably, the graded optical actuation utilized here did not synchronize simultaneously recorded neurons, but heterogeneity across the neuronal population resulted in a varied response to stimulation. Simulated multi-output feedback control provided better control of a heterogeneous population and demonstrated how the approach generalizes beyond single-neuron applications.Significance.To our knowledge, this work represents the first experimental application of state space model-based feedback control for optogenetic stimulation. In combination with linear quadratic optimal control, the approaches laid out and tested here should generalize to future problems involving the control of highly complex neural circuits. More generally, feedback control of neuronal circuits opens the door to adaptively interacting with the dynamics underlying sensory, motor, and cognitive signaling, enabling a deeper understanding of circuit function and ultimately the control of function in the face of injury or disease.

Adaptive latent state modeling of brain network dynamics with real-time learning rate optimization

Objective. Dynamic latent state models are widely used to characterize the dynamics of brain network activity for various neural signal types. To date, dynamic latent state models have largely been developed for stationary brain network dynamics. However, brain network dynamics can be non-stationary for example due to learning, plasticity or recording instability. To enable modeling these non-stationarities, two problems need to be resolved. First, novel methods should be developed that can adaptively update the parameters of latent state models, which is difficult due to the state being latent. Second, new methods are needed to optimize the adaptation learning rate, which specifies how fast new neural observations update the model parameters and can significantly influence adaptation accuracy.Approach. We develop a Rate Optimized-adaptive Linear State-Space Modeling (RO-adaptive LSSM) algorithm that solves these two problems. First, to enable adaptation, we derive a computation- and memory-efficient adaptive LSSM fitting algorithm that updates the LSSM parameters recursively and in real time in the presence of the latent state. Second, we develop a real-time learning rate optimization algorithm. We use comprehensive simulations of a broad range of non-stationary brain network dynamics to validate both algorithms, which together constitute the RO-adaptive LSSM.Main results. We show that the adaptive LSSM fitting algorithm can accurately track the broad simulated non-stationary brain network dynamics. We also find that the learning rate significantly affects the LSSM fitting accuracy. Finally, we show that the real-time learning rate optimization algorithm can run in parallel with the adaptive LSSM fitting algorithm. Doing so, the combined RO-adaptive LSSM algorithm rapidly converges to the optimal learning rate and accurately tracks non-stationarities.Significance. These algorithms can be used to study time-varying neural dynamics underlying various brain functions and enhance future neurotechnologies such as brain-machine interfaces and closed-loop brain stimulation systems.

Modelling and prediction of the dynamic responses of large-scale brain networks during direct electrical stimulation

Direct electrical stimulation can modulate the activity of brain networks for the treatment of several neurological and neuropsychiatric disorders and for restoring lost function. However, precise neuromodulation in an individual requires the accurate modelling and prediction of the effects of stimulation on the activity of their large-scale brain networks. Here, we report the development of dynamic input-output models that predict multiregional dynamics of brain networks in response to temporally varying patterns of ongoing microstimulation. In experiments with two awake rhesus macaques, we show that the activities of brain networks are modulated by changes in both stimulation amplitude and frequency, that they exhibit damping and oscillatory response dynamics, and that variabilities in prediction accuracy and in estimated response strength across brain regions can be explained by an at-rest functional connectivity measure computed without stimulation. Input-output models of brain dynamics may enable precise neuromodulation for the treatment of disease and facilitate the investigation of the functional organization of large-scale brain networks.

Multiscale low-dimensional motor cortical state dynamics predict naturalistic reach-and-grasp behavior

Motor function depends on neural dynamics spanning multiple spatiotemporal scales of population activity, from spiking of neurons to larger-scale local field potentials (LFP). How multiple scales of low-dimensional population dynamics are related in control of movements remains unknown. Multiscale neural dynamics are especially important to study in naturalistic reach-and-grasp movements, which are relatively under-explored. We learn novel multiscale dynamical models for spike-LFP network activity in monkeys performing naturalistic reach-and-grasps. We show low-dimensional dynamics of spiking and LFP activity exhibited several principal modes, each with a unique decay-frequency characteristic. One principal mode dominantly predicted movements. Despite distinct principal modes existing at the two scales, this predictive mode was multiscale and shared between scales, and was shared across sessions and monkeys, yet did not simply replicate behavioral modes. Further, this multiscale mode's decay-frequency explained behavior. We propose that multiscale, low-dimensional motor cortical state dynamics reflect the neural control of naturalistic reach-and-grasp behaviors.

Deep brain stimulation for psychiatric disorders: From focal brain targets to cognitive networks

Deep brain stimulation (DBS) is a promising intervention for treatment-resistant psychiatric disorders, particularly major depressive disorder (MDD) and obsessive-compulsive disorder (OCD). Up to 90% of patients who have not recovered with therapy or medication have reported benefit from DBS in open-label studies. Response rates in randomized controlled trials (RCTs), however, have been much lower. This has been argued to arise from surgical variability between sites, and recent psychiatric DBS research has focused on refining targeting through personalized imaging. Much less attention has been given to the fact that psychiatric disorders arise from dysfunction in distributed brain networks, and that DBS likely acts by altering communication within those networks. This is in part because psychiatric DBS research relies on subjective rating scales that make it difficult to identify network biomarkers. Here, we overview recent DBS RCT results in OCD and MDD, as well as the follow-on imaging studies. We present evidence for a new approach to studying DBS' mechanisms of action, focused on measuring objective cognitive/emotional deficits that underpin these and many other mental disorders. Further, we suggest that a focus on cognition could lead to reliable network biomarkers at an electrophysiologic level, especially those related to inter-regional synchrony of the local field potential (LFP). Developing the network neuroscience of DBS has the potential to finally unlock the potential of this highly specific therapy.

Modeling behaviorally relevant neural dynamics enabled by preferential subspace identification

Neural activity exhibits complex dynamics related to various brain functions, internal states and behaviors. Understanding how neural dynamics explain specific measured behaviors requires dissociating behaviorally relevant and irrelevant dynamics, which is not achieved with current neural dynamic models as they are learned without considering behavior. We develop preferential subspace identification (PSID), which is an algorithm that models neural activity while dissociating and prioritizing its behaviorally relevant dynamics. Modeling data in two monkeys performing three-dimensional reach and grasp tasks, PSID revealed that the behaviorally relevant dynamics are significantly lower-dimensional than otherwise implied. Moreover, PSID discovered distinct rotational dynamics that were more predictive of behavior. Furthermore, PSID more accurately learned behaviorally relevant dynamics for each joint and recording channel. Finally, modeling data in two monkeys performing saccades demonstrated the generalization of PSID across behaviors, brain regions and neural signal types. PSID provides a general new tool to reveal behaviorally relevant neural dynamics that can otherwise go unnoticed.

Models of communication and control for brain networks: distinctions, convergence, and future outlook

Recent advances in computational models of signal propagation and routing in the human brain have underscored the critical role of white-matter structure. A complementary approach has utilized the framework of network control theory to better understand how white matter constrains the manner in which a region or set of regions can direct or control the activity of other regions. Despite the potential for both of these approaches to enhance our understanding of the role of network structure in brain function, little work has sought to understand the relations between them. Here, we seek to explicitly bridge computational models of communication and principles of network control in a conceptual review of the current literature. By drawing comparisons between communication and control models in terms of the level of abstraction, the dynamical complexity, the dependence on network attributes, and the interplay of multiple spatiotemporal scales, we highlight the convergence of and distinctions between the two frameworks. Based on the understanding of the intertwined nature of communication and control in human brain networks, this work provides an integrative perspective for the field and outlines exciting directions for future work.

Digital Cardiovascular Biomarker Responses to Transcutaneous Cervical Vagus Nerve Stimulation: State-Space Modeling, Prediction, and Simulation

Background

Transcutaneous cervical vagus nerve stimulation (tcVNS) is a promising alternative to implantable stimulation of the vagus nerve. With demonstrated potential in myriad applications, ranging from systemic inflammation reduction to traumatic stress attenuation, closed-loop tcVNS during periods of risk could improve treatment efficacy and reduce ineffective delivery. However, achieving this requires a deeper understanding of biomarker changes over time.

Objective

The aim of the present study was to reveal the dynamics of relevant cardiovascular biomarkers, extracted from wearable sensing modalities, in response to tcVNS.

Methods

Twenty-four human subjects were recruited for a randomized double-blind clinical trial, for whom electrocardiography and photoplethysmography were used to measure heart rate and photoplethysmogram amplitude responses to tcVNS, respectively. Modeling these responses in state-space, we (1) compared the biomarkers in terms of their predictability and active vs sham differentiation, (2) studied the latency between stimulation onset and measurable effects, and (3) visualized the true and model-simulated biomarker responses to tcVNS.

Results

The models accurately predicted future heart rate and photoplethysmogram amplitude values with root mean square errors of approximately one-fifth the standard deviations of the data. Moreover, (1) the photoplethysmogram amplitude showed superior predictability (P=.03) and active vs sham separation compared to heart rate; (2) a consistent delay of greater than 5 seconds was found between tcVNS onset and cardiovascular effects; and (3) dynamic characteristics differentiated responses to tcVNS from the sham stimulation.

Conclusions

This work furthers the state of the art by modeling pertinent biomarker responses to tcVNS. Through subsequent analysis, we discovered three key findings with implications related to (1) wearable sensing devices for bioelectronic medicine, (2) the dominant mechanism of action for tcVNS-induced effects on cardiovascular physiology, and (3) the existence of dynamic biomarker signatures that can be leveraged when titrating therapy in closed loop.

Trial Registration

ClinicalTrials.gov NCT02992899; https://clinicaltrials.gov/ct2/show/NCT02992899

International Registered Report Identifier (IRRID)

RR2-10.1016/j.brs.2019.08.002

Signal recovery from stimulation artifacts in intracranial recordings with dictionary learning

OBJECTIVE

Electrical stimulation of the human brain is commonly used for eliciting and inhibiting neural activity for clinical diagnostics, modifying abnormal neural circuit function for therapeutics, and interrogating cortical connectivity. However, recording electrical signals with concurrent stimulation results in dominant electrical artifacts that mask the neural signals of interest. Here we develop a method to reproducibly and robustly recover neural activity during concurrent stimulation. We concentrate on signal recovery across an array of electrodes without channel-wise fine-tuning of the algorithm. Our goal includes signal recovery with trains of stimulation pulses, since repeated, high-frequency pulses are often required to induce desired effects in both therapeutic and research domains. We have made all of our code and data publicly available.

APPROACH

We developed an algorithm that automatically detects templates of artifacts across many channels of recording, creating a dictionary of learned templates using unsupervised clustering. The artifact template that best matches each individual artifact pulse is subtracted to recover the underlying activity. To assess the success of our method, we focus on whether it extracts physiologically interpretable signals from real recordings.

MAIN RESULTS

We demonstrate our signal recovery approach on invasive electrophysiologic recordings from human subjects during stimulation. We show the recovery of meaningful neural signatures in both electrocorticographic (ECoG) arrays and deep brain stimulation (DBS) recordings. In addition, we compared cortical responses induced by the stimulation of primary somatosensory (S1) by natural peripheral touch, as well as motor cortex activity with and without concurrent S1 stimulation.

SIGNIFICANCE

Our work will enable future advances in neural engineering with simultaneous stimulation and recording.

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.

State-Space Modeling and Fuzzy Feedback Control of Cognitive Stress

"Distress" or a substantial amount of stress may decrease brain functionality and cause neurological disorders. On the other hand, very low cognitive arousal may affect one's concentration and awareness. Data collected using wrist-worn wearable devices, in particular, skin conductance data, could be used to look into one's cognitive-stress-related arousal. Our goal here is to present excitatory and inhibitory wearable machine-interface (WMI) architectures to control one's cognitive-stress-related arousal state. We first present a model for skin conductance response events as a function of environmental stimuli associated with cognitive stress and relaxation. Then, we perform Bayesian filtering to estimate the hidden cognitive-stress-related arousal state. We finally close the loop using fuzzy control. In particular, we design two classes of controllers for our WMI architectures: (1) an inhibitory controller for reducing arousal and (2) an excitatory controller for increasing arousal. Our results illustrate that our simulated skin conductance responses are in agreement with experimental data. Moreover, we illustrate that our fuzzy control can successfully have both inhibitory and excitatory effects and regulate one's cognitive stress. In conclusion, in a simulation study based on experimental data, we have illustrated the feasibility of designing both excitatory and inhibitory WMI architectures. Since wearable devices can be used conveniently in one's daily life, the WMI architectures have a great potential to regulate one's cognitive stress seamlessly in real-world situations.

Explainable Artificial Intelligence for Neuroscience: Behavioral Neurostimulation

The use of Artificial Intelligence and machine learning in basic research and clinical neuroscience is increasing. AI methods enable the interpretation of large multimodal datasets that can provide unbiased insights into the fundamental principles of brain function, potentially paving the way for earlier and more accurate detection of brain disorders and better informed intervention protocols. Despite AI's ability to create accurate predictions and classifications, in most cases it lacks the ability to provide a mechanistic understanding of how inputs and outputs relate to each other. Explainable Artificial Intelligence (XAI) is a new set of techniques that attempts to provide such an understanding, here we report on some of these practical approaches. We discuss the potential value of XAI to the field of neurostimulation for both basic scientific inquiry and therapeutic purposes, as well as, outstanding questions and obstacles to the success of the XAI approach.

Adaptive delivery of continuous and delayed feedback deep brain stimulation - a computational study

Adaptive deep brain stimulation (aDBS) is a closed-loop method, where high-frequency DBS is turned on and off according to a feedback signal, whereas conventional high-frequency DBS (cDBS) is delivered permanently. Using a computational model of subthalamic nucleus and external globus pallidus, we extend the concept of adaptive stimulation by adaptively controlling not only continuous, but also demand-controlled stimulation. Apart from aDBS and cDBS, we consider continuous pulsatile linear delayed feedback stimulation (cpLDF), specifically designed to induce desynchronization. Additionally, we combine adaptive on-off delivery with continuous delayed feedback modulation by introducing adaptive pulsatile linear delayed feedback stimulation (apLDF), where cpLDF is turned on and off using pre-defined amplitude thresholds. By varying the stimulation parameters of cDBS, aDBS, cpLDF, and apLDF we obtain optimal parameter ranges. We reveal a simple relation between the thresholds of the local field potential (LFP) for aDBS and apLDF, the extent of the stimulation-induced desynchronization, and the integral stimulation time required. We find that aDBS and apLDF can be more efficient in suppressing abnormal synchronization than continuous simulation. However, apLDF still remains more efficient and also causes a stronger reduction of the LFP beta burst length. Hence, adaptive on-off delivery may further improve the intrinsically demand-controlled pLDF.