Model-based analysis and control of a network of basal ganglia spiking neurons in the normal and parkinsonian states

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.

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.

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.

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.

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.

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.

Design strategies for dynamic closed-loop optogenetic neurocontrol in vivo

OBJECTIVE

Controlling neural activity enables the possibility of manipulating sensory perception, cognitive processes, and body movement, in addition to providing a powerful framework for functionally disentangling the neural circuits that underlie these complex phenomena. Over the last decade, optogenetic stimulation has become an increasingly important and powerful tool for understanding neural circuit function, owing to the ability to target specific cell types and bidirectionally modulate neural activity. To date, most stimulation has been provided in open-loop or in an on/off closed-loop fashion, where previously-determined stimulation is triggered by an event. Here, we describe and demonstrate a design approach for precise optogenetic control of neuronal firing rate modulation using feedback to guide stimulation continuously.

APPROACH

Using the rodent somatosensory thalamus as an experimental testbed for realizing desired time-varying patterns of firing rate modulation, we utilized a moving average exponential filter to estimate firing rate online from single-unit spiking measured extracellularly. This estimate of instantaneous rate served as feedback for a proportional integral (PI) controller, which was designed during the experiment based on a linear-nonlinear Poisson (LNP) model of the neuronal response to light.

MAIN RESULTS

The LNP model fit during the experiment enabled robust closed-loop control, resulting in good tracking of sinusoidal and non-sinusoidal targets, and rejection of unmeasured disturbances. Closed-loop control also enabled manipulation of trial-to-trial variability.

SIGNIFICANCE

Because neuroscientists are faced with the challenge of dissecting the functions of circuit components, the ability to maintain control of a region of interest in spite of changes in ongoing neural activity will be important for disambiguating function within networks. Closed-loop stimulation strategies are ideal for control that is robust to such changes, and the employment of continuous feedback to adjust stimulation in real-time can improve the quality of data collected using optogenetic manipulation.

Toward a closed-loop deep brain stimulation in Parkinson's disease using local field potential in parkinsonian rat model

Deep brain stimulation (DBS) is an invasive method used for treating Parkinson's disease in its advanced stages. Nowadays, the initial adjustment of DBS parameters and their automatic matching proportion to the progression of the disease is viewed as one of the research areas discussed by the researchers, which is called closed-loop DBS. Various studies were conducted regarding finding the signal(s) which reflects different symptoms of the disease. Local Field Potential (LFP) is one of the signals that is suitable for using as feedback, because it can be recorded by the same implemented electrodes for stimulation. The present study aimed to identify the distinguishing features of patients from healthy individuals using LFP signals.

METHODS

In the present study, LFP was recorded from the rats in sham and parkinsonian model groups. After evaluating the signals in the frequency domain, sixty-six features were extracted from power spectral density of LFPs. The features were classified by Support Vector Machine (SVM) to determine the ability of features for separating parkinsonian rats from healthy ones. Finally, the most effective features were selected for distinguishing between the sham and parkinsonian model groups using a genetic algorithm.

RESULTS

The results indicated that the frequency domain features of LFP signals from rats have capacity of using them as a feedback for closed-loop DBS. The accuracy of the Support Vector Machine classification using all 66 features was 80.42% which increased to 84.41% using 38 features selected by genetic algorithm. The proposed method not only increase the accuracy, but it also reduce computation by decreasing the number of the effective features. The results indicate the significant capacity of the proposed method for identifying the effective high-frequency features to control the closed-loop DBS.

CONCLUSIONS

The ability of using LFP signals as feedback in closed-loop DBS was shown by extracting useful information in frequency bands below and above 100 Hz regarding LFP signals of parkinsonian rats and sham ones. Based on the results, features at frequencies above 100 Hz were more powerful and robust than below 100 Hz. The genetic algorithm was used for optimizing the classification problem.

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.

Synchronized activation of striatal direct and indirect pathways underlies the behavior in unilateral dopamine-depleted mice

For more than three decades it has been known, that striatal neurons become hyperactive after the loss of dopamine input, but the involvement of dopamine (DA) D1‐ or D2‐receptor‐expressing neurons has only been demonstrated indirectly. By recording neuronal activity using fluorescent calcium indicators in D1 or D2 eGFP‐expressing mice, we showed that following dopamine depletion, both types of striatal output neurons are involved in the large increase in neuronal activity generating a characteristic cell assembly of particular neurons that dominate the pattern. When we expressed channelrhodopsin in all the output neurons, light activation in freely moving animals, caused turning like that following dopamine loss. However, if the light stimulation was patterned in pulses the animals circled in the other direction. To explore the neuronal participation during this stimulation we infected normal mice with channelrhodopsin and calcium indicator in striatal output neurons. In slices made from these animals, continuous light stimulation for 15 s induced many cells to be active together and a particular dominant group of neurons, whereas light in patterned pulses activated fewer cells in more variable groups. These results suggest that the simultaneous activity of a large dominant group of striatal output neurons is intimately associated with parkinsonian symptoms.

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

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

Algorithmic design of a noise-resistant and efficient closed-loop deep brain stimulation system: A computational approach

Advances in the field of closed-loop neuromodulation call for analysis and modeling approaches capable of confronting challenges related to the complex neuronal response to stimulation and the presence of strong internal and measurement noise in neural recordings. Here we elaborate on the algorithmic aspects of a noise-resistant closed-loop subthalamic nucleus deep brain stimulation system for advanced Parkinson’s disease and treatment-refractory obsessive-compulsive disorder, ensuring remarkable performance in terms of both efficiency and selectivity of stimulation, as well as in terms of computational speed. First, we propose an efficient method drawn from dynamical systems theory, for the reliable assessment of significant nonlinear coupling between beta and high-frequency subthalamic neuronal activity, as a biomarker for feedback control. Further, we present a model-based strategy through which optimal parameters of stimulation for minimum energy desynchronizing control of neuronal activity are being identified. The strategy integrates stochastic modeling and derivative-free optimization of neural dynamics based on quadratic modeling. On the basis of numerical simulations, we demonstrate the potential of the presented modeling approach to identify, at a relatively low computational cost, stimulation settings potentially associated with a significantly higher degree of efficiency and selectivity compared with stimulation settings determined post-operatively. Our data reinforce the hypothesis that model-based control strategies are crucial for the design of novel stimulation protocols at the backstage of clinical applications.

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

A generalized predictive closed-loop control strategy to improve the basal ganglia activity patterns in Parkinson's disease (PD) is explored in this paper. Based on system identification, an input-output model is established to reveal the relationship between external stimulation and neuronal responses. The model contributes to the implementation of the generalized predictive control (GPC) algorithm that generates the optimal stimulation waveform to modulate the activities of neuronal nuclei. By analyzing the roles of two critical control parameters within the GPC law, optimal closed-loop control that has the capability of restoring the normal relay reliability of the thalamus with the least stimulation energy expenditure can be achieved. In comparison with open-loop deep brain stimulation and traditional static control schemes, the generalized predictive closed-loop control strategy can optimize the stimulation waveform without requiring any particular knowledge of the physiological properties of the system. This type of closed-loop control strategy generates an adaptive stimulation waveform with low energy expenditure with the potential to improve the treatments for PD.

Bioelectric Medicine and Devices for the Treatment of Spinal Cord Injury

Recovery of motor control is paramount for patients living with paralysis following spinal cord injury (SCI). While a cure or regenerative intervention remains on the horizon for the treatment of SCI, a number of neuroprosthetic devices have been employed to treat and mitigate the symptoms of paralysis associated with injuries to the spinal column and associated comorbidities. The recent success of epidural stimulation to restore voluntary motor function in the lower limbs of a small cohort of patients has breathed new life into the promise of electric-based medicine. Recently, a number of new organic and inorganic electronic devices have been developed for brain-computer interfaces to bypass the injury, for neurorehabilitation, bladder and bowel control, and the restoration of motor or sensory control. Herein, we discuss the recent advances in neuroprosthetic devices for treating SCI and highlight future design needs for closed-loop device systems.

A new bio-inspired stimulator to suppress hyper-synchronized neural firing in a cortical network

Hyper-synchronous neural oscillations are the character of several neurological diseases such as epilepsy. On the other hand, glial cells and particularly astrocytes can influence neural synchronization. Therefore, based on the recent researches, a new bio-inspired stimulator is proposed which basically is a dynamical model of the astrocyte biophysical model. The performance of the new stimulator is investigated on a large-scale, cortical network. Both excitatory and inhibitory synapses are also considered in the simulated spiking neural network. The simulation results show that the new stimulator has a good performance and is able to reduce recurrent abnormal excitability which in turn avoids the hyper-synchronous neural firing in the spiking neural network. In this way, the proposed stimulator has a demand controlled characteristic and is a good candidate for deep brain stimulation (DBS) technique to successfully suppress the neural hyper-synchronization.

Recovery of Dynamics and Function in Spiking Neural Networks with Closed-Loop Control

There is a growing interest in developing novel brain stimulation methods to control disease-related aberrant neural activity and to address basic neuroscience questions. Conventional methods for manipulating brain activity rely on open-loop approaches that usually lead to excessive stimulation and, crucially, do not restore the original computations performed by the network. Thus, they are often accompanied by undesired side-effects. Here, we introduce delayed feedback control (DFC), a conceptually simple but effective method, to control pathological oscillations in spiking neural networks (SNNs). Using mathematical analysis and numerical simulations we show that DFC can restore a wide range of aberrant network dynamics either by suppressing or enhancing synchronous irregular activity. Importantly, DFC, besides steering the system back to a healthy state, also recovers the computations performed by the underlying network. Finally, using our theory we identify the role of single neuron and synapse properties in determining the stability of the closed-loop system.

Brain stimulation is being used to ease symptoms in several neurological disorders in cases where pharmacological treatment is not effective (anymore). The most common way for stimulation so far has been to apply a fixed, predetermined stimulus irrespective of the actual state of the brain or the condition of the patient. Recently, alternative strategies such as event-triggered stimulation protocols have attracted the interest of researchers. In these protocols the state of the affected brain area is continuously monitored, but the stimulus is only applied if certain criteria are met. Here we go one step further and present a truly closed-loop stimulation protocol. That is, a stimulus is being continuously provided and the magnitude of the stimulus depends, at any point in time, on the ongoing neural activity dynamics of the affected brain area. This results not only in suppression of the pathological activity, but also in a partial recovery of the transfer function of the activity dynamics. Thus, the ability of the lesioned brain area to carry out relevant computations is restored up to a point as well.

Adaptive control of Parkinson's state based on a nonlinear computational model with unknown parameters

The objective here is to explore the use of adaptive input-output feedback linearization method to achieve an improved deep brain stimulation (DBS) algorithm for closed-loop control of Parkinson's state. The control law is based on a highly nonlinear computational model of Parkinson's disease (PD) with unknown parameters. The restoration of thalamic relay reliability is formulated as the desired outcome of the adaptive control methodology, and the DBS waveform is the control input. The control input is adjusted in real time according to estimates of unknown parameters as well as the feedback signal. Simulation results show that the proposed adaptive control algorithm succeeds in restoring the relay reliability of the thalamus, and at the same time achieves accurate estimation of unknown parameters. Our findings point to the potential value of adaptive control approach that could be used to regulate DBS waveform in more effective treatment of PD.

A tensor-product-kernel framework for multiscale neural activity decoding and control

Brain machine interfaces (BMIs) have attracted intense attention as a promising technology for directly interfacing computers or prostheses with the brain's motor and sensory areas, thereby bypassing the body. The availability of multiscale neural recordings including spike trains and local field potentials (LFPs) brings potential opportunities to enhance computational modeling by enriching the characterization of the neural system state. However, heterogeneity on data type (spike timing versus continuous amplitude signals) and spatiotemporal scale complicates the model integration of multiscale neural activity. In this paper, we propose a tensor-product-kernel-based framework to integrate the multiscale activity and exploit the complementary information available in multiscale neural activity. This provides a common mathematical framework for incorporating signals from different domains. The approach is applied to the problem of neural decoding and control. For neural decoding, the framework is able to identify the nonlinear functional relationship between the multiscale neural responses and the stimuli using general purpose kernel adaptive filtering. In a sensory stimulation experiment, the tensor-product-kernel decoder outperforms decoders that use only a single neural data type. In addition, an adaptive inverse controller for delivering electrical microstimulation patterns that utilizes the tensor-product kernel achieves promising results in emulating the responses to natural stimulation.

A combined method to estimate parameters of the thalamocortical model from a heavily noise-corrupted time series of action potential

A combined method composing of the unscented Kalman filter (UKF) and the synchronization-based method is proposed for estimating electrophysiological variables and parameters of a thalamocortical (TC) neuron model, which is commonly used for studying Parkinson's disease for its relay role of connecting the basal ganglia and the cortex. In this work, we take into account the condition when only the time series of action potential with heavy noise are available. Numerical results demonstrate that not only this method can estimate model parameters from the extracted time series of action potential successfully but also the effect of its estimation is much better than the only use of the UKF or synchronization-based method, with a higher accuracy and a better robustness against noise, especially under the severe noise conditions. Considering the rather important role of TC neuron in the normal and pathological brain functions, the exploration of the method to estimate the critical parameters could have important implications for the study of its nonlinear dynamics and further treatment of Parkinson's disease.

Closing the loop of deep brain stimulation

High-frequency deep brain stimulation is used to treat a wide range of brain disorders, like Parkinson's disease. The stimulated networks usually share common electrophysiological signatures, including hyperactivity and/or dysrhythmia. From a clinical perspective, HFS is expected to alleviate clinical signs without generating adverse effects. Here, we consider whether the classical open-loop HFS fulfills these criteria and outline current experimental or theoretical research on the different types of closed-loop DBS that could provide better clinical outcomes. In the first part of the review, the two routes followed by HFS-evoked axonal spikes are explored. In one direction, orthodromic spikes functionally de-afferent the stimulated nucleus from its downstream target networks. In the opposite direction, antidromic spikes prevent this nucleus from being influenced by its afferent networks. As a result, the pathological synchronized activity no longer propagates from the cortical networks to the stimulated nucleus. The overall result can be described as a reversible functional de-afferentation of the stimulated nucleus from its upstream and downstream nuclei. In the second part of the review, the latest advances in closed-loop DBS are considered. Some of the proposed approaches are based on mathematical models, which emphasize different aspects of the parkinsonian basal ganglia: excessive synchronization, abnormal firing-rate rhythms, and a deficient thalamo-cortical relay. The stimulation strategies are classified depending on the control-theory techniques on which they are based: adaptive and on-demand stimulation schemes, delayed and multi-site approaches, stimulations based on proportional and/or derivative control actions, optimal control strategies. Some of these strategies have been validated experimentally, but there is still a large reservoir of theoretical work that may point to ways of improving practical treatment.

Closed-loop control of the thalamocortical relay neuron's Parkinsonian state based on slow variable

A novel closed-loop control strategy is proposed to control Parkinsonian state based on a computational model. By modeling thalamocortical relay neurons under external electric field, a slow variable feedback control is applied to restore its relay functionality. Qualitative and quantitative analysis demonstrates the performance of feedback controller based on slow variable is more efficient compared with traditional feedback control based on fast variable. These findings point to the potential value of model-based design of feedback controllers for Parkinson's disease.

Control strategies for underactuated neural ensembles driven by optogenetic stimulation

Motivated by experiments employing optogenetic stimulation of cortical regions, we consider spike control strategies for ensembles of uncoupled integrate and fire neurons with a common conductance input. We construct strategies for control of spike patterns, that is, multineuron trains of action potentials, up to some maximal spike rate determined by the neural biophysics. We emphasize a constructive role for parameter heterogeneity, and find a simple rule for controllability in pairs of neurons. In particular, we determine parameters for which common drive is not limited to inducing synchronous spiking. For large ensembles, we determine how the number of controllable neurons varies with the number of observed (recorded) neurons, and what collateral spiking occurs in the full ensemble during control of the subensemble. While complete control of spiking in every neuron is not possible with a single input, we find that a degree of subensemble control is made possible by exploiting dynamical heterogeneity. As most available technologies for neural stimulation are underactuated, in the sense that the number of target neurons far exceeds the number of independent channels of stimulation, these results suggest partial control strategies that may be important in the development of sensory neuroprosthetics and other neurocontrol applications.

Adaptive inverse control of neural spatiotemporal spike patterns with a reproducing kernel Hilbert space (RKHS) framework

The precise control of spiking in a population of neurons via applied electrical stimulation is a challenge due to the sparseness of spiking responses and neural system plasticity. We pose neural stimulation as a system control problem where the system input is a multidimensional time-varying signal representing the stimulation, and the output is a set of spike trains; the goal is to drive the output such that the elicited population spiking activity is as close as possible to some desired activity, where closeness is defined by a cost function. If the neural system can be described by a time-invariant (homogeneous) model, then offline procedures can be used to derive the control procedure; however, for arbitrary neural systems this is not tractable. Furthermore, standard control methodologies are not suited to directly operate on spike trains that represent both the target and elicited system response. In this paper, we propose a multiple-input multiple-output (MIMO) adaptive inverse control scheme that operates on spike trains in a reproducing kernel Hilbert space (RKHS). The control scheme uses an inverse controller to approximate the inverse of the neural circuit. The proposed control system takes advantage of the precise timing of the neural events by using a Schoenberg kernel defined directly in the space of spike trains. The Schoenberg kernel maps the spike train to an RKHS and allows linear algorithm to control the nonlinear neural system without the danger of converging to local minima. During operation, the adaptation of the controller minimizes a difference defined in the spike train RKHS between the system and the target response and keeps the inverse controller close to the inverse of the current neural circuit, which enables adapting to neural perturbations. The results on a realistic synthetic neural circuit show that the inverse controller based on the Schoenberg kernel outperforms the decoding accuracy of other models based on the conventional rate representation of neural signal (i.e., spikernel and generalized linear model). Moreover, after a significant perturbation of the neuron circuit, the control scheme can successfully drive the elicited responses close to the original target responses.

Neural feedback for instantaneous spatiotemporal modulation of afferent pathways in bi-directional brain-machine interfaces

In bi-directional brain-machine interfaces (BMIs), precisely controlling the delivery of microstimulation, both in space and in time, is critical to continuously modulate the neural activity patterns that carry information about the state of the brain-actuated device to sensory areas in the brain. In this paper, we investigate the use of neural feedback to control the spatiotemporal firing patterns of neural ensembles in a model of the thalamocortical pathway. Control of pyramidal (PY) cells in the primary somatosensory cortex (S1) is achieved based on microstimulation of thalamic relay cells through multiple-input multiple-output (MIMO) feedback controllers. This closed loop feedback control mechanism is achieved by simultaneously varying the stimulation parameters across multiple stimulation electrodes in the thalamic circuit based on continuous monitoring of the difference between reference patterns and the evoked responses of the cortical PY cells. We demonstrate that it is feasible to achieve a desired level of performance by controlling the firing activity pattern of a few "key" neural elements in the network. Our results suggest that neural feedback could be an effective method to facilitate the delivery of information to the cortex to substitute lost sensory inputs in cortically controlled BMIs.