Optimal deep brain stimulation of the subthalamic nucleus--a computational study

Adaptive Stimulations in a Biophysical Network Model of Parkinson’s Disease

Deep brain stimulation (DBS)—through a surgically implanted electrode to the subthalamic nucleus (STN)—has become a widely used therapeutic option for the treatment of Parkinson’s disease and other neurological disorders. The standard conventional high-frequency stimulation (HF) that is currently used has several drawbacks. To overcome the limitations of HF, researchers have been developing closed-loop and demand-controlled, adaptive stimulation protocols wherein the amount of current that is delivered is turned on and off in real-time in accordance with a biophysical signal. Computational modeling of DBS in neural network models is an increasingly important tool in the development of new protocols that aid researchers in animal and clinical studies. In this computational study, we seek to implement a novel technique of DBS where we stimulate the STN in an adaptive fashion using the interspike time of the neurons to control stimulation. Our results show that our protocol eliminates bursts in the synchronized bursting neuronal activity of the STN, which is hypothesized to cause the failure of thalamocortical neurons (TC) to respond properly to excitatory cortical inputs. Further, we are able to significantly decrease the TC relay errors, representing potential therapeutics for Parkinson’s disease.

Delayed Feedback-Based Suppression of Pathological Oscillations in a Neural Mass Model

Suppression of excessively synchronous beta frequency (12-35 Hz) oscillatory activity in the basal ganglia is believed to correlate with the alleviation of hypokinetic motor symptoms of the Parkinson's disease. Delayed feedback is an effective strategy to interrupt the synchronization and has been used in the design of closed-loop neuromodulation methods computationally. Although tremendous efforts in this are being made by optimizing delayed feedback algorithm and stimulation waveforms, there are still remaining problems in the selection of effective parameters in the delayed feedback control schemes. In most delayed feedback neuromodulation strategies, the stimulation signal is obtained from the local field potential (LFP) of the excitatory subthalamic nucleus (STN) neurons and then is administered back to STN itself only. The inhibitory external globus pallidus (GPe) nucleus in the excitatory-inhibitory STN-GPe reciprocal network has not been involved in the design of the delayed feedback control strategies. Thus, considering the role of GPe, this paper proposes three schemes involving GPe in the design of the delayed feedback strategies and compared their effectiveness to the traditional paradigm using STN only. Based on a neural mass model of STN-GPe network having capability of simulating the LFP directly, the proposed stimulation strategies are tested and compared. Our simulation results show that the four types of delayed feedback control schemes are all effective, even if with a simple linear delayed feedback algorithm. But the three new control strategies we propose here further improve the control performance by enlarging the oscillatory suppression space and reducing the energy expenditure, suggesting that they may be more effective in applications. This paper may guide a new approach to optimize the closed-loop deep brain stimulation treatment to alleviate the Parkinsonian state by retargeting the measurement and stimulation nucleus.

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.

Deep brain stimulation: a review of the open neural engineering challenges

OBJECTIVE

Deep brain stimulation (DBS) is an established and valid therapy for a variety of pathological conditions ranging from motor to cognitive disorders. Still, much of the DBS-related mechanism of action is far from being understood, and there are several side effects of DBS whose origin is unclear. In the last years DBS limitations have been tackled by a variety of approaches, including adaptive deep brain stimulation (aDBS), a technique that relies on using chronically implanted electrodes on 'sensing mode' to detect the neural markers of specific motor symptoms and to deliver on-demand or modulate the stimulation parameters accordingly. Here we will review the state of the art of the several approaches to improve DBS and summarize the main challenges toward the development of an effective aDBS therapy.

APPROACH

We discuss models of basal ganglia disorders pathogenesis, hardware and software improvements for conventional DBS, and candidate neural and non-neural features and related control strategies for aDBS.

MAIN RESULTS

We identify then the main operative challenges toward optimal DBS such as (i) accurate target localization, (ii) increased spatial resolution of stimulation, (iii) development of in silico tests for DBS, (iv) identification of specific motor symptoms biomarkers, in particular (v) assessing how LFP oscillations relate to behavioral disfunctions, and (vi) clarify how stimulation affects the cortico-basal-ganglia-thalamic network to (vii) design optimal stimulation patterns.

SIGNIFICANCE

This roadmap will lead neural engineers novel to the field toward the most relevant open issues of DBS, while the in-depth readers might find a careful comparison of advantages and drawbacks of the most recent attempts to improve DBS-related neuromodulatory strategies.

Entrainment of a network of interacting neurons with minimum stimulating charge

Periodic pulse train stimulation is generically used to study the function of the nervous system and to counteract disease-related neuronal activity, e.g., collective periodic neuronal oscillations. The efficient control of neuronal dynamics without compromising brain tissue is key to research and clinical purposes. We here adapt the minimum charge control theory, recently developed for a single neuron, to a network of interacting neurons exhibiting collective periodic oscillations. We present a general expression for the optimal waveform, which provides an entrainment of a neural network to the stimulation frequency with a minimum absolute value of the stimulating current. As in the case of a single neuron, the optimal waveform is of bang-off-bang type, but its parameters are now determined by the parameters of the effective phase response curve of the entire network, rather than of a single neuron. The theoretical results are confirmed by three specific examples: two small-scale networks of FitzHugh-Nagumo neurons with synaptic and electric couplings, as well as a large-scale network of synaptically coupled quadratic integrate-and-fire neurons.

N-of-1 Trials for Closed-Loop Deep Brain Stimulation Devices

Closed-loop deep brain stimulation (DBS) devices hold great promise for treating various neurological and psychiatric conditions. Yet while these algorithmic-based devices provide personalized treatment to each patient, they also present uniquely individualized risks of physiological and psychological harms. These experimental devices are typically tested in randomized controlled trials, which may not be the optimum approach to identifying and assessing phenomenological harms they pose to patients. In this article, we contend that an N-of-1 trial design-which is being used ever more frequently to realize the goals of individualized, precision medicine-could provide beneficial phenomenological data about the potential risks of harm to properly inform the use of closed-loop DBS devices. Data from N-of-1 trials may provide patients, as well as their families and other caregivers, with better information on which to base informed choices about pursuing this type of treatment option.

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

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

Optimizing optogenetic stimulation protocols in auditory corticofugal neurons based on closed-loop spike feedback

OBJECTIVE

Optogenetics provides a means to probe functional connections between brain areas. By activating a set of presynaptic neurons and recording the activity from a downstream brain area, one can establish the sign and strength of a feedforward connection. One challenge is that there are virtually limitless patterns that can be used to stimulate a presynaptic brain area. Functional influences on downstream brain areas can depend not just on whether presynaptic neurons were activated, but how they were activated. Corticofugal axons from the auditory cortex (ACtx) heavily innervate the auditory tectum, the inferior colliculus (IC). Here, we sought to determine whether different modes of corticocollicular activation could titrate the strength of feedforward modulation of sound processing in IC neurons.

APPROACH

We used multi-channel electrophysiology and optogenetics to record from multiple regions of the IC in awake head-fixed mice while optogenetically stimulating ACtx neurons expressing Chronos, an ultra-fast channelrhodopsin. To identify cortical activation patterns associated with the strongest effects on IC firing rates, we employed a closed-loop evolutionary optimization procedure that tailored the voltage command signal sent to the laser based on spike feedback from single IC neurons.

MAIN RESULTS

Within minutes, our evolutionary search procedure converged on ACtx stimulation configurations that produced more effective and widespread enhancement of IC unit activity than generic activation parameters. Cortical modulation of midbrain spiking was bi-directional, as the evolutionary search procedure could be programmed to converge on activation patterns that either suppressed or enhanced sound-evoked IC firing rate.

SIGNIFICANCE

This study introduces a closed-loop optimization procedure to probe functional connections between brain areas. Our findings demonstrate that the influence of descending feedback projections on subcortical sensory processing can vary both in sign and degree depending on how cortical neurons are activated in time.

Noise-Induced Improvement of the Parkinsonian State: A Computational Study

The benefit of noise in improving the basal ganglia (BG) dysfunctions, especially Parkinsonian state, is explored in this paper. High frequency (≥ 100 Hz) deep brain stimulation (DBS), as a clinical effective stimulation method, has compelling and fantastic results in alleviating the motor symptoms of Parkinson's disease (PD). However, the mechanism of DBS is still unclear. And the selection of the DBS waveform parameters faces great challenges to further optimize the stimulation effects and to reduce its energy expenditure. Considering that the desynchronization of the BG neuronal activities is benefited from the forced high frequency regular spikes driven by standard high frequency DBS, we expect to explore a novel stimulation method that has capability of restoring the BG physiological firing patterns without introducing artificial high-frequency fires. In this paper, a colored noise stimulation is used as a neuromodulation method to disrupt the firing patterns of the pathological neuronal activities. A computational model of the BG that exhibits the intrinsic properties of the BG neurons and their interactions with the thalamic (Th) cells is employed. Based on the model, we investigate the effects of noise stimulation and explore the impacts of the noise stimulation parameters on both relay reliability of the Th neurons and energy expenditure of the stimulation. By comparison, it can be found that noise stimulation does not entrain the network to an artificial high-frequency firing state, but induces the pathological increased synchronous activities back to a normal physiological level. Moreover, besides the capability of restoring the neuronal state, the benefits of the noise also include its balanced waveform to avert potential tissue or electrode damage and its ability to reduce the energy expenditure to 50% less than that of the standard DBS, when the noise stimulation has low frequency (≤ 100 Hz) and appropriate intensity. Thus, the exploration of the optimal noise-induced improvement of the BG dysfunction is of great significance in treating symptoms of neurological disorders such as PD.

The onset mechanism of Parkinson's beta oscillations: A theoretical analysis

In this paper, we build a basal ganglia-cortex-thalamus model to study the oscillatory mechanisms and boundary conditions of the beta frequency band (13-30 Hz) that appears in the subthalamic nucleus. First, a theoretical oscillatory boundary formula is obtained in a simplified model by using the Laplace transform and linearization process of the system at fixed points. Second, we simulate the oscillatory boundary conditions through numerical calculations, which fit with our theoretical results very well, at least in the changing trend. We find that several critical coupling strengths in the model exert great effects on the oscillations, the mechanisms of which differ but can be explained in detail by our model and the oscillatory boundary formula. Specifically, we note that the relatively small or large sizes of the coupling strength from the fast-spiking interneurons to the medium spiny neurons and from the cortex to the fast-spiking interneurons both have obvious maintenance roles on the states. Similar phenomena have been reported in other neurological diseases, such as absence epilepsy. However, some of those interesting mutual regulation mechanisms in the model have rarely been considered in previous studies. In addition to the coupling weight in the pathway, in this work, we show that the delay is a key parameter that affects oscillations. On the one hand, the system needs a minimum delay to generate oscillations; on the other hand, in the appropriate range, a longer delay leads to a higher activation level of the subthalamic nucleus. In this paper, we study the oscillation activities that appear on the subthalamic nucleus. Moreover, all populations in the model show the dynamic behaviour of a synchronous resonance. Therefore, we infer that the mechanisms obtained can be expanded to explore the state of other populations, and that the model provides a unified framework for studying similar problems in the future. Moreover, the oscillatory boundary curves obtained are all critical conditions between the stable state and beta frequency oscillation. The method is also suitable for depicting other common frequency bands during brain oscillations, such as the alpha band (8-12 Hz), theta band (4-7 Hz) and delta band (1-3 Hz). Thus, the results of this work are expected to help us better understand the onset mechanism of parkinson's oscillations and can inspire related experimental research in this field.

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.

Irregularly timed electrical pulses reduce adaptation of retinal ganglion cells

OBJECTIVE

Retinal prostheses aim to provide visual percepts to blind people affected by diseases caused by photoreceptor degeneration. One of the main challenges presented by current devices is neural adaptation in the retina, which is believed to be the cause of fading-an effect where artificially produced percepts disappear over a short period of time, despite continuous stimulation of the retina. We aim to understand the neural adaptation generated in retinal ganglion cells (RGCs) during electrical stimulation.

APPROACH

Current visual prostheses use electrical pulses with fixed frequencies and amplitudes modulated over hundreds of milliseconds to stimulate the retina. However, in nature, neuronal spiking occurs with stochastic timing, hence the information received naturally from other neurons by RGCs is irregularly timed. We used a single epiretinal electrode to stimulate and compare rat RGC responses to stimulus trains of biphasic pulses delivered at regular and random inter-pulse intervals (IPI), the latter taken from an exponential distribution.

MAIN RESULTS

Our observations suggest that stimulation with random IPIs result in lower adaptation rates than stimulation with constant IPIs at frequencies of 50 Hz and 200 Hz. We also found a high proportion of lower amplitude action potentials, or spikelets. The spikelets were more prominent at high stimulation frequencies (50 Hz and 200 Hz) and were less susceptible to adaptation, but it was not clear if they propagated along the axon.

SIGNIFICANCE

Using random IPI stimulation in retinal prostheses reduces the decay of RGCs and this could potentially reduce fading of electrically induced visual perception.

An improved genetic algorithm for designing optimal temporal patterns of neural stimulation

OBJECTIVE

Electrical neuromodulation therapies typically apply constant frequency stimulation, but non-regular temporal patterns of stimulation may be more effective and more efficient. However, the design space for temporal patterns is exceedingly large, and model-based optimization is required for pattern design. We designed and implemented a modified genetic algorithm (GA) intended for design optimal temporal patterns of electrical neuromodulation.

APPROACH

We tested and modified standard GA methods for application to designing temporal patterns of neural stimulation. We evaluated each modification individually and all modifications collectively by comparing performance to the standard GA across three test functions and two biophysically-based models of neural stimulation.

MAIN RESULTS

The proposed modifications of the GA significantly improved performance across the test functions and performed best when all were used collectively. The standard GA found patterns that outperformed fixed-frequency, clinically-standard patterns in biophysically-based models of neural stimulation, but the modified GA, in many fewer iterations, consistently converged to higher-scoring, non-regular patterns of stimulation.

SIGNIFICANCE

The proposed improvements to standard GA methodology reduced the number of iterations required for convergence and identified superior solutions.

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

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

Nonlinear predictive control for adaptive adjustments of deep brain stimulation parameters in basal ganglia-thalamic network

The efficacy of deep brain stimulation (DBS) for Parkinson's disease (PD) depends in part on the post-operative programming of stimulation parameters. Closed-loop stimulation is one method to realize the frequent adjustment of stimulation parameters. This paper introduced the nonlinear predictive control method into the online adjustment of DBS amplitude and frequency. This approach was tested in a computational model of basal ganglia-thalamic network. The autoregressive Volterra model was used to identify the process model based on physiological data. Simulation results illustrated the efficiency of closed-loop stimulation methods (amplitude adjustment and frequency adjustment) in improving the relay reliability of thalamic neurons compared with the PD state. Besides, compared with the 130Hz constant DBS the closed-loop stimulation methods can significantly reduce the energy consumption. Through the analysis of inter-spike-intervals (ISIs) distribution of basal ganglia neurons, the evoked network activity by the closed-loop frequency adjustment stimulation was closer to the normal state.

A new approach to optimal control of conductance-based spiking neurons

This paper presents an algorithm for solving the minimum-energy optimal control problem of conductance-based spiking neurons. The basic procedure is (1) to construct a conductance-based spiking neuron oscillator as an affine nonlinear system, (2) to formulate the optimal control problem of the affine nonlinear system as a boundary value problem based on Pontryagin's maximum principle, and (3) to solve the boundary value problem using the homotopy perturbation method. The construction of the minimum-energy optimal control in the framework of the homotopy perturbation technique is novel and valid for a broad class of nonlinear conductance-based neuron models. The applicability of our method in the FitzHugh-Nagumo and Hindmarsh-Rose models is validated by simulations.

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 Control of Tremor-Predominant Parkinsonian State Based on Parameter Estimation

A significant feature of Parkinson's disease (PD) is the inability of the thalamus to respond faithfully to sensorimotor information from the cerebral cortex. This may be the result of abnormal oscillations in the basal ganglia (BG). Deep brain stimulation (DBS) is regarded as an effective method to modulate these pathological brain rhythmic activities. However, the selection of DBS parameters is challenging because the mechanism is not well understood. This work proposes the design of a closed-loop control strategy to automatically adjust the parameters of a DBS waveform based on a computational model. By estimating the synaptic input from BG to the thalamic neuron model as feedback variable, we designed and compared various control algorithms to counteract the effects of pathological oscillatory inputs. We then obtained optimal DBS parameters to modulate the tremor-predominant Parkinsonian state. We showed that even a simple proportional controller provides higher fidelity of thalamic relay of sensorimotor information and lower energy expenditure, as compared with classical open-loop DBS. Integral action further enhances DBS performance. Additionally, a positive bias voltage further improves the relay ability of the thalamus with decreased stimulation energy expenditure. These findings were conducive to the development of a more effective DBS to further improve the treatment of the PD.

A framework for identification of brain network dynamics using a novel binary noise modulated electrical stimulation pattern

Modeling and identification of brain network dynamics is of great importance both for understanding brain function and for closed-loop control of brain states. In this work, we present a multi-input-multi-output (MIMO) linear state-space model (LSSM) to describe the brain network dynamics in response to electrical stimulation. The LSSM maps the parameters of electrical stimulation, such as frequency, amplitude and pulse-width to recorded brain signals such as electrocorticography (ECoG) and electroencephalography (EEG). Effective identification of the LSSM in open-loop stimulation experiments, however, is strongly dependent on the open-loop input stimulation design. We propose a novel input design to accurately identify the LSSM by integrating the concept of binary noise (BN) with practical constraints on stimulation waveforms. The designed input pattern is a pulse train modulated by stochastic BN parameters. We show that this input pattern both satisfies the necessary spectral condition for accurate system identification and can incorporate any desired pulse shape. Using numerical experiments, we show that the quality of identification depends heavily on the input signal pattern and the proposed binary noise modulated pattern achieves satisfactory identification results, reducing the relative estimation error more than 300 times compared with step sequence modulated, single-sinusoid modulated and multi-sinusoids modulated input patterns.

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.

Analysis of Oscillatory Neural Activity in Series Network Models of Parkinson's Disease During Deep Brain Stimulation

Parkinson's disease is a progressive, neurodegenerative disorder, characterized by hallmark motor symptoms. It is associated with pathological, oscillatory neural activity in the basal ganglia. Deep brain stimulation (DBS) is often successfully used to treat medically refractive Parkinson's disease. However, the selection of stimulation parameters is based on qualitative assessment of the patient, which can result in a lengthy tuning period and a suboptimal choice of parameters. This study explores fourth-order, control theory-based models of oscillatory activity in the basal ganglia. Describing function analysis is applied to examine possible mechanisms for the generation of oscillations in interacting nuclei and to investigate the suppression of oscillations with high-frequency stimulation. The theoretical results for the suppression of the oscillatory activity obtained using both the fourth-order model, and a previously described second-order model, are optimized to fit clinically recorded local field potential data obtained from Parkinsonian patients with implanted DBS. Close agreement between the power of oscillations recorded for a range of stimulation amplitudes is observed ( R(2)=0.69-0.99 ). The results suggest that the behavior of the system and the suppression of pathological neural oscillations with DBS is well described by the macroscopic models presented. The results also demonstrate that in this instance, a second-order model is sufficient to model the clinical data, without the need for added complexity. Describing the system behavior with computationally efficient models could aid in the identification of optimal stimulation parameters for patients in a clinical environment.

Computational modeling of neurostimulation in brain diseases

Neurostimulation as a therapeutic tool has been developed and used for a range of different diseases such as Parkinson's disease, epilepsy, and migraine. However, it is not known why the efficacy of the stimulation varies dramatically across patients or why some patients suffer from severe side effects. This is largely due to the lack of mechanistic understanding of neurostimulation. Hence, theoretical computational approaches to address this issue are in demand. This chapter provides a review of mechanistic computational modeling of brain stimulation. In particular, we will focus on brain diseases, where mechanistic models (e.g., neural population models or detailed neuronal models) have been used to bridge the gap between cellular-level processes of affected neural circuits and the symptomatic expression of disease dynamics. We show how such models have been, and can be, used to investigate the effects of neurostimulation in the diseased brain. We argue that these models are crucial for the mechanistic understanding of the effect of stimulation, allowing for a rational design of stimulation protocols. Based on mechanistic models, we argue that the development of closed-loop stimulation is essential in order to avoid inference with healthy ongoing brain activity. Furthermore, patient-specific data, such as neuroanatomic information and connectivity profiles obtainable from neuroimaging, can be readily incorporated to address the clinical issue of variability in efficacy between subjects. We conclude that mechanistic computational models can and should play a key role in the rational design of effective, fully integrated, patient-specific therapeutic brain stimulation.

Improving desynchronization of Parkinsonian neuronal network via triplet-structure coordinated reset stimulation

We investigate how the triplet-structure coordinated reset stimulations (CRS), which acts on the GPe, STN and GPi within the basal ganglia-thalamocortical motor circuit, can destabilize the strong synchronous state and improve the reliability of thalamic relay in the parkinsonian network. It is shown that compared with the permanent (1:0 ON-OFF) CRS or the classic deep brain stimulation paradigm, the periodic m:n ON-OFF CRS (i.e., m ON-cycles stimulation followed by n OFF-cycles stimulation) can significantly desynchronize the neuronal network of Parkinson's disease, and evidently improve the fidelity of thalamic relay. In addition, the CRS-induced desynchronization can be greatly enhanced when the STN subpopulation within the pathologic network is subjected to the synaptic plasticity. Furthermore, the desynchronization and reliability can also be further improved as the closed-loop CRS strategy is introduced. The obtained results can be helpful for us to understand the pathophysiology mechanism of Parkinson's disease, even though the feasibility of CRS still needs to be explored in clinic.

Coordinated reset stimulation in a large-scale model of the STN-GPe circuit

Synchronization of populations of neurons is a hallmark of several brain diseases. Coordinated reset (CR) stimulation is a model-based stimulation technique which specifically counteracts abnormal synchrony by desynchronization. Electrical CR stimulation, e.g., for the treatment of Parkinson's disease (PD), is administered via depth electrodes. In order to get a deeper understanding of this technique, we extended the top-down approach of previous studies and constructed a large-scale computational model of the respective brain areas. Furthermore, we took into account the spatial anatomical properties of the simulated brain structures and incorporated a detailed numerical representation of 2 · 10⁴ simulated neurons. We simulated the subthalamic nucleus (STN) and the globus pallidus externus (GPe). Connections within the STN were governed by spike-timing dependent plasticity (STDP). In this way, we modeled the physiological and pathological activity of the considered brain structures. In particular, we investigated how plasticity could be exploited and how the model could be shifted from strongly synchronized (pathological) activity to strongly desynchronized (healthy) activity of the neuronal populations via CR stimulation of the STN neurons. Furthermore, we investigated the impact of specific stimulation parameters especially the electrode position on the stimulation outcome. Our model provides a step forward toward a biophysically realistic model of the brain areas relevant to the emergence of pathological neuronal activity in PD. Furthermore, our model constitutes a test bench for the optimization of both stimulation parameters and novel electrode geometries for efficient CR stimulation.

Closed-loop brain-machine-body interfaces for noninvasive rehabilitation of movement disorders

Traditional approaches for neurological rehabilitation of patients affected with movement disorders, such as Parkinson's disease (PD), dystonia, and essential tremor (ET) consist mainly of oral medication, physical therapy, and botulinum toxin injections. Recently, the more invasive method of deep brain stimulation (DBS) showed significant improvement of the physical symptoms associated with these disorders. In the past several years, the adoption of feedback control theory helped DBS protocols to take into account the progressive and dynamic nature of these neurological movement disorders that had largely been ignored so far. As a result, a more efficient and effective management of PD cardinal symptoms has emerged. In this paper, we review closed-loop systems for rehabilitation of movement disorders, focusing on PD, for which several invasive and noninvasive methods have been developed during the last decade, reducing the complications and side effects associated with traditional rehabilitation approaches and paving the way for tailored individual therapeutics. We then present a novel, transformative, noninvasive closed-loop framework based on force neurofeedback and discuss several future developments of closed-loop systems that might bring us closer to individualized solutions for neurological rehabilitation of movement disorders.

Effects of antidromic and orthodromic activation of STN afferent axons during DBS in Parkinson's disease: a simulation study

Recent studies suggest that subthalamic nucleus (STN)-Deep Brain Stimulation (DBS) may exert at least part of its therapeutic effect through the antidromic suppression of pathological oscillations in the cortex in 6-OHDA treated rats and in parkinsonian patients. STN-DBS may also activate STN neurons by initiating action potential propagation in the orthodromic direction, similarly resulting in suppression of pathological oscillations in the STN. While experimental studies have provided strong evidence in support of antidromic stimulation of cortical neurons, it is difficult to separate relative contributions of antidromic and orthodromic effects of STN-DBS. The aim of this computational study was to examine the effects of antidromic and orthodromic activation on neural firing patterns and beta-band (13-30 Hz) oscillations in the STN and cortex during DBS of STN afferent axons projecting from the cortex. High frequency antidromic stimulation alone effectively suppressed simulated beta activity in both the cortex and STN-globus pallidus externa (GPe) network. High frequency orthodromic stimulation similarly suppressed beta activity within the STN and GPe through the direct stimulation of STN neurons driven by DBS at the same frequency as the stimulus. The combined effect of both antidromic and orthodromic stimulation modulated cortical activity antidromically while simultaneously orthodromically driving STN neurons. While high frequency DBS reduced STN beta-band power, low frequency stimulation resulted in resonant effects, increasing beta-band activity, consistent with previous experimental observations. The simulation results indicate effective suppression of simulated oscillatory activity through both antidromic stimulation of cortical neurons and direct orthodromic stimulation of STN neurons. The results of the study agree with experimental recordings of STN and cortical neurons in rats and support the therapeutic potential of stimulation of cortical neurons.

Development of the Mayo Investigational Neuromodulation Control System: toward a closed-loop electrochemical feedback system for deep brain stimulation

OBJECT

Conventional deep brain stimulation (DBS) devices continue to rely on an open-loop system in which stimulation is independent of functional neural feedback. The authors previously proposed that as the foundation of a DBS "smart" device, a closed-loop system based on neurochemical feedback, may have the potential to improve therapeutic outcomes. Alterations in neurochemical release are thought to be linked to the clinical benefit of DBS, and fast-scan cyclic voltammetry (FSCV) has been shown to be effective for recording these evoked neurochemical changes. However, the combination of FSCV with conventional DBS devices interferes with the recording and identification of the evoked analytes. To integrate neurochemical recording with neurostimulation, the authors developed the Mayo Investigational Neuromodulation Control System (MINCS), a novel, wirelessly controlled stimulation device designed to interface with FSCV performed by their previously described Wireless Instantaneous Neurochemical Concentration Sensing System (WINCS).

METHODS

To test the functionality of these integrated devices, various frequencies of electrical stimulation were applied by MINCS to the medial forebrain bundle of the anesthetized rat, and striatal dopamine release was recorded by WINCS. The parameters for FSCV in the present study consisted of a pyramidal voltage waveform applied to the carbon-fiber microelectrode every 100 msec, ramping between -0.4 V and +1.5 V with respect to an Ag/AgCl reference electrode at a scan rate of either 400 V/sec or 1000 V/sec. The carbon-fiber microelectrode was held at the baseline potential of -0.4 V between scans.

RESULTS

By using MINCS in conjunction with WINCS coordinated through an optic fiber, the authors interleaved intervals of electrical stimulation with FSCV scans and thus obtained artifact-free wireless FSCV recordings. Electrical stimulation of the medial forebrain bundle in the anesthetized rat by MINCS elicited striatal dopamine release that was time-locked to stimulation and increased progressively with stimulation frequency.

CONCLUSIONS

Here, the authors report a series of proof-of-principle tests in the rat brain demonstrating MINCS to be a reliable and flexible stimulation device that, when used in conjunction with WINCS, performs wirelessly controlled stimulation concurrent with artifact-free neurochemical recording. These findings suggest that the integration of neurochemical recording with neurostimulation may be a useful first step toward the development of a closed-loop DBS system for human application.

Using a hybrid neuron in physiologically inspired models of the basal ganglia

Our current understanding of the basal ganglia (BG) has facilitated the creation of computational models that have contributed novel theories, explored new functional anatomy and demonstrated results complementing physiological experiments. However, the utility of these models extends beyond these applications. Particularly in neuromorphic engineering, where the basal ganglia's role in computation is important for applications such as power efficient autonomous agents and model-based control strategies. The neurons used in existing computational models of the BG, however, are not amenable for many low-power hardware implementations. Motivated by a need for more hardware accessible networks, we replicate four published models of the BG, spanning single neuron and small networks, replacing the more computationally expensive neuron models with an Izhikevich hybrid neuron. This begins with a network modeling action-selection, where the basal activity levels and the ability to appropriately select the most salient input is reproduced. A Parkinson's disease model is then explored under normal conditions, Parkinsonian conditions and during subthalamic nucleus deep brain stimulation (DBS). The resulting network is capable of replicating the loss of thalamic relay capabilities in the Parkinsonian state and its return under DBS. This is also demonstrated using a network capable of action-selection. Finally, a study of correlation transfer under different patterns of Parkinsonian activity is presented. These networks successfully captured the significant results of the originals studies. This not only creates a foundation for neuromorphic hardware implementations but may also support the development of large-scale biophysical models. The former potentially providing a way of improving the efficacy of DBS and the latter allowing for the efficient simulation of larger more comprehensive networks.

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.

Minimum energy control for in vitro neurons

OBJECTIVE

To demonstrate the applicability of optimal control theory for designing minimum energy charge-balanced input waveforms for single periodically-firing in vitro neurons from brain slices of Long-Evans rats.

APPROACH

The method of control uses the phase model of a neuron and does not require prior knowledge of the neuron's biological details. The phase model of a neuron is a one-dimensional model that is characterized by the neuron's phase response curve (PRC), a sensitivity measure of the neuron to a stimulus applied at different points in its firing cycle. The PRC for each neuron is experimentally obtained by measuring the shift in phase due to a short-duration pulse injected into the periodically-firing neuron at various phase values. Based on the measured PRC, continuous-time, charge-balanced, minimum energy control waveforms have been designed to regulate the next firing time of the neuron upon application at the onset of an action potential.

MAIN RESULT

The designed waveforms can achieve the inter-spike-interval regulation for in vitro neurons with energy levels that are lower than those of conventional monophasic pulsatile inputs of past studies by at least an order of magnitude. They also provide the advantage of being charge-balanced. The energy efficiency of these waveforms is also shown by performing several supporting simulations that compare the performance of the designed waveforms against that of phase shuffled surrogate inputs, variants of the minimum energy waveforms obtained from suboptimal PRCs, as well as pulsatile stimuli that are applied at the point of maximum PRC. It was found that the minimum energy waveforms perform better than all other stimuli both in terms of control and in the amount of energy used. Specifically, it was seen that these charge-balanced waveforms use at least an order of magnitude less energy than conventional monophasic pulsatile stimuli.

SIGNIFICANCE

The significance of this work is that it uses concepts from the theory of optimal control and introduces a novel approach in designing minimum energy charge-balanced input waveforms for neurons that are robust to noise and implementable in electrophysiological experiments.

The temporal pattern of stimulation may be important to the mechanism of deep brain stimulation

Deep brain stimulation (DBS) has emerged as an important and potentially powerful treatment option for the management of carefully selected patients with advanced Parkinson's disease (PD) who are not adequately controlled by standard medication therapy. Though considerable advances have been made, the mechanisms underlying the therapeutic effects of DBS remain unclear despite its clinical efficacy. It is now widely held that both excitation and inhibition can occur secondary to stimulation, and it is suspected that abnormal synchronized oscillations may also be important in the mechanism of DBS. Other potentially important processes, including blood flow changes, local and upstream neurogenesis, and the modulation of neurotransmitters through stimulation of bordering astrocytes are also being investigated. Recent research has suggested that the temporal pattern of DBS stimulation is also an important variable in DBS neuromodulation, yet the extent of its influence on DBS efficacy has yet to be determined. As high stimulation frequency alone does not appear to be sufficient for optimal symptom suppression, attention to stimulation pattern might lead to more effective symptom control and reduced side effects, possibly at a lower frequency. Stimulation pattern may be potentially amenable to therapeutic modulation and its role in the clinical efficacy of DBS should be addressed through further focus and research.

Improved efficacy of temporally non-regular deep brain stimulation in Parkinson's disease

High frequency deep brain stimulation is an effective therapy for motor symptoms in Parkinson's disease. However, the relative clinical efficacy of regular versus non-regular temporal patterns of stimulation in Parkinson's disease remains unclear. To determine the temporal characteristics of non-regular temporal patterns of stimulation important for the treatment of Parkinson's disease, we compared the efficacy of temporally regular stimulation with four non-regular patterns of stimulation in subjects with Parkinson's disease using an alternating finger tapping task. The patterns of stimulation were also evaluated in a biophysical model of the parkinsonian basal ganglia that exhibited prominent oscillatory activity in the beta frequency range. The temporal patterns of stimulation differentially improved motor task performance. Three of the non-regular patterns of stimulation improved performance of the finger tapping task more than temporally regular stimulation. In the computational model all patterns of deep brain stimulation suppressed beta band oscillatory activity, and the degree of suppression was strongly correlated with the clinical efficacy across stimulation patterns. The three non-regular patterns of stimulation that improved motor performance over regular stimulation also suppressed beta band oscillatory activity in the computational model more effectively than regular stimulation. These data demonstrate that the temporal pattern of stimulation is an important consideration for the clinical efficacy of deep brain stimulation in Parkinson's disease. Furthermore, non-regular patterns of stimulation may ameliorate motor symptoms and suppress pathological rhythmic activity in the basal ganglia more effectively than regular stimulation. Therefore, non-regular patterns of deep brain stimulation may have useful clinical and experimental applications.

Minimum energy desynchronizing control for coupled neurons

We employ optimal control theory to design an event-based, minimum energy, desynchronizing control stimulus for a network of pathologically synchronized, heterogeneously coupled neurons. This works by optimally driving the neurons to their phaseless sets, switching the control off, and letting the phases of the neurons randomize under intrinsic background noise. An event-based minimum energy input may be clinically desirable for deep brain stimulation treatment of neurological diseases, like Parkinson's disease. The event-based nature of the input results in its administration only when it is necessary, which, in general, amounts to fewer applications, and hence, less charge transfer to and from the tissue. The minimum energy nature of the input may also help prolong battery life for implanted stimulus generators. For the example considered, it is shown that the proposed control causes a considerable amount of randomization in the timing of each neuron's next spike, leading to desynchronization for the network.

What brain signals are suitable for feedback control of deep brain stimulation in Parkinson's disease?

Feedback control of deep brain stimulation (DBS) in Parkinson's disease has great potential to improve efficacy, reduce side effects, and decrease the cost of treatment. In this, the timing and intensity of stimulation are titrated according to biomarkers that capture current clinical state. Stimulation may be at standard high frequency or intelligently patterned to directly modify specific pathological rhythms. The search for and validation of appropriate feedback signals are therefore crucial. Signals recorded from the DBS electrode currently appear to be the most promising source of feedback. In particular, beta-frequency band oscillations in the local field potential recorded at the stimulation target may capture variation in bradykinesia and rigidity across patients, but this remains to be confirmed within patients. Biomarkers that reliably reflect other impairments, such as tremor, also need to be established. Finally, whether brain signals are causally important needs to be established before stimulation can be specifically patterned rather than delivered at empirically defined high frequency.

Simulation of cortico-basal ganglia oscillations and their suppression by closed loop deep brain stimulation

A new model of deep brain stimulation (DBS) is presented that integrates volume conduction effects with a neural model of pathological beta-band oscillations in the cortico-basal ganglia network. The model is used to test the clinical hypothesis that closed-loop control of the amplitude of DBS may be possible, based on the average rectified value of beta-band oscillations in the local field potential. Simulation of closed-loop high-frequency DBS was shown to yield energy savings, with the magnitude of the energy saved dependent on the strength of coupling between the subthalamic nucleus and the remainder of the cortico-basal ganglia network. When closed-loop DBS was applied to a strongly coupled cortico-basal ganglia network, the stimulation energy delivered over a 480 s period was reduced by up to 42%. Greater energy reductions were observed for weakly coupled networks, as the stimulation amplitude reduced to zero once the initial desynchronization had occurred. The results provide support for the application of closed-loop high-frequency DBS based on electrophysiological biomarkers.

Study of chaotic behavior of tremor of some Parkinsonians under deep brain stimulation

Deep Brain Stimulation, functional neurosurgery for Parkinson's disease treatment, has three parameters: frequency, pulse width, and voltage. They should be selected appropriately to achieve an effective treatment. In this research, we studied some nonlinear dynamics of Parkinsonian tremor under Deep Brain Stimulation. We recorded finger tremor signals of 8 patients at different voltages as data. To study tremor behavior variation at different voltages, we extracted some nonlinear dynamic features of the data. These features were: embedding space, correlation dimension, largest Lyapunov exponent, entropy and variance of embedding space along x, and y axes. We found that the largest Lyapunov exponents were positive and correlation dimensions of data were not integer, and also all embedding spaces at different voltages had attractors. These observations show that the tremor signal has chaotic behaviors. Also, embedding space variance along x, and y axes in all cases and entropy in the most of them had minimum values at highest voltages in comparison with other voltages. We plotted bar graphs of embedding space variances along x, and y axes at every patient's recorded voltages. A reduction procedure was seen after a threshold in all graphs. As a result, all the chaotic features change with the voltage variation. In the future, it could be possible to select the optimum stimulation voltages by using chaotic features of tremor.

Relative contributions of local cell and passing fiber activation and silencing to changes in thalamic fidelity during deep brain stimulation and lesioning: a computational modeling study

Deep brain stimulation (DBS) and lesioning are two surgical techniques used in the treatment of advanced Parkinson's disease (PD) in patients whose symptoms are not well controlled by drugs, or who experience dyskinesias as a side effect of medications. Although these treatments have been widely practiced, the mechanisms behind DBS and lesioning are still not well understood. The subthalamic nucleus (STN) and globus pallidus pars interna (GPi) are two common targets for both DBS and lesioning. Previous studies have indicated that DBS not only affects local cells within the target, but also passing axons within neighboring regions. Using a computational model of the basal ganglia-thalamic network, we studied the relative contributions of activation and silencing of local cells (LCs) and fibers of passage (FOPs) to changes in the accuracy of information transmission through the thalamus (thalamic fidelity), which is correlated with the effectiveness of DBS. Activation of both LCs and FOPs during STN and GPi-DBS were beneficial to the outcome of stimulation. During STN and GPi lesioning, effects of silencing LCs and FOPs were different between the two types of lesioning. For STN lesioning, silencing GPi FOPs mainly contributed to its effectiveness, while silencing only STN LCs did not improve thalamic fidelity. In contrast, silencing both GPi LCs and GPe FOPs during GPi lesioning contributed to improvements in thalamic fidelity. Thus, two distinct mechanisms produced comparable improvements in thalamic function: driving the output of the basal ganglia to produce tonic inhibition and silencing the output of the basal ganglia to produce tonic disinhibition. These results show the importance of considering effects of activating or silencing fibers passing close to the nucleus when deciding upon a target location for DBS or lesioning.