Conditions for the generation of beta oscillations in the subthalamic nucleus-globus pallidus network

Computational study of associations between the synaptic conductance of STN and GPe and the development of Parkinson's disease

There is evidence that the subthalamic nucleus (STN) and globus pallidus pars externa (GPe) involve in the development of Parkinson's disease, a neurodegenerative disorder characterized by motor and non-motor symptoms and loss of dopaminergic neurons in which the error index (EI) in firing patterns is widely used to address the related issues. Whether and how this interaction mechanism of STN and GPe affects EI in Parkinson's disease is uncertain. To account for this, we propose a kind of basal ganglia-thalamic network model associated with Parkinson's disease coupled with neurons, and investigate the effect of synaptic conductance of STN and GPe on EI in this network, as well as their internal relationship under EI as an index. The results show a relationship like a piecewise function between the error index and the slope of the state transition function of synaptic conductance from STN to GPe ( g snge ) and from GPe to STN ( g gesn ). And there is an approximate negative correlation between EI and g gesn . Increasing g snge and decreasing g gesn can improve the fidelity of thalamus information transmission and alleviate Parkinson's disease effectively. These obtained results can give some theoretical evidence that the abnormal synaptic releases of STN and GPe may be the symptoms of the development of Parkinson's disease, and further enrich the understanding of the pathogenesis and treatment mechanism of Parkinson's disease.

How to design optimal brain stimulation to modulate phase-amplitude coupling?

Objective.Phase-amplitude coupling (PAC), the coupling of the amplitude of a faster brain rhythm to the phase of a slower brain rhythm, plays a significant role in brain activity and has been implicated in various neurological disorders. For example, in Parkinson's disease, PAC between the beta (13-30 Hz) and gamma (30-100 Hz) rhythms in the motor cortex is exaggerated, while in Alzheimer's disease, PAC between the theta (4-8 Hz) and gamma rhythms is diminished. Modulating PAC (i.e. reducing or enhancing PAC) using brain stimulation could therefore open new therapeutic avenues. However, while it has been previously reported that phase-locked stimulation can increase PAC, it is unclear what the optimal stimulation strategy to modulate PAC might be. Here, we provide a theoretical framework to narrow down the experimental optimisation of stimulation aimed at modulating PAC, which would otherwise rely on trial and error.Approach.We make analytical predictions using a Stuart-Landau model, and confirm these predictions in a more realistic model of coupled neural populations.Main results.Our framework specifies the critical Fourier coefficients of the stimulation waveform which should be tuned to optimally modulate PAC. Depending on the characteristics of the amplitude response curve of the fast population, these components may include the slow frequency, the fast frequency, combinations of these, as well as their harmonics. We also show that the optimal balance of energy between these Fourier components depends on the relative strength of the endogenous slow and fast rhythms, and that the alignment of fast components with the fast rhythm should change throughout the slow cycle. Furthermore, we identify the conditions requiring to phase-lock stimulation to the fast and/or slow rhythms.Significance.Together, our theoretical framework lays the foundation for guiding the development of innovative and more effective brain stimulation aimed at modulating PAC for therapeutic benefit.

Computational models advance deep brain stimulation for Parkinson's disease

Deep brain stimulation(DBS) has become an effective intervention for advanced Parkinson's disease(PD), but the exact mechanism of DBS is still unclear. In this review, we discuss the history of DBS, the anatomy and internal architecture of the basal ganglia (BG), the abnormal pathological changes of the BG in PD, and how computational models can help understand and advance DBS. We also describe two types of models: mathematical theoretical models and clinical predictive models. Mathematical theoretical models simulate neurons or neural networks of BG to shed light on the mechanistic principle underlying DBS, while clinical predictive models focus more on patients' outcomes, helping to adapt treatment plans for each patient and advance novel electrode designs. Finally, we provide insights and an outlook on future technologies.

Mathematical derivation and mechanism analysis of beta oscillations in a cortex-pallidum model

In this paper, we develop a new cortex-pallidum model to study the origin mechanism of Parkinson's oscillations in the cortex. In contrast to many previous models, the globus pallidus internal (GPi) and externa (GPe) both exert direct inhibitory feedback to the cortex. Using Hopf bifurcation analysis, two new critical conditions for oscillations, which can include the self-feedback projection of GPe, are obtained. In this paper, we find that the average discharge rate (ADR) is an important marker of oscillations, which can divide Hopf bifurcations into two types that can uniformly be used to explain the oscillation mechanism. Interestingly, the ADR of the cortex first increases and then decreases with increasing coupling weights that are projected to the GPe. Regarding the Hopf bifurcation critical conditions, the quantitative relationship between the inhibitory projection and excitatory projection to the GPe is monotonically increasing; in contrast, the relationship between different coupling weights in the cortex is monotonically decreasing. In general, the oscillation amplitude is the lowest near the bifurcation points and reaches the maximum value with the evolution of oscillations. The GPe is an effective target for deep brain stimulation to alleviate oscillations in the cortex.

Estimation of the transmission delays in the basal ganglia of the macaque monkey and subsequent predictions about oscillatory activity under dopamine depletion

The timescales of the dynamics of a system depend on the combination of the timescales of its components and of its transmission delays between components. Here, we combine experimental stimulation data from 10 studies in macaque monkeys that reveal the timing of excitatory and inhibitory events in the basal ganglia circuit, to estimate its set of transmission delays. In doing so, we reveal possible inconsistencies in the existing data, calling for replications, and we propose two possible sets of transmission delays. We then integrate these delays in a model of the primate basal ganglia that does not rely on direct and indirect pathways' segregation and show that extrastriatal dopaminergic depletion in the external part of the globus pallidus and in the subthalamic nucleus is sufficient to generate β-band oscillations (in the high part, 20-35 Hz, of the band). More specifically, we show that D2 and D5 dopamine receptors in these nuclei play opposing roles in the emergence of these oscillations, thereby explaining how completely deactivating D5 receptors in the subthalamic nucleus can, paradoxically, cancel oscillations.

Structural constraints on the emergence of oscillations in multi-population neural networks

Oscillations arise in many real-world systems and are associated with both functional and dysfunctional states. Whether a network can oscillate can be estimated if we know the strength of interaction between nodes. But in real-world networks (in particular in biological networks) it is usually not possible to know the exact connection weights. Therefore, it is important to determine the structural properties of a network necessary to generate oscillations. Here, we provide a proof that uses dynamical system theory to prove that an odd number of inhibitory nodes and strong enough connections are necessary to generate oscillations in a single cycle threshold-linear network. We illustrate these analytical results in a biologically plausible network with either firing-rate based or spiking neurons. Our work provides structural properties necessary to generate oscillations in a network. We use this knowledge to reconcile recent experimental findings about oscillations in basal ganglia with classical findings.

Synaptic Changes in Pallidostriatal Circuits Observed in the Parkinsonian Model Triggers Abnormal Beta Synchrony with Accurate Spatio-temporal Properties across the Basal Ganglia

Excessive oscillatory activity across basal ganglia (BG) nuclei in the β frequencies (12-30 Hz) is a hallmark of Parkinson's disease (PD). While the link between oscillations and symptoms remains debated, exaggerated β oscillations constitute an important biomarker for therapeutic effectiveness in PD. The neuronal mechanisms of β-oscillation generation however remain unknown. Many existing models rely on a central role of the subthalamic nucleus (STN) or cortical inputs to BG. Contrarily, neural recordings and optogenetic manipulations in normal and parkinsonian rats recently highlighted the central role of the external pallidum (GPe) in abnormal β oscillations, while showing that the integrity of STN or motor cortex is not required. Here, we evaluate the mechanisms for the generation of abnormal β oscillations in a BG network model where neuronal and synaptic time constants, connectivity, and firing rate distributions are strongly constrained by experimental data. Guided by a mean-field approach, we show in a spiking neural network that several BG sub-circuits can drive oscillations. Strong recurrent STN-GPe connections or collateral intra-GPe connections drive γ oscillations (>40 Hz), whereas strong pallidostriatal loops drive low-β (10-15 Hz) oscillations. We show that pathophysiological strengthening of striatal and pallidal synapses following dopamine depletion leads to the emergence of synchronized oscillatory activity in the mid-β range with spike-phase relationships between BG neuronal populations in-line with experiments. Furthermore, inhibition of GPe, contrary to STN, abolishes oscillations. Our modeling study uncovers the neural mechanisms underlying PD β oscillations and may thereby guide the future development of therapeutic strategies.

Criticality supports cross-frequency cortical-thalamic information transfer during conscious states

Consciousness is thought to be regulated by bidirectional information transfer between the cortex and thalamus, but the nature of this bidirectional communication - and its possible disruption in unconsciousness - remains poorly understood. Here, we present two main findings elucidating mechanisms of corticothalamic information transfer during conscious states. First, we identify a highly preserved spectral channel of cortical-thalamic communication that is present during conscious states, but which is diminished during the loss of consciousness and enhanced during psychedelic states. Specifically, we show that in humans, mice, and rats, information sent from either the cortex or thalamus via δ/θ/α waves (∼1-13 Hz) is consistently encoded by the other brain region by high γ waves (52-104 Hz); moreover, unconsciousness induced by propofol anesthesia or generalized spike-and-wave seizures diminishes this cross-frequency communication, whereas the psychedelic 5-methoxy-N,N-dimethyltryptamine (5-MeO-DMT) enhances this low-to-high frequency interregional communication. Second, we leverage numerical simulations and neural electrophysiology recordings from the thalamus and cortex of human patients, rats, and mice to show that these changes in cross-frequency cortical-thalamic information transfer may be mediated by excursions of low-frequency thalamocortical electrodynamics toward/away from edge-of-chaos criticality, or the phase transition from stability to chaos. Overall, our findings link thalamic-cortical communication to consciousness, and further offer a novel, mathematically well-defined framework to explain the disruption to thalamic-cortical information transfer during unconscious states.

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

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

The Therapeutic Frequency Profile of Subthalamic Nucleus Deep Brain Stimulation in Rats Is Shaped by Antidromic Spike Failure

The therapeutic mechanisms of subthalamic nucleus (STN) deep brain stimulation (DBS) may depend on antidromic activation of cortex via the hyperdirect pathway. However, hyperdirect pathway neurons cannot reliably follow high-stimulation frequencies, and the spike failure rate appears to correlate with symptom relief as a function of stimulation frequency. We hypothesized that antidromic spike failure contributes to the cortical desynchronization caused by DBS. We measured in vivo evoked cortical activity in female Sprague Dawley rats and developed a computational model of cortical activation from STN DBS. We modeled stochastic antidromic spike failure to determine how spike failure affected the desynchronization of pathophysiological oscillatory activity in cortex. We found that high-frequency STN DBS desynchronized pathologic oscillations via the masking of intrinsic spiking through a combination of spike collision, refractoriness, and synaptic depletion. Antidromic spike failure shaped the parabolic relationship between DBS frequency and cortical desynchronization, with maximum desynchronization at ∼130 Hz. These findings reveal that antidromic spike failure plays a critical role in mediating the dependency of symptom relief on stimulation frequency.SIGNIFICANCE STATEMENT Deep brain stimulation (DBS) is a highly effective neuromodulation therapy, yet it remains uncertain why conventionally used stimulation frequencies (e.g., ∼130 Hz) are optimal. In this study, we demonstrate a potential explanation for the stimulation frequency dependency of DBS through a combination of in vivo experimental measurements and computational modeling. We show that high-frequency stimulation can desynchronize pathologic firing patterns in populations of neurons by inducing an informational lesion. However, sporadic spike failure at these high frequencies limits the efficacy of the informational lesion, yielding a parabolic profile with optimal effects at ∼130 Hz. This work provides a potential explanation for the therapeutic mechanism of DBS, and highlights the importance of considering spike failure in mechanistic models of DBS.

A model description of beta oscillations in the external globus pallidus

The external globus pallidus (GPe), a subcortical nucleus located in the indirect pathway of the basal ganglia, is widely considered to have tight associations with abnormal beta oscillations (13-30 Hz) observed in Parkinson's disease (PD). Despite that many mechanisms have been put forward to explain the emergence of these beta oscillations, however, it is still unclear the functional contributions of the GPe, especially, whether the GPe itself can generate beta oscillations. To investigate the role played by the GPe in producing beta oscillations, we employ a well described firing rate model of the GPe neural population. Through extensive simulations, we find that the transmission delay within the GPe-GPe pathway contributes significantly to inducing beta oscillations, and the impacts of the time constant and connection strength of the GPe-GPe pathway on generating beta oscillations are non-negligible. Moreover, the GPe firing patterns can be significantly modulated by the time constant and connection strength of the GPe-GPe pathway, as well as the transmission delay within the GPe-GPe pathway. Interestingly, both increasing and decreasing the transmission delay can push the GPe firing pattern from beta oscillations to other firing patterns, including oscillation and non-oscillation firing patterns. These findings suggest that if the transmission delays within the GPe are at least 9.8 ms, beta oscillations can be produced originally in the GPe neural population, which also may be the origin of PD-related beta oscillations and should be regarded as a promising target for treatments for PD.

The mechanism of Parkinson oscillation in the cortex: Possible evidence in a feedback model projecting from the globus pallidus to the cortex

The origin, location and cause of Parkinson's oscillation are not clear at present. In this paper, we establish a new cortex-basal ganglia model to study the origin mechanism of Parkinson beta oscillation. Unlike many previous models, this model includes two direct inhibitory projections from the globus pallidus external (GPe) segment to the cortex. We first obtain the critical calculation formula of Parkinson's oscillation by using the method of Quasilinear analysis. Different from previous studies, the formula obtained in this paper can include the self-feedback connection of GPe. Then, we use the bifurcation analysis method to systematically explain the influence of some key parameters on the oscillation. We find that the bifurcation principle of different cortical nuclei is different. In general, the increase of the discharge capacity of the nuclei will cause oscillation. In some special cases, the sharp reduction of the discharge rate of the nuclei will also cause oscillation. The direction of bifurcation simulation is consistent with the critical condition curve. Finally, we discuss the characteristics of oscillation amplitude. At the beginning of the oscillation, the amplitude is relatively small; with the evolution of oscillation, the amplitude will gradually strengthen. This is consistent with the experimental phenomenon. In most cases, the amplitude of cortical inhibitory nuclei (CIN) is greater than that of cortical excitatory nuclei (CEX), and the two direct inhibitory projections feedback from GPe can significantly reduce the amplitude gap between them. We calculate the main frequency of the oscillation generated in this model, which basically falls between 13 and 30 Hz, belonging to the typical beta frequency band oscillation. Some new results obtained in this paper can help to better understand the origin mechanism of Parkinson's disease and have guiding significance for the development of experiments.

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

Introduction

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

Methods

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

Results

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

Discussion

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

St18 specifies globus pallidus projection neuron identity in MGE lineage

The medial ganglionic eminence (MGE) produces both locally-projecting interneurons, which migrate long distances to structures such as the cortex as well as projection neurons that occupy subcortical nuclei. Little is known about what regulates the migratory behavior and axonal projections of these two broad classes of neurons. We find that St18 regulates the migration and morphology of MGE neurons in vitro. Further, genetic loss-of-function of St18 in mice reveals a reduction in projection neurons of the globus pallidus pars externa. St18 functions by influencing cell fate in MGE lineages as we observe a large expansion of nascent cortical interneurons at the expense of putative GPe neurons in St18 null embryos. Downstream of St18, we identified Cbx7, a component of Polycomb repressor complex 1, and find that it is essential for projection neuron-like migration but not morphology. Thus, we identify St18 as a key regulator of projection neuron vs. interneuron identity.

Subthalamic high-beta oscillation informs the outcome of deep brain stimulation in patients with Parkinson's disease

Background

The therapeutic effect of deep brain stimulation (DBS) of the subthalamic nucleus (STN) for Parkinson's disease (PD) is related to the modulation of pathological neural activities, particularly the synchronization in the β band (13–35 Hz). However, whether the local β activity in the STN region can directly predict the stimulation outcome remains unclear.

Objective

We tested the hypothesis that low-β (13–20 Hz) and/or high-β (20–35 Hz) band activities recorded from the STN region can predict DBS efficacy.

Methods

Local field potentials (LFPs) were recorded in 26 patients undergoing deep brain stimulation surgery in the subthalamic nucleus area. Recordings were made after the implantation of the DBS electrode prior to its connection to a stimulator. The maximum normalized powers in the theta (4–7 Hz), alpha (7–13 Hz), low-β (13–20 Hz), high-β (20–35 Hz), and low-γ (40–55 Hz) subbands in the postoperatively recorded LFP were correlated with the stimulation-induced improvement in contralateral tremor or bradykinesia–rigidity. The distance between the contact selected for stimulation and the contact with the maximum subband power was correlated with the stimulation efficacy. Following the identification of the potential predictors by the significant correlations, a multiple regression analysis was performed to evaluate their effect on the outcome.

Results

The maximum high-β power was positively correlated with bradykinesia–rigidity improvement (rs = 0.549, p < 0.0001). The distance to the contact with maximum high-β power was negatively correlated with bradykinesia–rigidity improvement (rs = −0.452, p < 0.001). No significant correlation was observed with low-β power. The maximum high-β power and the distance to the contact with maximum high-β power were both significant predictors for bradykinesia–rigidity improvement in the multiple regression analysis, explaining 37.4% of the variance altogether. Tremor improvement was not significantly correlated with any frequency.

Conclusion

High-β oscillations, but not low-β oscillations, recorded from the STN region with the DBS lead can inform stimulation-induced improvement in contralateral bradykinesia–rigidity in patients with PD. High-β oscillations can help refine electrode targeting and inform contact selection for DBS therapy.

The genesis and functional consequences of cortico-subthalamic beta augmentation and excessive subthalamic burst discharges after dopaminergic deprivation

The cardinal electrophysiological signs in Parkinson's disease (PD) include augmented beta oscillations in the motor cortex-subthalamic nucleus (MC-STN) axis and excessive burst discharges in STN. We have shown that excessive STN burst discharges have a direct causal relation with the locomotor deficits in PD. To investigate the correlation between the two cardinal signs, we characterized the courses of development of the electrophysiological abnormalities in the hemiparkinsonian rat model. The loss of dopaminergic neurons develops fast, and is histologically completed within 4-7 days of the lesion. The increase in STN burst discharges is limited to the lesioned side, and follows a very similar course. In contrast, beta augmentation has a bilateral presentation, and requires 14-21 days for full development. Behaviorally, the gross locomotor deficits in open field test and limb akinesia in stepping test match the foregoing fast and slow time courses, respectively. A further look into the spike entrainment shows that the oscillations in local field potential (LFP) of the MC effectively entrain the multi-unit (MU) spikes of MC, STN and entopeduncular nucleus (EPN), a rat homolog of human globus pallidus interna (GPi), whereas the LFP of STN or EPN (GPi) cannot entrain the spikes in MC. We conclude that excessive STN burst discharges are a direct consequence, whereas beta augmentation is probably a secondary or adaptive changes in the cortico-subcortical re-entrant loops, to dopaminergic deprivation. Beta augmentation is therefore not so consistently present as excessive STN burst discharges, but could signal more delicate derangements at the level of cortical programming in PD.

A translational perspective on pathophysiological changes of oscillatory activity in dystonia and parkinsonism

Intracerebral recordings from movement disorders patients undergoing deep brain stimulation have allowed the identification of pathophysiological patterns in oscillatory activity that correlate with symptom severity. Changes in oscillatory synchrony occur within and across brain areas, matching the classification of movement disorders as network disorders. However, the underlying mechanisms of oscillatory changes are difficult to assess in patients, as experimental interventions are technically limited and ethically problematic. This is why animal models play an important role in neurophysiological research of movement disorders. In this review, we highlight the contributions of translational research to the mechanistic understanding of pathological changes in oscillatory activity, with a focus on parkinsonism and dystonia, while addressing the limitations of current findings and proposing possible future directions.

Inhibitory Spike-Timing-Dependent Plasticity Can Account for Pathological Strengthening of Pallido-Subthalamic Synapses in Parkinson's Disease

Parkinson's disease (PD) is a neurodegenerative brain disorder associated with dysfunction of the basal ganglia (BG) circuitry. Dopamine (DA) depletion in experimental PD models leads to the pathological strengthening of pallido-subthalamic synaptic connections, contributing to the emergence of abnormally synchronized neuronal activity in the external segment of the globus pallidus (GPe) and subthalamic nucleus (STN). Augmented GPe-STN transmission following loss of DA was attributed to heterosynaptic plasticity mechanisms induced by cortico-subthalamic inputs. However, synaptic plasticity may play a role in this process. Here, by employing computational modeling we show that assuming inhibitory spike-timing-dependent plasticity (iSTDP) at pallido-subthalamic synapses can account for pathological strengthening of pallido-subthalamic synapses in PD by further promoting correlated neuronal activity in the GPe-STN network. In addition, we show that GPe-STN transmission delays can shape bistable activity-connectivity states due to iSTDP, characterized by strong connectivity and strong synchronized activity (pathological states) as opposed to weak connectivity and desynchronized activity (physiological states). Our results may shed light on how abnormal reshaping of GPe-STN connectivity by synaptic plasticity during parkinsonism is related to the PD pathophysiology and contribute to the development of therapeutic brain stimulation techniques targeting plasticity-induced rewiring of network connectivity.

Excitatory deep brain stimulation quenches beta oscillations arising in a computational model of the subthalamo-pallidal loop

Parkinson’s disease (PD) is associated with abnormal \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document}β band oscillations (13–30 Hz) in the cortico-basal ganglia circuits. Abnormally increased striato-pallidal inhibition and strengthening the synaptic coupling between subthalamic nucleus (STN) and globus pallidus externa (GPe), due to the loss of dopamine, are considered as the potential sources of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document}β oscillations in the basal ganglia. Deep brain stimulation (DBS) of the basal ganglia subregions is known as a way to reduce the pathological \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document}β oscillations and motor deficits related to PD. Despite the success of the DBS, its underlying mechanism is poorly understood and, there is controversy about the inhibitory or excitatory role of the DBS in the literature. Here, we utilized a computational network model of basal ganglia which consists of STN, GPe, globus pallidus interna, and thalamic neuronal population. This model can reproduce healthy and pathological \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document}β oscillations similar to what has been observed in experimental studies. Using this model, we investigated the effect of DBS to understand whether its effect is excitatory or inhibitory. Our results show that the excitatory DBS is able to quench the pathological synchrony and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document}β oscillations, while, applying inhibitory DBS failed to quench the PD signs. In light of simulation results, we conclude that the effect of the DBS on its target is excitatory.

Subthalamic Beta Activity in Parkinson's Disease May Be Linked to Dorsal Striatum Gray Matter Volume and Prefrontal Cortical Thickness: A Pilot Study

Background

Excessive oscillations at beta frequencies (13–35 Hz) in the subthalamic nucleus (STN) represent a pathophysiological hallmark of Parkinson's disease (PD), which correlates well with parkinsonian symptoms and is reduced in response to standard disease treatments. However, the association of disease-specific regional gray matter (GM) atrophy or cortical thickness (CT) with the presence of STN beta oscillatory activity has been poorly investigated but is of relevance given the potential of these variables for extracting information about PD pathophysiology. This exploratory study investigated the involvement of regional GM volume and CT in the basal ganglia-cortical network and its potential association with the presence of STN beta oscillatory activity in PD.

Methods

We acquired preoperative GM densities on T1-weighted magnetic resonance imaging scans and we carried out regional estimation of GM volume and CT. LFP activities from the STN were recorded post-operatively in 7 cognitively preserved PD patients off dopaminergic medication undergoing deep-brain stimulation surgery. Oscillatory beta power was determined by power spectral density of 4-min resting state STN LFP activity. Spearman partial correlations and regression analysis were used to screen the presence of STN beta power for their relationship with GM volume and CT measurements.

Results

After controlling for the effects of age, educational level, and disease duration, and after correcting for multiple testing, enhanced STN beta power showed significant and negative correlations between, first, volume of the right putamen and left caudate nucleus, and second, smaller CT in frontal regions involving the left rostral middle frontal gyrus (MFG) and left medial orbitofrontal gyrus. A lower volume in the right putamen and a lower CT in the left MFG demonstrated the strongest associations with increased STN beta power.

Conclusions

These tentative results seem to suggest that STN LFP beta frequencies may be mainly linked to different but ongoing parallel neurodegenerative processes, on the one hand, to GM volume reduction in dorsal striatum, and on the other hand, to CT reduction of prefrontal-“associative” regions. These findings could further delineate the brain structural interactions underpinning the exaggerated STN beta activity commonly observed in PD patients.

The Origin of Abnormal Beta Oscillations in the Parkinsonian Corticobasal Ganglia Circuits

Parkinson's disease (PD) is a neurodegenerative brain disorder associated with motor and nonmotor symptoms. Exaggerated beta band (15–30 Hz) neuronal oscillations are widely observed in corticobasal ganglia (BG) circuits during parkinsonism. Abnormal beta oscillations have been linked to motor symptoms of PD, but their exact relationship is poorly understood. Nevertheless, reduction of beta oscillations can induce therapeutic effects in PD patients. While it is widely believed that the external globus pallidus (GPe) and subthalamic nucleus (STN) are jointly responsible for abnormal rhythmogenesis in the parkinsonian BG, the role of other cortico-BG circuits cannot be ignored. To shed light on the origin of abnormal beta oscillations in PD, here we review changes of neuronal activity observed in experimental PD models and discuss how the cortex and different BG nuclei cooperate to generate and stabilize abnormal beta oscillations during parkinsonism. This may provide further insights into the complex relationship between abnormal beta oscillations and motor dysfunction in PD, which is crucial for potential target-specific therapeutic interventions in PD patients.

Transient Response of Basal Ganglia Network in Healthy and Low-Dopamine State

The basal ganglia (BG) are crucial for a variety of motor and cognitive functions. Changes induced by persistent low-dopamine (e.g., in Parkinson’s disease; PD) result in aberrant changes in steady-state population activity (β band oscillations) and the transient response of the BG. Typically, a brief cortical stimulation results in a triphasic response in the substantia nigra pars reticulata (SNr; an output of the BG). The properties of the triphasic responses are shaped by dopamine levels. While mechanisms underlying aberrant steady state activity are well studied, it is still unclear which BG interactions are crucial for the aberrant transient responses in the BG. Moreover, it is also unclear whether mechanisms underlying the aberrant changes in steady-state activity and transient response are the same. Here, we used numerical simulations of a network model of BG to identify the key factors that determine the shape of the transient responses. We show that an aberrant transient response of the SNr in the low-dopamine state involves changes in the direct pathway and the recurrent interactions within the globus pallidus externa (GPe) and between GPe and subthalamic nucleus (STN). However, the connections from D2-type spiny projection neurons (D2-SPN) to GPe are most crucial in shaping the transient response and by restoring them to their healthy level, we could restore the shape of transient response even in low-dopamine state. Finally, we show that the changes in BG that result in aberrant transient response are also sufficient to generate pathologic oscillatory activity in the steady state.

Spike-Timing-Dependent Plasticity Mediated by Dopamine and its Role in Parkinson's Disease Pathophysiology

Parkinson's disease (PD) is a multi-systemic neurodegenerative brain disorder. Motor symptoms of PD are linked to the significant dopamine (DA) loss in substantia nigra pars compacta (SNc) followed by basal ganglia (BG) circuit dysfunction. Increasing experimental and computational evidence indicates that (synaptic) plasticity plays a key role in the emergence of PD-related pathological changes following DA loss. Spike-timing-dependent plasticity (STDP) mediated by DA provides a mechanistic model for synaptic plasticity to modify synaptic connections within the BG according to the neuronal activity. To shed light on how DA-mediated STDP can shape neuronal activity and synaptic connectivity in the PD condition, we reviewed experimental and computational findings addressing the modulatory effect of DA on STDP as well as other plasticity mechanisms and discussed their potential role in PD pathophysiology and related network dynamics and connectivity. In particular, reshaping of STDP profiles together with other plasticity-mediated processes following DA loss may abnormally modify synaptic connections in competing pathways of the BG. The cascade of plasticity-induced maladaptive or compensatory changes can impair the excitation-inhibition balance towards the BG output nuclei, leading to the emergence of pathological activity-connectivity patterns in PD. Pre-clinical, clinical as well as computational studies reviewed here provide an understanding of the impact of synaptic plasticity and other plasticity mechanisms on PD pathophysiology, especially PD-related network activity and connectivity, after DA loss. This review may provide further insights into the abnormal structure-function relationship within the BG contributing to the emergence of pathological states in PD. Specifically, this review is intended to provide detailed information for the development of computational network models for PD, serving as testbeds for the development and optimization of invasive and non-invasive brain stimulation techniques. Computationally derived hypotheses may accelerate the development of therapeutic stimulation techniques and potentially reduce the number of related animal experiments.

A bidirectional Hopf bifurcation analysis of Parkinson's oscillation in a simplified basal ganglia model

In this paper, we study the parkinson oscillation mechanism in a computational model by bifurcation analysis and numerical simulation. Oscillatory activities can be induced by abnormal coupling weights and delays. The bidirectional Hopf bifurcation phenomena are found in simulations, which can uniformly explain the oscillation mechanism in this model. The Hopf1 represents the transition between the low firing rate stable state (SS) and oscillation state (OS), the Hopf2 represents the transition between the high firing rate stable state (HSS) and the OS, the mechanisms of them are different. The Hopf1 and Hopf2 bifurcations both show that when the state transfers from the stable region to the oscillation region, oscillatory activities always originate from the beta frequency band, and then gradually evolve into the alpha frequency band, the theta frequency band and delta frequency band in this model. We find that the changing trends of the DF and oscillation amplitude (OSAM) are contrary, oscillation activities in lower frequency band are more stable than that in higher frequency band. The effect of the delay in inhibitory pathways is greater than that of in excitatory pathways, and appropriate delays improve the discharge activation level (DAL) of the system. In all, we infer that oscillations can be induced by the follow factors: 1. Improvement of the DAL of the globus pallidus externa (GPe); 2. Reduce the DAL of the GPe from the HSS or the discharge saturation state; 3. The GPe can also resonate with the subthalamic nucleus (STN).

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

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

Modulation of dopamine tone induces frequency shifts in cortico-basal ganglia beta oscillations

Βeta oscillatory activity (human: 13-35 Hz; primate: 8-24 Hz) is pervasive within the cortex and basal ganglia. Studies in Parkinson's disease patients and animal models suggest that beta-power increases with dopamine depletion. However, the exact relationship between oscillatory power, frequency and dopamine tone remains unclear. We recorded neural activity in the cortex and basal ganglia of healthy non-human primates while acutely and chronically up- and down-modulating dopamine levels. We assessed changes in beta oscillations in patients with Parkinson's following acute and chronic changes in dopamine tone. Here we show beta oscillation frequency is strongly coupled with dopamine tone in both monkeys and humans. Power, coherence between single-units and local field potentials (LFP), spike-LFP phase-locking, and phase-amplitude coupling are not systematically regulated by dopamine levels. These results demonstrate that beta frequency is a key property of pathological oscillations in cortical and basal ganglia networks.

Long-Term Desynchronization by Coordinated Reset Stimulation in a Neural Network Model With Synaptic and Structural Plasticity

Several brain disorders are characterized by abnormal neuronal synchronization. To specifically counteract abnormal neuronal synchrony and, hence, related symptoms, coordinated reset (CR) stimulation was computationally developed. In principle, successive epochs of synchronizing and desynchronizing stimulation may reversibly move neural networks with plastic synapses back and forth between stable regimes with synchronized and desynchronized firing. Computationally derived predictions have been verified in pre-clinical and clinical studies, paving the way for novel therapies. However, as yet, computational models were not able to reproduce the clinically observed increase of desynchronizing effects of regularly administered CR stimulation intermingled by long stimulation-free epochs. We show that this clinically important phenomenon can be computationally reproduced by taking into account structural plasticity (SP), a mechanism that deletes or generates synapses in order to homeostatically adapt the firing rates of neurons to a set point-like target firing rate in the course of days to months. If we assume that CR stimulation favorably reduces the target firing rate of SP, the desynchronizing effects of CR stimulation increase after long stimulation-free epochs, in accordance with clinically observed phenomena. Our study highlights the pivotal role of stimulation- and dosing-induced modulation of homeostatic set points in therapeutic processes.

Neural signatures of hyperdirect pathway activity in Parkinson's disease

Parkinson's disease (PD) is characterised by the emergence of beta frequency oscillatory synchronisation across the cortico-basal-ganglia circuit. The relationship between the anatomy of this circuit and oscillatory synchronisation within it remains unclear. We address this by combining recordings from human subthalamic nucleus (STN) and internal globus pallidus (GPi) with magnetoencephalography, tractography and computational modelling. Coherence between supplementary motor area and STN within the high (21-30 Hz) but not low (13-21 Hz) beta frequency range correlated with 'hyperdirect pathway' fibre densities between these structures. Furthermore, supplementary motor area activity drove STN activity selectively at high beta frequencies suggesting that high beta frequencies propagate from the cortex to the basal ganglia via the hyperdirect pathway. Computational modelling revealed that exaggerated high beta hyperdirect pathway activity can provoke the generation of widespread pathological synchrony at lower beta frequencies. These findings suggest a spectral signature and a pathophysiological role for the hyperdirect pathway in PD.

Average beta burst duration profiles provide a signature of dynamical changes between the ON and OFF medication states in Parkinson's disease

Parkinson's disease motor symptoms are associated with an increase in subthalamic nucleus beta band oscillatory power. However, these oscillations are phasic, and there is a growing body of evidence suggesting that beta burst duration may be of critical importance to motor symptoms. This makes insights into the dynamics of beta bursting generation valuable, in particular to refine closed-loop deep brain stimulation in Parkinson's disease. In this study, we ask the question "Can average burst duration reveal how dynamics change between the ON and OFF medication states?". Our analysis of local field potentials from the subthalamic nucleus demonstrates using linear surrogates that the system generating beta oscillations is more likely to act in a non-linear regime OFF medication and that the change in a non-linearity measure is correlated with motor impairment. In addition, we pinpoint the simplest dynamical changes that could be responsible for changes in the temporal patterning of beta oscillations between medication states by fitting to data biologically inspired models, and simpler beta envelope models. Finally, we show that the non-linearity can be directly extracted from average burst duration profiles under the assumption of constant noise in envelope models. This reveals that average burst duration profiles provide a window into burst dynamics, which may underlie the success of burst duration as a biomarker. In summary, we demonstrate a relationship between average burst duration profiles, dynamics of the system generating beta oscillations, and motor impairment, which puts us in a better position to understand the pathology and improve therapies such as deep brain stimulation.

Leveraging deep learning to control neural oscillators

Modulation of the firing times of neural oscillators has long been an important control objective, with applications including Parkinson's disease, Tourette's syndrome, epilepsy, and learning. One common goal for such modulation is desynchronization, wherein two or more oscillators are stimulated to transition from firing in phase with each other to firing out of phase. The optimization of such stimuli has been well studied, but this typically relies on either a reduction of the dimensionality of the system or complete knowledge of the parameters and state of the system. This limits the applicability of results to real problems in neural control. Here, we present a trained artificial neural network capable of accurately estimating the effects of square-wave stimuli on neurons using minimal output information from the neuron. We then apply the results of this network to solve several related control problems in desynchronization, including desynchronizing pairs of neurons and achieving clustered subpopulations of neurons in the presence of coupling and noise.

Understanding the Role of Sensorimotor Beta Oscillations

Beta oscillations have been predominantly observed in sensorimotor cortices and basal ganglia structures and they are thought to be involved in somatosensory processing and motor control. Although beta activity is a distinct feature of healthy and pathological sensorimotor processing, the role of this rhythm is still under debate. Here we review recent findings about the role of beta oscillations during experimental manipulations (i.e., drugs and brain stimulation) and their alteration in aging and pathology. We show how beta changes when learning new motor skills and its potential to integrate sensory input with prior contextual knowledge. We conclude by discussing a novel methodological approach analyzing beta oscillations as a series of transient bursting events.

Model neocortical microcircuit supports beta and gamma rhythms

Gamma and beta rhythms in neocortical circuits are thought to be caused by distinct subcircuits involving different type of interneurons. However, it is not clear how these distinct but inter-linked intrinsic circuits interact with afferent drive to engender the two rhythms. We report a biophysical computational model to investigate the hypothesis that tonic and phasic drive might engender beta and gamma oscillations, respectively, in a neocortical circuit.

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

OBJECTIVE

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

APPROACH

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

MAIN RESULTS

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

SIGNIFICANCE

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

Interaction of Indirect and Hyperdirect Pathways on Synchrony and Tremor-Related Oscillation in the Basal Ganglia

Low-frequency oscillatory activity (3-9 Hz) and increased synchrony in the basal ganglia (BG) are recognized to be crucial for Parkinsonian tremor. However, the dynamical mechanism underlying the tremor-related oscillations still remains unknown. In this paper, the roles of the indirect and hyperdirect pathways on synchronization and tremor-related oscillations are considered based on a modified Hodgkin-Huxley model. Firstly, the effects of indirect and hyperdirect pathways are analysed individually, which show that increased striatal activity to the globus pallidus external (GPe) or strong cortical gamma input to the subthalamic nucleus (STN) is sufficient to promote synchrony and tremor-related oscillations in the BG network. Then, the mutual effects of both pathways are analysed by adjusting the related currents simultaneously. Our results suggest that synchrony and tremor-related oscillations would be strengthened if the current of these two paths are in relative imbalance. And the network tends to be less synchronized and less tremulous when the frequency of cortical input is in the theta band. These findings may provide novel treatments in the cortex and striatum to alleviate symptoms of tremor in Parkinson's disease.

EEG, MEG and neuromodulatory approaches to explore cognition: Current status and future directions

Neural oscillations and their association with brain states and cognitive functions have been object of extensive investigation over the last decades. Several electroencephalography (EEG) and magnetoencephalography (MEG) analysis approaches have been explored and oscillatory properties have been identified, in parallel with the technical and computational advancement. This review provides an up-to-date account of how EEG/MEG oscillations have contributed to the understanding of cognition. Methodological challenges, recent developments and translational potential, along with future research avenues, are discussed.

Facilitation of GluN2C-containing NMDA receptors in the external globus pallidus increases firing of fast spiking neurons and improves motor function in a hemiparkinsonian mouse model

Globus pallidus externa (GPe) is a nucleus in the basal ganglia circuitry involved in the control of movement. Recent studies have demonstrated a critical role of GPe cell types in Parkinsonism. Specifically increasing the function of parvalbumin (PV) neurons in the GPe has been found to facilitate motor function in a mouse model of Parkinson’s disease (PD). The knowledge of contribution of NMDA receptors to GPe function is limited. Here, we demonstrate that fast spiking neurons in the GPe express NMDA receptor currents sensitive to GluN2C/GluN2D-selective inhibitors and glycine site agonist with higher efficacy at GluN2C-containing receptors. Furthermore, using a novel reporter model, we demonstrate the expression of GluN2C subunits in PV neurons in the GPe which project to subthalamic nuclei. GluN2D subunit was also found to localize to PV neurons in GPe. Ablation of GluN2C subunit does not affect spontaneous firing of fast spiking neurons. In contrast, facilitating the function of GluN2C-containing receptors using glycine-site NMDA receptor agonists, D-cycloserine (DCS) or AICP, increased the spontaneous firing frequency of PV neurons in a GluN2C-dependent manner. Finally, we demonstrate that local infusion of DCS or AICP into the GPe improved motor function in a mouse model of PD. Together, these results demonstrate that GluN2C-containing receptors and potentially GluN2D-containing receptors in the GPe may serve as a therapeutic target for alleviating motor dysfunction in PD and related disorders.

Emergence of Beta Oscillations of a Resonance Model for Parkinson's Disease

In Parkinson's disease, the excess of beta oscillations in cortical-basal ganglia (BG) circuits has been correlated with normal movement suppression. In this paper, a physiologically based resonance model, generalizing an earlier model of the STN-GPe circuit, is employed to analyze critical dynamics of the occurrence of beta oscillations, which correspond to Hopf bifurcation. With the experimentally measured parameters, conditions for the occurrence of Hopf bifurcation with time delay are deduced by means of linear stability analysis, center manifold theorem, and normal form analysis. It is found that beta oscillations can be induced by increasing synaptic transmission delay. Furthermore, it is revealed that the oscillations originate from interaction among different synaptic connections. Our analytical results are consistent with the previous experimental and simulating findings, thus may provide a more systematic insight into the mechanisms underlying the transient beta bursts.

The theoretical mechanism of Parkinson's oscillation frequency bands: a computational model study

Excessive synchronous oscillation activities appear in the brain is a key pathological feature of Parkinson's disease, the mechanism of which is still unclear. Although some previous studies indicated that β oscillation (13-30 Hz) may directly originate in the network composed of the subthalamic nucleus (STN) and external globus pallidus (GPe) neurons, specific onset mechanisms of which are unclear, especially theoretical evidences in numerical simulation are still little. In this paper, we employ a STN-GPe mean-field model to explore the onset mechanism of Parkinson's oscillation. In addition to β oscillation, we find that some other common oscillation frequency bands can appear in this network, such as the α oscillation band (8-12 Hz), the θ oscillation band (4-7 Hz) and δ oscillation band (1-3 Hz). In addition to the coupling weight between the STN and GPe, the delay is also a critical factor to affect oscillatory activities, which can not be neglected compared to other parameters. Through simulation and analysis, we propose two possible theories may induce the system to transfer from the stable state to the oscillatory state in this model: (1). The oscillation activity can be induced when the firing activation level of the population increases to large enough; (2). In some special cases, the population may stay in the high firing rate stable state and the mean discharge rate of which is too large to induce oscillations, then oscillation activities may be induced as the MD decreases to moderate value. In most situations, the change trends of the MD and oscillation dominant frequency are contrary, which may be an important physiological phenomenon shown in this model. The delays and firing rates were obtained by simulating, which may be verified in the experiment in the future.

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

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

Subthalamic beta oscillations correlate with dopaminergic degeneration in experimental parkinsonism

Excessive beta activity has been shown in local field potential recordings from the cortico-basal ganglia loop of Parkinson's disease patients and in its various animal models. Recent evidence suggests that enhanced beta oscillations may play a central role in the pathophysiology of the disorder and that beta activity may be directly linked to the motor impairment. However, the temporal evolution of exaggerated beta oscillations during the ongoing dopaminergic neurodegeneration and its relation to the motor impairment and histological changes are still unknown. We investigated motor behavioral, in-vivo electrophysiological (subthalamic nucleus, motor cortex) and histological changes (striatum, substantia nigra compacta) 2, 5, 10 and 20-30 days after a 6-hydroxydopamine injection into the medial forebrain bundle in Wistar rats. We found strong correlations between subthalamic beta power and motor impairment. No correlation was found for beta power in the primary motor cortex. Only subthalamic but not cortical beta power was strongly correlated with the histological markers of the dopaminergic neurodegeneration. Significantly increased subthalamic beta oscillations could be detected before this increase was found in primary motor cortex. At the latest observation time point, a significantly higher percentage of long beta bursts was found. Our study is the first to show a strong relation between subthalamic beta power and the dopaminergic neurodegeneration. Thus, we provide additional evidence for an important pathophysiological role of subthalamic beta oscillations and prolonged beta bursts in Parkinson's disease.

Parvalbumin+ and Npas1+ Pallidal Neurons Have Distinct Circuit Topology and Function

The external globus pallidus (GPe) is a critical node within the basal ganglia circuit. Phasic changes in the activity of GPe neurons during movement and their alterations in Parkinson's disease (PD) argue that the GPe is important in motor control. Parvalbumin-positive (PV+) neurons and Npas1+ neurons are the two principal neuron classes in the GPe. The distinct electrophysiological properties and axonal projection patterns argue that these two neuron classes serve different roles in regulating motor output. However, the causal relationship between GPe neuron classes and movement remains to be established. Here, by using optogenetic approaches in mice (both males and females), we showed that PV+ neurons and Npas1+ neurons promoted and suppressed locomotion, respectively. Moreover, PV+ neurons and Npas1+ neurons are under different synaptic influences from the subthalamic nucleus (STN). Additionally, we found a selective weakening of STN inputs to PV+ neurons in the chronic 6-hydroxydopamine lesion model of PD. This finding reinforces the idea that the reciprocally connected GPe-STN network plays a key role in disease symptomatology and thus provides the basis for future circuit-based therapies.SIGNIFICANCE STATEMENT The external pallidum is a key, yet an understudied component of the basal ganglia. Neural activity in the pallidum goes awry in neurologic diseases, such as Parkinson's disease. While this strongly argues that the pallidum plays a critical role in motor control, it has been difficult to establish the causal relationship between pallidal activity and motor function/dysfunction. This was in part because of the cellular complexity of the pallidum. Here, we showed that the two principal neuron types in the pallidum have opposing roles in motor control. In addition, we described the differences in their synaptic influence. Importantly, our research provides new insights into the cellular and circuit mechanisms that explain the hypokinetic features of Parkinson's disease.

Functional segregation and integration within the human subthalamic nucleus from a micro- and meso-level perspective

The subthalamic nucleus (STN) is a core basal ganglia structure involved in the control of motor, cognitive, motivational and affective functions. The (challenged) tripartite subdivision hypothesis places these functions into distinct sensorimotor, cognitive/associative, and limbic subregions based on the topography of cortical projections. To a large extent, this hypothesis is used to motivate the choice of target coordinates for implantation of deep brain stimulation electrodes for treatment of neurological and psychiatric disorders. Yet, the parallel organization of basal ganglia circuits has been known to allow considerable cross-talk, which might contribute to the occurrence of neuropsychiatric side effects when stimulating the dorsolateral, putative sensorimotor, part of the STN for treatment of Parkinson's disease. Any functional segregation within the STN is expected to be reflected both at micro-level microscopy and meso-level neural population activity. As such, we review the current empirical evidence from anterograde tracing and immunocytochemistry studies and from local field potential recordings for delineating the STN into distinct subregions. The spatial distribution of immunoreactivity presents as a combination of gradients, and although neural activity in distinct frequency bands appears spatially clustered, there is substantial overlap in peak locations. We argue that regional specialization without sharply defined borders is likely most representative of the STN's functional organization.

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

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

Waveform changes with the evolution of beta bursts in the human subthalamic nucleus

OBJECTIVE

Phasic bursts of beta band synchronisation have been linked to motor impairment in Parkinson's disease (PD). However, little is known about what terminates bursts.

METHODS

We used the Hilbert-Huang transform to investigate beta bursts in the local field potential recorded from the subthalamic nucleus in nine patients with PD on and off levodopa.

RESULTS

The sharpness of the beta waveform extrema fell as burst amplitude dropped. Conversely, an index of phase slips between waveform extrema, and the power of concurrent theta activity increased as burst amplitude fell. Theta activity was also increased on levodopa when beta bursts were attenuated. These phenomena were associated with reduction in coupling between beta phase and high gamma activity amplitude. We discuss how these findings may suggest that beta burst termination is associated with relative desynchronization of the beta drive, increase in competing theta activity and increased phase slips in the beta activity.

CONCLUSIONS

We characterise the dynamical nature of beta bursts, thereby permitting inferences about underlying activities and, in particular, about why bursts terminate.

SIGNIFICANCE

Understanding the dynamical nature of beta bursts may help point to interventions that can cause their termination and potentially treat motor impairment in PD.

Dysregulation of external globus pallidus-subthalamic nucleus network dynamics in parkinsonian mice during cortical slow-wave activity and activation

KEY POINTS

Reciprocally connected GABAergic external globus pallidus (GPe) and glutamatergic subthalamic nucleus (STN) neurons form a key network within the basal ganglia. In Parkinson's disease and its models, abnormal rates and patterns of GPe-STN network activity are linked to motor dysfunction. Using cell class-specific optogenetic identification and inhibition during cortical slow-wave activity and activation, we report that, in dopamine-depleted mice, (1) D2 dopamine receptor expressing striatal projection neurons (D2-SPNs) discharge at higher rates, especially during cortical activation, (2) prototypic parvalbumin-expressing GPe neurons are excessively patterned by D2-SPNs even though their autonomous activity is upregulated, (3) despite being disinhibited, STN neurons are not hyperactive, and (4) STN activity opposes striatopallidal patterning. These data argue that in parkinsonian mice abnormal, temporally offset prototypic GPe and STN neuron firing results in part from increased striatopallidal transmission and that compensatory plasticity limits STN hyperactivity and cortical entrainment.

ABSTRACT

Reciprocally connected GABAergic external globus pallidus (GPe) and glutamatergic subthalamic nucleus (STN) neurons form a key, centrally positioned network within the basal ganglia. In Parkinson's disease and its models, abnormal rates and patterns of GPe-STN network activity are linked to motor dysfunction. Following the loss of dopamine, the activities of GPe and STN neurons become more temporally offset and strongly correlated with cortical oscillations below 40 Hz. Previous studies utilized cortical slow-wave activity and/or cortical activation (ACT) under anaesthesia to probe the mechanisms underlying the normal and pathological patterning of basal ganglia activity. Here, we combined this approach with in vivo optogenetic inhibition to identify and interrupt the activity of D2 dopamine receptor-expressing striatal projection neurons (D2-SPNs), parvalbumin-expressing prototypic GPe (PV GPe) neurons, and STN neurons. We found that, in dopamine-depleted mice, (1) the firing rate of D2-SPNs was elevated, especially during cortical ACT, (2) abnormal phasic suppression of PV GPe neuron activity was ameliorated by optogenetic inhibition of coincident D2-SPN activity, (3) autonomous PV GPe neuron firing ex vivo was upregulated, presumably through homeostatic mechanisms, (4) STN neurons were not hyperactive, despite being disinhibited, (5) optogenetic inhibition of the STN exacerbated abnormal GPe activity, and (6) exaggerated beta band activity was not present in the cortex or GPe-STN network. Together with recent studies, these data suggest that in dopamine-depleted mice abnormally correlated and temporally offset PV GPe and STN neuron activity is generated in part by elevated striatopallidal transmission, while compensatory plasticity prevents STN hyperactivity and limits cortical entrainment.

Uncoupling the roles of firing rates and spike bursts in shaping the STN-GPe beta band oscillations

The excess of 15-30 Hz (β-band) oscillations in the basal ganglia is one of the key signatures of Parkinson's disease (PD). The STN-GPe network is integral to generation and modulation of β band oscillations in basal ganglia. However, the role of changes in the firing rates and spike bursting of STN and GPe neurons in shaping these oscillations has remained unclear. In order to uncouple their effects, we studied the dynamics of STN-GPe network using numerical simulations. In particular, we used a neuron model, in which firing rates and spike bursting can be independently controlled. Using this model, we found that while STN firing rate is predictive of oscillations, GPe firing rate is not. The effect of spike bursting in STN and GPe neurons was state-dependent. That is, only when the network was operating in a state close to the border of oscillatory and non-oscillatory regimes, spike bursting had a qualitative effect on the β band oscillations. In these network states, an increase in GPe bursting enhanced the oscillations whereas an equivalent proportion of spike bursting in STN suppressed the oscillations. These results provide new insights into the mechanisms underlying the transient β bursts and how duration and power of β band oscillations may be controlled by an interplay of GPe and STN firing rates and spike bursts.