Beta-Band Resonance and Intrinsic Oscillations in a Biophysically Detailed Model of the Subthalamic Nucleus-Globus Pallidus Network

Beta-band power modulation in the human amygdala differentiates between go/no-go responses in an arm-reaching task

Objective. Traditionally known for its involvement in emotional processing, the amygdala's involvement in motor control remains relatively unexplored, with sparse investigations into the neural mechanisms governing amygdaloid motor movement and inhibition. This study aimed to characterize the amygdaloid beta-band (13-30 Hz) power between 'Go' and 'No-go' trials of an arm-reaching task.Approach. Ten participants with drug-resistant epilepsy implanted with stereoelectroencephalographic (SEEG) electrodes in the amygdala were enrolled in this study. SEEG data was recorded throughout discrete phases of a direct reach Go/No-go task, during which participants reached a touchscreen monitor or withheld movement based on a colored cue. Multitaper power analysis along with Wilcoxon signed-rank and Yates-correctedZtests were used to assess significant modulations of beta power between the Response and fixation (baseline) phases in the 'Go' and 'No-go' conditions.Main results. In the 'Go' condition, nine out of the ten participants showed a significant decrease in relative beta-band power during the Response phase (p⩽ 0.0499). In the 'No-go' condition, eight out of the ten participants presented a statistically significant increase in relative beta-band power during the response phase (p⩽ 0.0494). Four out of the eight participants with electrodes in the contralateral hemisphere and seven out of the eight participants with electrodes in the ipsilateral hemisphere presented significant modulation in beta-band power in both the 'Go' and 'No-go' conditions. At the group level, no significant differences were found between the contralateral and ipsilateral sides or between genders.Significance.This study reports beta-band power modulation in the human amygdala during voluntary movement in the setting of motor execution and inhibition. This finding supplements prior research in various brain regions associating beta-band power with motor control. The distinct beta-power modulation observed between these response conditions suggests involvement of amygdaloid oscillations in differentiating between motor inhibition and execution.

External segment of the globus pallidus in health and disease: Its interactions with the striatum and subthalamic nucleus

The external segment of the globus pallidus (GPe) has long been considered a homogeneous structure that receives inputs from the striatum and sends processed information to the subthalamic nucleus, composing a relay nucleus of the indirect pathway that contributes to movement suppression. Recent methodological revolution in rodents led to the identification of two distinct cell types in the GPe with different fiber connections. The GPe may be regarded as a dynamic, complex and influential center within the basal ganglia circuitry, rather than a simple relay nucleus. On the other hand, many studies have so far been performed in monkeys to clarify the functions of the basal ganglia in the healthy and diseased states, but have not paid much attention to such classification and functional differences of GPe neurons. In this minireview, we consider the knowledge on the rodent GPe and discuss its impact on the understanding of the basal ganglia circuitry in monkeys.

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

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

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 network configuration in Parkinsonian state compensates network activity change caused by loss of dopamine

Parkinson's disease is a movement disorder caused by dopamine depletion in the basal ganglia. Neural activity of the subthalamic nucleus (STN) and globus pallidus externus (GPe) in the basal ganglia are closely related to motor symptoms of Parkinson's disease. However, the pathogenesis of the disease and the transition from the normal state to the pathological state have yet to be elucidated. The functional organization of the GPe is gaining attention due to the recent finding that it consists of two distinct cell populations, namely prototypic GPe neurons and arkypallidal neurons. Identifying connectivity structures between these cell populations, as well as STN neurons, in relation to the dependence of the network activity on the dopaminergic effects is vital. In the present study, using a computational model of the STN-GPe network, we explored biologically plausible connectivity structures between these cell populations. We evaluated the experimentally reported neural activities of these cell types to elucidate the effects of dopaminergic modulation and changes caused by chronic dopamine depletion, such as strengthened connections in the neural activity of the STN-GPe network. Our results indicate that the arkypallidal neurons receive cortical inputs separately from the source for prototypic and STN neurons, suggesting that arkypallidal neurons might be responsible for an additional pathway with the cortex. Furthermore, changes caused by chronic dopamine depletion compensate for the loss of dopaminergic modulation. Changes caused by dopamine depletion itself likely induce the pathological activity observed in patients with Parkinson's disease. However, such changes counteract those of firing rates caused by loss of dopaminergic modulation. In addition, we observed that the STN-GPe tends to exhibit activity with pathological characteristics as side effects.

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.

EEG Power spectra and subcortical pathology in chronic disorders of consciousness

BACKGROUND

Despite a growing understanding of disorders of consciousness following severe brain injury, the association between long-term impairment of consciousness, spontaneous brain oscillations, and underlying subcortical damage, and the ability of such information to aid patient diagnosis, remains incomplete.

METHODS

Cross-sectional observational sample of 116 patients with a disorder of consciousness secondary to brain injury, collected prospectively at a tertiary center between 2011 and 2013. Multimodal analyses relating clinical measures of impairment, electroencephalographic measures of spontaneous brain activity, and magnetic resonance imaging data of subcortical atrophy were conducted in 2018.

RESULTS

In the final analyzed sample of 61 patients, systematic associations were found between electroencephalographic power spectra and subcortical damage. Specifically, the ratio of beta-to-delta relative power was negatively associated with greater atrophy in regions of the bilateral thalamus and globus pallidus (both left > right) previously shown to be preferentially atrophied in chronic disorders of consciousness. Power spectrum total density was also negatively associated with widespread atrophy in regions of the left globus pallidus, right caudate, and in the brainstem. Furthermore, we showed that the combination of demographics, encephalographic, and imaging data in an analytic framework can be employed to aid behavioral diagnosis.

CONCLUSIONS

These results ground, for the first time, electroencephalographic presentation detected with routine clinical techniques in the underlying brain pathology of disorders of consciousness and demonstrate how multimodal combination of clinical, electroencephalographic, and imaging data can be employed in potentially mitigating the high rates of misdiagnosis typical of this patient cohort.

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.

Topographic connectivity and cellular profiling reveal detailed input pathways and functionally distinct cell types in the subthalamic nucleus

The subthalamic nucleus (STN) controls psychomotor activity and is an efficient therapeutic deep brain stimulation target in individuals with Parkinson's disease. Despite evidence indicating position-dependent therapeutic effects and distinct functions within the STN, the input circuit and cellular profile in the STN remain largely unclear. Using neuroanatomical techniques, we construct a comprehensive connectivity map of the indirect and hyperdirect pathways in the mouse STN. Our circuit- and cellular-level connectivities reveal a topographically graded organization with three types of indirect and hyperdirect pathways (external globus pallidus only, STN only, and collateral). We confirm consistent pathways into the human STN by 7 T MRI-based tractography. We identify two functional types of topographically distinct glutamatergic STN neurons (parvalbumin [PV+/-]) with synaptic connectivity from indirect and hyperdirect pathways. Glutamatergic PV+ STN neurons contribute to burst firing. These data suggest a complex interplay of information integration within the basal ganglia underlying coordinated movement control and therapeutic effects.

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).

Active Dendrites and Local Field Potentials: Biophysical Mechanisms and Computational Explorations

Neurons and glial cells are endowed with membranes that express a rich repertoire of ion channels, transporters, and receptors. The constant flux of ions across the neuronal and glial membranes results in voltage fluctuations that can be recorded from the extracellular matrix. The high frequency components of this voltage signal contain information about the spiking activity, reflecting the output from the neurons surrounding the recording location. The low frequency components of the signal, referred to as the local field potential (LFP), have been traditionally thought to provide information about the synaptic inputs that impinge on the large dendritic trees of various neurons. In this review, we discuss recent computational and experimental studies pointing to a critical role of several active dendritic mechanisms that can influence the genesis and the location-dependent spectro-temporal dynamics of LFPs, spanning different brain regions. We strongly emphasize the need to account for the several fast and slow dendritic events and associated active mechanisms - including gradients in their expression profiles, inter- and intra-cellular spatio-temporal interactions spanning neurons and glia, heterogeneities and degeneracy across scales, neuromodulatory influences, and activitydependent plasticity - towards gaining important insights about the origins of LFP under different behavioral states in health and disease. We provide simple but essential guidelines on how to model LFPs taking into account these dendritic mechanisms, with detailed methodology on how to account for various heterogeneities and electrophysiological properties of neurons and synapses while studying LFPs.

Connectivity and Functionality of the Globus Pallidus Externa Under Normal Conditions and Parkinson's Disease

The globus pallidus externa (GPe) functions as a central hub in the basal ganglia for processing motor and non-motor information through the creation of complex connections with the other basal ganglia nuclei and brain regions. Recently, with the adoption of sophisticated genetic tools, substantial advances have been made in understanding the distinct molecular, anatomical, electrophysiological, and functional properties of GPe neurons and non-neuronal cells. Impairments in dopamine transmission in the basal ganglia contribute to Parkinson's disease (PD), the most common movement disorder that severely affects the patients' life quality. Altered GPe neuron activity and synaptic connections have also been found in both PD patients and pre-clinical models. In this review, we will summarize the main findings on the composition, connectivity and functionality of different GPe cell populations and the potential GPe-related mechanisms of PD symptoms to better understand the cell type and circuit-specific roles of GPe in both normal and PD conditions.

A novel low-cost electrode for recording the local field potential of freely moving rat's brain

Local field potentials (LFPs) are involved in almost all cognitive activities of animals. Several kinds of recording electrodes are used for recording LFPs in freely moving animals, including commercial and homemade electrodes. However, commercial recording electrodes are expensive, and their relatively fixed size often causes a steric hindrance effect, especially when combining deep brain stimulation (DBS) with LFP recording, which may not always satisfy the aim of researchers. Currently, an increasing number of researchers are designing their own recording electrodes to lower research costs. Nevertheless, there is no simple universal method to produce low-cost recording electrodes with a specific size according to the target brain area. Thus, we developed a simple method for quickly producing low-cost multiple-channel recording electrodes. To inspect the effectiveness of our self-designed electrode, LFPs were recorded in a Parkinson’s disease (PD) rat model, and an electrical stimulation electrode was implanted into the subthalamic nucleus to verify the space-saving ability of the self-designed recording electrode. The results showed that <30 min was needed to prepare an electrode and that the electrode materials cost <5 dollars. Further investigations showed that our electrode successfully recorded the beta oscillations (12–40 Hz) in the PD rat model. Thus, this method will greatly reduce the cost of recording electrodes and save time for researchers. Additionally, the small size of the electrode will further facilitate DBS research.

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.

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

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

Nonlinear pharmacodynamics of levodopa through Parkinson's disease progression

The effect of levodopa in alleviating the symptoms of Parkinson's disease is altered in a highly nonlinear manner as the disease progresses. This can be attributed to different compensation mechanisms taking place in the basal ganglia where the dopaminergic neurons are progressively lost. This alteration in the effect of levodopa complicates the optimization of a drug regimen. The present work aims at investigating the nonlinear dynamics of Parkinson's disease and its therapy through mechanistic mathematical modeling. Using a holistic approach, a pharmacokinetic model of levodopa was combined to a dopamine dynamics and a neurocomputational model of basal ganglia. The influence of neuronal death on these different mechanisms was also integrated. Using this model, we were able to investigate the nonlinear relationships between the levodopa plasma concentration, the dopamine brain concentration, and a response to a motor task. Variations in dopamine concentrations in the brain for different levodopa doses were also studied. Finally, we investigated the narrowing of a levodopa therapeutic index with the progression of the disease as a result of these nonlinearities. In conclusion, various consequences of nonlinear dynamics in Parkinson's disease treatment were studied by developing an integrative model. This model paves the way toward individualization of a dosing regimen. Using sensor based information, the parameters of the model could be fitted to individual data to propose optimal individual regimens.

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

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

Simulation of Closed-Loop Deep Brain Stimulation Control Schemes for Suppression of Pathological Beta Oscillations in Parkinson's Disease

This study presents a computational model of closed-loop control of deep brain stimulation (DBS) for Parkinson's disease (PD) to investigate clinically viable control schemes for suppressing pathological beta-band activity. Closed-loop DBS for PD has shown promising results in preliminary clinical studies and offers the potential to achieve better control of patient symptoms and side effects with lower power consumption than conventional open-loop DBS. However, extensive testing of algorithms in patients is difficult. The model presented provides a means to explore a range of control algorithms in silico and optimize control parameters before preclinical testing. The model incorporates (i) the extracellular DBS electric field, (ii) antidromic and orthodromic activation of STN afferent fibers, (iii) the LFP detected at non-stimulating contacts on the DBS electrode and (iv) temporal variation of network beta-band activity within the thalamo-cortico-basal ganglia loop. The performance of on-off and dual-threshold controllers for suppressing beta-band activity by modulating the DBS amplitude were first verified, showing levels of beta suppression and reductions in power consumption comparable with previous clinical studies. Proportional (P) and proportional-integral (PI) closed-loop controllers for amplitude and frequency modulation were then investigated. A simple tuning rule was derived for selecting effective PI controller parameters to target long duration beta bursts while respecting clinical constraints that limit the rate of change of stimulation parameters. Of the controllers tested, PI controllers displayed superior performance for regulating network beta-band activity whilst accounting for clinical considerations. Proportional controllers resulted in undesirable rapid fluctuations of the DBS parameters which may exceed clinically tolerable rate limits. Overall, the PI controller for modulating DBS frequency performed best, reducing the mean error by 83% compared to DBS off and the mean power consumed to 25% of that utilized by open-loop DBS. The network model presented captures sufficient physiological detail to act as a surrogate for preclinical testing of closed-loop DBS algorithms using a clinically accessible biomarker, providing a first step for deriving and testing novel, clinically suitable closed-loop DBS controllers.