Computational Models Describing Possible Mechanisms for Generation of Excessive Beta Oscillations in Parkinson's Disease

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.

Investigation of the mechanism of action of deep brain stimulation for the treatment of Parkinson's disease

Parkinson's disease (PD) is a severe, progressive, neurological disorder. PD is not a single disease, but rather resembles a syndrome. PD includes two types of pathogenesis (i.e., classical PD and new PD). Clinically, PD patients present with a range of motor symptoms including decreased spontaneous movement, bradykinesia, muscle rigidity, changes in speech, and resting tremors. PD patients also often exhibit non-motor symptoms such as fatigue, sleep disorders, and emotional and mental health disturbances. Deep brain stimulation (DBS) performed in clinical neurosurgery has demonstrated considerable efficacy in the treatment of dyskinesia that occurs in PD patients. However, the specific neural mechanism of DBS remains unknown and is limited by several shortcomings that have hampered the popularization and development of the procedure. To address this issue, this study established a theoretical model of DBS for PD to investigate and understand the mechanism of DBS using several artificial intelligence (AI) algorithms. This model was used to investigate both classical PD and unheard-of new PD. The research described in this paper was as follows: a single neuron was used to establish a theoretical model of the basal ganglia circuit and to simulate the characteristic indicators of the potential release of the basal ganglia circuit in both normal and PD states. The state of the deep brain electrical stimulation in PD was then analyzed to identify the critical electrical stimulation index and the optimal target. We showed that the use of AI algorithms such as particle swarm optimization and other AI algorithms was beneficial for more detailed exploration and understanding of the mechanisms of DBS compared to those used in previous studies. This discovery may lead to advances in DBS technology and provide better treatment options for neurological diseases such as PD.

Oscillatory vs. non-oscillatory subthalamic beta activity in Parkinson's disease

Parkinson's disease is characterized by exaggerated beta activity (13-35 Hz) in cortico-basal ganglia motor loops. Beta activity includes both periodic fluctuations (i.e. oscillatory activity) and aperiodic fluctuations reflecting spiking activity and excitation/inhibition balance (i.e. non-oscillatory activity). However, the relative contribution, dopamine dependency and clinical correlations of oscillatory vs. non-oscillatory beta activity remain unclear. We recorded, modelled and analysed subthalamic local field potentials in parkinsonian patients at rest while off or on medication. Autoregressive modelling with additive 1/f noise clarified the relationships between measures of beta activity in the time domain (i.e. amplitude and duration of beta bursts) or in the frequency domain (i.e. power and sharpness of the spectral peak) and oscillatory vs. non-oscillatory activity: burst duration and spectral sharpness are specifically sensitive to oscillatory activity, whereas burst amplitude and spectral power are ambiguously sensitive to both oscillatory and non-oscillatory activity. Our experimental data confirmed the model predictions and assumptions. We subsequently analysed the effect of levodopa, obtaining strong-to-extreme Bayesian evidence that oscillatory beta activity is reduced in patients on vs. off medication, with moderate evidence for absence of modulation of the non-oscillatory component. Finally, specifically the oscillatory component of beta activity correlated with the rate of motor progression of the disease. Methodologically, these results provide an integrative understanding of beta-based biomarkers relevant for adaptive deep brain stimulation. Biologically, they suggest that primarily the oscillatory component of subthalamic beta activity is dopamine dependent and may play a role not only in the pathophysiology but also in the progression of Parkinson's disease. KEY POINTS: Beta activity in Parkinson's disease includes both true periodic fluctuations (i.e. oscillatory activity) and aperiodic fluctuations reflecting spiking activity and synaptic balance (i.e. non-oscillatory activity). The relative contribution, dopamine dependency and clinical correlations of oscillatory vs. non-oscillatory beta activity remain unclear. Burst duration and spectral sharpness are specifically sensitive to oscillatory activity, while burst amplitude and spectral power are ambiguously sensitive to both oscillatory and non-oscillatory activity. Only the oscillatory component of subthalamic beta activity is dopamine-dependent. Stronger beta oscillatory activity correlates with faster motor progression of the disease.

Local field potential (LFP) power and phase-amplitude coupling (PAC) changes in the striatum and motor cortex reflect neural mechanisms associated with bradykinesia and rigidity during D2R suppression in an animal model

Impairments in motor control are the primary feature of Parkinson's disease, which is caused by dopaminergic imbalance in the basal ganglia. Identification of neural biomarkers of dopamine D2 receptor (D2R) suppression would be useful for monitoring the progress of neuropathologies and effects of treatment. Male Swiss albino ICR mice were deeply anesthetized, and electrodes were implanted in the striatum and motor cortex to record local field potential (LFP). Haloperidol (HAL), a D2R antagonist, was administered to induce decreased D2R activity. Following HAL treatment, the mice showed significantly decreased movement velocity in open field test, increased latency to descend in a bar test, and decreased latency to fall in a rotarod test. LFP signals during HAL-induced immobility (open field test) and catalepsy (bar test) were analyzed. Striatal low-gamma (30.3-44.9 Hz) power decreased during immobility periods, but during catalepsy, delta power (1-4 Hz) increased, beta1(13.6-18 Hz) and low-gamma powers decreased, and high-gamma (60.5-95.7 Hz) power increased. Striatal delta-high-gamma phase-amplitude coupling (PAC) was significantly increased during catalepsy but not immobility. In the motor cortex, during HAL-induced immobility, beta1 power significantly increased and low-gamma power decreased, but during HAL-induced catalepsy, low-gamma and beta1 powers decreased and high-gamma power increased. Delta-high-gamma PAC in the motor cortex significantly increased during catalepsy but not during immobility. Altogether, the present study demonstrated changes in delta, beta1 and gamma powers and delta-high-gamma PAC in the striatum and motor cortex in association with D2R suppression. In particular, delta power in the striatum and delta-high-gamma PAC in the striatum and motor cortex appear to represent biomarkers of neural mechanisms associated with bradykinesia and rigidity.

Average power and burst analysis revealed complementary information on drug-related changes of motor performance in Parkinson's disease

In patients with Parkinson's disease (PD), suppression of beta and increase in gamma oscillations in the subthalamic nucleus (STN) have been associated with both levodopa treatment and motor functions. Recent results suggest that modulation of the temporal dynamics of theses oscillations (bursting activity) might contain more information about pathological states and behaviour than their average power. Here we directly compared the information provided by power and burst analyses about the drug-related changes in STN activities and their impact on motor performance within PD patients. STN local field potential (LFP) signals were recorded from externalized patients performing self-paced movements ON and OFF levodopa. When normalised across medication states, both power and burst analyses showed an increase in low-beta oscillations in the dopamine-depleted state during rest. When normalised within-medication state, both analyses revealed that levodopa increased movement-related modulation in the alpha and low-gamma bands, with higher gamma activity around movement predicting faster reaches. Finally, burst analyses helped to reveal opposite drug-related changes in low- and high-beta frequency bands, and identified additional within-patient relationships between high-beta bursting and movement performance. Our findings suggest that although power and burst analyses share a lot in common they also provide complementary information on how STN-LFP activity is associated with motor performance, and how levodopa treatment may modify these relationships in a way that helps explain drug-related changes in motor performance. Different ways of normalisation in the power analysis can reveal different information. Similarly, the burst analysis is sensitive to how the threshold is defined - either for separate medication conditions separately, or across pooled conditions. In addition, the burst interpretation has far-reaching implications about the nature of neural oscillations - whether the oscillations happen as isolated burst-events or are they sustained phenomena with dynamic amplitude variations? This can be different for different frequency bands, and different for different medication states even for the same frequency band.

Excessive α-β Oscillations Mark Enlarged Motor Sign Severity and Parkinson's Disease Duration

BACKGROUND

β Oscillations in the subthalamic nucleus (STN) have been proven to contribute to Parkinson's disease (PD), but the exact borders of β subbands vary substantially across the studies, and information regarding heterogeneity of β rhythmic activity is still limited. Recently, α oscillations in the basal ganglia have also become the focus of PD research.

OBJECTIVES

The aim was to study rhythmic oscillations in the STN in PD patients to identify different subbands with stable oscillatory peaks within a broad α-β range and to establish their associations with motor symptoms.

METHODS

Local field potentials inside the STN were recorded during deep brain stimulation (DBS) surgeries. After calculating power spectra and extracting an aperiodic component, oscillatory peaks in the 8- to 35-Hz range with amplitude exceeding 90th percentile were clustered into three bands. Peak parameters were estimated for two lower subbands. Clinical features were compared in patients with and without oscillation peaks in the lowest α-β subband.

RESULTS

We isolated α-β (8-15 Hz), β (15-25 Hz), and β-γ (25-35 Hz) subbands within the 8- to 35-Hz spectral range using oscillatory parameters and Ward's hierarchical clustering. Additional α-β oscillatory peaks were found in about half of patients with β peaks; they were located more ventrally compared to β. We have found a significant increase in disease duration, bradykinesia, and rigidity scores in the group with additional α-β peaks.

CONCLUSIONS

Increased α-β oscillations may emerge as additional phenomena complementing β oscillations; they may mark disease progression in PD and affect DBS stimulation setup. © 2023 International Parkinson and Movement Disorder Society.

Multi-band oscillations emerge from a simple spiking network

In the brain, coherent neuronal activities often appear simultaneously in multiple frequency bands, e.g., as combinations of alpha (8-12 Hz), beta (12.5-30 Hz), and gamma (30-120 Hz) oscillations, among others. These rhythms are believed to underlie information processing and cognitive functions and have been subjected to intense experimental and theoretical scrutiny. Computational modeling has provided a framework for the emergence of network-level oscillatory behavior from the interaction of spiking neurons. However, due to the strong nonlinear interactions between highly recurrent spiking populations, the interplay between cortical rhythms in multiple frequency bands has rarely been theoretically investigated. Many studies invoke multiple physiological timescales (e.g., various ion channels or multiple types of inhibitory neurons) or oscillatory inputs to produce rhythms in multi-bands. Here, we demonstrate the emergence of multi-band oscillations in a simple network consisting of one excitatory and one inhibitory neuronal population driven by constant input. First, we construct a data-driven, Poincaré section theory for robust numerical observations of single-frequency oscillations bifurcating into multiple bands. Then, we develop model reductions of the stochastic, nonlinear, high-dimensional neuronal network to capture the appearance of multi-band dynamics and the underlying bifurcations theoretically. Furthermore, when viewed within the reduced state space, our analysis reveals conserved geometrical features of the bifurcations on low-dimensional dynamical manifolds. These results suggest a simple geometric mechanism behind the emergence of multi-band oscillations without appealing to oscillatory inputs or multiple synaptic or neuronal timescales. Thus, our work points to unexplored regimes of stochastic competition between excitation and inhibition behind the generation of dynamic, patterned neuronal activities.

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.

Distinct cortico-striatal compartments drive competition between adaptive and automatized behavior

Cortical and basal ganglia circuits play a crucial role in the formation of goal-directed and habitual behaviors. In this study, we investigate the cortico-striatal circuitry involved in learning and the role of this circuitry in the emergence of inflexible behaviors such as those observed in addiction. Specifically, we develop a computational model of cortico-striatal interactions that performs concurrent goal-directed and habit learning. The model accomplishes this by distinguishing learning processes in the dorsomedial striatum (DMS) that rely on reward prediction error signals as distinct from the dorsolateral striatum (DLS) where learning is supported by salience signals. These striatal subregions each operate on unique cortical input: the DMS receives input from the prefrontal cortex (PFC) which represents outcomes, and the DLS receives input from the premotor cortex which determines action selection. Following an initial learning of a two-alternative forced choice task, we subjected the model to reversal learning, reward devaluation, and learning a punished outcome. Behavior driven by stimulus-response associations in the DLS resisted goal-directed learning of new reward feedback rules despite devaluation or punishment, indicating the expression of habit. We repeated these simulations after the impairment of executive control, which was implemented as poor outcome representation in the PFC. The degraded executive control reduced the efficacy of goal-directed learning, and stimulus-response associations in the DLS were even more resistant to the learning of new reward feedback rules. In summary, this model describes how circuits of the dorsal striatum are dynamically engaged to control behavior and how the impairment of executive control by the PFC enhances inflexible behavior.

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.

When do bursts matter in the primary motor cortex? Investigating changes in the intermittencies of beta rhythms associated with movement states

Brain activity exhibits significant temporal structure that is not well captured in the power spectrum. Recently, attention has shifted to characterising the properties of intermittencies in rhythmic neural activity (i.e. bursts), yet the mechanisms that regulate them are unknown. Here, we present evidence from electrocorticography recordings made over the motor cortex to show that the statistics of bursts, such as duration or amplitude, in the beta frequency (14-30 Hz) band, significantly aid the classification of motor states such as rest, movement preparation, execution, and imagery. These features reflect nonlinearities not detectable in the power spectrum, with states increasing in nonlinearity from movement execution to preparation to rest. Further, we show using a computational model of the cortical microcircuit, constrained to account for burst features, that modulations of laminar specific inhibitory interneurons are responsible for the temporal organisation of activity. Finally, we show that the temporal characteristics of spontaneous activity can be used to infer the balance of cortical integration between incoming sensory information and endogenous activity. Critically, we contribute to the understanding of how transient brain rhythms may underwrite cortical processing, which in turn, could inform novel approaches for brain state classification, and modulation with novel brain-computer interfaces.

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.

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.

Identifying control ensembles for information processing within the cortico-basal ganglia-thalamic circuit

In situations featuring uncertainty about action-reward contingencies, mammals can flexibly adopt strategies for decision-making that are tuned in response to environmental changes. Although the cortico-basal ganglia thalamic (CBGT) network has been identified as contributing to the decision-making process, it features a complex synaptic architecture, comprised of multiple feed-forward, reciprocal, and feedback pathways, that complicate efforts to elucidate the roles of specific CBGT populations in the process by which evidence is accumulated and influences behavior. In this paper we apply a strategic sampling approach, based on Latin hypercube sampling, to explore how variations in CBGT network properties, including subpopulation firing rates and synaptic weights, map to variability of parameters in a normative drift diffusion model (DDM), representing algorithmic aspects of information processing during decision-making. Through the application of canonical correlation analysis, we find that this relationship can be characterized in terms of three low-dimensional control ensembles within the CBGT network that impact specific qualities of the emergent decision policy: responsiveness (a measure of how quickly evidence evaluation gets underway, associated with overall activity in corticothalamic and direct pathways), pliancy (a measure of the standard of evidence needed to commit to a decision, associated largely with overall activity in components of the indirect pathway of the basal ganglia), and choice (a measure of commitment toward one available option, associated with differences in direct and indirect pathways across action channels). These analyses provide mechanistic predictions about the roles of specific CBGT network elements in tuning the way that information is accumulated and translated into decision-related behavior.

Biophysical and Architectural Mechanisms of Subthalamic Theta under Response Conflict

The cortico-basal ganglia circuit is needed to suppress prepotent actions and to facilitate controlled behavior. Under conditions of response conflict, the frontal cortex and subthalamic nucleus (STN) exhibit increased spiking and theta band power, which are linked to adaptive regulation of behavioral output. The electrophysiological mechanisms underlying these neural signatures of impulse control remain poorly understood. To address this lacuna, we constructed a novel large-scale, biophysically principled model of the subthalamopallidal (STN-globus pallidus externus) network and examined the mechanisms that modulate theta power and spiking in response to cortical input. Simulations confirmed that theta power does not emerge from intrinsic network dynamics but is robustly elicited in response to cortical input as burst events representing action selection dynamics. Rhythmic burst events of multiple cortical populations, representing a state of conflict where cortical motor plans vacillate in the theta range, led to prolonged STN theta and increased spiking, consistent with empirical literature. Notably, theta band signaling required NMDA, but not AMPA, currents, which were in turn related to a triphasic STN response characterized by spiking, silence, and bursting periods. Finally, theta band resonance was also strongly modulated by architectural connectivity, with maximal theta arising when multiple cortical populations project to individual STN "conflict detector" units because of an NMDA-dependent supralinear response. Our results provide insights into the biophysical principles and architectural constraints that give rise to STN dynamics during response conflict, and how their disruption can lead to impulsivity and compulsivity.SIGNIFICANCE STATEMENT The subthalamic nucleus exhibits theta band power modulation related to cognitive control over motor actions during conditions of response conflict. However, the mechanisms of such dynamics are not understood. Here we developed a novel biophysically detailed and data-constrained large-scale model of the subthalamopallidal network, and examined the impacts of cellular and network architectural properties that give rise to theta dynamics. Our investigations implicate an important role for NMDA receptors and cortico-subthalamic nucleus topographical connectivities in theta power modulation.

Dorsal-to-ventral imbalance in the superior longitudinal fasciculus mediates methylphenidate's effect on beta oscillations in ADHD

While pharmacological treatment with methylphenidate (MPH) is a first line intervention for ADHD, its mechanisms of action have yet to be elucidated. We here seek to identify the white matter tracts that mediate MPH's effect on beta oscillations. We implemented a double-blind placebo-controlled crossover design, where boys diagnosed with ADHD underwent behavioral and MEG measurements during a spatial attention task while on and off MPH. The results were compared with an age/IQ-matched control group. Estimates of white matter tracts were obtained using diffusion tensor imaging (DTI). Via a stepwise model selection strategy, we identified the fiber tracts (regressors) significantly predicting values of the dependent variables of interest (i.e., oscillatory power, behavioral performance, and clinical symptoms): the anterior thalamic radiation (ATR), the superior longitudinal fasciculus ("parietal endings") (SLFp), and superior longitudinal fasciculus ("temporal endings") (SLFt). ADHD symptoms severity was associated with lower fractional anisotropy (FA) within the ATR. In addition, individuals with relatively higher FA in SLFp compared to SLFt, led to stronger behavioral effects of MPH in the form of faster and more accurate responses. Furthermore, the same parietotemporal FA gradient explained the effects of MPH on beta modulation: subjects with ADHD exhibiting higher FA in SLFp compared to SLFt also displayed greater effects of MPH on beta power during response preparation. Our data suggest that the behavioral deficits and aberrant oscillatory modulations observed in ADHD depend on a possibly detrimental structural connectivity imbalance within the SLF, caused by a diffusivity gradient in favor of parietal rather than temporal, fiber tracts.

Stimulating at the right time to recover network states in a model of the cortico-basal ganglia-thalamic circuit

Synchronization of neural oscillations is thought to facilitate communication in the brain. Neurodegenerative pathologies such as Parkinson’s disease (PD) can result in synaptic reorganization of the motor circuit, leading to altered neuronal dynamics and impaired neural communication. Treatments for PD aim to restore network function via pharmacological means such as dopamine replacement, or by suppressing pathological oscillations with deep brain stimulation. We tested the hypothesis that brain stimulation can operate beyond a simple “reversible lesion” effect to augment network communication. Specifically, we examined the modulation of beta band (14–30 Hz) activity, a known biomarker of motor deficits and potential control signal for stimulation in Parkinson’s. To do this we setup a neural mass model of population activity within the cortico-basal ganglia-thalamic (CBGT) circuit with parameters that were constrained to yield spectral features comparable to those in experimental Parkinsonism. We modulated the connectivity of two major pathways known to be disrupted in PD and constructed statistical summaries of the spectra and functional connectivity of the resulting spontaneous activity. These were then used to assess the network-wide outcomes of closed-loop stimulation delivered to motor cortex and phase locked to subthalamic beta activity. Our results demonstrate that the spatial pattern of beta synchrony is dependent upon the strength of inputs to the STN. Precisely timed stimulation has the capacity to recover network states, with stimulation phase inducing activity with distinct spectral and spatial properties. These results provide a theoretical basis for the design of the next-generation brain stimulators that aim to restore neural communication in disease.

Diseases of the brain lead to a wide range of disabling symptoms for patients, by affecting their ability to move or think properly. These symptoms arise from disruption to both the organization of networks in the brain, but also the timing of neural activity that propagates around it. Treatments for disease with drugs can restore the organization of these networks to some extent, yet it is very difficult to deliver drugs with good spatial or temporal selectivity. Brain stimulation provides one way in which to improve the spatial specificity of treatment, yet understanding how to stimulate at the right time to achieve the best outcome for patients, remains an outstanding question. In this work we use simulations of an important circuit involved in Parkinson’s disease that has parameters chosen to reflect recordings made in animal models of the disease. Using this computer model, we show how brain rhythms can act as signatures of underlying changes in networks. Further, we simulate intervention with temporally precise stimulation to show how future approaches to brain stimulation can act to restore or even augment neural networks following their degeneration in disease.

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.

Magnetoencephalography detects phase-amplitude coupling in Parkinson's disease

To characterize Parkinson’s disease, abnormal phase-amplitude coupling is assessed in the cortico-basal circuit using invasive recordings. It is unknown whether the same phenomenon might be found in regions other than the cortico-basal ganglia circuit. We hypothesized that using magnetoencephalography to assess phase-amplitude coupling in the whole brain can characterize Parkinson’s disease. We recorded resting-state magnetoencephalographic signals in patients with Parkinson’s disease and in healthy age- and sex-matched participants. We compared whole-brain signals from the two groups, evaluating the power spectra of 3 frequency bands (alpha, 8–12 Hz; beta, 13–25 Hz; gamma, 50–100 Hz) and the coupling between gamma amplitude and alpha or beta phases. Patients with Parkinson’s disease showed significant beta–gamma phase-amplitude coupling that was widely distributed in the sensorimotor, occipital, and temporal cortices; healthy participants showed such coupling only in parts of the somatosensory and temporal cortices. Moreover, beta- and gamma-band power differed significantly between participants in the two groups (P < 0.05). Finally, beta–gamma phase-amplitude coupling in the sensorimotor cortices correlated significantly with motor symptoms of Parkinson’s disease (P < 0.05); beta- and gamma-band power did not. We thus demonstrated that beta–gamma phase-amplitude coupling in the resting state characterizes Parkinson’s disease.

Deep brain stimulation for movement disorder treatment: exploring frequency-dependent efficacy in a computational network model

A large-scale computational model of the basal ganglia network and thalamus is proposed to describe movement disorders and treatment effects of deep brain stimulation (DBS). The model of this complex network considers three areas of the basal ganglia region: the subthalamic nucleus (STN) as target area of DBS, the globus pallidus, both pars externa and pars interna (GPe-GPi), and the thalamus. Parkinsonian conditions are simulated by assuming reduced dopaminergic input and corresponding pronounced inhibitory or disinhibited projections to GPe and GPi. Macroscopic quantities are derived which correlate closely to thalamic responses and hence motor programme fidelity. It can be demonstrated that depending on different levels of striatal projections to the GPe and GPi, the dynamics of these macroscopic quantities (synchronisation index, mean synaptic activity and response efficacy) switch from normal to Parkinsonian conditions. Simulating DBS of the STN affects the dynamics of the entire network, increasing the thalamic activity to levels close to normal, while differing from both normal and Parkinsonian dynamics. Using the mentioned macroscopic quantities, the model proposes optimal DBS frequency ranges above 130 Hz.

Identification of an early-stage Parkinson's disease neuromarker using event-related potentials, brain network analytics and machine-learning

OBJECTIVE

The purpose of this study is to explore the possibility of developing a biomarker that can discriminate early-stage Parkinson's disease from healthy brain function using electroencephalography (EEG) event-related potentials (ERPs) in combination with Brain Network Analytics (BNA) technology and machine learning (ML) algorithms.

BACKGROUND

Currently, diagnosis of PD depends mainly on motor signs and symptoms. However, there is need for biomarkers that detect PD at an earlier stage to allow intervention and monitoring of potential disease-modifying therapies. Cognitive impairment may appear before motor symptoms, and it tends to worsen with disease progression. While ERPs obtained during cognitive tasks performance represent processing stages of cognitive brain functions, they have not yet been established as sensitive or specific markers for early-stage PD.

METHODS

Nineteen PD patients (disease duration of ≤2 years) and 30 healthy controls (HC) underwent EEG recording while performing visual Go/No-Go and auditory Oddball cognitive tasks. ERPs were analyzed by the BNA technology, and a ML algorithm identified a combination of features that distinguish early PD from HC. We used a logistic regression classifier with a 10-fold cross-validation.

RESULTS

The ML algorithm identified a neuromarker comprising 15 BNA features that discriminated early PD patients from HC. The area-under-the-curve of the receiver-operating characteristic curve was 0.79. Sensitivity and specificity were 0.74 and 0.73, respectively. The five most important features could be classified into three cognitive functions: early sensory processing (P50 amplitude, N100 latency), filtering of information (P200 amplitude and topographic similarity), and response-locked activity (P-200 topographic similarity preceding the motor response in the visual Go/No-Go task).

CONCLUSIONS

This pilot study found that BNA can identify patients with early PD using an advanced analysis of ERPs. These results need to be validated in a larger PD patient sample and assessed for people with premotor phase of PD.

Improved alpha-beta power reduction via combined electrical and ultrasonic stimulation in a parkinsonian cortex-basal ganglia-thalamus computational model

Objective. To investigate computationally the interaction of combined electrical and ultrasonic modulation of isolated neurons and of the parkinsonian cortex-basal ganglia-thalamus loop.Approach. Continuous-wave or pulsed electrical and ultrasonic neuromodulation is applied to isolated Otsuka plateau-potential generating subthalamic nucleus (STN) and Pospischil regular, fast and low-threshold spiking cortical cells in a temporally alternating or simultaneous manner. Similar combinations of electrical/ultrasonic waveforms are applied to a parkinsonian biophysical cortex-basal ganglia-thalamus neuronal network. Ultrasound-neuron interaction is modelled respectively for isolated neurons and the neuronal network with the NICE and SONIC implementations of the bilayer sonophore underlying mechanism. Reduction inα-βspectral energy is used as a proxy to express improvement in Parkinson's disease by insonication and electrostimulation.Main results. Simultaneous electro-acoustic stimulation achieves a given level of neuronal activity at lower intensities compared to the separate stimulation modalities. Conversely, temporally alternating stimulation with50 Hzelectrical and ultrasound pulses is capable of eliciting100 HzSTN firing rates. Furthermore, combination of ultrasound with hyperpolarizing currents can alter cortical cell relative spiking regimes. In the parkinsonian neuronal network, continuous-wave and pulsed ultrasound reduce pathological oscillations by different mechanisms. High-frequency pulsed separated electrical and ultrasonic deep brain stimulation (DBS) reduce pathologicalα-βpower by entraining STN-neurons. In contrast, continuous-wave ultrasound reduces pathological oscillations by silencing the STN. Compared to the separated stimulation modalities, temporally simultaneous or alternating electro-acoustic stimulation can achieve higher reductions inα-βpower for the same safety contraints on electrical/ultrasonic intensity.Significance. Focused ultrasound has the potential of becoming a non-invasive alternative of conventional DBS for the treatment of Parkinson's disease. Here, we elaborate on proposed benefits of combined electro-acoustic stimulation in terms of improved dynamic range, efficiency, spatial resolution, and neuronal selectivity.

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).

Mathematical model of subthalamic nucleus neuron: Characteristic activity patterns and bifurcation analysis

The subthalamic nucleus (STN) has an important role in the pathophysiology of the basal ganglia in Parkinson's disease. The ability of STN cells to generate bursting rhythms under either transient or sustained hyperpolarization may underlie the excessively synchronous beta rhythms observed in Parkinson's disease. In this study, we developed a conductance-based single compartment model of an STN neuron, which is able to generate characteristic activity patterns observed in experiments including hyperpolarization-induced bursts and post-inhibitory rebound bursts. This study focused on the role of three currents in rhythm generation: T-type calcium (CaT) current, L-type calcium (CaL) current, and hyperpolarization-activated cyclic nucleotide-gated (HCN) current. To investigate the effects of these currents in rhythm generation, we performed a bifurcation analysis using slow variables in these currents. Bifurcation analysis showed that the HCN current promotes single-spike activity patterns rather than bursting in agreement with experimental results. It also showed that the CaT current is necessary for characteristic bursting activity patterns. In particular, the CaT current enables STN neurons to generate these activity patterns under hyperpolarizing stimuli. The CaL current enriches and reinforces these characteristic activity patterns. In hyperpolarization-induced bursts or post-inhibitory rebound bursts, the CaL current allows STN neurons to generate long bursting patterns. Thus, the bifurcation analysis explained the synergistic interaction of the CaT and CaL currents, which enables STN neurons to respond to hyperpolarizing stimuli in a salient way. The results of this study implicate the importance of CaT and CaL currents in the pathophysiology of the basal ganglia in Parkinson's disease.

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.

Optimal closed-loop deep brain stimulation using multiple independently controlled contacts

Deep brain stimulation (DBS) is a well-established treatment option for a variety of neurological disorders, including Parkinson’s disease and essential tremor. The symptoms of these disorders are known to be associated with pathological synchronous neural activity in the basal ganglia and thalamus. It is hypothesised that DBS acts to desynchronise this activity, leading to an overall reduction in symptoms. Electrodes with multiple independently controllable contacts are a recent development in DBS technology which have the potential to target one or more pathological regions with greater precision, reducing side effects and potentially increasing both the efficacy and efficiency of the treatment. The increased complexity of these systems, however, motivates the need to understand the effects of DBS when applied to multiple regions or neural populations within the brain. On the basis of a theoretical model, our paper addresses the question of how to best apply DBS to multiple neural populations to maximally desynchronise brain activity. Central to this are analytical expressions, which we derive, that predict how the symptom severity should change when stimulation is applied. Using these expressions, we construct a closed-loop DBS strategy describing how stimulation should be delivered to individual contacts using the phases and amplitudes of feedback signals. We simulate our method and compare it against two others found in the literature: coordinated reset and phase-locked stimulation. We also investigate the conditions for which our strategy is expected to yield the most benefit.

In this paper we use computer models of brain tissue to derive an optimal control algorithm for a recently developed new generation of deep brain stimulation (DBS) devices. DBS is a treatment for a variety of neurological disorders including Parkinson’s disease, essential tremor, depression and pain. There is a growing amount of evidence to suggest that delivering stimulation according to feedback from patients, or closed-loop, has the potential to improve the efficacy, efficiency and side effects of the treatment. An important recent development in DBS technology are electrodes with multiple independently controllable contacts and this paper is a theoretical study into the effects of using this new technology. On the basis of a theoretical model, we devise a closed-loop strategy and address the question of how to best apply DBS across multiple contacts to maximally desynchronise neural populations. We demonstrate using numerical simulation that, for the systems we consider, our methods are more effective than two well-known alternatives, namely phase-locked stimulation and coordinated reset. We also predict that the benefits of using multiple contacts should depend strongly on the intrinsic neuronal response. The insights from this work should lead to a better understanding of how to implement and optimise closed-loop multi-contact DBS systems which in turn should lead to more effective and efficient DBS treatments.

On the Role of Arkypallidal and Prototypical Neurons for Phase Transitions in the External Pallidum

The external pallidum (globus pallidus pars externa [GPe]) plays a central role for basal ganglia functions and dynamics and, consequently, has been included in most computational studies of the basal ganglia. These studies considered the GPe as a homogeneous neural population. However, experimental studies have shown that the GPe contains at least two distinct cell types (prototypical and arkypallidal cells). In this work, we provide in silico insight into how pallidal heterogeneity modulates dynamic regimes inside the GPe and how they affect the GPe response to oscillatory input. We derive a mean-field model of the GPe system from a microscopic spiking neural network of recurrently coupled prototypical and arkypallidal neurons. Using bifurcation analysis, we examine the influence of dopamine-dependent changes of intrapallidal connectivity on the GPe dynamics. We find that increased self-inhibition of prototypical cells can induce oscillations, whereas increased inhibition of prototypical cells by arkypallidal cells leads to the emergence of a bistable regime. Furthermore, we show that oscillatory input to the GPe, arriving from striatum, leads to characteristic patterns of cross-frequency coupling observed at the GPe. Based on these findings, we propose two different hypotheses of how dopamine depletion at the GPe may lead to phase-amplitude coupling between the parkinsonian beta rhythm and a GPe-intrinsic γ rhythm. Finally, we show that these findings generalize to realistic spiking neural networks of sparsely coupled Type I excitable GPe neurons.SIGNIFICANCE STATEMENT Our work provides (1) insight into the theoretical implications of a dichotomous globus pallidus pars externa (GPe) organization, and (2) an exact mean-field model that allows for future investigations of the relationship between GPe spiking activity and local field potential fluctuations. We identify the major phase transitions that the GPe can undergo when subject to static or periodic input and link these phase transitions to the emergence of synchronized oscillations and cross-frequency coupling in the basal ganglia. Because of the close links between our model and experimental findings on the structure and dynamics of prototypical and arkypallidal cells, our results can be used to guide both experimental and computational studies on the role of the GPe for basal ganglia dynamics in health and disease.

Neuro4PD: An Initial Neurorobotics Model of Parkinson's Disease

In this work, we present the first steps toward the creation of a new neurorobotics model of Parkinson's Disease (PD) that embeds, for the first time in a real robot, a well-established computational model of PD. PD mostly affects the modulation of movement in humans. The number of people suffering from this neurodegenerative disease is set to double in the next 15 years and there is still no cure. With the new model we were capable to further explore the dynamics of the disease using a humanoid robot. Results show that the embedded model under both conditions, healthy and parkinsonian, was capable of performing a simple behavioural task with different levels of motor disturbance. We believe that this neurorobotics model is a stepping stone to the development of more sophisticated models that could eventually test and inform new PD therapies and help to reduce and replace animals in research.

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.

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.

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.

Model-Based Closed-Loop Suppression of Parkinsonian Beta Band Oscillations Through Origin Analysis

Excessive beta band (13-30 Hz) oscillations have been observed in the basal ganglia (BG) of patients with Parkinson's disease (PD). Understanding the origin and transmission of beta band oscillations are important to improve treatments of PD, such as closed-loop deep brain stimulation (DBS). This paper proposed a model-based closed-loop GPi stimulation system to suppress pathological beta band oscillations of BG. The feedback nucleus was selected through the analysis of GPi oscillations variation when different synaptic currents were blocked, mainly projections from globus pallidus external (GPe), the subthalamic nucleus (STN) and striatum. Since simulation results proved the important role of synaptic current from GPe in shaping the excessive GPi beta band oscillations, the local field potential (LFP) of GPe was chosen as the feedback signal. That is to say, the feedback nucleus was selected based on the origin analysis of the pathological GPi beta band oscillation. The closed-loop algorithm was the multiplication of linear delayed feedback of the filtered GPe-LFP and modeled synaptic dynamics from GPe to GPi. Thus, the formed stimulation waveform was synaptic current like shape, which was proved to be more energy efficient than open-loop continuous DBS in suppressing GPi beta band oscillation. With the development of DBS devices, the efficiency of this closed-loop stimulation could be testified in animal model and clinical.

Dysregulation of excitatory neural firing replicates physiological and functional changes in aging visual cortex

The mammalian visual system has been the focus of countless experimental and theoretical studies designed to elucidate principles of neural computation and sensory coding. Most theoretical work has focused on networks intended to reflect developing or mature neural circuitry, in both health and disease. Few computational studies have attempted to model changes that occur in neural circuitry as an organism ages non-pathologically. In this work we contribute to closing this gap, studying how physiological changes correlated with advanced age impact the computational performance of a spiking network model of primary visual cortex (V1). Our results demonstrate that deterioration of homeostatic regulation of excitatory firing, coupled with long-term synaptic plasticity, is a sufficient mechanism to reproduce features of observed physiological and functional changes in neural activity data, specifically declines in inhibition and in selectivity to oriented stimuli. This suggests a potential causality between dysregulation of neuron firing and age-induced changes in brain physiology and functional performance. While this does not rule out deeper underlying causes or other mechanisms that could give rise to these changes, our approach opens new avenues for exploring these underlying mechanisms in greater depth and making predictions for future experiments.

Brain rhythm bursts are enhanced by multiplicative noise

Many healthy and pathological brain rhythms, including beta and gamma rhythms and essential tremor, are suspected to be induced by noise. This yields randomly occurring, brief epochs of higher amplitude oscillatory activity known as "bursts," the statistics of which are important for proper neural function. Here, we consider a more realistic model with both multiplicative and additive noise instead of only additive noise, to understand how state-dependent fluctuations further affect rhythm induction. For illustrative purposes, we calibrate the model at the lower end of the beta band that relates to movement; parameter tuning can extend the relevance of our analysis to the higher frequency gamma band or to lower frequency essential tremors. A stochastic Wilson-Cowan model for reciprocally as well as self-coupled excitatory (E) and inhibitory (I) populations is analyzed in the parameter regime where the noise-free dynamics spiral in to a fixed point. Noisy oscillations known as quasi-cycles are then generated by stochastic synaptic inputs. The corresponding dynamics of E and I local field potentials can be studied using linear stochastic differential equations subject to both additive and multiplicative noises. As the prevalence of bursts is proportional to the slow envelope of the E and I firing activities, we perform an envelope-phase decomposition using the stochastic averaging method. The resulting envelope dynamics are uni-directionally coupled to the phase dynamics as in the case of additive noise alone but both dynamics involve new noise-dependent terms. We derive the stationary probability and compute power spectral densities of envelope fluctuations. We find that multiplicative noise can enhance network synchronization by reducing the magnitude of the negative real part of the complex conjugate eigenvalues. Higher noise can lead to a "virtual limit cycle," where the deterministically stable eigenvalues around the fixed point acquire a positive real part, making the system act more like a noisy limit cycle rather than a quasi-cycle. Multiplicative noise can thus exacerbate synchronization and possibly contribute to the onset of symptoms in certain motor diseases.

Insights on the role of external globus pallidus in controlling absence seizures

Absence epilepsy, characterized by transient loss of awareness and bilaterally synchronous 2-4 Hz spike and wave discharges (SWDs) on electroencephalography (EEG) during absence seizures, is generally believed to arise from abnormal interactions between the cerebral cortex (Ctx) and thalamus. Recent animal electrophysiological studies suggested that changing the neural activation level of the external globus pallidus (GPe) neurons can remarkably modify firing rates of the thalamic reticular nucleus (TRN) neurons through the GABAergic GPe-TRN pathway. However, the existing experimental evidence does not provide a clear answer as to whether the GPe-TRN pathway contributes to regulating absence seizures. Here, using a biophysically based mean-field model of the GPe-corticothalamic (GCT) network, we found that both directly decreasing the strength of the GPe-TRN pathway and inactivating GPe neurons can effectively suppress absence seizures. Also, the pallido-cortical pathway and the recurrent connection of GPe neurons facilitate the regulation of absence seizures through the GPe-TRN pathway. Specifically, in the controllable situation, enhancing the coupling strength of either of the two pathways can successfully terminate absence seizures. Moreover, the competition between the GPe-TRN and pallido-cortical pathways may lead to the GPe bidirectionally controlling absence seizures, and this bidirectional control manner can be significantly modulated by the Ctx-TRN pathway. Importantly, when the strength of the Ctx-TRN pathway is relatively strong, the bidirectional control of absence seizures by changing GPe neural activities can be observed at both weak and strong strengths of the pallido-cortical pathway.These findings suggest that the GPe-TRN pathway may have crucial functional roles in regulating absence seizures, which may provide a testable hypothesis for further experimental studies and new perspectives on the treatment of absence epilepsy.

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.

Evaluation of Frequency-Dependent Effects of Deep Brain Stimulation in a Cortex-Basal Ganglia-Thalamus Network Model of Parkinson's Disease

Parkinson's disease (PD) is a chronic neurodegenerative disease whose motor symptoms are accompanied by an exaggerated power in the alpha-beta (7-35Hz) band and an increased synchronization of neurons encompassing the cortex-basal ganglia-thalamus network. Currently, deep brain stimulation (DBS) is used as an effective therapy for reducing the excessive power and synchrony observed in brain circuits, thereby ameliorating the PD symptoms. In the present study, we used a biologically plausible computational model of cortex-basal ganglia-thalamus network, which represents both healthy and PD conditions, to systematically investigate the effects of DBS frequency on the model outputs. DBS was applied to the subthalamic nucleus (STN) at different stimulation frequencies (40Hz to 300Hz). Spike train variability and spectral power in the 7-35Hz band were measured from the several nuclei represented in the model. In addition, the magnitude squared coherence between the nuclei was assessed. An increased DBS frequency tended to produce interspike intervals (ISIs) with higher variability as compared to PD condition. Also, DBS significantly reduced the alpha-beta power for almost all brain nuclei. The median of the magnitude-squared coherence matrix (which is a metric of global network synchronization) decreased significantly with the increase of DBS frequency.

Optimal Control Perspective on Parkinson's Disease: Increased Delay Between State Estimator and Controller Produces Tremor

Parkinson's disease produces tremor in a large subset of patients despite generally inhibiting movement. The pathophysiology of parkinsonian tremor is unclear, leading to uncertainty in how and why treatments reduce tremor with varying effectiveness. Models for parkinsonian tremor attempt to explain the underlying principles of tremor generation in the central nervous system, often focusing on neural activity of specific substructures. In contrast, control system approaches to modeling the human motor system provide qualitative results that help inform conclusions from clinical studies. This article uses an optimal control approach to investigate the hypothesis that an increased delay in the central nervous system-unaccounted by delay compensation mechanisms-produces parkinsonian tremor. This hypothesis is motivated by the excessive inhibition projected from the basal ganglia to the thalamus in Parkinson's disease. The thalamus relays signals from the cerebellum to the primary motor cortex: previous mapping of optimal control components indicates this prospective delay exists between the estimator (cerebellum) and controller (primary motor cortex). Simulations demonstrate realistic tremor in a neuromuscular model of the wrist. In addition, changes to effort sensitivity in the optimal controller may account for some clinical features of parkinsonian tremor, including the characteristics of re-emergent tremor and the time-varying amplitude and frequency of tremor. Contextualization of the optimal control model with physiological models and clinical observations provides insight into the potential role of the basal ganglia and cerebello-thalamo-cortical circuit and how treatments like dopaminergic medications and deep brain stimulation reduce tremor.

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.

Subthalamic nucleus activity dynamics and limb movement prediction in Parkinson's disease

Whilst exaggerated bursts of beta frequency band oscillatory synchronization in the subthalamic nucleus have been associated with motor impairment in Parkinson's disease, a plausible mechanism linking the two phenomena has been lacking. Here we test the hypothesis that increased synchronization denoted by beta bursting might compromise information coding capacity in basal ganglia networks. To this end we recorded local field potential activity in the subthalamic nucleus of 18 patients with Parkinson's disease as they executed cued upper and lower limb movements. We used the accuracy of local field potential-based classification of the limb to be moved on each trial as an index of the information held by the system with respect to intended action. Machine learning using the naïve Bayes conditional probability model was used for classification. Local field potential dynamics allowed accurate prediction of intended movements well ahead of their execution, with an area under the receiver operator characteristic curve of 0.80 ± 0.04 before imperative cues when the demanded action was known ahead of time. The presence of bursts of local field potential activity in the alpha, and even more so, in the beta frequency band significantly compromised the prediction of the limb to be moved. We conclude that low frequency bursts, particularly those in the beta band, restrict the capacity of the basal ganglia system to encode physiologically relevant information about intended actions. The current findings are also important as they suggest that local subthalamic activity may potentially be decoded to enable effector selection, in addition to force control in restorative brain-machine interface applications.

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.

Phase-dependence of response curves to deep brain stimulation and their relationship: from essential tremor patient data to a Wilson-Cowan model

Essential tremor manifests predominantly as a tremor of the upper limbs. One therapy option is high-frequency deep brain stimulation, which continuously delivers electrical stimulation to the ventral intermediate nucleus of the thalamus at about 130 Hz. Constant stimulation can lead to side effects, it is therefore desirable to find ways to stimulate less while maintaining clinical efficacy. One strategy, phase-locked deep brain stimulation, consists of stimulating according to the phase of the tremor. To advance methods to optimise deep brain stimulation while providing insights into tremor circuits, we ask the question: can the effects of phase-locked stimulation be accounted for by a canonical Wilson-Cowan model? We first analyse patient data, and identify in half of the datasets significant dependence of the effects of stimulation on the phase at which stimulation is provided. The full nonlinear Wilson-Cowan model is fitted to datasets identified as statistically significant, and we show that in each case the model can fit to the dynamics of patient tremor as well as to the phase response curve. The vast majority of top fits are stable foci. The model provides satisfactory prediction of how patient tremor will react to phase-locked stimulation by predicting patient amplitude response curves although they were not explicitly fitted. We also approximate response curves of the significant datasets by providing analytical results for the linearisation of a stable focus model, a simplification of the Wilson-Cowan model in the stable focus regime. We report that the nonlinear Wilson-Cowan model is able to describe response to stimulation more precisely than the linearisation.

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.

The globus pallidus orchestrates abnormal network dynamics in a model of Parkinsonism

The dynamical properties of cortico-basal ganglia (CBG) circuits are dramatically altered following the loss of dopamine in Parkinson’s disease (PD). The neural circuit dysfunctions associated with PD include spike-rate alteration concomitant with excessive oscillatory spike-synchronization in the beta frequency range (12–30 Hz). Which neuronal circuits orchestrate and propagate these abnormal neural dynamics in CBG remains unknown. In this work, we combine in vivo electrophysiological recordings with advanced optogenetic manipulations in normal and 6-OHDA rats to shed light on the mechanistic principle underlying circuit dysfunction in PD. Our results show that abnormal neural dynamics present in a rat model of PD do not rely on cortical or subthalamic nucleus activity but critically dependent on globus pallidus (GP) integrity. Our findings highlight the pivotal role played by the GP which operates as a hub nucleus capable of orchestrating firing rate and synchronization changes across CBG circuits both in normal and pathological conditions.

Oscillatory changes between basal ganglia nuclei occur in Parkinson’s disease. Here the authors determine that the globus pallidus is the source of beta oscillation generation in a rodent model of the disease.

Basal ganglia oscillations as biomarkers for targeting circuit dysfunction in Parkinson's disease

Oscillations are a naturally occurring phenomenon in highly interconnected dynamical systems. However, it is thought that excessive synchronized oscillations in brain circuits can be detrimental for many brain functions by disrupting neuronal information processing. Because synchronized basal ganglia oscillations are a hallmark of Parkinson's disease (PD), it has been suggested that aberrant rhythmic activity associated with symptoms of the disease could be used as a physiological biomarker to guide pharmacological and electrical neuromodulatory interventions. We here briefly review the various manifestations of basal ganglia oscillations observed in human subjects and in animal models of PD. In this context, we also review the evidence supporting a pathophysiological role of different oscillations for the suppression of voluntary movements as well as for the induction of excessive motor activity. In light of these findings, it is discussed how oscillations could be used to guide a more precise targeting of dysfunctional circuits to obtain improved symptomatic treatment of PD.

Basal ganglia role in learning rewarded actions and executing previously learned choices: Healthy and diseased states

The basal ganglia (BG) is a collection of nuclei located deep beneath the cerebral cortex that is involved in learning and selection of rewarded actions. Here, we analyzed BG mechanisms that enable these functions. We implemented a rate model of a BG-thalamo-cortical loop and simulated its performance in a standard action selection task. We have shown that potentiation of corticostriatal synapses enables learning of a rewarded option. However, these synapses became redundant later as direct connections between prefrontal and premotor cortices (PFC-PMC) were potentiated by Hebbian learning. After we switched the reward to the previously unrewarded option (reversal), the BG was again responsible for switching to the new option. Due to the potentiated direct cortical connections, the system was biased to the previously rewarded choice, and establishing the new choice required a greater number of trials. Guided by physiological research, we then modified our model to reproduce pathological states of mild Parkinson's and Huntington's diseases. We found that in the Parkinsonian state PMC activity levels become extremely variable, which is caused by oscillations arising in the BG-thalamo-cortical loop. The model reproduced severe impairment of learning and predicted that this is caused by these oscillations as well as a reduced reward prediction signal. In the Huntington state, the potentiation of the PFC-PMC connections produced better learning, but altered BG output disrupted expression of the rewarded choices. This resulted in random switching between rewarded and unrewarded choices resembling an exploratory phase that never ended. Along with other computational studies, our results further reconcile the apparent contradiction between the critical involvement of the BG in execution of previously learned actions and yet no impairment of these actions after BG output is ablated by lesions or deep brain stimulation. We predict that the cortico-BG-thalamo-cortical loop conforms to previously learned choice in healthy conditions, but impedes those choices in disease states.