Computational models of basal ganglia dysfunction: the dynamics is in the details

Transmission of delta band (0.5-4 Hz) oscillations from the globus pallidus to the substantia nigra pars reticulata in dopamine depletion

Parkinson's disease (PD) and animal models of PD feature enhanced oscillations in several frequency bands in the basal ganglia (BG). Past research has emphasized the enhancement of 13-30 Hz beta oscillations. Recently, however, oscillations in the delta band (0.5-4 Hz) have been identified as a robust predictor of dopamine loss and motor dysfunction in several BG regions in mouse models of PD. In particular, delta oscillations in the substantia nigra pars reticulata (SNr) were shown to lead oscillations in motor cortex (M1) and persist under M1 lesion, but it is not clear where these oscillations are initially generated. In this paper, we use a computational model to study how delta oscillations may arise in the SNr due to projections from the globus pallidus externa (GPe). We propose a network architecture that incorporates inhibition in SNr from oscillating GPe neurons and other SNr neurons. In our simulations, this configuration yields firing patterns in model SNr neurons that match those measured in vivo. In particular, we see the spontaneous emergence of near-antiphase active-predicting and inactive-predicting neural populations in the SNr, which persist under the inclusion of STN inputs based on experimental recordings. These results demonstrate how delta oscillations can propagate through BG nuclei despite imperfect oscillatory synchrony in the source site, narrowing down potential targets for the source of delta oscillations in PD models and giving new insight into the dynamics of SNr oscillations.

Model-based quantitative optimization of deep brain stimulation and prediction of parkinson's states

Although the exact etiology of Parkinson's disease (PD) is still unknown, there are a variety of treatments available to alleviate its symptoms according to the development stage of PD. Deep brain stimulation (DBS), the most common surgical treatment for advanced PD, accurately locates and implants stimulating electrodes at specific targets in the brain to deliver high-frequency electrical stimulation that alters the excitability of the corresponding nuclei. However, for different patients and stages of PD development, there exists a choice of the optimal DBS protocol. In this paper, we propose a quantitative method (multi-dimensional feature indexes) to determine the stimulation pattern, stimulation parameters, and target of DBS from the perspective of the network model. On the other hand, based on this method, the development of PD can be predicted so that timely treatment can be given to patients. Simulation results show that, first, different network states can be distinguished by extracting features of the firing activity of neuronal populations within the basal ganglia network system. Secondly, the optimal DBS treatment can be selected by comparing the feature indexes vectors of the pre- and post-state of the network after the action of different modes of DBS. Lastly, the evolution of the network state from normal to pathological is simulated. The critical point of network state transitions is determined. These results provide a quantitative and qualitative method for determining the optimal regimen for DBS for PD, which is helpful for clinical practice.

Reaching and Grasping Movements in Parkinson's Disease: A Review

Parkinson's disease (PD) is known to affect the brain motor circuits involving the basal ganglia (BG) and to induce, among other signs, general slowness and paucity of movements. In upper limb movements, PD patients show a systematic prolongation of movement duration while maintaining a sufficient level of endpoint accuracy. PD appears to cause impairments not only in movement execution, but also in movement initiation and planning, as revealed by abnormal preparatory activity of motor-related brain areas. Grasping movement is affected as well, particularly in the coordination of the hand aperture with the transport phase. In the last fifty years, numerous behavioral studies attempted to clarify the mechanisms underlying these anomalies, speculating on the plausible role that the BG-thalamo-cortical circuitry may play in normal and pathological motor control. Still, many questions remain open, especially concerning the management of the speed-accuracy tradeoff and the online feedback control. In this review, we summarize the literature results on reaching and grasping in parkinsonian patients. We analyze the relevant hypotheses on the origins of dysfunction, by focusing on the motor control aspects involved in the different movement phases and the corresponding role played by the BG. We conclude with an insight into the innovative stimulation techniques and computational models recently proposed, which might be helpful in further clarifying the mechanisms through which PD affects reaching and grasping movements.

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.

Imbalanced basal ganglia connectivity is associated with motor deficits and apathy in Huntington's disease

The gating of movement depends on activity within the cortico-striato-thalamic loops. Within these loops, emerging from the cells of the striatum, run two opponent pathways—the direct and indirect basal ganglia pathways. Both are complex and polysynaptic, but the overall effect of activity within these pathways is thought to encourage and inhibit movement, respectively. In Huntington’s disease, the preferential early loss of striatal neurons forming the indirect pathway is thought to lead to disinhibition, giving rise to the characteristic motor features of the condition. But early Huntington’s disease is also associated with apathy, a loss of motivation and failure to engage in goal-directed movement. We hypothesized that in Huntington’s disease, motor signs and apathy may be selectively correlated with indirect and direct pathway dysfunction, respectively.

We used spectral dynamic casual modelling of resting-state functional MRI data to model effective connectivity in a model of these cortico-striatal pathways. We tested both of these hypotheses in vivo for the first time in a large cohort of patients with prodromal Huntington’s disease. Using an advanced approach at the group level we combined parametric empirical Bayes and Bayesian model reduction procedures to generate a large number of competing models and compare them using Bayesian model comparison. With this automated Bayesian approach, associations between clinical measures and connectivity parameters emerge de novo from the data.

We found very strong evidence (posterior probability > 0.99) to support both of our hypotheses. First, more severe motor signs in Huntington’s disease were associated with altered connectivity in the indirect pathway components of our model and, by comparison, loss of goal-direct behaviour or apathy, was associated with changes in the direct pathway component.

The empirical evidence we provide here demonstrates that imbalanced basal ganglia connectivity may play an important role in the pathogenesis of some of commonest and disabling features of Huntington’s disease and may have important implications for therapeutics.

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.

A change of mind: Globus pallidus activity and effective connectivity during changes in choice selections

The basal ganglia are a group of interconnected subcortical nuclei that plays a key role in multiple motor and cognitive processes, in a close interplay with several cortical regions. Two conflicting theories postulate that the basal ganglia pathways can either foster or suppress the cortico-striatal output or, alternatively, they can stabilize or destabilize the cortico-striatal circuit dynamics. These different approaches significantly impact the understanding of observable behaviours and cognitive processes in healthy, as well as clinical populations. We investigated the predictions of these models in healthy participants (N = 28), using dynamic causal modeling of fMRI BOLD activity to estimate time- and context-dependent changes in the indirect pathway effective connectivity, in association with repetitions or changes of choice selections. We used two multi-option tasks that required the participants to adapt to uncontrollable environmental changes, by performing sequential choice selections, with and without value-based feedbacks. We found that, irrespective of the task, the trials that were characterized by changes in choice selections (switch trials) were associated with a neural response that mostly overlapped with a network commonly described for the encoding of uncertainty. More interestingly, dynamic causal modeling and family-wise model comparison identified with high likelihood a directed causal relation from the external to the internal part of the globus pallidus (i.e., the short indirect pathway in the basal ganglia), in association with the switch trials. This finding supports the hypothesis that the short indirect pathway in the basal ganglia drives instability in the network dynamics, resulting in changes in choice selection.

Basal Ganglia and Thalamic Contributions to Language Function: Insights from A Parallel Distributed Processing Perspective

Cerebral representations are encoded as patterns of activity involving billions of neurons. Parallel distributed processing (PDP) across these neuronal populations provides the basis for a number of emergent properties: 1) processing occurs and knowledge (long term memories) is stored (as synaptic connection strengths) in exactly the same networks; 2) networks have the capacity for setting into stable attractor states corresponding to concepts, symbols, implicit rules, or data transformations; 3) networks provide the scaffold for the acquisition of knowledge but knowledge is acquired through experience; 4) PDP networks are adept at incorporating the statistical regularities of experience as well as frequency and age of acquisition effects; 5) networks enable content-addressable memory; 6) because knowledge is distributed throughout networks, they exhibit the property of graceful degradation; 7) networks intrinsically provide the capacity for inference. This paper details the features of the basal ganglia and thalamic systems (recurrent and distributed connectivity) that support PDP. The PDP lens and an understanding of the attractor trench dynamics of the basal ganglia provide a natural explanation for the peculiar dysfunctions of Parkinson's disease and the mechanisms by which dopamine deficiency is causal. The PDP lens, coupled with the fact that the basal ganglia of humans bears strong homology to the basal ganglia of lampreys and the central complex of arthropods, reveals that the fundamental function of the basal ganglia is computational and involves the reduction of the vast dimensionality of a complex multi-dimensional array of sensorimotor input into the optimal choice from a small repertoire of behavioral options - the essence of reactive intention (automatic responses to sensory input). There is strong evidence that the sensorimotor basal ganglia make no contributions to cognitive or motor function in humans but can cause serious dysfunction when pathological. It appears that humans, through the course of evolution, have developed cortical capacities (working memory and volitional and reactive attention) for managing sensory input, however complex, that obviate the need for the basal ganglia. The functions of the dorsal tier thalamus, however, even viewed with an understanding of the properties of population encoded representations, remain somewhat more obscure. Possibilities include the enabling of attractor state constellations that optimize function by taking advantage of simultaneous input from multiple cortical areas; selective engagement of cortical representations; and support of the gamma frequency synchrony that enables binding of the multiple network representations that comprise a full concept representation.

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.

Simple models including energy and spike constraints reproduce complex activity patterns and metabolic disruptions

In this work, we introduce new phenomenological neuronal models (eLIF and mAdExp) that account for energy supply and demand in the cell as well as the inactivation of spike generation how these interact with subthreshold and spiking dynamics. Including these constraints, the new models reproduce a broad range of biologically-relevant behaviors that are identified to be crucial in many neurological disorders, but were not captured by commonly used phenomenological models. Because of their low dimensionality eLIF and mAdExp open the possibility of future large-scale simulations for more realistic studies of brain circuits involved in neuronal disorders. The new models enable both more accurate modeling and the possibility to study energy-associated disorders over the whole time-course of disease progression instead of only comparing the initially healthy status with the final diseased state. These models, therefore, provide new theoretical and computational methods to assess the opportunities of early diagnostics and the potential of energy-centered approaches to improve therapies.

Neurons, even “at rest”, require a constant supply of energy to function. They cannot sustain high-frequency activity over long periods because of regulatory mechanisms, such as adaptation or sodium channels inactivation, and metabolic limitations. These limitations are especially severe in many neuronal disorders, where energy can become insufficient and make the neuronal response change drastically, leading to increased burstiness, network oscillations, or seizures. Capturing such behaviors and impact of energy constraints on them is an essential prerequisite to study disorders such as Parkinson’s disease and epilepsy. However, energy and spiking constraints are not present in any of the standard neuronal models used in computational neuroscience. Here we introduce models that provide a simple and scalable way to account for these features, enabling large-scale theoretical and computational studies of neurological disorders and activity patterns that could not be captured by previously used models. These models provide a way to study energy-associated disorders over the whole time-course of disease progression, and they enable a better assessment of energy-centered approaches to improve therapies.

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.

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 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.

Model-based optimized phase-deviation deep brain stimulation for Parkinson 's disease

High-frequency deep brain stimulation (HF-DBS) of the subthalamic nucleus (STN), globus pallidus interna (GPi) and globus pallidus externa (GPe) are often considered as effective methods for the treatment of Parkinson's disease (PD). However, the stimulation of a single nucleus by HF-DBS can cause specific physical damage, produce side effects and usually consume more electrical energy. Therefore, we use a biophysically-based model of basal ganglia-thalamic circuits to explore more effective stimulation patterns to reduce adverse effects and save energy. In this paper, we computationally investigate the combined DBS of two nuclei with the phase deviation between two stimulation waveforms (CDBS). Three different stimulation combination strategies are proposed, i.e., STN and GPe CDBS (SED), STN and GPi CDBS (SID), as well as GPi and GPe CDBS (GGD). Resultantly, it is found that anti-phase CDBS is more effective in improving parkinsonian dynamical properties, including desynchronization of neurons and the recovery of the thalamus relay ability. Detailed simulation investigation shows that anti-phase SED and GGD are superior to SID. Besides, the energy consumption can be largely reduced by SED and GGD (72.5% and 65.5%), compared to HF-DBS. These results provide new insights into the optimal stimulation parameter and target choice of PD, which may be helpful for the clinical practice.

Cellular and Synaptic Dysfunctions in Parkinson's Disease: Stepping out of the Striatum

The basal ganglia (BG) are a collection of interconnected subcortical nuclei that participate in a great variety of functions, ranging from motor programming and execution to procedural learning, cognition, and emotions. This network is also the region primarily affected by the degeneration of midbrain dopaminergic neurons localized in the substantia nigra pars compacta (SNc). This degeneration causes cellular and synaptic dysfunctions in the BG network, which are responsible for the appearance of the motor symptoms of Parkinson’s disease. Dopamine (DA) modulation and the consequences of its loss on the striatal microcircuit have been extensively studied, and because of the discrete nature of DA innervation of other BG nuclei, its action outside the striatum has been considered negligible. However, there is a growing body of evidence supporting functional extrastriatal DA modulation of both cellular excitability and synaptic transmission. In this review, the functional relevance of DA modulation outside the striatum in both normal and pathological conditions will be discussed.

Insights into Parkinson's disease from computational models of the basal ganglia

Movement disorders arise from the complex interplay of multiple changes to neural circuits. Successful treatments for these disorders could interact with these complex changes in myriad ways, and as a consequence their mechanisms of action and their amelioration of symptoms are incompletely understood. Using Parkinson's disease as a case study, we review here how computational models are a crucial tool for taming this complexity, across causative mechanisms, consequent neural dynamics and treatments. For mechanisms, we review models that capture the effects of losing dopamine on basal ganglia function; for dynamics, we discuss models that have transformed our understanding of how beta-band (15-30 Hz) oscillations arise in the parkinsonian basal ganglia. For treatments, we touch on the breadth of computational modelling work trying to understand the therapeutic actions of deep brain stimulation. Collectively, models from across all levels of description are providing a compelling account of the causes, symptoms and treatments for Parkinson's disease.

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

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