Mean-field modeling of the basal ganglia-thalamocortical system. II Dynamics of parkinsonian oscillations

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.

Multi-timescale neuromodulation strategy for closed-loop deep brain stimulation in Parkinson's disease

Objective.Beta triggered closed-loop deep brain stimulation (DBS) shows great potential for improving the efficacy while reducing side effect for Parkinson's disease. However, there remain great challenges due to the dynamics and stochasticity of neural activities. In this study, we aimed to tune the amplitude of beta oscillations with different time scales taking into account influence of inherent variations in the basal ganglia-thalamus-cortical circuit.Approach. A dynamic basal ganglia-thalamus-cortical mean-field model was established to emulate the medication rhythm. Then, a dynamic target model was designed to embody the multi-timescale dynamic of beta power with milliseconds, seconds and minutes. Moreover, we proposed a closed-loop DBS strategy based on a proportional-integral-differential (PID) controller with the dynamic control target. In addition, the bounds of stimulation amplitude increments and different parameters of the dynamic target were considered to meet the clinical constraints. The performance of the proposed closed-loop strategy, including beta power modulation accuracy, mean stimulation amplitude, and stimulation variation were calculated to determine the PID parameters and evaluate neuromodulation performance in the computational dynamic mean-field model.Main results. The Results show that the dynamic basal ganglia-thalamus-cortical mean-field model simulated the medication rhythm with the fasted and the slowest rate. The dynamic control target reflected the temporal variation in beta power from milliseconds to minutes. With the proposed closed-loop strategy, the beta power tracked the dynamic target with a smoother stimulation sequence compared with closed-loop DBS with the constant target. Furthermore, the beta power could be modulated to track the control target under different long-term targets, modulation strengths, and bounds of the stimulation increment.Significance. This work provides a new method of closed-loop DBS for multi-timescale beta power modulation with clinical constraints.

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.

Modeling Instantaneous Firing Rate of Deep Brain Stimulation Target Neuronal Ensembles in the Basal Ganglia and Thalamus

OBJECTIVE

Deep brain stimulation (DBS) is an effective treatment for movement disorders, including Parkinson disease and essential tremor. However, the underlying mechanisms of DBS remain elusive. Despite the capability of existing models in interpreting experimental data qualitatively, there are very few unified computational models that quantitatively capture the dynamics of the neuronal activity of varying stimulated nuclei-including subthalamic nucleus (STN), substantia nigra pars reticulata (SNr), and ventral intermediate nucleus (Vim)-across different DBS frequencies.

MATERIALS AND METHODS

Both synthetic and experimental data were used in the model fitting; the synthetic data were generated by an established spiking neuron model that was reported in our previous work, and the experimental data were provided using single-unit microelectrode recordings (MERs) during DBS (microelectrode stimulation). Based on these data, we developed a novel mathematical model to represent the firing rate of neurons receiving DBS, including neurons in STN, SNr, and Vim-across different DBS frequencies. In our model, the DBS pulses were filtered through a synapse model and a nonlinear transfer function to formulate the firing rate variability. For each DBS-targeted nucleus, we fitted a single set of optimal model parameters consistent across varying DBS frequencies.

RESULTS

Our model accurately reproduced the firing rates observed and calculated from both synthetic and experimental data. The optimal model parameters were consistent across different DBS frequencies.

CONCLUSIONS

The result of our model fitting was in agreement with experimental single-unit MER data during DBS. Reproducing neuronal firing rates of different nuclei of the basal ganglia and thalamus during DBS can be helpful to further understand the mechanisms of DBS and to potentially optimize stimulation parameters based on their actual effects on neuronal activity.

A dynamic computational model of the parallel circuit on the basal ganglia-cortex associated with Parkinson's disease dementia

The cognitive impairment will gradually appear over time in Parkinson's patients, which is closely related to the basal ganglia-cortex network. This network contains two parallel circuits mediated by putamen and caudate nucleus, respectively. Based on the biophysical mean-field model, we construct a dynamic computational model of the parallel circuit in the basal ganglia-cortex network associated with Parkinson's disease dementia. The simulated results show that the decrease of power ratio in the prefrontal cortex is mainly caused by dopamine depletion in the caudate nucleus and is less related to that in the putamen, which indicates Parkinson's disease dementia may be caused by a lesion of the caudate nucleus rather than putamen. Furthermore, the underlying dynamic mechanism behind the decrease of power ratio is investigated by bifurcation analysis, which demonstrates that the decrease of power ratio is due to the change of brain discharge pattern from the limit cycle mode to the point attractor mode. More importantly, the spatiotemporal course of dopamine depletion in Parkinson's disease patients is well simulated, which states that with the loss of dopaminergic neurons projecting to the striatum, motor dysfunction of Parkinson's disease is first observed, whereas cognitive impairment occurs after a period of onset of motor dysfunction. These results are helpful to understand the pathogenesis of cognitive impairment and provide insights into the treatment of Parkinson's disease dementia.

Suppression of absence seizures by using different stimulations in a reduced corticothalamic-basal ganglion-pedunculopontine nucleus model

Coupled neural network models are playing an increasingly important part in the modulation of absence seizures today. However, it is currently unclear how basal ganglia, corticothalamic network and pedunculopontine nucleus can coordinate with each other to develop a whole coupling circuit, theoretically. In addition, it is still difficult to select effective parameters of electrical stimulation on the regulation of absence seizures in clinical trials. Therefore, to develop a coupled model and reduce computation cost, a new model constructed by a simplified basal ganglion, two corticothalamic circuits and a pedunculopontine nucleus was proposed. Further, to seek better inhibition therapy, three electrical stimulations, high frequency stimulation (HFS), 1:0 coordinate reset stimulation (CRS) and 3:2 CRS, were applied to the thalamic reticular nucleus (RE) in the first corticothalamic circuit in the coupled model. The simulation results revealed that increasing the frequency and pulse width of an electrical stimulation within a certain range can also suppress seizures. Under the same parameters of electrical stimulation, the inhibitory effect of HFS on seizures was better than that of 1:0 CRS and 3:2 CRS. The research established a reduced corticothalamic-basal ganglion-pedunculopontine nucleus model, which lays a theoretical foundation for future optimal parameters selection of electrical stimulation. We hope that the findings will provide new insights into the role of theoretical models in absence seizures.

Dopamine depletion leads to pathological synchronization of distinct basal ganglia loops in the beta band

Motor symptoms of Parkinson's Disease (PD) are associated with dopamine deficits and pathological oscillation of basal ganglia (BG) neurons in the β range ([12-30] Hz). However, how dopamine depletion affects the oscillation dynamics of BG nuclei is still unclear. With a spiking neurons model, we here capture the features of BG nuclei interactions leading to oscillations in dopamine-depleted condition. We highlight that both the loop between subthalamic nucleus (STN) and Globus Pallidus pars externa (GPe) and the loop between striatal fast spiking and medium spiny neurons and GPe display resonances in the β range, and synchronize to a common β frequency through interaction. Crucially, the synchronization depends on dopamine depletion: the two loops are largely independent for high levels of dopamine, but progressively synchronize as dopamine is depleted due to the increased strength of the striatal loop. The model is validated against recent experimental reports on the role of cortical inputs, STN and GPe activity in the generation of β oscillations. Our results highlight the role of the interplay between the GPe-STN and the GPe-striatum loop in generating sustained β oscillations in PD subjects, and explain how this interplay depends on the level of dopamine. This paves the way to the design of therapies specifically addressing the onset of pathological β oscillations.

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.

The adjustment mechanism of the spike and wave discharges in thalamic neurons: a simulation analysis

Different from many previous theoretical studies, this paper explores the regulatory mechanism of the spike and wave discharges (SWDs) in the reticular thalamic nucleus (TRN) by a dynamic computational model. We observe that the SWDs appears in the TRN by changing the coupling weights and delays in the thalamocortical circuit. The abundant poly-spikes wave discharges is also induced when the delay increases to large enough. These discharges can be inhibited by tuning the inhibitory output from the basal ganglia to the thalamus. The mechanisms of these waves can be explained in this model together with simulation results, which are different from the mechanisms in the cortex. The TRN is an important target in treating epilepsy, and the results may be a theoretical evidence for experimental study in the future.

Regulating absence seizures by tri-phase delay stimulation applied to globus pallidus internal

In this paper, a reduced globus pallidus internal (GPI)-corticothalamic (GCT) model is developed, and a tri-phase delay stimulation (TPDS) with sequentially applying three pulses on the GPI representing the inputs from the striatal D ₁ neurons, subthalamic nucleus (STN), and globus pallidus external (GPE), respectively, is proposed. The GPI is evidenced to control absence seizures characterized by 2 Hz-4 Hz spike and wave discharge (SWD). Hence, based on the basal ganglia-thalamocortical (BGCT) model, we firstly explore the triple effects of D _l-GPI, GPE-GPI, and STN-GPI pathways on seizure patterns. Then, using the GCT model, we apply the TPDS on the GPI to potentially investigate the alternative and improved approach if these pathways to the GPI are blocked. The results show that the striatum D ₁, GPE, and STN can indeed jointly and significantly affect seizure patterns. In particular, the TPDS can effectively reproduce the seizure pattern if the D ₁-GPI, GPE-GPI, and STN-GPI pathways are cut off. In addition, the seizure abatement can be obtained by well tuning the TPDS stimulation parameters. This implies that the TPDS can play the surrogate role similar to the modulation of basal ganglia, which hopefully can be helpful for the development of the brain-computer interface in the clinical application of epilepsy.

The inhibition mechanism of epilepsy disease in a computational model

BACKGROUND:

The mechanism of prevention and treatment of epilepsy is a hot issue in theoretical research.

OBJECTIVE:

In this paper, we studied the control mechanism of the generalized spike-and-wave discharges (GSWD) by different types of external electrical stimulation acting on the subthalamic nucleus (STN) in a computational model.

METHODS:

Firstly, we analyzed the pathological mechanism of seizures, which were induced by different parameters in the thalamocortical (TC) circuit. Then, a voltage V was exerted in the STN. At last, we used the sine wave and square wave current stimulation in the STN.

RESULTS:

We found that seizures can be inhibited by tuning stimulus intensity into suitable range, and the direction of adjustment depended on the size of the parameter. We observed that the seizure can also be inhibited by tuning different parameters in current.

CONCLUSIONS:

Different inhibition mechanisms can be explained in this model, which may provide theoretical evidences for selecting the optimal treatment scheme in the clinical.

A data-informed mean-field approach to mapping of cortical parameter landscapes

Constraining the many biological parameters that govern cortical dynamics is computationally and conceptually difficult because of the curse of dimensionality. This paper addresses these challenges by proposing (1) a novel data-informed mean-field (MF) approach to efficiently map the parameter space of network models; and (2) an organizing principle for studying parameter space that enables the extraction biologically meaningful relations from this high-dimensional data. We illustrate these ideas using a large-scale network model of the Macaque primary visual cortex. Of the 10-20 model parameters, we identify 7 that are especially poorly constrained, and use the MF algorithm in (1) to discover the firing rate contours in this 7D parameter cube. Defining a "biologically plausible" region to consist of parameters that exhibit spontaneous Excitatory and Inhibitory firing rates compatible with experimental values, we find that this region is a slightly thickened codimension-1 submanifold. An implication of this finding is that while plausible regimes depend sensitively on parameters, they are also robust and flexible provided one compensates appropriately when parameters are varied. Our organizing principle for conceptualizing parameter dependence is to focus on certain 2D parameter planes that govern lateral inhibition: Intersecting these planes with the biologically plausible region leads to very simple geometric structures which, when suitably scaled, have a universal character independent of where the intersections are taken. In addition to elucidating the geometry of the plausible region, this invariance suggests useful approximate scaling relations. Our study offers, for the first time, a complete characterization of the set of all biologically plausible parameters for a detailed cortical model, which has been out of reach due to the high dimensionality of parameter space.

Computational neuronal correlation with enhanced synchronized activity in the basal ganglia and the slowing of thalamic theta and alpha rhythms in Parkinson's disease

The aim of this work is computationally to correlate the synchronized neuronal activity of basal ganglia and slowing in theta and alpha rhythms in electroencephalogram (EEG) signal in thalamic region in case of dopamine depletion and decrease of synaptic connections. The used network topology is a scale-free network with constant node degree. The dopamine-modulated type Izikhevich neuron model is used for modeling the striatal region, consisting of fast-spiking interneurons, D1 and D2 type dopamine expressing medium spiny neurons. On the other hand, the ordinary Izikhevich neuron model is used in the modeling of extrastriatal basal ganglia (BG) regions where globus pallidus (GP) subregion neurons have also dopamine-dependent parameters. The thalamic region of the network is mass modeled including inhibitory input from basal ganglia. Depending on the decrease of synaptic connections and dopamine level, the synchronization among basal ganglia neuron populations is investigated. The effect of synaptic delay on synchronization is also considered. It is observed that the decrease of dopamine neurotransmitter and decrease in the number of synaptic connections cause an increased synchronous activity in BG. Also, slowing in theta and alpha bands in thalamus EEG signals is observed. This shows the causal relation between synchronization and power shifting to lower frequency components in the case of neurodegenerative diseases such as Parkinson's disease (PD).

The effect of external voltage stimulation on absence seizures

BACKGROUND:

Absence epilepsy (AE) is a systemic disease of the brain, which mainly occurs during childhood and adolescence. The control mechanism is still unclear, and few theoretical studies have been conducted to investigate this.

OBJECTIVE:

In this paper, we employed external direct voltage stimulation in the subthalamic nucleus to explore mechanisms that inhibit absence seizures.

METHODS:

All simulation results are obtained by the four-order Runge-Kutta method in the MATLAB environment. The inhibition mechanism can be inferred from the results.

RESULTS:

We found that the seizures may be inhibited by tuning the strength of the voltage to suitable ranges. This regulation may be achieved through the competition between the inhibitory projections from the basal ganglia to the thalamus.

CONCLUSION:

Because the mechanism underlying the treatment of epilepsy with a uniform direct current electric field is unclear, we hope that these results can inspire further experimental studies.

The therapeutic mechanism of epilepsy seizures in different target areas: Research on a theoretical model

BACKGROUND

The selection of optimal target areas in the surgical treatment of epilepsy is always a difficult problem in medicine.

OBJECTIVE

We employed a theoretical calculation model to explore the control mechanism of seizures by an external voltage stimulus acting in different nerve nuclei.

METHODS

Theoretical analysis and numerical simulation were combined.

RESULTS

The globus pallidus, excitatory pyramidal neurons, striatal D1 neurons, thalamic reticular nucleus and specific relay nuclei were selected, we analyzed that the electrical stimulation has different effects in these target areas.

CONCLUSIONS

The data selected were reasonable in study, the results may give a theoretical support for similar studies in clinical.

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.

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.

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.

A biologically constrained spiking neural network model of the primate basal ganglia with overlapping pathways exhibits action selection

Action selection has been hypothesized to be a key function of the basal ganglia, yet the nuclei involved, their interactions and the importance of the direct/indirect pathway segregation in such process remain debated. Here, we design a spiking computational model of the monkey basal ganglia derived from a previously published population model, initially parameterized to reproduce electrophysiological activity at rest and to embody as much quantitative anatomical data as possible. As a particular feature, both models exhibit the strong overlap between the direct and indirect pathways that has been documented in non-human primates. Here, we first show how the translation from a population to an individual neuron model was achieved, with the addition of a minimal number of parameters. We then show that our model performs action selection, even though it was built without any assumption on the activity carried out during behaviour. We investigate the mechanisms of this selection through circuit disruptions and found an instrumental role of the off-centre/on-surround structure of the MSN-STN-GPi circuit, as well as of the MSN-MSN and FSI-MSN projections. This validates their potency in enabling selection. We finally study the pervasive centromedian and parafascicular thalamic inputs that reach all basal ganglia nuclei and whose influence is therefore difficult to anticipate. Our model predicts that these inputs modulate the responsiveness of action selection, making them a candidate for the regulation of the speed-accuracy trade-off during decision-making.

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.

A review of computational modeling and deep brain stimulation: applications to Parkinson's disease

Biophysical computational models are complementary to experiments and theories, providing powerful tools for the study of neurological diseases. The focus of this review is the dynamic modeling and control strategies of Parkinson's disease (PD). In previous studies, the development of parkinsonian network dynamics modeling has made great progress. Modeling mainly focuses on the cortex-thalamus-basal ganglia (CTBG) circuit and its sub-circuits, which helps to explore the dynamic behavior of the parkinsonian network, such as synchronization. Deep brain stimulation (DBS) is an effective strategy for the treatment of PD. At present, many studies are based on the side effects of the DBS. However, the translation from modeling results to clinical disease mitigation therapy still faces huge challenges. Here, we introduce the progress of DBS improvement. Its specific purpose is to develop novel DBS treatment methods, optimize the treatment effect of DBS for each patient, and focus on the study in closed-loop DBS. Our goal is to review the inspiration and insights gained by combining the system theory with these computational models to analyze neurodynamics and optimize DBS treatment.

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

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

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.

Regulation and control roles of the basal ganglia in the development of absence epileptiform activities

Absence epileptiform activities are traditionally considered to be primarily induced by abnormal interactions between the cortical and thalamic neurons, which form the thalamocortical circuit in the brain. The basal ganglia, as an organizational unit in the brain, has close input and output relationships with the thalamocortical circuit. Although several studies report that the basal ganglia may participate in controlling and regulating absence epileptiform activities, to date, there have been no studies regarding whether the basal ganglia directly cause absence epileptiform activities. In this paper, we built a basal ganglia-corticothalamic network model to determine the role of basal ganglia in this disease. We determined that absence epileptiform activities might be directly induced by abnormal coupling strengths on certain pivotal pathways in the basal ganglia. These epileptiform activities can be well controlled by the coupling strengths of three major pathways that project from the thalamocortical network to the basal ganglia. The results implied that the substantia nigra pars compacta (SNc) can be considered to be the effective treatment target area for inhibiting epileptiform activities, which supports the observations of previous studies. Particularly, as a major contribution of this paper, we determined that the final presentation position of the epileptic slow spike waves is not limited to the cerebral cortex; these waves may additionally appear in the thalamus, striatal medium spiny neurons, striatal fast spiking interneuron, the SNc, subthalamic nucleus, substantia nigra pars reticulata and globus pallidus pars externa. In addition, consistent with several previous studies, the delay in the network was observed to be a critical factor for inducing transitions between different types of absence epileptiform activities. Our new model not only explains the onset and control mechanism but also provides a unified framework to study similar problems in neuron systems.

Neural field theory of evoked response potentials in a spherical brain geometry

Evoked response potentials (ERPs) are calculated in spherical and planar geometries using neural field theory of the corticothalamic system. The ERP is modeled as an impulse response and the resulting modal effects of spherical corticothalamic dynamics are explored, showing that results for spherical and planar geometries converge in the limit of large brain size. Cortical modal effects can lead to a double-peak structure in the ERP time series. It is found that the main difference between infinite planar geometry and spherical geometry is that the ERP peak is sharper and stronger in the spherical geometry. It is also found that the magnitude of the response decreases with increasing spatial width of the stimulus at the cortex. The peak is slightly delayed at large angles from the stimulus point, corresponding to group velocities of 6-10 m s^{-1}. Strong modal effects are found in the spherical geometry, with the lowest few modes sufficing to describe the main features of ERPs, except very near to spatially narrow stimuli.

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

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

The beta oscillation conditions in a simplified basal ganglia network

Parkinson's disease is a type of motor dysfunction disease that is induced mainly by abnormal interactions between the subthalamic nucleus (STN) and globus pallidus (GP) neurons. Periodic oscillatory activities with frequencies of 13-30 Hz are the main physiological characteristics of Parkinson's disease. In this paper, we built a class of STN-GP networks to explore beta oscillation conditions. A theoretical formula was obtained for generating oscillations without internal GP connections. Based on this formula, we studied the effects of cortex inputs, striatum inputs, coupling weights and delays on oscillation conditions, and the theoretical results are in good agreement with the numerical results. The onset mechanism can be explained by the model, and the internal GP connection has little effect on oscillations. Finally, we compared oscillation conditions with those in previous studies and found that the delays and coupling weights required for generating oscillations may decrease as the number of nuclei increases. We hope that the results obtained will inspire future theoretical and experimental studies.

Suppression of Parkinsonian Beta Oscillations by Deep Brain Stimulation: Determination of Effective Protocols

A neural field model of the corticothalamic-basal ganglia system is developed that describes enhanced beta activity within subthalamic and pallidal circuits in Parkinson's disease (PD) via system resonances. A model of deep brain stimulation (DBS) of typical clinical targets, the subthalamic nucleus (STN) and globus pallidus internus (GPi), is added and studied for several distinct stimulation protocols that are used for treatment of the motor symptoms of PD and that reduce pathological beta band activity (13-30 Hz) in the corticothalamic-basal ganglia network. The resulting impact of DBS on enhanced beta activity in the STN and GPi, as well as cortico-subthalamic and cortico-pallidal coherence, are studied. Both STN-DBS and GPi-DBS are found to be effective for suppressing peak STN and GPi power in the beta band, with GPi-DBS being slightly more effective in both the STN and the GPi for all stimulus protocols tested. The largest decrease in cortico-STN coherence is observed during STN-DBS, whereas GPi-DBS is most effective for reducing cortico-GPi coherence. A reduction of the pathologically large STN connection strengths that define the parkinsonian state results in enhanced 6 Hz activity and could thus represent a compensatory mechanism that has the side effect of driving parkinsonian tremor-like oscillations. This model provides a method for systematically testing effective DBS protocols that agrees with experimental and clinical findings. Furthermore, the model suggests GPi-DBS and STN-DBS have distinct impacts on elevated synchronization between the basal ganglia and motor cortex in PD.

Bayesian adaptive dual control of deep brain stimulation in a computational model of Parkinson's disease

In this paper, we present a novel Bayesian adaptive dual controller (ADC) for autonomously programming deep brain stimulation devices. We evaluated the Bayesian ADC's performance in the context of reducing beta power in a computational model of Parkinson's disease, in which it was tasked with finding the set of stimulation parameters which optimally reduced beta power as fast as possible. Here, the Bayesian ADC has dual goals: (a) to minimize beta power by exploiting the best parameters found so far, and (b) to explore the space to find better parameters, thus allowing for better control in the future. The Bayesian ADC is composed of two parts: an inner parameterized feedback stimulator and an outer parameter adjustment loop. The inner loop operates on a short time scale, delivering stimulus based upon the phase and power of the beta oscillation. The outer loop operates on a long time scale, observing the effects of the stimulation parameters and using Bayesian optimization to intelligently select new parameters to minimize the beta power. We show that the Bayesian ADC can efficiently optimize stimulation parameters, and is superior to other optimization algorithms. The Bayesian ADC provides a robust and general framework for tuning stimulation parameters, can be adapted to use any feedback signal, and is applicable across diseases and stimulator designs.

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.

Generic dynamic causal modelling: An illustrative application to Parkinson's disease

We present a technical development in the dynamic causal modelling of electrophysiological responses that combines qualitatively different neural mass models within a single network. This affords the option to couple various cortical and subcortical nodes that differ in their form and dynamics. Moreover, it enables users to implement new neural mass models in a straightforward and standardized way. This generic framework hence supports flexibility and facilitates the exploration of increasingly plausible models. We illustrate this by coupling a basal ganglia-thalamus model to a (previously validated) cortical model developed specifically for motor cortex. The ensuing DCM is used to infer pathways that contribute to the suppression of beta oscillations induced by dopaminergic medication in patients with Parkinson's disease. Experimental recordings were obtained from deep brain stimulation electrodes (implanted in the subthalamic nucleus) and simultaneous magnetoencephalography. In line with previous studies, our results indicate a reduction of synaptic efficacy within the circuit between the subthalamic nucleus and external pallidum, as well as reduced efficacy in connections of the hyperdirect and indirect pathway leading to this circuit. This work forms the foundation for a range of modelling studies of the synaptic mechanisms (and pathophysiology) underlying event-related potentials and cross-spectral densities.

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.

The oscillatory boundary conditions of different frequency bands in Parkinson's disease

Parkinson's disease (PD) is a neurodegenerative disease that is common in the elderly population. The most important pathological change in PD is the degeneration and death of dopaminergic neurons in the substantia nigra of the midbrain, which results in a decrease in the dopamine (DA) content of the striatum. The exact cause of this pathological change is still unknown. Numerous studies have shown that the evolution of PD is associated with abnormal oscillatory activities in the basal ganglia, with different oscillation frequency ranges, such as the typical beta band (13-30 Hz), the alpha band (8-12 Hz), the theta band (4-7 Hz) and the delta band (1-3 Hz). Although some studies have implied that abnormal interactions between the subthalamic nucleus (STN) and globus pallidus (GP) neurons may be a key factor required to induce these oscillations, the relative mechanism is still unclear. The effects of other nerve nuclei in the basal ganglia, such as the striatum, on these oscillations are still unknown. The thalamus and cortex both have close input and output relationships with the basal ganglia, and many previous studies have indicated that they may also exert effects on Parkinson's disease oscillation, but the mechanisms involved are unclear. In this paper, we built a corticothalamic-basal ganglia (CTBG) mean firing-rate model to explore the onset mechanisms of these different oscillation phenomena. We found that, in addition to the STN-GP network, Parkinson's disease oscillations may also be induced by changing the coupling strength and delays in other pathways. Different frequency bands appear in the oscillating region, and various boundary conditions are depicted in parameter diagrams. The onset mechanism is well explained both by the model and by the numerical simulation results. Therefore, this model provides a unifying framework for studying the mechanism of Parkinson's disease oscillations, and we hope that the results obtained in this work can inspire future experimental studies.

Modeling and Analysis of Beta Oscillations in the Basal Ganglia

Enhanced beta (12-30 Hz) oscillatory activity in the basal ganglia (BG) is a prominent feature of the Parkinsonian state in animal models and in patients with Parkinson's disease. Increased beta oscillations are associated with severe dopaminergic striatal depletion. However, the mechanisms underlying these pathological beta oscillations remain elusive. Inspired by the experimental observation that only subsets of neurons within each nucleus in the BG exhibit oscillatory activities, a computational model of the BG-thalamus neuronal network is proposed, which is characterized by subdivided nuclei within the BG. Using different currents externally applied to the neurons within a given nucleus, neurons behave according to one of the two subgroups, named "-N" and "-P," where "-N" and "-P" denote the normal and the Parkinsonian states, respectively. The ratio of "-P" to "-N" neurons indicates the degree of the Parkinsonian state. Simulation results show that if "-P" neurons have a high degree of connectivity in the subthalamic nucleus (STN), they will have a significant downstream effect on the generation of beta oscillations in the globus pallidus. Interestingly, however, the generation of beta oscillations in the STN is independent of the selection of the "-P" neurons in the external segment of the globus pallidus (GPe), despite the reciprocal structure between STN and GPe. This computational model may pave the way to revealing the mechanism of such pathological behaviors in a realistic way that can replicate experimental observations. The simulation results suggest that the STN is more suitable than GPe as a deep brain stimulation target.

Quantitative theory of deep brain stimulation of the subthalamic nucleus for the suppression of pathological rhythms in Parkinson's disease

Deep brain stimulation (DBS) of the subthalamic nucleus (STN) is modeled to explore the mechanisms of this effective, but poorly understood, treatment for motor symptoms of drug-refractory Parkinson's disease and dystonia. First, a neural field model of the corticothalamic-basal ganglia (CTBG) system is developed that reproduces key clinical features of Parkinson's disease, including its characteristic 4-8 Hz and 13-30 Hz electrophysiological signatures. Deep brain stimulation of the STN is then modeled and shown to suppress the pathological 13-30 Hz (beta) activity for physiologically realistic and optimized stimulus parameters. This supports the idea that suppression of abnormally coherent activity in the CTBG system is a major factor in DBS therapy for Parkinson's disease, by permitting normal dynamics to resume. At high stimulus intensities, nonlinear effects in the target population mediate wave-wave interactions between resonant beta activity and the stimulus pulse train, leading to complex spectral structure that shows remarkable similarity to that seen in steady-state evoked potential experiments.

Credibility, Replicability, and Reproducibility in Simulation for Biomedicine and Clinical Applications in Neuroscience

Modeling and simulation in computational neuroscience is currently a research enterprise to better understand neural systems. It is not yet directly applicable to the problems of patients with brain disease. To be used for clinical applications, there must not only be considerable progress in the field but also a concerted effort to use best practices in order to demonstrate model credibility to regulatory bodies, to clinics and hospitals, to doctors, and to patients. In doing this for neuroscience, we can learn lessons from long-standing practices in other areas of simulation (aircraft, computer chips), from software engineering, and from other biomedical disciplines. In this manuscript, we introduce some basic concepts that will be important in the development of credible clinical neuroscience models: reproducibility and replicability; verification and validation; model configuration; and procedures and processes for credible mechanistic multiscale modeling. We also discuss how garnering strong community involvement can promote model credibility. Finally, in addition to direct usage with patients, we note the potential for simulation usage in the area of Simulation-Based Medical Education, an area which to date has been primarily reliant on physical models (mannequins) and scenario-based simulations rather than on numerical simulations.

Control of absence epilepsy seizures in specific relay nuclei of thalamus

In this paper, we used a classic basal ganglia-corticothalamic model(BGCT) to study the onset and control mechanism of absence epilepsy in specific relay nuclei (SRN) of thalamus. It was found that the seizure state may appear in SRN by turning the coupling strength -v_sr and signal transmission delay τ on the route "Thalamic reticular nuclei (TRN) of thalamus ⟶ SRN". With increasing of -v_sr, the seizure state appeared two times, and its onset mechanism has not been discussed in previous studies. The seizure activity can be well controlled by adjusting the activation level of the substantia nigra pars reticulata (SNr) in basal ganglia, which is a main output tissue to the corticothalamic system through two direct inhibitory pathways "SNr ⟶ SRN" and "SNr ⟶ TRN" in our model. We found that the interesting bidirectional regulation phenomenon appeared as considering the single pathway "SNr ⟶ SRN" and "SNr ⟶ TRN", or when they coexisted in one network, the mechanism of which is also different from some previous theoretical studies. At last, we pointed out that the mechanism obtained above can also explain the onset and control of the poly-spikes slow wave appeared in SRN by turning τ to large enough. Therefore, the results in the paper will further deepen our understanding of the generation and control mechanism of epilepsy disease.

Controlling mechanism of absence seizures by deep brain stimulus applied on subthalamic nucleus

Based on a classical model of the basal ganglia thalamocortical network, in this paper, we employed a type of the deep brain stimulus voltage on the subthalamic nucleus to study the control mechanism of absence epilepsy seizures. We found that the seizure can be well controlled by turning the period and the duration of current stimulation into suitable ranges. It is the very interesting bidirectional periodic adjustment phenomenon. These parameters are easily regulated in clinical practice, therefore, the results obtained in this paper may further help us to understand the treatment mechanism of the epilepsy seizure.

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

The development, simulation, and analysis of mathematical models offer helpful tools for integrating experimental findings and exploring or suggesting possible explanatory mechanisms. As models relating to basal ganglia dysfunction have proliferated, however, there has not always been consistency among their findings. This work points out several ways in which biological details, relating to ionic currents and synaptic pathways, can influence the dynamics of models of the basal ganglia under parkinsonian conditions and hence may be important for inclusion in models. It also suggests some additional useful directions for future modeling studies relating to basal ganglia dysfunction.

Unified neural field theory of brain dynamics underlying oscillations in Parkinson's disease and generalized epilepsies

The mechanisms underlying pathologically synchronized neural oscillations in Parkinson's disease (PD) and generalized epilepsies are explored in parallel via a physiologically-based neural field model of the corticothalamic-basal ganglia (CTBG) system. The basal ganglia (BG) are approximated as a single effective population and their roles in the modulation of oscillatory dynamics of the corticothalamic (CT) system and vice versa are analyzed. In addition to normal EEG rhythms, enhanced activity around 4 Hz and 20 Hz exists in the model, consistent with the characteristic frequencies observed in PD. These rhythms result from resonances in loops formed between the BG and CT populations, analogous to those that underlie epileptic oscillations in a previous CT model, and which are still present in the combined CTBG system. Dopamine depletion is argued to weaken the dampening of these loop resonances in PD, and network connections then explain the significant coherence observed between BG, thalamic, and cortical population activity around 4-8 Hz and 20 Hz. Parallels between the afferent and efferent connection sites of the thalamic reticular nucleus (TRN) and BG predict low dopamine to correspond to a reduced likelihood of tonic-clonic (grand mal) seizures, which agrees with experimental findings. Furthermore, the model predicts an increased likelihood of absence (petit mal) seizure resulting from pathologically low dopamine levels in accordance with experimental observations. Suppression of absence seizure activity is demonstrated when afferent and efferent BG connections to the CT system are strengthened, which is consistent with other CTBG modeling studies. The BG are demonstrated to have a suppressive effect on activity of the CTBG system near tonic-clonic seizure states, which provides insight into the reported efficacy of current treatments in BG circuits. Sleep states of the TRN are also found to suppress pathological PD activity in accordance with observations. Overall, the findings demonstrate strong parallels between coherent oscillations in generalized epilepsies and PD, and provide insights into possible comorbidities.

Modulation of Parkinsonian State With Uncertain Disturbance Based on Sliding Mode Control

Parkinson's disease (PD) is a degenerative disorder of central nervous system that endangers the olds' health seriously. The motor symptoms of PD can be attributed to the distorted relay reliability of thalamus to cortical sensorimotor input that results from the increase of inhibitory input from internal segment of the globus pallidum (GPi). Based on this, we construct the GPi-thalamocortical computational model to generate the normal and pathological firing patterns by varying GPi spike train input. A kind of closed-loop deep brain stimulation (DBS) strategy is proposed here. Our control objective is to make the controlled membrane potential of the thalamic neuron return to the normal firing pattern. The control input that directly acts on the thalamus is the DBS waveform, which is adjusted in real time according to the feedback signal. Aimed at a certain system without the change of object parameters or stochastic disturbance, the input-output feedback linearization method is able to eliminate the error between the system output and the desired output. When uncertain elements taken into consideration in the system, the simulation results indicate that sliding mode control scheme provides better effectiveness and higher robustness.

Control of Absence Seizures by the Thalamic Feed-Forward Inhibition

As a subtype of idiopathic generalized epilepsies, absence epilepsy is believed to be caused by pathological interactions within the corticothalamic (CT) system. Using a biophysical mean-field model of the CT system, we demonstrate here that the feed-forward inhibition (FFI) in thalamus, i.e., the pathway from the cerebral cortex (Ctx) to the thalamic reticular nucleus (TRN) and then to the specific relay nuclei (SRN) of thalamus that are also directly driven by the Ctx, may participate in controlling absence seizures. In particular, we show that increasing the excitatory Ctx-TRN coupling strength can significantly suppress typical electrical activities during absence seizures. Further, investigation demonstrates that the GABA_A- and GABA_B-mediated inhibitions in the TRN-SRN pathway perform combination roles in the regulation of absence seizures. Overall, these results may provide an insightful mechanistic understanding of how the thalamic FFI serves as an intrinsic regulator contributing to the control of absence seizures.

Eliminating Absence Seizures through the Deep Brain Stimulation to Thalamus Reticular Nucleus

Deep brain stimulation (DBS) can play a crucial role in the modulation of absence seizures, yet relevant biophysical mechanisms are not completely established. In this paper, on the basis of a biophysical mean-field model, we investigate a typical absence epilepsy activity by introducing slow kinetics of GABA_B receptors on thalamus reticular nucleus (TRN). We find that the region of spike and slow-wave discharges (SWDs) can be reduced greatly when we add the DBS to TRN. Furthermore, we systematically explore how the corresponding stimulation parameters including frequency, amplitude and positive input duration suppress the SWDs under certain conditions. It is shown that the SWDs can be controlled as key stimulation parameters are suitably chosen. The results in this paper can be helpful for researchers to understand the thalamus stimulation in treating epilepsy patients, and provide theoretical basis for future experimental and clinical studies.

A new EEG synchronization strength analysis method: S-estimator based normalized weighted-permutation mutual information

Synchronization is an important mechanism for understanding information processing in normal or abnormal brains. In this paper, we propose a new method called normalized weighted-permutation mutual information (NWPMI) for double variable signal synchronization analysis and combine NWPMI with S-estimator measure to generate a new method named S-estimator based normalized weighted-permutation mutual information (SNWPMI) for analyzing multi-channel electroencephalographic (EEG) synchronization strength. The performances including the effects of time delay, embedding dimension, coupling coefficients, signal to noise ratios (SNRs) and data length of the NWPMI are evaluated by using Coupled Henon mapping model. The results show that the NWPMI is superior in describing the synchronization compared with the normalized permutation mutual information (NPMI). Furthermore, the proposed SNWPMI method is applied to analyze scalp EEG data from 26 amnestic mild cognitive impairment (aMCI) subjects and 20 age-matched controls with normal cognitive function, who both suffer from type 2 diabetes mellitus (T2DM). The proposed methods NWPMI and SNWPMI are suggested to be an effective index to estimate the synchronization strength.

Disinhibition-Induced Delayed Onset of Epileptic Spike-Wave Discharges in a Five Variable Model of Cortex and Thalamus

Based on a modified neural field network model composed of cortex and thalamus, we here propose a computational framework to investigate the onset control of absence seizure, which is characterized by the spike-wave discharges. Firstly, we briefly demonstrate the existence of various transition types in Taylor's model by increasing the thalamic input. Furthermore, after the disinhibitory function is reasonably introduced into the Taylor's model, we can observe the occurrence of various transition states of firing patterns with different dominant frequencies as the thalamic input is varied under different disinhibitory effects onto the pyramidal neural population. Interestingly, it is found that the onset of spike-wave discharges can be delayed as the disinhibitory input is considered. More importantly, we explore bifurcation mechanism of firing transitions as some key parameters are changed. And also, we observe other dynamical states, such as simple oscillations and saturated discharges with different spatial scales, which are consistent with previous theoretical or experimental findings.

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

In Parkinson's disease, an increase in beta oscillations within the basal ganglia nuclei has been shown to be associated with difficulty in movement initiation. An important role in the generation of these oscillations is thought to be played by the motor cortex and by a network composed of the subthalamic nucleus (STN) and the external segment of globus pallidus (GPe). Several alternative models have been proposed to describe the mechanisms for generation of the Parkinsonian beta oscillations. However, a recent experimental study of Tachibana and colleagues yielded results which are challenging for all published computational models of beta generation. That study investigated how the presence of beta oscillations in a primate model of Parkinson's disease is affected by blocking different connections of the STN-GPe circuit. Due to a large number of experimental conditions, the study provides strong constraints that any mechanistic model of beta generation should satisfy. In this paper we present two models consistent with the data of Tachibana et al. The first model assumes that Parkinsonian beta oscillation are generated in the cortex and the STN-GPe circuits resonates at this frequency. The second model additionally assumes that the feedback from STN-GPe circuit to cortex is important for maintaining the oscillations in the network. Predictions are made about experimental evidence that is required to differentiate between the two models, both of which are able to reproduce firing rates, oscillation frequency and effects of lesions carried out by Tachibana and colleagues. Furthermore, an analysis of the models reveals how the amplitude and frequency of the generated oscillations depend on parameters.

Critical Roles of the Direct GABAergic Pallido-cortical Pathway in Controlling Absence Seizures

The basal ganglia (BG), serving as an intermediate bridge between the cerebral cortex and thalamus, are believed to play crucial roles in controlling absence seizure activities generated by the pathological corticothalamic system. Inspired by recent experiments, here we systematically investigate the contribution of a novel identified GABAergic pallido-cortical pathway, projecting from the globus pallidus externa (GPe) in the BG to the cerebral cortex, to the control of absence seizures. By computational modelling, we find that both increasing the activation of GPe neurons and enhancing the coupling strength of the inhibitory pallido-cortical pathway can suppress the bilaterally synchronous 2-4 Hz spike and wave discharges (SWDs) during absence seizures. Appropriate tuning of several GPe-related pathways may also trigger the SWD suppression, through modulating the activation level of GPe neurons. Furthermore, we show that the previously discovered bidirectional control of absence seizures due to the competition between other two BG output pathways also exists in our established model. Importantly, such bidirectional control is shaped by the coupling strength of this direct GABAergic pallido-cortical pathway. Our work suggests that the novel identified pallido-cortical pathway has a functional role in controlling absence seizures and the presented results might provide testable hypotheses for future experimental studies.