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

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.

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

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

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.

Control of epileptic activities in a cortex network of multiple coupled neural populations under electromagnetic induction

Epilepsy is believed to be associated with the abnormal synchronous neuronal activity in the brain, which results from large groups or circuits of neurons. In this paper, we choose to focus on the temporal lobe epilepsy, and establish a cortex network of multiple coupled neural populations to explore the epileptic activities under electromagnetic induction. We demonstrate that the epileptic activities can be controlled and modulated by electromagnetic induction and coupling among regions. In certain regions, these two types of control are observed to show exactly reverse effects. The results show that the strong electromagnetic induction is conducive to eliminating the epileptic seizures. The coupling among regions has a conduction effect that the previous normal background activity of the region gives way to the epileptic discharge, owing to coupling with spike wave discharge regions. Overall, these results highlight the role of electromagnetic induction and coupling among the regions in controlling and modulating epileptic activities, and might provide novel insights into the treatments of epilepsy.

Segregation, integration and balance in resting-state brain functional networks associated with bipolar disorder symptoms

Bipolar disorder (BD) is a serious mental disorder involving widespread abnormal interactions between brain regions, and it is believed to be associated with imbalanced functions in the brain. However, how this brain imbalance underlies distinct BD symptoms remains poorly understood. Here, we used a nested-spectral partition (NSP) method to study the segregation, integration, and balance in resting-state brain functional networks in BD patients and healthy controls (HCs). We first confirmed that there was a high deviation in the brain functional network toward more segregation in BD patients than in HCs and that the limbic system had the largest alteration. Second, we demonstrated a network balance of segregation and integration that corresponded to lower anxiety in BD patients but was not related to other symptoms. Subsequently, based on a machine-learning approach, we identified different system-level mechanisms underlying distinct BD symptoms and found that the features related to the brain network balance could predict BD symptoms better than graph theory analyses. Finally, we studied attention-deficit/hyperactivity disorder (ADHD) symptoms in BD patients and identified specific patterns that distinctly predicted ADHD and BD scores, as well as their shared common domains. Our findings supported an association of brain imbalance with anxiety symptom in BD patients and provided a potential network signature for diagnosing BD. These results contribute to further understanding the neuropathology of BD and to screening ADHD in BD patients.

Brain diffusion tensor imaging reveals altered connections and networks in epilepsy patients

Introduction

Accumulating evidence shows that epilepsy is a disease caused by brain network dysfunction. This study explored changes in brain network structure in epilepsy patients based on graph analysis of diffusion tensor imaging data.

Methods

The brain structure networks of 42 healthy control individuals and 26 epilepsy patients were constructed. Using graph theory analysis, global and local network topology parameters of the brain structure network were calculated, and changes in global and local characteristics of the brain network in epilepsy patients were quantitatively analyzed.

Results

Compared with the healthy control group, the epilepsy patient group showed lower global efficiency, local efficiency, clustering coefficient, and a longer shortest path length. Both healthy control individuals and epilepsy patients showed small-world attributes, with no significant difference between groups. The epilepsy patient group showed lower nodal local efficiency and nodal clustering coefficient in the right olfactory cortex and right rectus and lower nodal degree centrality in the right olfactory cortex and the left paracentral lobular compared with the healthy control group. In addition, the epilepsy patient group showed a smaller fiber number of edges in specific regions of the frontal lobe, temporal lobe, and default mode network, indicating reduced connection strength.

Discussion

Epilepsy patients exhibited lower global and local brain network properties as well as reduced white matter fiber connectivity in key brain regions. These findings further support the idea that epilepsy is a brain network disorder.

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.

Closed-loop controller based on reference signal tracking for absence seizures

Absent epilepsy is a kind of refractory epilepsy, which is characterized by 2–4 Hz spike and wave discharges (SWDs) in electroencephalogram. Open-loop deep brain stimulation (DBS) targeting the thalamic reticular nucleus (TRN) is an effective method to treat absent epilepsy by eliminating SWDs in the brain. Compared with open-loop DBS, closed-loop DBS has been recognized by researchers for its advantages of significantly inhibiting seizures and having fewer side effects. Since traditional trial-and-error methods for adjusting closed-loop controller parameters are too dependent on the experience of doctors, in this paper we designed two proportional integral (PI) controllers based on the basal ganglia-cortical-thalamic model, whose PI parameters are calculated from the stability of the system. The two PI controllers can automatically adjust the frequency and amplitude of DBS respectively according to the change of the firing rate detected by substantia nigra pars reticulata (SNr). The parameters of the PI controller are calculated based on the Routh-Hurwitz stability criterion of a linear system which transformed by the original system using controlled auto-regressive (CAR) model and recursive least squares (RLS) method. Numerical simulation results show that both PI controllers significantly destroy the SWDs of the cerebral cortex and restore it to the other two normal discharge modes according to the different target firing rate, which supplies a promising brain stimulation strategy.

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.

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.

Connective profiles and antagonism between dynamic and static connectivity underlying generalized epilepsy

This study aims to characterize the connective profiles and the coupling relationship between dynamic and static functional connectivity (dFC and sFC) in large-scale brain networks in patients with generalized epilepsy (GE). Functional, structural and diffuse MRI data were collected from 83 patients with GE and 106 matched healthy controls (HC). Resting-state BOLD time course was deconvolved to neural time course using a blind hemodynamic deconvolution method. Then, five connective profiles, including the structural connectivity (SC) and BOLD/neural time course-derived sFC/dFC networks, were constructed based on the proposed whole brain atlas. Network-level weighted correlation probability (NWCP) were proposed to evaluate the association between dFC and sFC. Both the BOLD signal and neural time course showed highly concordant findings and the present study emphasized the consistent findings between two functional approaches. The patients with GE showed hypervariability and enhancement of FC, and notably decreased SC in the subcortical network. Besides, increased dFC, weaker anatomic links, and complex alterations of sFC were observed in the default mode network of GE. Moreover, significantly increased SC and predominantly increased sFC were found in the frontoparietal network. Remarkably, antagonism between dFC and sFC was observed in large-scale networks in HC, while patients with GE showed significantly decreased antagonism in core epileptic networks. In sum, our study revealed distinct connective profiles in different epileptic networks and provided new clues to the brain network mechanism of epilepsy from the perspective of antagonism between dynamic and static functional connectivity.

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.

Closed-Loop Control of Absence Seizures Inspired by Feedback Modulation of Basal Ganglia to the Corticothalamic Circuit

Basal ganglia (BG) has been demonstrated to play the role of modulation for absence seizure generated in the corticothalamic (CT) circuit. But it is unknown what the principle of modulation is and how to improve the modulation if BG fails to hold back the absence seizures. Although neurostimulation has been surgically employed to improve the clinical symptom of patients with epilepsy, the mechanism underlying the neurostimulation regulation is still unclear. In addition, it is not clear what sort of the spatiotemporal patterned stimulation protocols can effectively abate absence seizures with less side effect and energy consumption. Here, we address these issues on the previously proposed BG-CT model. In particular, we develop a reduced corticothalamic (RCT) moldel by viewing BG as a 2I:3O feedback modulator. By calculating the mean firing rate (MFR) and triggering mean firing rate (TMFR), we find that absence seizures can be induced or abated using the neurostimulations through driving the MFRs of the related neurons to fall into or be kicked out of the regions bounded by the TMFRs. In particular, closed-loop m:n ON-OFF anodic-cathodic-cathodic (ACC) triphase coordinated resetting stimulation (CRS) applied on the CT circuit and designed with the TMFR of subthalamic nucleus (STN) in BG could achieve the satisfying abatement effects of absence seizures with the least current consumption.

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.

Epileptic Focus Localization via Brain Network Analysis on Riemannian Manifolds

OBJECTIVE

Brain network connectivity analysis plays an important role in computer-aided automatic localization of seizure onset zone (SOZ) from Intracranial Electroencephalography (iEEG). However, how to accurately compute brain network dynamics is still not well addressed. This work aims to develop an effective measure to find out the dynamics for SOZ localization.

METHODS

Given multiple-channel iEEG signals, the ictal process involves continuous changes of information propagation. In each time slot, the connectivity relationship between channels can be represented as a matrix. Since the matrices from different time slots do not lie on vector spaces, the similarity between them cannot be computed directly. In this paper, we regard the matrices as points on a Riemannian manifold, so that the similarity can be measured by the geodesic distance on the manifold. It addresses the information-losing problem in existing methods using a vector to approximate a matrix. With the Riemannian method, the brain network dynamics are figured out by clustering methods. A temporal segmentation process is applied to refine the segments for SOZ localization.

RESULTS

Our method is evaluated on six epilepsy patients, and the SOZ localization performance is evaluated by the area under the curve (AUC) score. Overall, our method obtains an average AUC score of 0.875, which outperforms the existing approaches.

CONCLUSION

Our method preserves more information in measuring the relationship between brain connectivity descriptors, thus is more robust for SOZ localization.

SIGNIFICANCE

Our method has great potentials for clinical epilepsy treatments.

Unified analysis of global and focal aspects of absence epilepsy via neural field theory of the corticothalamic system

Absence epilepsy is characterized by a sudden paroxysmal loss of consciousness accompanied by oscillatory activity propagating over many brain areas. Although primary generalized absence seizures are supported by the global corticothalamic system, converging experimental evidence supports a focal theory of absence epilepsy. Here a physiology-based corticothalamic model is investigated with spatial heterogeneity due to focal epilepsy to unify global and focal aspects of absence epilepsy. Numeric and analytic calculations are employed to investigate the emergent spatiotemporal dynamics as well as their underlying dynamical mechanisms. They can be categorized into three scenarios: suppressed epilepsy, focal seizures, or generalized seizures, as summarized from a phase diagram vs focal width and characteristic axon range. The corresponding temporal frequencies and spatial extents of cortical waves in generalized seizures and focal seizures agree well with experimental observations of global and focal aspects of absence epilepsy, respectively. The emergence of the spatiotemporal dynamics corresponding to focal seizures provides a biophysical explanation of the temporally higher frequency but spatially more localized cortical waves observed in genetic rat models that display characteristics of human absence epilepsy. Predictions are also presented for further experimental test.

Bistable Firing Pattern in a Neural Network Model

Excessively high, neural synchronization has been associated with epileptic seizures, one of the most common brain diseases worldwide. A better understanding of neural synchronization mechanisms can thus help control or even treat epilepsy. In this paper, we study neural synchronization in a random network where nodes are neurons with excitatory and inhibitory synapses, and neural activity for each node is provided by the adaptive exponential integrate-and-fire model. In this framework, we verify that the decrease in the influence of inhibition can generate synchronization originating from a pattern of desynchronized spikes. The transition from desynchronous spikes to synchronous bursts of activity, induced by varying the synaptic coupling, emerges in a hysteresis loop due to bistability where abnormal (excessively high synchronous) regimes exist. We verify that, for parameters in the bistability regime, a square current pulse can trigger excessively high (abnormal) synchronization, a process that can reproduce features of epileptic seizures. Then, we show that it is possible to suppress such abnormal synchronization by applying a small-amplitude external current on > 10% of the neurons in the network. Our results demonstrate that external electrical stimulation not only can trigger synchronous behavior, but more importantly, it can be used as a means to reduce abnormal synchronization and thus, control or treat effectively epileptic seizures.

Pivotal Role of Subcortical Structures as a Network Hub in Focal Epilepsy: Evidence from Graph Theoretical Analysis Based on Diffusion-Tensor Imaging

Background and Purpose

There is accumulating evidence that epilepsy is caused by network dysfunction. We evaluated the hub reorganization of subcortical structures in patients with focal epilepsy using graph theoretical analysis based on diffusion-tensor imaging (DTI). In addition, we investigated differences in the values of diffusion tensors and scalars, fractional anisotropy (FA), and mean diffusivity (MD) of subcortical structures between patients with focal epilepsy and healthy subjects.

Methods

One hundred patients with focal epilepsy and normal magnetic resonance imaging (MRI) findings and 80 age- and sex-matched healthy subjects were recruited prospectively. All subjects underwent DTI to obtain data suitable for graph theoretical analysis. We investigated the differences in the node strength, cluster coefficient, eigenvector centrality, page-rank centrality measures, FA, and MD of subcortical structures between patients with epilepsy and healthy subjects.

Results

After performing multiple corrections, the cluster coefficient and the eigenvector centrality of the globus pallidus were higher in patients with epilepsy than in healthy subjects (p=0.006 and p=0.008, respectively). In addition, the strength and the page-rank centrality of the globus pallidus tended to be higher in patients with epilepsy than in healthy subjects (p=0.092 and p=0.032, respectively). The cluster coefficient of the putamen was lower in patients with epilepsy than in healthy subjects (p=0.004). The FA values of the caudate nucleus and thalamus were significantly lower in patients with epilepsy than in healthy subjects (p=0.009 and p=0.007, respectively), whereas the MD value of the thalamus was higher than that in healthy subjects (p=0.005).

Conclusions

We discovered the presence of hub reorganization of subcortical structures in focal epilepsy patients with normal MRI findings, suggesting that subcortical structures play a pivotal role as a hub in the epilepsy network. These findings further reinforce the idea that epilepsy is a network disease.

Analytically determining frequency and amplitude of spontaneous alpha oscillation in Jansen's neural mass model using the describing function method

Spontaneous alpha oscillations are a ubiquitous phenomenon in the brain and play a key role in neural information processing and various cognitive functions. Jansen's neural mass model (NMM) was initially proposed to study the origin of alpha oscillations. Most of previous studies of the spontaneous alpha oscillations in the NMM were conducted using numerical methods. In this study, we aim to propose an analytical approach using the describing function method to elucidate the spontaneous alpha oscillation mechanism in the NMM. First, the sigmoid nonlinear function in the NMM is approximated by its describing function, allowing us to reformulate the NMM and derive its standard form composed of one nonlinear part and one linear part. Second, by conducting a theoretical analysis, we can assess whether or not the spontaneous alpha oscillation would occur in the NMM and, furthermore, accurately determine its amplitude and frequency. The results reveal analytically that the interaction between linearity and nonlinearity of the NMM plays a key role in generating the spontaneous alpha oscillations. Furthermore, strong nonlinearity and large linear strength are required to generate the spontaneous alpha oscillations.

The generation mechanism of spike-and-slow wave discharges appearing on thalamic relay nuclei

In this paper, we use a model modified from classic corticothalamic network(CT) to explore the mechanism of absence seizures appearing on specific relay nuclei (SRN) of the thalamus. It is found that typical seizure states appear on SRN through tuning several critical connection strengths in the model. In view of previous experimental and theoretical works which were mainly on epilepsy seizure phenomena appearing on excitatory pyramidal neurons (EPN) of the cortex, this is a novel model to consider the seizure observed on thalamus. In particular, the onset mechanism is different from previous theoretical studies. Inspired by some previous clinical and experimental studies, we employ the external stimuli voltage on EPN and SRN in the network, and observe that the seizure can be well inhibited by tuning the stimulus intensity appropriately. We further explore the effect of the signal transmission delays on seizures, and found that the polyspike phenomenon appears only when the delay is sufficiently large. The experimental data also confirmed our model. Since there is a complex network in the brain and all organizations are interacting closely with each other, the results obtained in this paper provide not only biological insights into the regulatory mechanisms but also a reference for the prevention and treatment of epilepsy in future.

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.

Stimulus-induced transitions between spike-wave discharges and spindles with the modulation of thalamic reticular nucleus

It is believed that thalamic reticular nucleus (TRN) controls spindles and spike-wave discharges (SWD) in seizure or sleeping processes. The dynamical mechanisms of spatiotemporal evolutions between these two types of activity, however, are not well understood. In light of this, we first use a single-compartment thalamocortical neural field model to investigate the effects of TRN on occurrence of SWD and its transition. Results show that the increasing inhibition from TRN to specific relay nuclei (SRN) can lead to the transition of system from SWD to slow-wave oscillation. Specially, it is shown that stimulations applied in the cortical neuronal populations can also initiate the SWD and slow-wave oscillation from the resting states under the typical inhibitory intensity from TRN to SRN. Then, we expand into a 3-compartment coupled thalamocortical model network in linear and circular structures, respectively, to explore the spatiotemporal evolutions of wave states in different compartments. The main results are: (i) for the open-ended model network, SWD induced by stimulus in the first compartment can be transformed into sleep-like slow UP-DOWN and spindle states as it propagates into the downstream compartments; (ii) for the close-ended model network, weak stimulations performed in the first compartment can result in the consistent experimentally observed spindle oscillations in all three compartments; in contrast, stronger periodic single-pulse stimulations applied in the first compartment can induce periodic transitions between SWD and spindle oscillations. Detailed investigations reveal that multi-attractor coexistence mechanism composed of SWD, spindles and background state underlies these state evolutions. What's more, in order to demonstrate the state evolution stability with respect to the topological structures of neural network, we further expand the 3-compartment coupled network into 10-compartment coupled one, with linear and circular structures, and nearest-neighbor (NN) coupled network as well as its realization of small-world (SW) topology via random rewiring, respectively. Interestingly, for the cases of linear and circular connetivities, qualitatively similar results were obtained in addition to the more irregularity of firings. However, SWD can be eventually transformed into the consistent low-amplitude oscillations for both NN and SW networks. In particular, SWD evolves into the slow spindling oscillations and background tonic oscillations within the NN and SW network, respectively. Our modeling and simulation studies highlight the effect of network topology in the evolutions of SWD and spindling oscillations, which provides new insights into the mechanisms of cortical seizures development.

The role of the basal ganglia in the control of seizure

Epilepsy is a network disorder and each type of seizure involves distinct cortical and subcortical network, differently implicated in the control and propagation of the ictal activity. The role of the basal ganglia has been revealed in several cases of focal and generalized seizures. Here, we review the data that show the implication of the basal ganglia in absence, temporal lobe, and neocortical seizures in animal models (rodent, cat, and non-human primate) and in human. Based on these results and the advancement of deep brain stimulation for Parkinson's disease, basal ganglia neuromodulation has been tested with some success that can be equally seen as promising or disappointing. The effect of deep brain stimulation can be considered promising with a 76% in seizure reduction in temporal lobe epilepsy patients, but also disappointing, since only few patients have become seizure free and the antiepileptic effects have been highly variable among patients. This variability could probably be explained by the heterogeneity among the patients included in these clinical studies. To illustrate the importance of specific network identification, electrophysiological activity of the putamen and caudate nucleus has been recorded during penicillin-induced pre-frontal and motor seizures in one monkey. While an increase of the firing rate was found in putamen and caudate nucleus during pre-frontal seizures, only the activity of the putamen cells was increased during motor seizures. These preliminary results demonstrate the implication of the basal ganglia in two types of neocortical seizures and the necessity of studying the network to identify the important nodes implicated in the propagation and control of each type of seizure.

Combined Effects of Feedforward Inhibition and Excitation in Thalamocortical Circuit on the Transitions of Epileptic Seizures

The mechanisms underlying electrophysiologically observed two-way transitions between absence and tonic-clonic epileptic seizures in cerebral cortex remain unknown. The interplay within thalamocortical network is believed to give rise to these epileptic multiple modes of activity and transitions between them. In particular, it is thought that in some areas of cortex there exists feedforward inhibition from specific relay nucleus of thalamus (TC) to inhibitory neuronal population (IN) which has even more stronger functions on cortical activities than the known feedforward excitation from TC to excitatory neuronal population (EX). Inspired by this, we proposed a modified computational model by introducing feedforward inhibitory connectivity within thalamocortical circuit, to systematically investigate the combined effects of feedforward inhibition and excitation on transitions of epileptic seizures. We first found that the feedforward excitation can induce the transition from tonic oscillation to spike and wave discharges (SWD) in cortex, i.e., the epileptic tonic-absence seizures, with the fixed weak feedforward inhibition. Thereinto, the phase of absence seizures corresponding to strong feedforward excitation can be further transformed into the clonic oscillations with the increasing of feedforward inhibition, representing the epileptic absence-clonic seizures. We also observed the other fascinating dynamical states, such as periodic 2/3/4-spike and wave discharges, reversed SWD and clonic oscillations, as well as saturated firings. More importantly, we can identify the stable parameter regions representing the tonic-clonic oscillations and SWD discharges of epileptic seizures on the 2-D plane composed of feedforward inhibition and excitation, where the physiologically plausible transition pathways between tonic-clonic and absence seizures can be figured out. These results indicate the functional role of feedforward pathways in controlling epileptic seizures and the modified thalamocortical model may provide a guide for future efforts to mechanistically link feedforward pathways in the pathogenesis of epileptic seizures.

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.

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.

Stimulus-induced Epileptic Spike-Wave Discharges in Thalamocortical Model with Disinhibition

Epileptic absence seizure characterized by the typical 2–4 Hz spike-wave discharges (SWD) are known to arise due to the physiologically abnormal interactions within the thalamocortical network. By introducing a second inhibitory neuronal population in the cortical system, here we propose a modified thalamocortical field model to mathematically describe the occurrences and transitions of SWD under the mutual functions between cortex and thalamus, as well as the disinhibitory modulations of SWD mediated by the two different inhibitory interneuronal populations. We first show that stimulation can induce the recurrent seizures of SWD in the modified model. Also, we demonstrate the existence of various types of firing states including the SWD. Moreover, we can identify the bistable parametric regions where the SWD can be both induced and terminated by stimulation perturbations applied in the background resting state. Interestingly, in the absence of stimulation disinhibitory functions between the two different interneuronal populations can also both initiate and abate the SWD, which suggests that the mechanism of disinhibition is comparable to the effect of stimulation in initiating and terminating the epileptic SWD. Hopefully, the obtained results can provide theoretical evidences in exploring dynamical mechanism of epileptic seizures.

The Role of Striatal Feedforward Inhibition in the Maintenance of Absence Seizures

Absence seizures are characterized by brief interruptions of conscious experience accompanied by oscillations of activity synchronized across many brain areas. Although the dynamics of the thalamocortical circuits are traditionally thought to underlie absence seizures, converging experimental evidence supports the key involvement of the basal ganglia (BG). In this theoretical work, we argue that the BG are essential for the maintenance of absence seizures. To this end, we combine analytical calculations with numerical simulations to investigate a computational model of the BG-thalamo-cortical network. We demonstrate that abnormally strong striatal feedforward inhibition can promote synchronous oscillatory activity that persists in the network over several tens of seconds as observed during seizures. We show that these maintained oscillations result from an interplay between the negative feedback through the cortico-subthalamo-nigral pathway and the striatal feedforward inhibition. The negative feedback promotes epileptic oscillations whereas the striatal feedforward inhibition suppresses the positive feedback provided by the cortico-striato-nigral pathway. Our theory is consistent with experimental evidence regarding the influence of BG on seizures (e.g., with the fact that a pharmacological blockade of the subthalamo-nigral pathway suppresses seizures). It also accounts for the observed strong suppression of the striatal output during seizures. Our theory predicts that well-timed transient excitatory inputs to the cortex advance the termination of absence seizures. In contrast with the thalamocortical theory, it also predicts that reducing the synaptic transmission along the cortico-subthalamo-nigral pathway while keeping constant the average firing rate of substantia nigra pars reticulata reduces the incidence of seizures.

SIGNIFICANCE STATEMENT

Absence seizures are characterized by brief interruptions of consciousness accompanied by abnormal brain oscillations persisting tens of seconds. Thalamocortical circuits are traditionally thought to underlie absence seizures. However, recent experiments have highlighted the key role of the basal ganglia (BG). This work argues for a novel theory according to which the BG drive the oscillatory patterns of activity occurring during the seizures. It demonstrates that abnormally strong striatal feedforward inhibition promotes synchronous oscillatory activity in the BG-thalamo-cortical network and relate this property to the observed strong suppression of the striatal output during seizures. The theory is compatible with virtually all known experimental results, and it predicts that well-timed transient excitatory inputs to the cortex advance the termination of absence seizures.

Regulation of Irregular Neuronal Firing by Autaptic Transmission

The importance of self-feedback autaptic transmission in modulating spike-time irregularity is still poorly understood. By using a biophysical model that incorporates autaptic coupling, we here show that self-innervation of neurons participates in the modulation of irregular neuronal firing, primarily by regulating the occurrence frequency of burst firing. In particular, we find that both excitatory and electrical autapses increase the occurrence of burst firing, thus reducing neuronal firing regularity. In contrast, inhibitory autapses suppress burst firing and therefore tend to improve the regularity of neuronal firing. Importantly, we show that these findings are independent of the firing properties of individual neurons, and as such can be observed for neurons operating in different modes. Our results provide an insightful mechanistic understanding of how different types of autapses shape irregular firing at the single-neuron level, and they highlight the functional importance of autaptic self-innervation in taming and modulating neurodynamics.

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.