Synchronous high-frequency oscillations in inhibitory-dominant network motifs consisting of three dentate gyrus-CA3 systems.

Studies on the structural-functional connectomes of the human brain have demonstrated the existence of synchronous firings in a specific brain network motif. In particular, synchronization of high-frequency oscillations (HFOs) has been observed in the experimental data sets of temporal lobe epilepsy (TLE). In addition, both clinical and experimental evidences have accumulated to demonstrate the effect of electrical stimulation on TLE, which, however, remains largely unexplored. In this work, we first employ our previously proposed dentate gyrus (DG)-CA3 network model to investigate the influence of an external electrical stimulus on the HFO transitions. The results indicate that the reinforcing stimulus can induce the HFO transitions of the DG-CA3 system from the gamma band to the fast ripples band. Along with that, the consistent oscillations of neurons within DG-CA3 can also be enhanced with the increasing of stimulus. Then, we expand into a simple motif of three coupled DG-CA3 systems in both the feedforward inhibition and feedback inhibition connections, to investigate the synchronous evolutions of HFOs by regulating both the stimulation strength and inhibitory function. It is shown that the comprehensive effects, which lead to band transition, are independent of the motif configurations. The enhanced external electrical stimulus weakens the synchronism and correlation of connected motifs. In contrast, we demonstrate that the increased inhibitory coupling could facilitate correlation to some extent. Overall, our work highlights the possible origin of synchronous HFOs of hippocampal motifs governed by external inputs and inhibitory connection, which might contribute to a better understanding of the interplay between synchronization dynamics and epileptic structure in the human brain.

Effects of brain-derived neurotrophic factor and noise on transitions in temporal lobe epilepsy in a hippocampal network.

Brain-derived neurotrophic factor (BDNF) has recently been implicated in the modulation of receptor activation leading to dynamic state transitions in temporal lobe epilepsy (TLE). In addition, the crucial role of neuronal noise in these transitions has been studied in electrophysiological experiments. However, the precise role of these factors during seizure generation in TLE is not known. Building on a previously proposed model of an epileptogenic hippocampal network, we included the actions of BDNF-regulated receptors and intrinsic noise. We found that the effects of both BDNF and noise can increase the activation of N-methyl-D-aspartate receptors leading to excessive C a 2 + flux, which induces abnormal fast spiking and bursting. Our results indicate that the combined effects have a strong influence on the seizure-generating network, resulting in higher firing frequency and amplitude. As correlations between firing increase, the synchronization of the entire network increases, a marker of the ictogenic transitions from normal to seizures-like dynamics. Our work on the effects of BDNF dynamics in a noisy environment might lead to an improved model-based understanding of the pathological mechanisms in TLE.

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 pacemaker role of thalamic reticular nucleus in controlling spike-wave discharges and spindles.

Absence epilepsy, characterized by 2-4 Hz spike-wave discharges (SWDs), can be caused by pathological interactions within the thalamocortical system. Cortical spindling oscillations are also demonstrated to involve the oscillatory thalamocortical rhythms generated by the synaptic circuitry of the thalamus and cortex. This implies that SWDs and spindling oscillations can share the common thalamocortical mechanism. Additionally, the thalamic reticular nucleus (RE) is hypothesized to regulate the onsets and propagations of both the epileptic SWDs and sleep spindles. Based on the proposed single-compartment thalamocortical neural field model, we firstly investigate the stimulation effect of RE on the initiations, terminations, and transitions of SWDs. It is shown that the activations and deactivations of RE triggered by single-pulse stimuli can drive the cortical subsystem to behave as the experimentally observed onsets and self-abatements of SWDs, as well as the transitions from 2-spike and wave discharges (2-SWDs) to SWDs. In particular, with increasing inhibition from RE to the specific relay nucleus (TC), rich transition behaviors in cortex can be obtained through the upstream projection path, RE→TC→Cortex. Although some of the complex dynamical patterns can be expected from the earlier single compartment thalamocortical model, the effect of brain network topology on the emergence of SWDs and spindles, as well as the transitions between them, has not been fully investigated. We thereby develop a spatially extended 3-compartment coupled network model with open-/closed-end connective configurations, to investigate the spatiotemporal effect of RE on the SWDs and spindles. Results show that the degrees of activations of RE1 can induce the rich spatiotemporal evolution properties including the propagations from SWDs to spindles within different compartments and the transitions between them, through the RE1→TC1→Cortex1 and Cortex1→Cortex2→Cortex3 projecting paths, respectively. Overall, those results imply that RE possesses the pacemaker function in controlling SWDs and spindling oscillations, which computationally provide causal support for the involvement of RE in absence seizures and sleep spindles.

Improving desynchronization of Parkinsonian neuronal network via triplet-structure coordinated reset stimulation.

We investigate how the triplet-structure coordinated reset stimulations (CRS), which acts on the GPe, STN and GPi within the basal ganglia-thalamocortical motor circuit, can destabilize the strong synchronous state and improve the reliability of thalamic relay in the parkinsonian network. It is shown that compared with the permanent (1:0 ON-OFF) CRS or the classic deep brain stimulation paradigm, the periodic m:n ON-OFF CRS (i.e., m ON-cycles stimulation followed by n OFF-cycles stimulation) can significantly desynchronize the neuronal network of Parkinson's disease, and evidently improve the fidelity of thalamic relay. In addition, the CRS-induced desynchronization can be greatly enhanced when the STN subpopulation within the pathologic network is subjected to the synaptic plasticity. Furthermore, the desynchronization and reliability can also be further improved as the closed-loop CRS strategy is introduced. The obtained results can be helpful for us to understand the pathophysiology mechanism of Parkinson's disease, even though the feasibility of CRS still needs to be explored in clinic.

The seizure classification of focal epilepsy based on the network motif analysis.

Due to the complexity of focal epilepsy and its risk for transiting to the generalized epilepsy, the development of reliable classification methods to accurately predict and classify focal and generalized seizures is critical for the clinical management of patients with epilepsy. In order to holistically understand the seizure propagation behavior of focal epilepsy, we propose a three-node motif reduced network by respectively simplifying the focal region, surrounding healthy region and their critical regions as the single node. Because three-node motif can richly characterize information evolutions, the motif analysis method could comprehensively investigate the seizure behavior of focal epilepsy. Firstly, we define a new seizure propagation marker value to capture the seizure onsets and intensity. Based on the three-node motif analysis, it is shown that the focal seizure and spreading can be categorized as inhibitory seizure, focal seizure, focal-critical seizure and generalized seizures, respectively. The four types of seizures correspond to specific modal types respectively, reflecting the strong correlation between seizure behavior and information flow evolution. In addition, it is found that the intensity difference of outflow and inflow information from the critical node (connection heterogeneity) and the excitability of the critical node significantly affected the distribution and transition of the four seizure types. In particular, the method of local linear stability analysis also verifies the effectiveness of four types of seizures classification. In sum, this paper computationally confirms the complex dynamic behavior of focal seizures, and the study of criticality is helpful to propose novel seizure control strategies.

The distribution and heterogeneity of excitability in focal epileptic network potentially contribute to the seizure propagation.

Introduction: Existing dynamical models can explain the transmigration mechanisms involved in seizures but are limited to a single modality. Combining models with networks can reproduce scaled epileptic dynamics. And the structure and coupling interactions of the network, as well as the heterogeneity of both the node and network activities, may influence the final state of the network model. Methods: We built a fully connected network with focal nodes prominently interacting and established a timescale separated epileptic network model. The factors affecting epileptic network seizure were explored by varying the connectivity patterns of focal network nodes and modulating the distribution of network excitability. Results: The whole brain network topology as the brain activity foundation affects the consistent delayed clustering seizure propagation. In addition, the network size and distribution heterogeneity of the focal excitatory nodes can influence seizure frequency. With the increasing of the network size and averaged excitability level of focal network, the seizure period decreases. In contrast, the larger heterogeneity of excitability for focal network nodes can lower the functional activity level (average degree) of focal network. There are also subtle effects of focal network topologies (connection patterns of excitatory nodes) that cannot be ignored along with non-focal nodes. Discussion: Unraveling the role of excitatory factors in seizure onset and propagation can be used to understand the dynamic mechanisms and neuromodulation of epilepsy, with profound implications for the treatment of epilepsy and even for the understanding of the brain.

Putative cause of seizure-induced cognitive alterations: The oscillatory reconfiguration of seizure network.

Introduction: The dynamic reconfiguration of network oscillations is connected with cognitive processes. Changes in how neural networks and signaling pathways work are crucial to how epilepsy and related conditions develop. Specifically, there is evidence that prolonged or recurrent seizures may induce or exacerbate cognitive impairment. However, it still needs to be determined how the seizure brain configures its functional structure to shape the battle of strong local oscillations vs. slow global oscillations in the network to impair cognitive function. Methods: In this paper, we aim to deduce the network mechanisms underlying seizure-induced cognitive impairment by comparing the evolution of strong local oscillations with slow global oscillations and their link to the resting state of healthy controls. Here, we construct a dynamically efficient network of pathological seizures by calculating the synchrony and directionality of information flow between nine patients' SEEG signals. Then, using a pattern-based method, we found hierarchical modules in the brain's functional network and measured the functional balance between the network's local strong and slow global oscillations. Results and discussion: According to the findings, a tremendous rise in strong local oscillations during seizures and an increase in slow global oscillations after seizures corresponded to the initiation and recovery of cognitive impairment. Specifically, during the interictal period, local strong and slow global oscillations are in metastable balance, which is the same as a normal cognitive process and can be switched easily. During the pre-ictal period, the two show a bimodal pattern of separate peaks that cannot be easily switched, and some flexibility is lost. During the seizure period, a single-peak pattern with negative peaks is showcased, and the network eventually transitions to a very intense strong local oscillation state. These results shed light on the mechanism behind network oscillations in epilepsy-induced cognitive impairment. On the other hand, the differential (similarity) of oscillatory reorganization between the local (non) epileptogenic network and the global network may be an emergency protective mechanism of the brain, preventing the spread of pathological information flow to more healthy brain regions.

Deep-layer motif method for estimating information flow between EEG signals.

Accurate identification for the information flow between epileptic seizure signals is the key to construct the directional epileptic brain network which can be used to localize epileptic focus. In this paper, our concern is on how to improve the direction identification of information flow and also investigate how it can be cut off or weakened. In view of this, we propose the deep-layer motif method. Based on the directional index (DI) estimation using permutation conditional mutual information, the effectiveness of the proposed deep-layer motif method is numerically assessed with the coupled mass neural model. Furthermore, we investigate the robustness of this method in considering the interference of autaptic coupling, time delay and short-term plasticity. Results show that compared to the simple 1-layer motif method, the 2nd- and 3rd-layer motif methods have the dominant enhancement effects for the direction identification. In particular, deep-layer motif method possesses good anti-jamming performance and good robustness in calculating DI. In addition, we investigate the effect of deep brain stimulation (DBS) on the information flow. It is found that this deep-layer motif method is still superior to the single-layer motif method in direction identification and is robust to weak DBS. However, the high-frequency strong DBS can effectively decrease the DI suggesting the weakened information flow. These results may give new insights into the seizure detection and control.

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.

Sharp decrease in the Laplacian matrix rank of phase-space graphs: a potential biomarker in epilepsy.

In this paper, phase space reconstruction from stereo-electroencephalography data of ten patients with focal epilepsy forms a series of graphs. Those obtained graphs reflect the transition characteristics of brain dynamical system from pre-seizure to seizure of epilepsy. Interestingly, it is found that the rank of Laplacian matrix of these graphs has a sharp decrease when a seizure is close to happen, which thus might be viewed as a new potential biomarker in epilepsy. In addition, the reliability of this method is numerically verified with a coupled mass neural model. In particular, our simulation suggests that this potential biomarker can play the roles of predictive effect or delayed awareness, depending on the bias current of the Gaussian noise. These results may give new insights into the seizure detection.

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.

Transition Dynamics of a Dentate Gyrus-CA3 Neuronal Network during Temporal Lobe Epilepsy.

In temporal lobe epilepsy (TLE), the variation of chemical receptor expression underlies the basis of neural network activity shifts, resulting in neuronal hyperexcitability and epileptiform discharges. However, dynamical mechanisms involved in the transitions of TLE are not fully understood, because of the neuronal diversity and the indeterminacy of network connection. Hence, based on Hodgkin-Huxley (HH) type neurons and Pinsky-Rinzel (PR) type neurons coupling with glutamatergic and GABAergic synaptic connections respectively, we propose a computational framework which contains dentate gyrus (DG) region and CA3 region. By regulating the concentration range of N-methyl-D-aspartate-type glutamate receptor (NMDAR), we demonstrate the pyramidal neuron can generate transitions from interictal to seizure discharges. This suggests that enhanced endogenous activity of NMDAR contributes to excitability in pyramidal neuron. Moreover, we conclude that excitatory discharges in CA3 region vary considerably on account of the excitatory currents produced by the excitatory pyramidal neuron. Interestingly, by changing the backprojection connection, we find that glutamatergic type backprojection can promote the dominant frequency of firings and further motivate excitatory counterpropagation from CA3 region to DG region. However, GABAergic type backprojection can reduce firing rate and block morbid counterpropagation, which may be factored into the terminations of TLE. In addition, neuronal diversity dominated network shows weak correlation with different backprojections. Our modeling and simulation studies provide new insights into the mechanisms of seizures generation and connectionism in local hippocampus, along with the synaptic mechanisms of this disease.

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.

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.

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.

Disinhibition-induced transitions between absence and tonic-clonic epileptic seizures.

Electrophysiological experiments have long revealed the existence of two-way transitions between absence and tonic-clonic epileptic seizures in the cerebral cortex. Based on a modified spatially-extended Taylor &Baier neural field model, we here propose a computational framework to mathematically describe the transition dynamics between these epileptic seizures. We first demonstrate the existence of various transition types that are induced by disinhibitory functions between two inhibitory variables in an isolated Taylor &Baier model. Moreover, we show that these disinhibition-induced transitions can lead to stable tonic-clonic oscillations as well as periodic spike with slow-wave discharges, which are the hallmark of absence seizures. We also observe fascinating dynamical states, such as periodic 2-spike with slow-wave discharges, tonic death, bursting oscillations, as well as saturated firing. Most importantly, we identify paths that represent physiologically plausible transitions between absence and tonic-clonic seizures in the modified spatially-extended Taylor &Baier model.

Hopf bifurcation and bursting synchronization in an excitable systems with chemical delayed coupling.

In this paper we consider the Hopf bifurcation and synchronization in the two coupled Hindmarsh-Rose excitable systems with chemical coupling and time-delay. We surveyed the conditions for Hopf bifurcations by means of dynamical bifurcation analysis and numerical simulation. The results show that the coupled excitable systems with no delay have supercritical Hopf bifurcation, while the delayed system undergoes Hopf bifurcations at critical time delays when coupling strength lies in a particular region. We also investigated the effect of the delay on the transition of bursting synchronization in the coupled system. The results are helpful for us to better understand the dynamical properties of excitable systems and the biological mechanism of information encoding and cognitive activity.