A computational study of stimulus driven epileptic seizure abatement

An exploratory computational analysis in mice brain networks of widespread epileptic seizure onset locations along with potential strategies for effective intervention and propagation control

Mean-field models have been developed to replicate key features of epileptic seizure dynamics. However, the precise mechanisms and the role of the brain area responsible for seizure onset and propagation remain incompletely understood. In this study, we employ computational methods within The Virtual Brain framework and the Epileptor model to explore how the location and connectivity of an Epileptogenic Zone (EZ) in a mouse brain are related to focal seizures (seizures that start in one brain area and may or may not remain localized), with a specific focus on the hippocampal region known for its association with epileptic seizures. We then devise computational strategies to confine seizures (prevent widespread propagation), simulating medical-like treatments such as tissue resection and the application of an anti-seizure drugs or neurostimulation to suppress hyperexcitability. Through selectively removing (blocking) specific connections informed by the structural connectome and graph network measurements or by locally reducing outgoing connection weights of EZ areas, we demonstrate that seizures can be kept constrained around the EZ region. We successfully identified the minimal connections necessary to prevent widespread seizures, with a particular focus on minimizing surgical or medical intervention while simultaneously preserving the original structural connectivity and maximizing brain functionality.

Optogenetic stimulation of the superior colliculus suppresses genetic absence seizures

While anti-seizure medications are effective for many patients, nearly one-third of individuals have seizures that are refractory to pharmacotherapy. Prior studies using evoked preclinical seizure models have shown that pharmacological activation or excitatory optogenetic stimulation of the deep and intermediate layers of the superior colliculus (DLSC) display multi-potent anti-seizure effects. Here we monitored and modulated DLSC activity to suppress spontaneous seizures in the WAG/Rij genetic model of absence epilepsy. Female and male WAG/Rij adult rats were employed as study subjects. For electrophysiology studies, we recorded single unit activity from microwire arrays placed within the DLSC. For optogenetic experiments, animals were injected with virus coding for channelrhodopsin-2 or a control vector, and we compared the efficacy of continuous neuromodulation to that of closed-loop neuromodulation paradigms. For each, we compared three stimulation frequencies on a within-subject basis (5, 20, 100 Hz). For closed-loop stimulation, we detected seizures in real time based on the EEG power within the characteristic frequency band of spike-and-wave discharges (SWDs). We quantified the number and duration of each SWD during each 2 h-observation period. Following completion of the experiment, virus expression and fibre-optic placement was confirmed. We found that single-unit activity within the DLSC decreased seconds prior to SWD onset and increased during and after seizures. Nearly 40% of neurons displayed suppression of firing in response to the start of SWDs. Continuous optogenetic stimulation of the DLSC (at each of the three frequencies) resulted in a significant reduction of SWDs in males and was without effect in females. In contrast, closed-loop neuromodulation was effective in both females and males at all three frequencies. These data demonstrate that activity within the DLSC is suppressed prior to SWD onset, increases at SWD onset, and that excitatory optogenetic stimulation of the DLSC exerts anti-seizure effects against absence seizures. The striking difference between open- and closed-loop neuromodulation approaches underscores the importance of the stimulation paradigm in determining therapeutic effects.

Regulating epileptiform discharges by heterogeneous interneurons in thalamocortical model

Inhibitory interneurons in the cortex are abundant and have diverse roles, classified as parvalbumin (PV), somatostatin (SOM), and vasoactive intestinal polypeptide (VIP) according to chemically defined categories. Currently, their involvement with seizures has been partially uncovered in physiological terms. Here, we propose a corticothalamic model containing heterogeneous interneurons to study the effects of various interneurons on absence seizure dynamics by means of optogenetic stimulation. First, the important role of feedforward inhibition caused by SRN→PV→PN projections on seizures is verified. Then, we demonstrate that light activation targeting either PV or SOM INs can control seizures. Finally, with different inhibition contributions from PV INs and SOM INs, the possible disinhibitory effect of blue light acting on VIP INs is mainly discussed. The results suggest that depending on the inhibition degree of both types, the disinhibition brought about by the VIP INs will trigger seizures, will control seizures, and will not work or cause the PNs to tend toward a high saturation state with high excitability. The circuit mechanism and the related bifurcation characteristics in various cases are emphatically revealed. In the model presented, in addition to Hopf and saddle-node bifurcations, the system may also undergo period-doubling and torus bifurcations under stimulus action, with more complex dynamics. Our work may provide a theoretical basis for understanding and further exploring the role of heterogeneous interneurons, in particular, the VIP INs, a novel target, in absence seizures.

Glycoprotein VI interplay with fibrin(ogen) in thrombosis

Platelets play a central role in the arrest of bleeding. The ability of platelets to engage with extracellular matrix proteins of the subendothelium has long been recognized as a pivotal platelet attribute, underpinning adequate hemostasis. The propensity of platelets to rapidly bind and functionally respond to collagen was one of the earliest documented events in platelet biology. The receptor primarily responsible for mediating platelet/collagen responses was identified as glycoprotein (GP) VI and successfully cloned in 1999. Since that time, this receptor has held the attention of many research groups, and through these efforts, we now have an excellent understanding of the roles of GPVI as a platelet- and megakaryocyte-specific adheso-signaling receptor in platelet biology. GPVI is considered a viable antithrombotic target, as data obtained from groups across the world is consistent with GPVI being less involved in physiological hemostatic processes but participating in arterial thrombosis. This review will highlight the key aspects of GPVI contributions to platelet biology and concentrate on the interaction with recently identified ligands, with a focus on fibrin and fibrinogen, discussing the role of these interactions in the growth and stability of thrombi. We will also discuss important therapeutic developments that target GPVI to modulate platelet function while minimizing bleeding outcomes.

Closed-loop optogenetic control of the dynamics of neural activity in non-human primates

Electrical neurostimulation is effective in the treatment of neurological disorders, but associated recording artefacts generally limit its applications to open-loop stimuli. Real-time and continuous closed-loop control of brain activity can, however, be achieved by pairing concurrent electrical recordings and optogenetics. Here we show that closed-loop optogenetic stimulation with excitatory opsins enables the precise manipulation of neural dynamics in brain slices from transgenic mice and in anaesthetized non-human primates. The approach generates oscillations in quiescent tissue, enhances or suppresses endogenous patterns in active tissue and modulates seizure-like bursts elicited by the convulsant 4-aminopyridine. A nonlinear model of the phase-dependent effects of optical stimulation reproduced the modulation of cycles of local-field potentials associated with seizure oscillations, as evidenced by the systematic changes in the variability and entropy of the phase-space trajectories of seizures, which correlated with changes in their duration and intensity. We also show that closed-loop optogenetic neurostimulation could be delivered using intracortical optrodes incorporating light-emitting diodes. Closed-loop optogenetic approaches may be translatable to therapeutic applications in humans.

Dynamic effect of electromagnetic induction on epileptic waveform

BACKGROUND

Electromagnetic induction has recently been considered as an important factor affecting the activity of neurons. However, as an important form of intervention in epilepsy treatment, few people have linked the two, especially the related dynamic mechanisms have not been explained clearly.

METHODS

Considering that electromagnetic induction has some brain area dependence, we proposed a modified two-compartment cortical thalamus model and set eight different key bifurcation parameters to study the transition mechanisms of epilepsy. We compared and analyzed the application and getting rid of memristors of single-compartment and coupled models. In particular, we plotted bifurcation diagrams to analyze the dynamic mechanisms behind abundant discharge activities, which mainly involved Hopf bifurcations (HB), fold of cycle bifurcations (LPC) and torus bifurcations (TR).

RESULTS

The results show that the coupled model can trigger more discharge states due to the driving effect between compartments. Moreover, the most remarkable finding of this study is that the memristor shows two sides. On the one hand, it may reduce tonic discharges. On the other hand, it may cause new pathological states.

CONCLUSIONS

The work explains the control effect of memristors on different brain regions and lays a theoretical foundation for future targeted therapy. Finally, it is hoped that our findings will provide new insights into the role of electromagnetic induction in absence seizures.

A Model for the Propagation of Seizure Activity in Normal Brain Tissue

Epilepsies are characterized by paroxysmal electrophysiological events and seizures, which can propagate across the brain. One of the main unsolved questions in epilepsy is how epileptic activity can invade normal tissue and thus propagate across the brain. To investigate this question, we consider three computational models at the neural network scale to study the underlying dynamics of seizure propagation, understand which specific features play a role, and relate them to clinical or experimental observations. We consider both the internal connectivity structure between neurons and the input properties in our characterization. We show that a paroxysmal input is sometimes controlled by the network while in other instances, it can lead the network activity to itself produce paroxysmal activity, and thus will further propagate to efferent networks. We further show how the details of the network architecture are essential to determine this switch to a seizure-like regime. We investigated the nature of the instability involved and in particular found a central role for the inhibitory connectivity. We propose a probabilistic approach to the propagative/non-propagative scenarios, which may serve as a guide to control the seizure by using appropriate stimuli.

Transition behavior of the seizure dynamics modulated by the astrocyte inositol triphosphate noise

Epilepsy is a neurological disorder with recurrent seizures, which convey complex dynamical characteristics including chaos and randomness. Until now, the underlying mechanism has not been fully elucidated, especially the bistable property beneath the epileptic random induction phenomena in certain conditions. Inspired by the recent finding that astrocyte GTPase-activating protein (G-protein)-coupled receptors could be involved in stochastic epileptic seizures, we proposed a neuron-astrocyte network model, incorporating the noise of the astrocytic second messenger, inositol triphosphate (IP3) that is modulated by G-protein-coupled receptor activation. Based on this model, we have statistically analyzed the transitions of epileptic seizures by performing repeatable simulation trials. Our simulation results show that the increase in the IP3 noise intensity induces depolarization-block epileptic seizures together with an increase in neuronal firing frequency, consistent with corresponding experiments. Meanwhile, the bistable states of the seizure dynamics were present under certain noise intensities, during which the neuronal firing pattern switches between regular sparse spiking and epileptic seizure states. This random presence of epileptic seizures is absent when the noise intensity continues to increase, accompanying with an increase in the epileptic depolarization block duration. The simulation results also shed light on the fact that calcium signals in astrocytes play significant roles in the pattern formations of the epileptic seizure. Our results provide a potential pathway for understanding the epileptic randomness in certain conditions.

Role of coupling distances in a coupled thalamocortical network for regulation of epilepsy

The recent theoretical modeling of coupled cortical thalamic network is an important advance toward the spatiotemporal dynamics of the brain. However, the diversity of coupling distances is ignored, and the better choice of deep brain stimulation (DBS) parameters to control epilepsy is still a challenge so far. A modeling object of this paper is to establish a coupled cortical thalamic model with uncertain coupling distances including nine combinations. Based on the pathways formed by pyramidal neuronal population (PY), thalamic reticular nucleus (RE) and thalamic relay nucleus (TC), we simulate the spike-wave discharges (SWD) at 2-4Hz which are the main manifestations of absence episodes. It is demonstrated that combination (1/3, 1/9) between the left and right ventricles is the optimal coupling distance of the proposed model by analyzing the percentage of SWD. A stimulating object of this paper is to find an optimum parameter range of DBS. One of the important results is that the number of SWD is inversely proportional to the amplitude, another one is that the number of SWD shows a U-shaped trend with the change of frequency. The present study has laidtheoryfoundationforthebrainplasticity, which will provide an important theoretical basis and direction for the treatment of absence epilepsy in the future. In brief, hopefully our simulation results will provide some help to patients.

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.

Mechanism analysis for excitatory interneurons dominating poly-spike wave and optimization of electrical stimulation

In addition to inhibitory interneurons, there exist excitatory interneurons (EINs) in the cortex, which mainly have excitatory projections to pyramidal neurons. In this study, we improve a thalamocortical model by introducing EIN, investigate the dominant role of EIN in generating spike and slow wave discharges (SWDs), and consider a non-rectangular pulse to control absence seizures. First, we display here that the improved model can reproduce typical SWDs of absence seizures. Moreover, we focus on the function of EIN by means of bifurcation analysis and find that EIN can induce transition behaviors under Hopf-type and fold limit cycle bifurcations. Specifically, the system has three stable solutions composing a tri-stable region. In this region, there are three attraction basins, which hints that external stimulation can drive the system trajectory from one basin to another, thereby eliminating abnormal oscillations. Furthermore, we compare the increasing ramp with rectangular pulse and optimize stimulation waveforms from the perspective of electrical charges input. The controlling role of the single increasing ramp to absence seizures is remarkable and the optimal stimulus parameters have been found theoretically. This work provides a computational model containing EIN and a theoretical basis for future physiological experiments and clinical research studies.

The Critical Modulatory Role of Spiny Stellate Cells in Seizure Onset Based on Dynamic Analysis of a Neural Mass Model

Growing evidence suggests that excitatory neurons in the brain play a significant role in seizure generation. Nonetheless, spiny stellate cells are cortical excitatory non-pyramidal neurons in the brain, whose basic role in seizure occurrence is not well understood. In the present research, we study the critical role of spiny stellate cells or the excitatory interneurons (EI), for the first time, in epileptic seizure generation using an extended neural mass model inspired by a thalamocortical model originally introduced by another research group. Applying bifurcation analysis on this modified model, we investigated the rich dynamics corresponding to the epileptic seizure onset and transition between interictal and ictal states caused by EI connectivity to other cell types. Our results indicate that the transition between interictal and ictal states (preictal signal) corresponds to a supercritical Hopf bifurcation, and thus, the extended model suggests that before seizure onset, the amplitude and frequency of neural activities gradually increase. Moreover, we showed that (1) the altered function of GABAergic and glutamatergic receptors of EI can cause seizure, and (2) the pathway between the thalamic relay nucleus and EI facilitates the transition from interictal to ictal activity by decreasing the preictal period. Thereafter, we considered both sensory and cortical periodic inputs to study model responses to various harmonic stimulations. Bifurcation analysis of the model, in this case, suggests that the initial state of the model might be the main cause for the transition between interictal and ictal states as the stimulus frequency changes. The extended thalamocortical model shows also that the amplitude jump phenomenon and non-linear resonance behavior result from the preictal state of the modified model. These results can be considered as a step forward to a deeper understanding of the mechanisms underlying the transition from normal activities to epileptic activities.

Regulatory Mechanism for Absence Seizures in Bidirectional Interactive Thalamocortical Model via Different Targeted Therapy Schemes

Recent clinical practice has found that the spike-wave discharge (SWD) scopes of absence seizures change from small cortical region to large thalamocortical networks, which has also been proved by theoretical simulation. The best biophysics explanation is that there are interactions between coupled cortico-thalamic and thalamocortical circuits. To agree with experiment results and describe the phenomena better, we constructed a coupled thalamocortical model with bidirectional channel (CTMBC) to account for the causes of absence seizures which are connected by the principle of two-way communication of neural pathways. By adjusting the coupling strength of bidirectional pathways, the spike-wave discharges are reproduced. Regulatory mechanism for absence seizures is further applied to CTMBC via four different targeted therapy schemes, such as deep brain stimulation (DBS), charge-balanced biphasic pulse (CBBP), coordinated reset stimulation (CRS) 1 : 0, and (CRS) 3 : 2. The new CTMBC model shows that neurodiversity in bidirectional interactive channel could supply theory reference for the bidirectional communication mode of thalamocortical networks and the hypothesis validation of pathogenesis.

Altered communication dynamics reflect cognitive deficits in temporal lobe epilepsy

OBJECTIVE

Although temporal lobe epilepsy (TLE) is recognized as a system-level disorder, little work has investigated pathoconnectomics from a dynamic perspective. By leveraging computational simulations that quantify patterns of information flow across the connectome, we tested the hypothesis that network communication is abnormal in this condition, studied the interplay between hippocampal- and network-level disease effects, and assessed associations with cognition.

METHODS

We simulated signal spreading via a linear threshold model that temporally evolves on a structural graph derived from diffusion-weighted magnetic resonance imaging (MRI), comparing a homogeneous group of 31 patients with histologically proven hippocampal sclerosis to 31 age- and sex-matched healthy controls. We evaluated the modulatory effects of structural alterations of the neocortex and hippocampus on network dynamics. Furthermore, multivariate statistics addressed the relationship with cognitive parameters.

RESULTS

We observed a slowing of in- and out-spreading times across multiple areas bilaterally, indexing delayed information flow, with the strongest effects in ipsilateral frontotemporal regions, thalamus, and hippocampus. Effects were markedly reduced when controlling for hippocampal volume but not cortical thickness, underscoring the central role of the hippocampus in whole-brain disease expression. Multivariate analysis associated slower spreading time in frontoparietal, limbic, default mode, and subcortical networks with impairment across tasks tapping into sensorimotor, executive, memory, and verbal abilities.

SIGNIFICANCE

Moving beyond descriptions of static topology toward the formulation of brain dynamics, our work provides novel insight into structurally mediated network dysfunction and demonstrates that altered whole-brain communication dynamics contribute to common cognitive difficulties in TLE.

Active probing to highlight approaching transitions to ictal states in coupled neural mass models

The extraction of electrophysiological features that reliably forecast the occurrence of seizures is one of the most challenging goals in epilepsy research. Among possible approaches to tackle this problem is the use of active probing paradigms in which responses to stimuli are used to detect underlying system changes leading up to seizures. This work evaluates the theoretical and mechanistic underpinnings of this strategy using two coupled populations of the well-studied Wendling neural mass model. Different model settings are evaluated, shifting parameters (excitability, slow inhibition, or inter-population coupling gains) from normal towards ictal states while probing stimuli are applied every 2 seconds to the input of either one or both populations. The correlation between the extracted features and the ictogenic parameter shifting indicates if the impending transition to the ictal state may be identified in advance. Results show that not only can the response to the probing stimuli forecast seizures but this is true regardless of the altered ictogenic parameter. That is, similar feature changes are highlighted by probing stimuli responses in advance of the seizure including: increased response variance and lag-1 autocorrelation, decreased skewness, and increased mutual information between the outputs of both model subsets. These changes were mostly restricted to the stimulated population, showing a local effect of this perturbational approach. The transition latencies from normal activity to sustained discharges of spikes were not affected, suggesting that stimuli had no pro-ictal effects. However, stimuli were found to elicit interictal-like spikes just before the transition to the ictal state. Furthermore, the observed feature changes highlighted by probing the neuronal populations may reflect the phenomenon of critical slowing down, where increased recovery times from perturbations may signal the loss of a systems' resilience and are common hallmarks of an impending critical transition. These results provide more evidence that active probing approaches highlight information about underlying system changes involved in ictogenesis and may be able to play a role in assisting seizure forecasting methods which can be incorporated into early-warning systems that ultimately enable closing the loop for targeted seizure-controlling interventions.

Dynamic Transitions of Epilepsy Waveforms Induced by Astrocyte Dysfunction and Electrical Stimulation

Experimental studies have shown that astrocytes participate in epilepsy through inducing the release of glutamate. Meanwhile, considering the disinhibition circuit among inhibitory neuronal populations with different time scales and the feedforward inhibition connection from thalamic relay nucleus to cortical inhibitory neuronal population, here, we propose a modified thalamocortical field model to systematically investigate the mechanism of epilepsy. Firstly, our results show that rich firing activities can be induced by astrocyte dysfunction, including high or low saturated state, high- or low-frequency clonic, spike-wave discharge (SWD), and tonic. More importantly, with the enhancement of feedforward inhibition connection, SWD and tonic oscillations will disappear. In other words, all these pathological waveforms can be suppressed or eliminated. Then, we explore the control effects after different external stimulations applying to thalamic neuronal population. We find that single-pulse stimulation can not only suppress but also induce pathological firing patterns, such as SWD, tonic, and clonic oscillations. And we further verify that deep brain stimulation can control absence epilepsy by regulating the amplitude and pulse width of stimulation. In addition, based on our modified model, 3 : 2 coordinated reset stimulation strategies with different intensities are compared and a more effective and safer stimulation mode is proposed. Our conclusions are expected to give more theoretical insights into the treatment of epilepsy.

Control analysis of electrical stimulation for epilepsy waveforms in a thalamocortical network

Physiological experiments and computational models both show that the thalamic reticular nucleus (RE) participates in inducing various firing patterns of cortex. Absence seizure, featured by 2-4 Hz spike-wave discharges (SWD) oscillation, is a high incidence of disease in children. Lots of electrophysiological experiments have verified the correlation between absence seizures and RE, however, the dynamical mechanisms are not well understood. Based on previous Taylor model, we firstly study the effects of external input and self-inhibition of RE on epilepsy transition. We show that increasing external input and self-inhibition of RE can lead the system from epileptic state to normal state, and vice versa. Next, we explore two stimulus strategies added in RE and various transition behaviors can be induced, such as high saturated state to clonic. Meanwhile, as the intensity of stimulation increasing, they can not only suppress the SWD, but also produce tonic-clonic oscillation. Finally, the control of DBS on single neuron cluster and two neuron clusters are compared and we find stimulating RE and TC simultaneously is a superior mode to stimulate anyone of RE or TC. It is hoped that the results we obtained will have an enlightenment on clinical treatment.

Neural mass modeling of slow-fast dynamics of seizure initiation and abortion

Epilepsy is a dynamic and complex neurological disease affecting about 1% of the worldwide population, among which 30% of the patients are drug-resistant. Epilepsy is characterized by recurrent episodes of paroxysmal neural discharges (the so-called seizures), which manifest themselves through a large-amplitude rhythmic activity observed in depth-EEG recordings, in particular in local field potentials (LFPs). The signature characterizing the transition to seizures involves complex oscillatory patterns, which could serve as a marker to prevent seizure initiation by triggering appropriate therapeutic neurostimulation methods. To investigate such protocols, neurophysiological lumped-parameter models at the mesoscopic scale, namely neural mass models, are powerful tools that not only mimic the LFP signals but also give insights on the neural mechanisms related to different stages of seizures. Here, we analyze the multiple time-scale dynamics of a neural mass model and explain the underlying structure of the complex oscillations observed before seizure initiation. We investigate population-specific effects of the stimulation and the dependence of stimulation parameters on synaptic timescales. In particular, we show that intermediate stimulation frequencies (>20 Hz) can abort seizures if the timescale difference is pronounced. Those results have the potential in the design of therapeutic brain stimulation protocols based on the neurophysiological properties of tissue.

Spontaneous transitions to focal-onset epileptic seizures: A dynamical study

Given the complex temporal evolution of epileptic seizures, understanding their dynamic nature might be beneficial for clinical diagnosis and treatment. Yet, the mechanisms behind, for instance, the onset of seizures are still unknown. According to an existing classification, two basic types of dynamic onset patterns plus a number of more complex onset waveforms can be distinguished. Here, we introduce a basic three-variable model with two time scales to study potential mechanisms of spontaneous seizure onset. We expand the model to demonstrate how coupling of oscillators leads to more complex seizure onset waveforms. Finally, we test the response to pulse perturbation as a potential biomarker of interictal changes.

Dynamical mesoscale model of absence seizures in genetic models

A mesoscale network model is proposed for the development of spike and wave discharges (SWDs) in the cortico-thalamo-cortical (C-T-C) circuit. It is based on experimental findings in two genetic models of childhood absence epilepsy–rats of WAG/Rij and GAERS strains. The model is organized hierarchically into two levels (brain structures and individual neurons) and composed of compartments for representation of somatosensory cortex, reticular and ventroposteriomedial thalamic nuclei. The cortex and the two thalamic compartments contain excitatory and inhibitory connections between four populations of neurons. Two connected subnetworks both including relevant parts of a C-T-C network responsible for SWD generation are modelled: a smaller subnetwork for the focal area in which the SWD generation can take place, and a larger subnetwork for surrounding areas which can be only passively involved into SWDs, but which is mostly responsible for normal brain activity. This assumption allows modeling of both normal and SWD activity as a dynamical system (no noise is necessary), providing reproducibility of results and allowing future analysis by means of theory of dynamical system theories. The model is able to reproduce most time-frequency changes in EEG activity accompanying the transition from normal to epileptiform activity and back. Three different mechanisms of SWD initiation reported previously in experimental studies were successfully reproduced in the model. The model incorporates also a separate mechanism for the maintenance of SWDs based on coupling analysis from experimental data. Finally, the model reproduces the possibility to stop ongoing SWDs with high frequency electrical stimulation, as described in the literature.

Modeling regional changes in dynamic stability during sleep and wakefulness

Global brain states are frequently placed within a unidimensional continuum by correlational studies, ranging from states of deep unconsciousness to ordinary wakefulness. An alternative is their multidimensional and mechanistic characterization in terms of different cognitive capacities, using computational models to reproduce the underlying neural dynamics. We explore this alternative by introducing a semi-empirical model linking regional activation and long-range functional connectivity in the different brain states visited during the natural wake-sleep cycle. Our model combines functional magnetic resonance imaging (fMRI) data, in vivo estimates of structural connectivity, and anatomically-informed priors to constrain the independent variation of regional activation. The best fit to empirical data was achieved using priors based on functionally coherent networks, with the resulting model parameters dividing the cortex into regions presenting opposite dynamical behavior. Frontoparietal regions approached a bifurcation from dynamics at a fixed point governed by noise, while sensorimotor regions approached a bifurcation from oscillatory dynamics. In agreement with human electrophysiological experiments, sleep onset induced subcortical deactivation with low correlation, which was subsequently reversed for deeper stages. Finally, we introduced periodic forcing of variable intensity to simulate external perturbations, and identified the key regions relevant for the recovery of wakefulness from deep sleep. Our model represents sleep as a state with diminished perceptual gating and the latent capacity for global accessibility that is required for rapid arousals. To the extent that the qualitative characterization of local dynamics is exhausted by the dichotomy between unstable and stable behavior, our work highlights how expanding the model parameter space can describe states of consciousness in terms of multiple dimensions with interpretations given by the choice of anatomically-informed priors.

A practical guide to methodological considerations in the controllability of structural brain networks

OBJECTIVE

Predicting how the brain can be driven to specific states by means of internal or external control requires a fundamental understanding of the relationship between neural connectivity and activity. Network control theory is a powerful tool from the physical and engineering sciences that can provide insights regarding that relationship; it formalizes the study of how the dynamics of a complex system can arise from its underlying structure of interconnected units.

APPROACH

Given the recent use of network control theory in neuroscience, it is now timely to offer a practical guide to methodological considerations in the controllability of structural brain networks. Here we provide a systematic overview of the framework, examine the impact of modeling choices on frequently studied control metrics, and suggest potentially useful theoretical extensions. We ground our discussions, numerical demonstrations, and theoretical advances in a dataset of high-resolution diffusion imaging with 730 diffusion directions acquired over approximately 1 h of scanning from ten healthy young adults.

MAIN RESULTS

Following a didactic introduction of the theory, we probe how a selection of modeling choices affects four common statistics: average controllability, modal controllability, minimum control energy, and optimal control energy. Next, we extend the current state-of-the-art in two ways: first, by developing an alternative measure of structural connectivity that accounts for radial propagation of activity through abutting tissue, and second, by defining a complementary metric quantifying the complexity of the energy landscape of a system. We close with specific modeling recommendations and a discussion of methodological constraints.

SIGNIFICANCE

Our hope is that this accessible account will inspire the neuroimaging community to more fully exploit the potential of network control theory in tackling pressing questions in cognitive, developmental, and clinical neuroscience.

Unified dynamics of interictal events and absence seizures

The dynamics of interictal events between absence seizures and their relationship to seizures themselves are investigated by employing a neural field model of the corticothalamic system. Interictal events are modeled as being due to transient parameter excursions beyond the seizure threshold, in the present case by sufficiently temporally varying the connection strength between the cerebral cortex and the thalamus. Increasing connection strength drives the system into ∼3-Hz seizure oscillations via a supercritical Hopf bifurcation once the linear instability threshold is passed. Depending on the time course of the excursion above threshold, different interictal activity event dynamics are seen in the time series of corticothalamic fields. These resemble experimental interictal time series observed via electroencephalography. It is found that the morphology of these events depends on the magnitude and duration of the excursion above threshold. For a large-amplitude excursion of short duration, events resemble interictal spikes, where one large spike is seen, followed by small damped oscillations. For a short excursion with long duration, events like observed interictal periodic sharp waves are seen. When both amplitude and duration above threshold are large, seizure oscillations are seen. Using these outcomes, proximity to seizure can be estimated and tracked.

Robust closed-loop control of spike-and-wave discharges in a thalamocortical computational model of absence epilepsy

In this paper, we investigate the abatement of spike-and-wave discharges in a thalamocortical model using a closed-loop brain stimulation method. We first explore the complex states and various transitions in the thalamocortical computational model of absence epilepsy by using bifurcation analysis. We demonstrate that the Hopf and double cycle bifurcations are the key dynamical mechanisms of the experimental observed bidirectional communications during absence seizures through top-down cortical excitation and thalamic feedforward inhibition. Then, we formulate the abatement of epileptic seizures to a closed-loop tracking control problem. Finally, we propose a neural network based sliding mode feedback control system to drive the dynamics of pathological cortical area to track the desired normal background activities. The control system is robust to uncertainties and disturbances, and its stability is guaranteed by Lyapunov stability theorem. Our results suggest that the seizure abatement can be modeled as a tracking control problem and solved by a robust closed-loop control method, which provides a promising brain stimulation strategy.

Controlling seizure propagation in large-scale brain networks

Information transmission in the human brain is a fundamentally dynamic network process. In partial epilepsy, this process is perturbed and highly synchronous seizures originate in a local network, the so-called epileptogenic zone (EZ), before recruiting other close or distant brain regions. We studied patient-specific brain network models of 15 drug-resistant epilepsy patients with implanted stereotactic electroencephalography (SEEG) electrodes. Each personalized brain model was derived from structural data of magnetic resonance imaging (MRI) and diffusion tensor weighted imaging (DTI), comprising 88 nodes equipped with region specific neural mass models capable of demonstrating a range of epileptiform discharges. Each patient's virtual brain was further personalized through the integration of the clinically hypothesized EZ. Subsequent simulations and connectivity modulations were performed and uncovered a finite repertoire of seizure propagation patterns. Across patients, we found that (i) patient-specific network connectivity is predictive for the subsequent seizure propagation pattern; (ii) seizure propagation is characterized by a systematic sequence of brain states; (iii) propagation can be controlled by an optimal intervention on the connectivity matrix; (iv) the degree of invasiveness can be significantly reduced via the proposed seizure control as compared to traditional resective surgery. To stop seizures, neurosurgeons typically resect the EZ completely. We showed that stability analysis of the network dynamics, employing structural and dynamical information, estimates reliably the spatiotemporal properties of seizure propagation. This suggests novel less invasive paradigms of surgical interventions to treat and manage partial epilepsy.

Computer modelling of connectivity change suggests epileptogenesis mechanisms in idiopathic generalised epilepsy

Patients with idiopathic generalised epilepsy (IGE) typically have normal conventional magnetic resonance imaging (MRI), hence diagnosis based on MRI is challenging. Anatomical abnormalities underlying brain dysfunctions in IGE are unclear and their relation to the pathomechanisms of epileptogenesis is poorly understood.

In this study, we applied connectometry, an advanced quantitative neuroimaging technique for investigating localised changes in white-matter tissues in vivo. Analysing white matter structures of 32 subjects we incorporated our in vivo findings in a computational model of seizure dynamics to suggest a plausible mechanism of epileptogenesis.

Patients with IGE have significant bilateral alterations in major white-matter fascicles. In the cingulum, fornix, and superior longitudinal fasciculus, tract integrity is compromised, whereas in specific parts of tracts between thalamus and the precentral gyrus, tract integrity is enhanced in patients. Combining these alterations in a logistic regression model, we computed the decision boundary that discriminated patients and controls. The computational model, informed with the findings on the tract abnormalities, specifically highlighted the importance of enhanced cortico-reticular connections along with impaired cortico-cortical connections in inducing pathological seizure-like dynamics.

We emphasise taking directionality of brain connectivity into consideration towards understanding the pathological mechanisms; this is possible by combining neuroimaging and computational modelling. Our imaging evidence of structural alterations suggest the loss of cortico-cortical and enhancement of cortico-thalamic fibre integrity in IGE. We further suggest that impaired connectivity from cortical regions to the thalamic reticular nucleus offers a therapeutic target for selectively modifying the brain circuit for reversing the mechanisms leading to epileptogenesis.

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Significant focal alterations along major white-matter fascicles in IGE patients are characterised.

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Increased white matter integrity found in thalamo-cortical connections.

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Decreased white matter integrity found in cortico-cortical connections.

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Disease mechanism is investigated by combining the neuroimaging findings with a dynamical model of seizure activity.

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Model implicates cortical projections to the thalamic reticular nucleus in IGE.

Collective excitability in a mesoscopic neuronal model of epileptic activity

At the mesoscopic scale, the brain can be understood as a collection of interacting neuronal oscillators, but the extent to which its sustained activity is due to coupling among brain areas is still unclear. Here we address this issue in a simplified situation by examining the effect of coupling between two cortical columns described via Jansen-Rit neural mass models. Our results show that coupling between the two neuronal populations gives rise to stochastic initiations of sustained collective activity, which can be interpreted as epileptic events. For large enough coupling strengths, termination of these events results mainly from the emergence of synchronization between the columns, and thus it is controlled by coupling instead of noise. Stochastic triggering and noise-independent durations are characteristic of excitable dynamics, and thus we interpret our results in terms of collective excitability.

Seizure pathways: A model-based investigation

We present the results of a model inversion algorithm for electrocorticography (ECoG) data recorded during epileptic seizures. The states and parameters of neural mass models were tracked during a total of over 3000 seizures from twelve patients with focal epilepsy. These models provide an estimate of the effective connectivity within intracortical circuits over the time course of seizures. Observing the dynamics of effective connectivity provides insight into mechanisms of seizures. Estimation of patients seizure dynamics revealed: 1) a highly stereotyped pattern of evolution for each patient, 2) distinct sub-groups of onset mechanisms amongst patients, and 3) different offset mechanisms for long and short seizures. Stereotypical dynamics suggest that, once initiated, seizures follow a deterministic path through the parameter space of a neural model. Furthermore, distinct sub-populations of patients were identified based on characteristic motifs in the dynamics at seizure onset. There were also distinct patterns between long and short duration seizures that were related to seizure offset. Understanding how these different patterns of seizure evolution arise may provide new insights into brain function and guide treatment for epilepsy, since specific therapies may have preferential effects on the various parameters that could potentially be individualized. Methods that unite computational models with data provide a powerful means to generate testable hypotheses for further experimental research. This work provides a demonstration that the hidden connectivity parameters of a neural mass model can be dynamically inferred from data. Our results underscore the power of theoretical models to inform epilepsy management. It is our hope that this work guides further efforts to apply computational models to clinical data.

The Relationship Between Ictal Multi-Unit Activity and the Electrocorticogram

During neocortical seizures in patients with epilepsy, microelectrode array recordings from the ictal core show a strong correlation between the fast, cellular spiking activities and the low-frequency component of the potential field, reflected in the electrocorticogram (ECoG). Here, we model the relationship between the cellular spike activity and this low-frequency component as the input and output signals of a linear time invariant system. Our approach is based on the observation that this relationship can be characterized by a so-called sinc function, the unit impulse response of an ideal (brick-wall) filter. Accordingly, using a brick-wall filter, we are able to convert ictal cellular spike inputs into an output that significantly correlates with the observed seizure activity in the ECoG (r = 0.40 - 0.56,p < 0.01) , while ECoG recordings of subsequent seizures within patients also show significant, but lower, correlations (r = 0.10 - 0.30,p < 0.01) . Furthermore, we can produce seizure-like output signals using synthetic spike trains with ictal properties. We propose a possible physiological mechanism to explain the observed properties associated with an ideal filter, and discuss the potential use of our approach for the evaluation of anticonvulsant strategies.

Predicting the spatiotemporal diversity of seizure propagation and termination in human focal epilepsy

Recent studies have shown that seizures can spread and terminate across brain areas via a rich diversity of spatiotemporal patterns. In particular, while the location of the seizure onset area is usually invariant across seizures in an individual patient, the source of traveling (2–3 Hz) spike-and-wave discharges during seizures can either move with the slower propagating ictal wavefront or remain stationary at the seizure onset area. Furthermore, although many focal seizures terminate synchronously across brain areas, some evolve into distinct ictal clusters and terminate asynchronously. Here, we introduce a unifying perspective based on a new neural field model of epileptic seizure dynamics. Two main mechanisms, the co-existence of wave propagation in excitable media and coupled-oscillator dynamics, together with the interaction of multiple time scales, account for the reported diversity. We confirm our predictions in seizures and tractography data obtained from patients with pharmacologically resistant epilepsy. Our results contribute toward patient-specific seizure modeling.

A major goal of epilepsy research is understanding the spatiotemporal dynamics of seizure. Here, the authors extend the Epileptor neural mass model into a neural field model, in order to provide a unified and patient-specific model of seizure initiation, propagation, and termination.

Network dynamics in the healthy and epileptic developing brain

Electroencephalography (EEG) allows recording of cortical activity at high temporal resolution. EEG recordings can be summarized along different dimensions using network-level quantitative measures, such as channel-to-channel correlation, or band power distributions across channels. These reveal network patterns that unfold over a range of different timescales and can be tracked dynamically. Here we describe the dynamics of network state transitions in EEG recordings of spontaneous brain activity in normally developing infants and infants with severe early infantile epileptic encephalopathies (n = 8, age: 1–8 months). We describe differences in measures of EEG dynamics derived from band power, and correlation-based summaries of network-wide brain activity. We further show that EEGs from different patient groups and controls may be distinguishable on a small set of the novel quantitative measures introduced here, which describe dynamic network state switching. Quantitative measures related to the sharpness of switching from one correlation pattern to another show the largest differences between groups. These findings reveal that the early epileptic encephalopathies are associated with characteristic dynamic features at the network level. Quantitative network-based analyses like the one presented here may in the future inform the clinical use of quantitative EEG for diagnosis.

Characterisation of ictal and interictal states of epilepsy: A system dynamic approach of principal dynamic modes analysis

Epilepsy is a brain disorder characterised by the recurrent and unpredictable interruptions of normal brain function, called epileptic seizures. The present study attempts to derive new diagnostic indices which may delineate between ictal and interictal states of epilepsy. To achieve this, the nonlinear modeling approach of global principal dynamic modes (PDMs) is adopted to examine the functional connectivity of the temporal and frontal lobes with the occipital brain segment using an ensemble of paediatric EEGs having the presence of epileptic seizure. The distinct spectral characteristics of global PDMs are found to be in line with the neural rhythms of brain dynamics. Moreover, we find that the linear trends of associated nonlinear functions (ANFs) associated with the 2nd and 4th global PDMs (representing delta, theta and alpha bands) of Fp1–F3 may differentiate between ictal and interictal states of epilepsy. These findings suggest that global PDMs and their associated ANFs may offer potential utility as diagnostic neural measures for ictal and interictal states of epilepsy.

Dynamics underlying interictal to ictal transition in temporal lobe epilepsy: insights from a neural mass model

We propose an approach that combines a neural mass model and clinical intracranial electroencephalographic (iEEG) recordings to explore the potential pathophysiological mechanisms (at the neuronal population level) of ictogenesis. Thirty iEEG recordings from 10 temporal lobe epilepsy (TLE) patients around seizure onset were investigated. Physiologically meaningful parameters [average excitatory (A_e ), slow (B), and fast (G) inhibitory synaptic gain] were identified during interictal to ictal transition. Four ratios (A_e /G, A_e /B, A_e /(B + G), and B/G) were derived from these parameters, and their evolution over time was analyzed. The excitation/inhibition ratio increased around seizure onset and decreased before seizure offset, indicating the impairment and re-emergence of excitation/inhibition balance around seizure onset and before seizure offset, respectively. Moreover, the slow inhibition may have an earlier effect on excitation/inhibition imbalance. We confirm the decrease in excitation/inhibition ratio upon seizure termination in human temporal lobe epilepsy, as revealed by optogenetic approaches both in vivo in animal models and in vitro. The increase in excitation/inhibition ratio around seizure occurrence could be an indicator to detect seizures.

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.

A new description of epileptic seizures based on dynamic analysis of a thalamocortical model

Increasing evidence suggests that the brain dynamics can be interpreted from the viewpoint of nonlinear dynamical systems. The aim of this paper is to investigate the behavior of a thalamocortical model from this perspective. The model includes both cortical and sensory inputs that can affect the dynamic nature of the model. Driving response of the model subjected to various harmonic stimulations is considered to identify the effects of stimulus parameters on the cortical output. Detailed numerical studies including phase portraits, Poincare maps and bifurcation diagrams reveal a wide range of complex dynamics including period doubling and chaos in the output. Transition between different states can occur as the stimulation parameters are changed. In addition, the amplitude jump phenomena and hysteresis are shown to be possible as a result of the bending in the frequency response curve. These results suggest that the jump phenomenon due to the brain nonlinear resonance can be responsible for the transitions between ictal and interictal states.

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.

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.

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.

Prediction of the Seizure Suppression Effect by Electrical Stimulation via a Computational Modeling Approach

In this paper, we identified factors that can affect seizure suppression via electrical stimulation by an integrative study based on experimental and computational approach. Preferentially, we analyzed the characteristics of seizure-like events (SLEs) using our previous in vitro experimental data. The results were analyzed in two groups classified according to the size of the effective region, in which the SLE was able to be completely suppressed by local stimulation. However, no significant differences were found between these two groups in terms of signal features or propagation characteristics (i.e., propagation delays, frequency spectrum, and phase synchrony). Thus, we further investigated important factors using a computational model that was capable of evaluating specific influences on effective region size. In the proposed model, signal transmission between neurons was based on two different mechanisms: synaptic transmission and the electrical field effect. We were able to induce SLEs having similar characteristics with differentially weighted adjustments for the two transmission methods in various noise environments. Although the SLEs had similar characteristics, their suppression effects differed. First of all, the suppression effect occurred only locally where directly received the stimulation effect in the high noise environment, but it occurred in the entire network in the low noise environment. Interestingly, in the same noise environment, the suppression effect was different depending on SLE propagation mechanism; only a local suppression effect was observed when the influence of the electrical field transmission was very weak, whereas a global effect was observed with a stronger electrical field effect. These results indicate that neuronal activities synchronized by a strong electrical field effect respond more sensitively to partial changes in the entire network. In addition, the proposed model was able to predict that stimulation of a seizure focus region is more effective for suppression. In conclusion, we confirmed the possibility of a computational model as a simulation tool to analyze the efficacy of deep brain stimulation (DBS) and investigated the key factors that determine the size of an effective region in seizure suppression via electrical stimulation.

Mechanisms underlying different onset patterns of focal seizures

Focal seizures are episodes of pathological brain activity that appear to arise from a localised area of the brain. The onset patterns of focal seizure activity have been studied intensively, and they have largely been distinguished into two types-low amplitude fast oscillations (LAF), or high amplitude spikes (HAS). Here we explore whether these two patterns arise from fundamentally different mechanisms. Here, we use a previously established computational model of neocortical tissue, and validate it as an adequate model using clinical recordings of focal seizures. We then reproduce the two onset patterns in their most defining properties and investigate the possible mechanisms underlying the different focal seizure onset patterns in the model. We show that the two patterns are associated with different mechanisms at the spatial scale of a single ECoG electrode. The LAF onset is initiated by independent patches of localised activity, which slowly invade the surrounding tissue and coalesce over time. In contrast, the HAS onset is a global, systemic transition to a coexisting seizure state triggered by a local event. We find that such a global transition is enabled by an increase in the excitability of the "healthy" surrounding tissue, which by itself does not generate seizures, but can support seizure activity when incited. In our simulations, the difference in surrounding tissue excitability also offers a simple explanation of the clinically reported difference in surgical outcomes. Finally, we demonstrate in the model how changes in tissue excitability could be elucidated, in principle, using active stimulation. Taken together, our modelling results suggest that the excitability of the tissue surrounding the seizure core may play a determining role in the seizure onset pattern, as well as in the surgical outcome.

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.

Understanding Epileptiform After-Discharges as Rhythmic Oscillatory Transients

Electro-cortical activity in patients with epilepsy may show abnormal rhythmic transients in response to stimulation. Even when using the same stimulation parameters in the same patient, wide variability in the duration of transient response has been reported. These transients have long been considered important for the mapping of the excitability levels in the epileptic brain but their dynamic mechanism is still not well understood. To investigate the occurrence of abnormal transients dynamically, we use a thalamo-cortical neural population model of epileptic spike-wave activity and study the interaction between slow and fast subsystems. In a reduced version of the thalamo-cortical model, slow wave oscillations arise from a fold of cycles (FoC) bifurcation. This marks the onset of a region of bistability between a high amplitude oscillatory rhythm and the background state. In vicinity of the bistability in parameter space, the model has excitable dynamics, showing prolonged rhythmic transients in response to suprathreshold pulse stimulation. We analyse the state space geometry of the bistable and excitable states, and find that the rhythmic transient arises when the impending FoC bifurcation deforms the state space and creates an area of locally reduced attraction to the fixed point. This area essentially allows trajectories to dwell there before escaping to the stable steady state, thus creating rhythmic transients. In the full thalamo-cortical model, we find a similar FoC bifurcation structure. Based on the analysis, we propose an explanation of why stimulation induced epileptiform activity may vary between trials, and predict how the variability could be related to ongoing oscillatory background activity. We compare our dynamic mechanism with other mechanisms (such as a slow parameter change) to generate excitable transients, and we discuss the proposed excitability mechanism in the context of stimulation responses in the epileptic cortex.

Predicting neurosurgical outcomes in focal epilepsy patients using computational modelling

See Eissa and Schevon (doi:10.1093/aww332) for a scientific commentary on this article.

Surgery can be a last resort for patients with intractable, medically refractory epilepsy. For many of these patients, however, there is substantial risk that the surgery will be ineffective. The prediction of who is likely to benefit from a surgical approach is crucial for being able to inform patients better, conduct principled prospective clinical trials, and ultimately tailor therapeutic approaches to these patients more effectively. Dynamical computational models, informed with patient data, can be used to make predictions and give mechanistic insight. In this study, we develop patient-specific dynamical network models of epileptogenic cortex. We infer the network connectivity matrix from non-seizure electrographic recordings of patients and use these connectivity matrices as the network structure in our model. The model simulates the dynamics of a bi-stable switch at every node in this network, meaning that every node starts in a background state, but has the ability to transit to a co-existing seizure state. Whether a transition happens in a node is partly determined by the stochastic nature of the input to the node, but also by the input the node receives from other connected nodes in the network. By conducting simulations with such a model, we can detect the average transition time for nodes in a given network, and therefore define nodes with a short transition time as highly epileptogenic. In a retrospective study, we found that in some patients the regions with high epileptogenicity in the model overlap with those identified clinically as the seizure onset zone. Moreover, it was found that the resection of these regions in the model reduces the overall likelihood of a seizure. Following removal of these regions in the model, we predicted surgical outcomes and compared these to actual patient outcomes. Our predictions were found to be 81.3% accurate on a dataset of 16 patients with intractable epilepsy. Intriguingly, in patients with unsuccessful outcomes, the proposed computational approach is able to suggest alternative resection sites. The model presented here gives mechanistic insight as to why surgery may be unsuccessful in some patients. This may aid clinicians in presurgical evaluation by providing a tool to explore various surgical options, offering complementary information to existing clinical techniques.