Seizures, refractory status epilepticus, and depolarization block as endogenous brain activities

Brain sodium MRI-derived priors support the estimation of epileptogenic zones using personalized model-based methods in epilepsy

Patients presenting with drug-resistant epilepsy are eligible for surgery aiming to remove the regions involved in the production of seizure activities, the so-called epileptogenic zone network (EZN). Thus the accurate estimation of the EZN is crucial. Data-driven, personalized virtual brain models derived from patient-specific anatomical and functional data are used in Virtual Epileptic Patient (VEP) to estimate the EZN via optimization methods from Bayesian inference. The Bayesian inference approach used in previous VEP integrates priors, based on the features of stereotactic-electroencephalography (SEEG) seizures' recordings. Here, we propose new priors, based on quantitative 23Na-MRI. The 23Na-MRI data were acquired at 7T and provided several features characterizing the sodium signal decay. The hypothesis is that the sodium features are biomarkers of neuronal excitability related to the EZN and will add additional information to VEP estimation. In this paper, we first proposed the mapping from 23Na-MRI features to predict the EZN via a machine learning approach. Then, we exploited these predictions as priors in the VEP pipeline. The statistical results demonstrated that compared with the results from current VEP, the result from VEP based on 23Na-MRI prior has better balanced accuracy, and the similar weighted harmonic mean of the precision and recall.

Recent Progress in Brain Network Models for Medical Applications: A Review

Importance: Pathological perturbations of the brain often spread via connectome to fundamentally alter functional consequences. By integrating multimodal neuroimaging data with mathematical neural mass modeling, brain network models (BNMs) enable to quantitatively characterize aberrant network dynamics underlying multiple neurological and psychiatric disorders. We delved into the advancements of BNM-based medical applications, discussed the prevalent challenges within this field, and provided possible solutions and future directions. Highlights: This paper reviewed the theoretical foundations and current medical applications of computational BNMs. Composed of neural mass models, the BNM framework allows to investigate large-scale brain dynamics behind brain diseases by linking the simulated functional signals to the empirical neurophysiological data, and has shown promise in exploring neuropathological mechanisms, elucidating therapeutic effects, and predicting disease outcome. Despite that several limitations existed, one promising trend of this research field is to precisely guide clinical neuromodulation treatment based on individual BNM simulation. Conclusion: BNM carries the potential to help understand the mechanism underlying how neuropathology affects brain network dynamics, further contributing to decision-making in clinical diagnosis and treatment. Several constraints must be addressed and surmounted to pave the way for its utilization in the clinic.

Dynamical modulation of hypersynchronous seizure onset with transcranial magneto-acoustic stimulation in a hippocampal computational model

Hypersynchronous (HYP) seizure onset is one of the frequently observed seizure-onset patterns in temporal lobe epileptic animals and patients, often accompanied by hippocampal sclerosis. However, the exact mechanisms and ion dynamics of the transition to HYP seizures remain unclear. Transcranial magneto-acoustic stimulation (TMAS) has recently been proposed as a novel non-invasive brain therapy method to modulate neurological disorders. Therefore, we propose a biophysical computational hippocampal network model to explore the evolution of HYP seizure caused by changes in crucial physiological parameters and design an effective TMAS strategy to modulate HYP seizure onset. We find that the cooperative effects of abnormal glial uptake strength of potassium and excessive bath potassium concentration could produce multiple discharge patterns and result in transitions from the normal state to the HYP seizure state and ultimately to the depolarization block state. Moreover, we find that the pyramidal neuron and the PV+ interneuron in HYP seizure-onset state exhibit saddle-node-on-invariant-circle/saddle homoclinic (SH) and saddle-node/SH at onset/offset bifurcation pairs, respectively. Furthermore, the response of neuronal activities to TMAS of different ultrasonic waveforms revealed that lower sine wave stimulation can increase the latency of HYP seizures and even completely suppress seizures. More importantly, we propose an ultrasonic parameter area that not only effectively regulates epileptic rhythms but also is within the safety limits of ultrasound neuromodulation therapy. Our results may offer a more comprehensive understanding of the mechanisms of HYP seizure and provide a theoretical basis for the application of TMAS in treating specific types of seizures.

Bifurcations and bursting in the Epileptor

The Epileptor is a phenomenological model for seizure activity that is used in a personalized large-scale brain modeling framework, the Virtual Epileptic Patient, with the aim of improving surgery outcomes for drug-resistant epileptic patients. Transitions between interictal and ictal states are modeled as bifurcations, enabling the definition of seizure classes in terms of onset/offset bifurcations. This establishes a taxonomy of seizures grounded in their essential underlying dynamics and the Epileptor replicates the activity of the most common class, as observed in patients with focal epilepsy, which is characterized by square-wave bursting properties. The Epileptor also encodes an additional mechanism to account for interictal spikes and spike and wave discharges. Here we use insights from a more generic model for square-wave bursting, based on the Unfolding Theory approach, to guide the bifurcation analysis of the Epileptor and gain a deeper understanding of the model and the role of its parameters. We show how the Epileptor's parameters can be modified to produce activities for other seizures classes of the taxonomy, as observed in patients, so that the large-scale brain models could be further personalized. Some of these classes have already been described in the literature in the Epileptor, others, predicted by the generic model, are new. Finally, we unveil how the interaction with the additional mechanism for spike and wave discharges alters the bifurcation structure of the main burster.

Nonequilibrium indicator for the onset of epileptic seizure

The occurrence of spontaneous bursts of uncontrolled electrical activity between neurons can disrupt normal brain function and lead to epileptic seizures. Despite extensive research, the mechanisms underlying seizure onset remain unclear. This study investigates the onset of seizures from the perspective of nonequilibrium statistical physics. By analyzing the probability flux within the framework of the nonequilibrium potential-flux landscape, we establish a connection between seizure dynamics and nonequilibrium. Our findings demonstrate that the degree of nonequilibrium is sensitive to the onset of epileptic seizures. This result offers an alternative perspective on assessing seizure onset in epilepsy.

From phenomenological to biophysical models of seizures

Epilepsy is a complex disease that requires various approaches for its study. In this short review, we discuss the contribution of theoretical and computational models. The review presents theoretical frameworks that underlie the understanding of certain seizure properties and their classification based on their dynamical properties at the onset and offset of seizures. Dynamical system tools are valuable resources in the study of seizures. By analyzing the complex, dynamic behavior of seizures, these tools can provide insights into seizure mechanisms and offer a framework for their classification. Additionally, computational models have high potential for clinical applications, as they can be used to develop more accurate diagnostic and personalized medicine tools. We discuss various modeling approaches that span different scales and levels, while also questioning the neurocentric view, and emphasize the importance of considering glial cells. Finally, we explore the epistemic value provided by this type of approach.

Personalized whole brain modeling of status epilepticus

How status epilepticus (SE) is generated and propagates in the brain is not known. As for seizures, a patient-specific approach is necessary, and the analysis should be performed at the whole brain level. Personalized brain models can be used to study seizure genesis and propagation at the whole brain scale in The Virtual Brain (TVB), using the Epileptor mathematical construct. Building on the fact that SE is part of the repertoire of activities that the Epileptor can generate, we present the first attempt to model SE at the whole brain scale in TVB, using data from a patient who experienced SE during presurgical evaluation. Simulations reproduced the patterns found with SEEG recordings. We find that if, as expected, the pattern of SE propagation correlates with the properties of the patient's structural connectome, SE propagation also depends upon the global state of the network, i.e., that SE propagation is an emergent property. We conclude that individual brain virtualization can be used to study SE genesis and propagation. This type of theoretical approach may be used to design novel interventional approaches to stop SE. This paper was presented at the 8th London-Innsbruck Colloquium on Status Epilepticus and Acute Seizures held in September 2022.

Estimating the Parameters of the Epileptor Model for Epileptic Seizure Suppression

Epilepsy is one of the most common brain disorders worldwide, affecting millions of people every year. Given the partially successful existing treatments for epileptiform activity suppression, dynamic mathematical models have been proposed with the purpose of better understanding the factors that might trigger an epileptic seizure and how to mitigate it, among which Epileptor stands out, due to its relative simplicity and consistency with experimental observations. Recent studies using this model have provided evidence that establishing a feedback-based control approach is possible. However, for this strategy to work properly, Epileptor's parameters, which describe the dynamic characteristics of a seizure, must be known beforehand. Therefore, this work proposes a methodology for estimating such parameters based on a successive optimization technique. The results show that it is feasible to approximate their values as they converge to reference values based on different initial conditions, which are modeled by an uncertainty factor or noise addition. Also, interictal (healthy) and ictal (ongoing seizure) conditions, as well as time resolution, must be taken into account for an appropriate estimation. At last, integrating such a parameter estimation approach with observers and controllers for purposes of seizure suppression is carried out, which might provide an interesting alternative for seizure suppression in practice in the future.

A unified physiological framework of transitions between seizures, sustained ictal activity and depolarization block at the single neuron level

The majority of seizures recorded in humans and experimental animal models can be described by a generic phenomenological mathematical model, the Epileptor. In this model, seizure-like events (SLEs) are driven by a slow variable and occur via saddle node (SN) and homoclinic bifurcations at seizure onset and offset, respectively. Here we investigated SLEs at the single cell level using a biophysically relevant neuron model including a slow/fast system of four equations. The two equations for the slow subsystem describe ion concentration variations and the two equations of the fast subsystem delineate the electrophysiological activities of the neuron. Using extracellular K⁺ as a slow variable, we report that SLEs with SN/homoclinic bifurcations can readily occur at the single cell level when extracellular K⁺ reaches a critical value. In patients and experimental models, seizures can also evolve into sustained ictal activity (SIA) and depolarization block (DB), activities which are also parts of the dynamic repertoire of the Epileptor. Increasing extracellular concentration of K⁺ in the model to values found during experimental status epilepticus and DB, we show that SIA and DB can also occur at the single cell level. Thus, seizures, SIA, and DB, which have been first identified as network events, can exist in a unified framework of a biophysical model at the single neuron level and exhibit similar dynamics as observed in the Epileptor.Author Summary: Epilepsy is a neurological disorder characterized by the occurrence of seizures. Seizures have been characterized in patients in experimental models at both macroscopic and microscopic scales using electrophysiological recordings. Experimental works allowed the establishment of a detailed taxonomy of seizures, which can be described by mathematical models. We can distinguish two main types of models. Phenomenological (generic) models have few parameters and variables and permit detailed dynamical studies often capturing a majority of activities observed in experimental conditions. But they also have abstract parameters, making biological interpretation difficult. Biophysical models, on the other hand, use a large number of variables and parameters due to the complexity of the biological systems they represent. Because of the multiplicity of solutions, it is difficult to extract general dynamical rules. In the present work, we integrate both approaches and reduce a detailed biophysical model to sufficiently low-dimensional equations, and thus maintaining the advantages of a generic model. We propose, at the single cell level, a unified framework of different pathological activities that are seizures, depolarization block, and sustained ictal activity.

Burster Reconstruction Considering Unmeasurable Variables in the Epileptor Model

Epilepsy is one of the most common brain disorders worldwide, affecting millions of people every year. Although significant effort has been put into better understanding it and mitigating its effects, the conventional treatments are not fully effective. Advances in computational neuroscience, using mathematical dynamic models that represent brain activities at different scales, have enabled addressing epilepsy from a more theoretical standpoint. In particular, the recently proposed Epileptor model stands out among these models, because it represents well the main features of seizures, and the results from its simulations have been consistent with experimental observations. In addition, there has been an increasing interest in designing control techniques for Epileptor that might lead to possible realistic feedback controllers in the future. However, such approaches rely on knowing all of the states of the model, which is not the case in practice. The work explored in this letter aims to develop a state observer to estimate Epileptor's unmeasurable variables, as well as reconstruct the respective so-called bursters. Furthermore, an alternative modeling is presented for enhancing the convergence speed of an observer. The results show that the proposed approach is efficient under two main conditions: when the brain is undergoing a seizure and when a transition from the healthy to the epileptiform activity occurs.

Modeling seizures: From single neurons to networks

Dynamical system tools offer a complementary approach to detailed biophysical seizure modeling, with a high potential for clinical applications. This review describes the theoretical framework that provides a basis for theorizing certain properties of seizures and for their classification according to their dynamical properties at onset and offset. We describe various modeling approaches spanning different scales, from single neurons to large-scale networks. This narrative review provides an accessible overview of this field, including non-exhaustive examples of key recent works.

The Kainic Acid Models of Temporal Lobe Epilepsy

Experimental models of epilepsy are useful to identify potential mechanisms of epileptogenesis, seizure genesis, comorbidities, and treatment efficacy. The kainic acid (KA) model is one of the most commonly used. Several modes of administration of KA exist, each producing different effects in a strain-, species-, gender-, and age-dependent manner. In this review, we discuss the advantages and limitations of the various forms of KA administration (systemic, intrahippocampal, and intranasal), as well as the histologic, electrophysiological, and behavioral outcomes in different strains and species. We attempt a personal perspective and discuss areas where work is needed. The diversity of KA models and their outcomes offers researchers a rich palette of phenotypes, which may be relevant to specific traits found in patients with temporal lobe epilepsy.

Perturbations both trigger and delay seizures due to generic properties of slow-fast relaxation oscillators

The mechanisms underlying the emergence of seizures are one of the most important unresolved issues in epilepsy research. In this paper, we study how perturbations, exogenous or endogenous, may promote or delay seizure emergence. To this aim, due to the increasingly adopted view of epileptic dynamics in terms of slow-fast systems, we perform a theoretical analysis of the phase response of a generic relaxation oscillator. As relaxation oscillators are effectively bistable systems at the fast time scale, it is intuitive that perturbations of the non-seizing state with a suitable direction and amplitude may cause an immediate transition to seizure. By contrast, and perhaps less intuitively, smaller amplitude perturbations have been found to delay the spontaneous seizure initiation. By studying the isochrons of relaxation oscillators, we show that this is a generic phenomenon, with the size of such delay depending on the slow flow component. Therefore, depending on perturbation amplitudes, frequency and timing, a train of perturbations causes an occurrence increase, decrease or complete suppression of seizures. This dependence lends itself to analysis and mechanistic understanding through methods outlined in this paper. We illustrate this methodology by computing the isochrons, phase response curves and the response to perturbations in several epileptic models possessing different slow vector fields. While our theoretical results are applicable to any planar relaxation oscillator, in the motivating context of epilepsy they elucidate mechanisms of triggering and abating seizures, thus suggesting stimulation strategies with effects ranging from mere delaying to full suppression of seizures.

Despite its simplicity, the modelling of epileptic dynamics as a slow-fast transition between low and high activity states mediated by some slow feedback variable is a relatively novel albeit fruitful approach. This study is the first, to our knowledge, characterizing the response of such slow-fast models of epileptic brain to perturbations by computing its isochrons. Besides its numerical computation, we theoretically determine which factors shape the geometry of isochrons for planar slow-fast oscillators. As a consequence, we introduce a theoretical approach providing a clear understanding of the response of perturbations of slow-fast oscillators. Within the epilepsy context, this elucidates the origin of the contradictory role of interictal epileptiform discharges in the transition to seizure, manifested by both pro-convulsive and anti-convulsive effect depending on the amplitude, frequency and timing. More generally, this paper provides theoretical framework highlighting the role of the slow flow component on the response to perturbations in relaxation oscillators, pointing to the general phenomena in such slow-fast oscillators ubiquitous in biological systems.

Falling off a limit cycle using phase-agnostic stimuli: Applications to clinical oscillopathies

For over a century, physiological studies have shown that precisely timed pulses can switch off a biological oscillator. This empiric finding has shaped our mechanistic understanding of how perturbations start, stop, and reset biological oscillators and has led to treatments that suppress pathological oscillations using electrical pulses given within specified therapeutic phase windows. Here, we present evidence, using numerical simulations of models of epileptic seizures and reentrant tachycardia, that the phase window can be opened to the entire cycle using novel complex stimulus waveforms. Our results reveal that the trajectories are displaced by such phase-agnostic stimuli off the oscillator's limit cycle and corralled into a region where oscillation is suppressed, irrespective of the phase at which the stimulus was applied. Our findings suggest the need for broadening theoretical understanding of how complex perturbing waveforms interact with biological oscillators to access their arrhythmic states. In clinical practice, oscillopathies may be treated more effectively with non-traditional stimulus waveforms that obviate the need for phase specificity.

Evidence for spreading seizure as a cause of theta-alpha activity electrographic pattern in stereo-EEG seizure recordings

Intracranial electroencephalography is a standard tool in clinical evaluation of patients with focal epilepsy. Various early electrographic seizure patterns differing in frequency, amplitude, and waveform of the oscillations are observed. The pattern most common in the areas of seizure propagation is the so-called theta-alpha activity (TAA), whose defining features are oscillations in the θ - α range and gradually increasing amplitude. A deeper understanding of the mechanism underlying the generation of the TAA pattern is however lacking. In this work we evaluate the hypothesis that the TAA patterns are caused by seizures spreading across the cortex. To do so, we perform simulations of seizure dynamics on detailed patient-derived cortical surfaces using the spreading seizure model as well as reference models with one or two homogeneous sources. We then detect the occurrences of the TAA patterns both in the simulated stereo-electroencephalographic signals and in the signals of recorded epileptic seizures from a cohort of fifty patients, and we compare the features of the groups of detected TAA patterns to assess the plausibility of the different models. Our results show that spreading seizure hypothesis is qualitatively consistent with the evidence available in the seizure recordings, and it can explain the features of the detected TAA groups best among the examined models.

An Efficient Approach to Define the Input Stimuli to Suppress Epileptic Seizures Described by the Epileptor Model

Epilepsy affects about 70 million people in the world. Every year, approximately 2.4 million people are diagnosed with epilepsy, two-thirds of them will not know the etiology of their disease, and 1% of these individuals will decease as a consequence of it. Due to the inherent complexity of predicting and explaining it, the mathematical model Epileptor was recently developed to reproduce seizure-like events, also providing insights to improve the understanding of the neural dynamics in the interictal and ictal periods, although the physics behind each parameter and variable of the model is not fully established in the literature. This paper introduces an approach to design a feedback-based controller for suppressing epileptic seizures described by Epileptor. Our work establishes how the nonlinear dynamics of this disorder can be written in terms of a combination of linear sub-models employing an exact solution. Additionally, we show how a feedback control gain can be computed to suppress seizures, as well as how specific shapes applied as input stimuli for this purpose can be obtained. The practical application of the approach is discussed and the results show that the proposed technique is promising for developing controllers in this field.

A taxonomy of seizure dynamotypes

Seizures are a disruption of normal brain activity present across a vast range of species and conditions. We introduce an organizing principle that leads to the first objective Taxonomy of Seizure Dynamics (TSD) based on bifurcation theory. The ‘dynamotype’ of a seizure is the dynamic composition that defines its observable characteristics, including how it starts, evolves and ends. Analyzing over 2000 focal-onset seizures from multiple centers, we find evidence of all 16 dynamotypes predicted in TSD. We demonstrate that patients’ dynamotypes evolve during their lifetime and display complex but systematic variations including hierarchy (certain types are more common), non-bijectivity (a patient may display multiple types) and pairing preference (multiple types may occur during one seizure). TSD provides a way to stratify patients in complement to present clinical classifications, a language to describe the most critical features of seizure dynamics, and a framework to guide future research focused on dynamical properties.

Epileptic seizures have been recognized for centuries. But it was only in the 1930s that it was realized that seizures are the result of out-of-control electrical activity in the brain. By placing electrodes on the scalp, doctors can identify when and where in the brain a seizure begins. But they cannot tell much about how the seizure behaves, that is, how it starts, stops or spreads to other areas. This makes it difficult to control and prevent seizures. It also helps explain why almost a third of patients with epilepsy continue to have seizures despite being on medication.

Saggio, Crisp et al. have now approached this problem from a new angle using methods adapted from physics and engineering. In these fields, “dynamics research” has been used with great success to predict and control the behavior of complex systems like electrical power grids. Saggio, Crisp et al. reasoned that applying the same approach to the brain would reveal the dynamics of seizures and that such information could then be used to categorize seizures into groups with similar properties. This would in effect create for seizures what the periodic table is for the elements.

Applying the dynamics research method to seizure data from more than a hundred patients from across the world revealed 16 types of seizure dynamics. These “dynamotypes” had distinct characteristics. Some were more common than others, and some tended to occur together. Individual patients showed different dynamotypes over time. By constructing a way to classify seizures based on the relationships between the dynamotypes, Saggio, Crisp et al. provide a new tool for clinicians and researchers studying epilepsy.

Previous clinical tools have focused on the physical symptoms of a seizure (referred to as the phenotype) or its potential genetic causes (genotype). The current approach complements these tools by adding the dynamotype: how seizures start, spread and stop in the brain. This approach has the potential to lead to new branches of research and better understanding and treatment of seizures.

Dynamical Mechanisms of Interictal Resting-State Functional Connectivity in Epilepsy

Drug-resistant focal epilepsy is a large-scale brain networks disorder characterized by altered spatiotemporal patterns of functional connectivity (FC), even during interictal resting state (RS). Although RS-FC-based metrics can detect these changes, results from RS functional magnetic resonance imaging (RS-fMRI) studies are unclear and difficult to interpret, and the underlying dynamical mechanisms are still largely unknown. To better capture the RS dynamics, we phenomenologically extended the neural mass model of partial seizures, the Epileptor, by including two neuron subpopulations of epileptogenic and nonepileptogenic type, making it capable of producing physiological oscillations in addition to the epileptiform activity. Using the neuroinformatics platform The Virtual Brain, we reconstructed 14 epileptic and 5 healthy human (of either sex) brain network models (BNMs), based on individual anatomical connectivity and clinically defined epileptogenic heatmaps. Through systematic parameter exploration and fitting to neuroimaging data, we demonstrated that epileptic brains during interictal RS are associated with lower global excitability induced by a shift in the working point of the model, indicating that epileptic brains operate closer to a stable equilibrium point than healthy brains. Moreover, we showed that functional networks are unaffected by interictal spikes, corroborating previous experimental findings; additionally, we observed higher excitability in epileptogenic regions, in agreement with the data. We shed light on new dynamical mechanisms responsible for altered RS-FC in epilepsy, involving the following two key factors: (1) a shift of excitability of the whole brain leading to increased stability; and (2) a locally increased excitability in the epileptogenic regions supporting the mixture of hyperconnectivity and hypoconnectivity in these areas.

SIGNIFICANCE STATEMENT Advances in functional neuroimaging provide compelling evidence for epilepsy-related brain network alterations, even during the interictal resting state (RS). However, the dynamical mechanisms underlying these changes are still elusive. To identify local and network processes behind the RS-functional connectivity (FC) spatiotemporal patterns, we systematically manipulated the local excitability and the global coupling in the virtual human epileptic patient brain network models (BNMs), complemented by the analysis of the impact of interictal spikes and fitting to the neuroimaging data. Our results suggest that a global shift of the dynamic working point of the brain model, coupled with locally hyperexcitable node dynamics of the epileptogenic networks, provides a mechanistic explanation of the epileptic processes during the interictal RS period. These, in turn, are associated with the changes in FC.

The Bayesian Virtual Epileptic Patient: A probabilistic framework designed to infer the spatial map of epileptogenicity in a personalized large-scale brain model of epilepsy spread

Despite the importance and frequent use of Bayesian frameworks in brain network modeling for parameter inference and model prediction, the advanced sampling algorithms implemented in probabilistic programming languages to overcome the inference difficulties have received relatively little attention in this context. In this technical note, we propose a probabilistic framework, namely the Bayesian Virtual Epileptic Patient (BVEP), which relies on the fusion of structural data of individuals to infer the spatial map of epileptogenicity in a personalized large-scale brain model of epilepsy spread. To invert the individualized whole-brain model employed in this study, we use the recently developed algorithms known as No-U-Turn Sampler (NUTS) as well as Automatic Differentiation Variational Inference (ADVI). Our results indicate that NUTS and ADVI accurately estimate the degree of epileptogenicity of brain regions, therefore, the hypothetical brain areas responsible for the seizure initiation and propagation, while the convergence diagnostics and posterior behavior analysis validate the reliability of the estimations. Moreover, we illustrate the efficiency of the transformed non-centered parameters in comparison to centered form of parameterization. The Bayesian framework used in this work proposes an appropriate patient-specific strategy for estimating the epileptogenicity of the brain regions to improve outcome after epilepsy surgery.

The hidden repertoire of brain dynamics and dysfunction

The purpose of this paper is to describe a framework for the understanding of rules that govern how neural system dynamics are coordinated to produce behavior. The framework, structured flows on manifolds (SFM), posits that neural processes are flows depicting system interactions that occur on relatively low-dimension manifolds, which constrain possible functional configurations. Although this is a general framework, we focus on the application to brain disorders. We first explain the Epileptor, a phenomenological computational model showing fast and slow dynamics, but also a hidden repertoire whose expression is similar to refractory status epilepticus. We suggest that epilepsy represents an innate brain state whose potential may be realized only under certain circumstances. Conversely, deficits from damage or disease processes, such as stroke or dementia, may reflect both the disease process per se and the adaptation of the brain. SFM uniquely captures both scenarios. Finally, we link neuromodulation effects and switches in functional network configurations to fast and slow dynamics that coordinate the expression of SFM in the context of cognition. The tools to measure and model SFM already exist, giving researchers access to the dynamics of neural processes that support the concomitant dynamics of the cognitive and behavioral processes.

Effects of Single Cage Housing on Stress, Cognitive, and Seizure Parameters in the Rat and Mouse Pilocarpine Models of Epilepsy

Many experimental approaches require housing rodents in individual cages, including in epilepsy research. However, rats and mice are social animals; and individual housing constitutes a stressful situation. The goal of the present study was to determine the effects of individual housing as compared to conditions maintaining social contact on stress markers and epilepsy. Control male mice socially housed during pretest and then transferred to individual cages for six weeks displayed anhedonia, increased anxiety and biological markers of stress as compared to pretest values or mice kept socially housed during six weeks. Pilocarpine (pilo)-treated mice housed together showed increased levels of anhedonia, anxiety and stress markers as well as decreased cognitive performance as compared to the control group. The differences were more significant in pilo-treated mice housed individually. Anxiety correlated linearly with cognitive performance and stress markers independently of the experimental conditions. In the male rat pilo model, seizures were sixteen times more frequent in singly housed animals as compared to animals kept in pairs. Daily interactions with an experimenter in otherwise singly housed animals was sufficient to produce results identical to those found in animals kept in pairs. We propose that social isolation produces a severe phenotype in terms of stress and seizure frequency as compared to animals maintaining social contact (at least in these two models), a factor that needs to be taken into account for data interpretation, in particular for preclinical studies.

Outgrowing seizures in Childhood Absence Epilepsy: time delays and bistability

We formulate a conductance-based model for a 3-neuron motif associated with Childhood Absence Epilepsy (CAE). The motif consists of neurons from the thalamic relay (TC) and reticular nuclei (RT) and the cortex (CT). We focus on a genetic defect common to the mouse homolog of CAE which is associated with loss of GABA_A receptors on the TC neuron, and the fact that myelination of axons as children age can increase the conduction velocity between neurons. We show the combination of low GABA_A mediated inhibition of TC neurons and the long corticothalamic loop delay gives rise to a variety of complex dynamics in the motif, including bistability. This bistability disappears as the corticothalamic conduction delay shortens even though GABA_A activity remains impaired. Thus the combination of deficient GABA_A activity and changing axonal myelination in the corticothalamic loop may be sufficient to account for the clinical course of CAE.

Postictal electroencephalographic (EEG) suppression: A stereo-EEG study of 100 focal to bilateral tonic-clonic seizures

OBJECTIVES

We aimed to describe intracerebral aspects of postictal generalized electroencephalography suppression (PGES) following focal to bilateral tonic-clonic ("secondarily generalized tonic-clonic") seizures (GTCS) recorded using stereoelectroencephalographic (SEEG), and to correlate these with electroclinical features.

METHODS

Three independent observers scored semiologic and SEEG features. Patient and epilepsy characteristics were collected. Descriptive statistics and multivariate analysis were performed. The operational definition of PGES on SEEG used strict criteria (absence of visible signal at 20 μV/mm amplitude, in all readable channels). Postictal regional suppression (RS) was identified if only a subset of implanted electrodes showed absence of signal.

RESULTS

We evaluated 100 seizures in 52 patients. Interobserver agreement was good (κ 0.72 for clinical features and 0.73 for EEG features). PGES was present in 27 of 100 and RS without PGES present in 42 of 100 seizures. Region of RS included epileptogenic zone in 43 of 51 (86%). No effect of sampling (multilobar or bilateral exploration) was seen. Oral tonicity (mouth opening and/or tonic vocalization during the tonic phase of GTCS) was associated with the presence of PGES (P = 0.029; negative predictive value [NPV] 0.91). Bilateral upper limb extension during the tonic phase correlated with PGES (P = 0.041; NPV 0.85). Association of both oral tonicity and bilateral upper limb extension had a high NPV of 0.96.

SIGNIFICANCE

SEEG recordings confirm true absence of signal during postictal EEG suppression. PGES is unlikely when both upper limb extension and oral tonicity are absent. We hypothesize that bilateral tonic seizure discharge at bulbar level brainstem regions is associated with the production of oral signs and may relate to mechanisms of PGES.

Dynamics of coupled mode solitons in bursting neural networks

Using an electrically coupled chain of Hindmarsh-Rose neural models, we analytically derived the nonlinearly coupled complex Ginzburg-Landau equations. This is realized by superimposing the lower and upper cutoff modes of wave propagation and by employing the multiple scale expansions in the semidiscrete approximation. We explore the modified Hirota method to analytically obtain the bright-bright pulse soliton solutions of our nonlinearly coupled equations. With these bright solitons as initial conditions of our numerical scheme, and knowing that electrical signals are the basis of information transfer in the nervous system, it is found that prior to collisions at the boundaries of the network, neural information is purely conveyed by bisolitons at lower cutoff mode. After collision, the bisolitons are completely annihilated and neural information is now relayed by the upper cutoff mode via the propagation of plane waves. It is also shown that the linear gain of the system is inextricably linked to the complex physiological mechanisms of ion mobility, since the speeds and spatial profiles of the coupled nerve impulses vary with the gain. A linear stability analysis performed on the coupled system mainly confirms the instability of plane waves in the neural network, with a glaring example of the transition of weak plane waves into a dark soliton and then static kinks. Numerical simulations have confirmed the annihilation phenomenon subsequent to collision in neural systems. They equally showed that the symmetry breaking of the pulse solution of the system leaves in the network static internal modes, sometime referred to as Goldstone modes.

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.

Individual brain structure and modelling predict seizure propagation

See Lytton (doi:10.1093/awx018) for a scientific commentary on this article.Neural network oscillations are a fundamental mechanism for cognition, perception and consciousness. Consequently, perturbations of network activity play an important role in the pathophysiology of brain disorders. When structural information from non-invasive brain imaging is merged with mathematical modelling, then generative brain network models constitute personalized in silico platforms for the exploration of causal mechanisms of brain function and clinical hypothesis testing. We here demonstrate with the example of drug-resistant epilepsy that patient-specific virtual brain models derived from diffusion magnetic resonance imaging have sufficient predictive power to improve diagnosis and surgery outcome. In partial epilepsy, seizures originate in a local network, the so-called epileptogenic zone, before recruiting other close or distant brain regions. We create personalized large-scale brain networks for 15 patients and simulate the individual seizure propagation patterns. Model validation is performed against the presurgical stereotactic electroencephalography data and the standard-of-care clinical evaluation. We demonstrate that the individual brain models account for the patient seizure propagation patterns, explain the variability in postsurgical success, but do not reliably augment with the use of patient-specific connectivity. Our results show that connectome-based brain network models have the capacity to explain changes in the organization of brain activity as observed in some brain disorders, thus opening up avenues towards discovery of novel clinical interventions.

Time evolution of interhemispheric coupling in a model of focal neocortical epilepsy in mice

Epilepsy is characterized by substantial network rearrangements leading to spontaneous seizures and little is known on how an epileptogenic focus impacts on neural activity in the contralateral hemisphere. Here, we used a model of unilateral epilepsy induced by injection of the synaptic blocker tetanus neurotoxin (TeNT) in the mouse primary visual cortex (V1). Local field potential (LFP) signals were simultaneously recorded from both hemispheres of each mouse in acute phase (peak of toxin action) and chronic condition (completion of TeNT effects). To characterize the neural electrical activities the corresponding LFP signals were analyzed with several methods of time series analysis. For the epileptic mice, the spectral analysis showed that TeNT determines a power redistribution among the different neurophysiological bands in both acute and chronic phases. Using linear and nonlinear interdependence measures in both time and frequency domains, it was found in the acute phase that TeNT injection promotes a reduction of the interhemispheric coupling for high frequencies (12-30 Hz) and small time lag (<20 ms), whereas an increase of the coupling is present for low frequencies (0.5-4 Hz) and long time lag (>40 ms). On the other hand, the chronic period is characterized by a partial or complete recovery of the interhemispheric interdependence level. Granger causality test and symbolic transfer entropy indicate a greater driving influence of the TeNT-injected side on activity in the contralateral hemisphere in the chronic phase. Lastly, based on experimental observations, we built a computational model of LFPs to investigate the role of the ipsilateral inhibition and exicitatory interhemispheric connections in the dampening of the interhemispheric coupling. The time evolution of the interhemispheric coupling in such a relevant model of epilepsy has been addressed here.

Dynamic transition of neuronal firing induced by abnormal astrocytic glutamate oscillation

The gliotransmitter glutamate released from astrocytes can modulate neuronal firing by activating neuronal N-methyl-D-aspartic acid (NMDA) receptors. This enables astrocytic glutamate(AG) to be involved in neuronal physiological and pathological functions. Based on empirical results and classical neuron-glial "tripartite synapse" model, we propose a practical model to describe extracellular AG oscillation, in which the fluctuation of AG depends on the threshold of calcium concentration, and the effect of AG degradation is considered as well. We predict the seizure-like discharges under the dysfunction of AG degradation duration. Consistent with our prediction, the suppression of AG uptake by astrocytic transporters, which operates by modulating the AG degradation process, can account for the emergence of epilepsy.

The Diathesis-Epilepsy Model: How Past Events Impact the Development of Epilepsy and Comorbidities

In epilepsy, seizures and comorbidities (e.g., cognitive deficits and depression) occur when specific thresholds are crossed. These thresholds depend on the diathesis (or vulnerability) of a given individual. The diathesis is controlled by multiple genetic and environmental factors. Diathesis changes over multiple timescales: on a daily basis, and as part of the development/aging processes, etc. The diathesis-epilepsy model introduced here provides a conceptual framework to understand how past events (e.g., a very stressful event) can directly influence the occurrence of epilepsy and comorbidities later in life. Experimental evidence supports this model, and the existence of biomarkers predictive of a vulnerability state have led to the development of preventive therapeutic strategies. Epigenetic modifications could be a key determinant of diathesis. Their role is discussed.

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.

Spreading depression: epilepsy's wave of death

Seizures may trigger spreading depression in brainstem nuclei, leading to central cardiorespiratory collapse and sudden unexpected death in epilepsy (Aiba and Noebels, this issue).

Multistability in Large Scale Models of Brain Activity

Noise driven exploration of a brain network’s dynamic repertoire has been hypothesized to be causally involved in cognitive function, aging and neurodegeneration. The dynamic repertoire crucially depends on the network’s capacity to store patterns, as well as their stability. Here we systematically explore the capacity of networks derived from human connectomes to store attractor states, as well as various network mechanisms to control the brain’s dynamic repertoire. Using a deterministic graded response Hopfield model with connectome-based interactions, we reconstruct the system’s attractor space through a uniform sampling of the initial conditions. Large fixed-point attractor sets are obtained in the low temperature condition, with a bigger number of attractors than ever reported so far. Different variants of the initial model, including (i) a uniform activation threshold or (ii) a global negative feedback, produce a similarly robust multistability in a limited parameter range. A numerical analysis of the distribution of the attractors identifies spatially-segregated components, with a centro-medial core and several well-delineated regional patches. Those different modes share similarity with the fMRI independent components observed in the “resting state” condition. We demonstrate non-stationary behavior in noise-driven generalizations of the models, with different meta-stable attractors visited along the same time course. Only the model with a global dynamic density control is found to display robust and long-lasting non-stationarity with no tendency toward either overactivity or extinction. The best fit with empirical signals is observed at the edge of multistability, a parameter region that also corresponds to the highest entropy of the attractors.

Recent developments in non-invasive brain imaging allow reconstructing axonal tracts in the human brain and building realistic network models of the human brain. These models resemble brain systems in their network character and allow deciphering how different regions share signals and process information. Inspired by the metastable dynamics of the spin glass model in statistical physics, we systematically explore the brain network’s capacity to process information and investigate novel avenues how to enhance it. In particular, we study how the brain activates and switches between different functional networks across time. Such non-stationary behavior has been observed in human brain imaging data and hypothesized to be linked to information processsing. To shed light on the conditions under which large-scale brain network models exhibit such dynamics, we characterize the principal network patterns and confront them with modular structures observed both in graph theoretical analysis and resting-state functional Magnetic Resonance Imaging (rs-fMRI).

Computational modeling of seizure dynamics using coupled neuronal networks: factors shaping epileptiform activity

Epileptic seizure dynamics span multiple scales in space and time. Understanding seizure mechanisms requires identifying the relations between seizure components within and across these scales, together with the analysis of their dynamical repertoire. Mathematical models have been developed to reproduce seizure dynamics across scales ranging from the single neuron to the neural population. In this study, we develop a network model of spiking neurons and systematically investigate the conditions, under which the network displays the emergent dynamic behaviors known from the Epileptor, which is a well-investigated abstract model of epileptic neural activity. This approach allows us to study the biophysical parameters and variables leading to epileptiform discharges at cellular and network levels. Our network model is composed of two neuronal populations, characterized by fast excitatory bursting neurons and regular spiking inhibitory neurons, embedded in a common extracellular environment represented by a slow variable. By systematically analyzing the parameter landscape offered by the simulation framework, we reproduce typical sequences of neural activity observed during status epilepticus. We find that exogenous fluctuations from extracellular environment and electro-tonic couplings play a major role in the progression of the seizure, which supports previous studies and further validates our model. We also investigate the influence of chemical synaptic coupling in the generation of spontaneous seizure-like events. Our results argue towards a temporal shift of typical spike waves with fast discharges as synaptic strengths are varied. We demonstrate that spike waves, including interictal spikes, are generated primarily by inhibitory neurons, whereas fast discharges during the wave part are due to excitatory neurons. Simulated traces are compared with in vivo experimental data from rodents at different stages of the disorder. We draw the conclusion that slow variations of global excitability, due to exogenous fluctuations from extracellular environment, and gap junction communication push the system into paroxysmal regimes. We discuss potential mechanisms underlying such machinery and the relevance of our approach, supporting previous detailed modeling studies and reflecting on the limitations of our methodology.

Neurons communicate via different types of synapses on very fast time scales. The combination of hundred thousand of such interconnected cells within a fluctuating extracellular environment forms a complex network that gives rise to function and behavior via the formation of dynamical patterns of activity. In the context of epilepsy, the functional properties of the network at the source of a seizure are disrupted by a possibly large set of factors at the cellular and molecular levels. It is therefore needed to sacrifice some biological accuracy to model seizure dynamics in favor of macroscopic realizations. Here, we present a neuronal network model that convenes both neuronal and network representations with the goal to describe brain dynamics involved in the development of epilepsy. We compare our modeling results with animal in vivo recordings to validate our approach in the context of seizures. Such system-level methodology has significant bearing in understanding neuronal network dynamics that entangle multiple synaptic and extracellular modalities.