Dynamics of epileptic phenomena determined from statistics of ictal transitions

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.

Chaotic and stochastic dynamics of epileptiform-like activities in sclerotic hippocampus resected from patients with pharmacoresistant epilepsy

The types of epileptiform activity occurring in the sclerotic hippocampus with highest incidence are interictal-like events (II) and periodic ictal spiking (PIS). These activities are classified according to their event rates, but it is still unclear if these rate differences are consequences of underlying physiological mechanisms. Identifying new and more specific information related to these two activities may bring insights to a better understanding about the epileptogenic process and new diagnosis. We applied Poincaré map analysis and Recurrence Quantification Analysis (RQA) onto 35 in vitro electrophysiological signals recorded from slices of 12 hippocampal tissues surgically resected from patients with pharmacoresistant temporal lobe epilepsy. These analyzes showed that the II activity is related to chaotic dynamics, whereas the PIS activity is related to deterministic periodic dynamics. Additionally, it indicates that their different rates are consequence of different endogenous dynamics. Finally, by using two computational models we were able to simulate the transition between II and PIS activities. The RQA was applied to different periods of these simulations to compare the recurrences between artificial and real signals, showing that different ranges of regularity-chaoticity can be directly associated with the generation of PIS and II activities.

Temporal lobe epilepsy (TLE) is the most prevalent type of epilepsy in adults and hippocampal sclerosis is the major pathophysiological substrate of pharmaco-refractory TLE. Different patterns of epileptiform-like activity have been described in human hippocampal sclerosis, but the standard analysis applied to characterize the activities usually do not consider the nonlinear features that epileptiform patterns exhibit. Here, using Poincaré map and Recurrence Quantitative Analysis we characterized the most prevalent type of epileptiform-like activities—interictal-like events (II) and periodic ictal spiking (PIS), recorded in vitro from resected hippocampi of pharmacoresistant patients with TLE—according to their levels of stochasticity, chaoticity and determinism. The II activities showed to be more chaotic with complex rhythmicity than PIS activities. The nonlinear dynamic differences between II and PIS leads us to conjecture that they are expressions of different seizure susceptibility. We also identified that each hippocampal subfield expresses II and PIS activities in a specific and different way. Finally, from the modulation of internal parameters of two computational models, we show the conversion of one type of activity into the other, showing how specific neuron networks synchronize over time, leading to II and PIS activities and then into a generalized seizure.

Optimization of epilepsy surgery through virtual resections on individual structural brain networks

The success of epilepsy surgery in patients with refractory epilepsy depends upon correct identification of the epileptogenic zone (EZ) and an optimal choice of the resection area. In this study we developed individualized computational models based upon structural brain networks to explore the impact of different virtual resections on the propagation of seizures. The propagation of seizures was modelled as an epidemic process [susceptible-infected-recovered (SIR) model] on individual structural networks derived from presurgical diffusion tensor imaging in 19 patients. The candidate connections for the virtual resection were all connections from the clinically hypothesized EZ, from which the seizures were modelled to start, to other brain areas. As a computationally feasible surrogate for the SIR model, we also removed the connections that maximally reduced the eigenvector centrality (EC) (large values indicate network hubs) of the hypothesized EZ, with a large reduction meaning a large effect. The optimal combination of connections to be removed for a maximal effect were found using simulated annealing. For comparison, the same number of connections were removed randomly, or based on measures that quantify the importance of a node or connection within the network. We found that 90% of the effect (defined as reduction of EC of the hypothesized EZ) could already be obtained by removing substantially less than 90% of the connections. Thus, a smaller, optimized, virtual resection achieved almost the same effect as the actual surgery yet at a considerably smaller cost, sparing on average 27.49% (standard deviation: 4.65%) of the connections. Furthermore, the maximally effective connections linked the hypothesized EZ to hubs. Finally, the optimized resection was equally or more effective than removal based on structural network characteristics both regarding reducing the EC of the hypothesized EZ and seizure spreading. The approach of using reduced EC as a surrogate for simulating seizure propagation can suggest more restrictive resection strategies, whilst obtaining an almost optimal effect on reducing seizure propagation, by taking into account the unique topology of individual structural brain networks of patients.

The role of interictal discharges in ictogenesis - A dynamical perspective

Interictal epileptiform discharge (IED) is a traditional hallmark of epileptic tissue that is generated by the synchronous activity of a population of neurons. Interictal epileptiform discharges represent a heterogeneous group of pathological activities that differ in shape, duration, spatiotemporal distribution, underlying cellular and network mechanisms, and their relationship to seizure genesis. The exact role of IEDs in epilepsy is still not well understood, and there remains a persistent dichotomy about the impact on IEDs on seizures. Proseizure, antiseizure, and no impact on ictogenesis have all been described in previous studies. In this article, we review the existing knowledge on the role of interictal discharges in seizure genesis, and we discuss how dynamical approaches to ictogenesis can explain the existing dichotomy about the multifaceted role of IEDs in ictogenesis. This article is part of the Special Issue "NEWroscience 2018".

The use of computational models in the management and prognosis of refractory epilepsy: A critical evaluation

PURPOSE

Drug resistant epilepsy (DRE) affects approximately 30 percent of individuals with epilepsy worldwide. Surgery remains the most effective treatment for individuals with DRE, but referral to surgery is low and only about 60 percent of individuals who undergo surgery experience seizure control postoperatively. The present paper evaluates the evidence for using computational models in the prediction of surgical resection sites and surgical outcomes for patients with DRE.

METHODS

We conducted a search in the Medline data base using the terms "refractory epilepsy", "drug-resistant epilepsy", "surgery", "computational model", and "artificial intelligence". Inclusion: original articles in English and case reports from 2000 to 2020. Reviews were excluded.

RESULTS

Clinical applications of computational models may lead to increased utilisation of surgical services through improving our ability to predict outcomes and by improving surgical outcomes outright. The identification and optimisation of nodes that are crucial for the genesis and propagation of epileptiform activity offers the most promising clinical applications of computational models discussed herein.

CONCLUSION

Advances in computational models may in the future significantly increase the application and efficacy of surgery for patients with DRE by optimising the site and amount of cortex to resect, but more research is needed before it achieves therapeutic utility.

Noise amplification precedes extreme epileptic events on human EEG

Extreme events are rare and sudden abnormal deviations of the system's behavior from a typical state. Statistical analysis reveals that if the time series contains extreme events, its distribution has a heavy tail. In dynamical systems, extreme events often occur due to developing instability preceded by noise amplification. Here, we apply this theory to analyze generalized epileptic seizures in the human brain. First, we demonstrate that the time series of electroencephalogram (EEG) spectral power in a frequency band of 1-5 Hz obeys a heavy-tailed distribution, confirming the presence of extreme events. Second, we report that noise on EEG signals gradually increases before the seizure onset. Thus, we hypothesize that generalized epileptic seizures in humans are the extreme events emerging from instability accompanied by preictal noise amplification similar to other dynamical systems.

Delta-gamma phase-amplitude coupling as a biomarker of postictal generalized EEG suppression

Postictal generalized EEG suppression is the state of suppression of electrical activity at the end of a seizure. Prolongation of this state has been associated with increased risk of sudden unexpected death in epilepsy, making characterization of underlying electrical rhythmic activity during postictal suppression an important step in improving epilepsy treatment. Phase-amplitude coupling in EEG reflects cognitive coding within brain networks and some of those codes highlight epileptic activity; therefore, we hypothesized that there are distinct phase-amplitude coupling features in the postictal suppression state that can provide an improved estimate of this state in the context of patient risk for sudden unexpected death in epilepsy. We used both intracranial and scalp EEG data from eleven patients (six male, five female; age range 21–41 years) containing 25 seizures, to identify frequency dynamics, both in the ictal and postictal EEG suppression states. Cross-frequency coupling analysis identified that during seizures there was a gradual decrease of phase frequency in the coupling between delta (0.5–4 Hz) and gamma (30+ Hz), which was followed by an increased coupling between the phase of 0.5–1.5 Hz signal and amplitude of 30–50 Hz signal in the postictal state as compared to the pre-seizure baseline. This marker was consistent across patients. Then, using these postictal-specific features, an unsupervised state classifier—a hidden Markov model—was able to reliably classify four distinct states of seizure episodes, including a postictal suppression state. Furthermore, a connectome analysis of the postictal suppression states showed increased information flow within the network during postictal suppression states as compared to the pre-seizure baseline, suggesting enhanced network communication. When the same tools were applied to the EEG of an epilepsy patient who died unexpectedly, ictal coupling dynamics disappeared and postictal phase-amplitude coupling remained constant throughout. Overall, our findings suggest that there are active postictal networks, as defined through coupling dynamics that can be used to objectively classify the postictal suppression state; furthermore, in a case study of sudden unexpected death in epilepsy, the network does not show ictal-like phase-amplitude coupling features despite the presence of convulsive seizures, and instead demonstrates activity similar to postictal. The postictal suppression state is a period of elevated network activity as compared to the baseline activity which can provide key insights into the epileptic pathology.

Transitions between neocortical seizure and non-seizure-like states and their association with presynaptic glutamate release

The transition between seizure and non-seizure states in neocortical epileptic networks is governed by distinct underlying dynamical processes. Based on the gamma distribution of seizure and inter-seizure durations, over time, seizures are highly likely to self-terminate; whereas, inter-seizure durations have a low chance of transitioning back into a seizure state. Yet, the chance of a state transition could be formed by multiple overlapping, unknown synaptic mechanisms. To identify the relationship between the underlying synaptic mechanisms and the chance of seizure-state transitions, we analyzed the skewed histograms of seizure durations in human intracranial EEG and seizure-like events (SLEs) in local field potential activity from mouse neocortical slices, using an objective method for seizure state classification. While seizures and SLE durations were demonstrated to have a unimodal distribution (gamma distribution shape parameter >1), suggesting a high likelihood of terminating, inter-SLE intervals were shown to have an asymptotic exponential distribution (gamma distribution shape parameter <1), suggesting lower probability of cessation. Then, to test cellular mechanisms for these distributions, we studied the modulation of synaptic neurotransmission during, and between, the in vitro SLEs. Using simultaneous local field potential and whole-cell voltage clamp recordings, we found a suppression of presynaptic glutamate release at SLE termination, as demonstrated by electrically- and optogenetically-evoked excitatory postsynaptic currents (EPSCs), and focal hypertonic sucrose application. Adenosine A1 receptor blockade interfered with the suppression of this release, changing the inter-SLE shape parameter from asymptotic exponential to unimodal, altering the chance of state transition occurrence with time. These findings reveal a critical role for presynaptic glutamate release in determining the chance of neocortical seizure state transitions.

Glial Modulation of Electrical Rhythms in a Neuroglial Network Model of Epilepsy

OBJECTIVE

An important EEG-based biomarker for epilepsy is the phase-amplitude cross-frequency coupling (PAC) of electrical rhythms; however, the underlying pathways of these pathologic markers are not always clear. Since glial cells have been shown to play an active role in neuroglial networks, it is likely that some of these PAC markers are modulated via glial effects.

METHODS

We developed a 4-unit hybrid model of a neuroglial network, consisting of 16 sub-units, that combines a mechanistic representation of neurons with an oscillator-based Cognitive Rhythm Generator (CRG) representation of glial cells-astrocytes and microglia. The model output was compared with recorded generalized tonic-clonic patient data, both in terms of PAC features, and state classification using an unsupervised hidden Markov model (HMM).

RESULTS

The neuroglial model output showed PAC features similar to those observed in epileptic seizures. These generated PAC features were able to accurately identify spontaneous epileptiform discharges (SEDs) as seizure-like states, as well as a postictal-like state following the long-duration SED, when applied to the HMM machine learning algorithm trained on patient data. The evolution profile of the maximal PAC during the SED compared well with patient data, showing similar association with the duration of the postictal state.

CONCLUSION

The hybrid neuroglial network model was able to generate PAC features similar to those observed in ictal and postictal epileptic states, which has been used for state classification and postictal state duration prediction.

SIGNIFICANCE

Since PAC biomarkers are important for epilepsy research and postictal state duration has been linked with risk of sudden unexplained death in epilepsy, this model suggests glial synaptic effects as potential targets for further analysis and treatment.

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.

Effects of physiological parameter evolution on the dynamics of tonic-clonic seizures

The temporal and spectral characteristics of tonic-clonic seizures are investigated using a neural field model of the corticothalamic system in the presence of a temporally varying connection strength between the cerebral cortex and thalamus. Increasing connection strength drives the system into ∼ 10 Hz seizure oscillations once a threshold is passed and a subcritical Hopf bifurcation occurs. In this study, the spectral and temporal characteristics of tonic-clonic seizures are explored as functions of the relevant properties of physiological connection strengths, such as maximum strength, time above threshold, and the ramp rate at which the strength increases or decreases. Analysis shows that the seizure onset time decreases with the maximum connection strength and time above threshold, but increases with the ramp rate. Seizure duration and offset time increase with maximum connection strength, time above threshold, and rate of change. Spectral analysis reveals that the power of nonlinear harmonics and the duration of the oscillations increase as the maximum connection strength and the time above threshold increase. A secondary limit cycle at ∼ 18 Hz, termed a saddle-cycle, is also seen during seizure onset and becomes more prominent and robust with increasing ramp rate. If the time above the threshold is too small, the system does not reach the 10 Hz limit cycle, and only exhibits 18 Hz saddle-cycle oscillations. It is also seen that the time to reach the saturated large amplitude limit-cycle seizure oscillation from both the instability threshold and from the end of the saddle-cycle oscillations is inversely proportional to the square root of the ramp rate.

Epileptic seizures in a heterogeneous excitatory network with short-term plasticity

Epilepsy involves a diverse group of abnormalities, including molecular and cellular disorders. These abnormalities prove to be associated with the changes in local excitability and synaptic dynamics. Correspondingly, the epileptic processes including onset, propagation and generalized seizure may be related with the alterations of excitability and synapse. In this paper, three regions, epileptogenic zone (EZ), propagation area and normal region, were defined and represented by neuronal population model with heterogeneous excitability, respectively. In order to describe the synaptic behavior that the strength was enhanced and maintained at a high level for a short term under a high frequency spike train, a novel activity-dependent short-term plasticity model was proposed. Bifurcation analysis showed that the presence of hyperexcitability could increase the seizure susceptibility of local area, leading to epileptic discharges first seen in the EZ. Meanwhile, recurrent epileptic activities might result in the transition of synaptic strength from weak state to high level, augmenting synaptic depolarizations in non-epileptic neurons as the experimental findings. Numerical simulation based on a full-connected weighted network could qualitatively demonstrate the epileptic process that the propagation area and normal region were successively recruited by the EZ. Furthermore, cross recurrence plot was used to explore the synchronization between neuronal populations, and the global synchronization index was introduced to measure the global synchronization. Results suggested that the synchronization between the EZ and other region was significantly enhanced with the occurrence of seizure. Interestingly, the desynchronization phenomenon was also observed during seizure initiation and propagation as reported before. Therefore, heterogeneous excitability and short-term plasticity are believed to play an important role in the epileptic process. This study may provide novel insights into the mechanism of epileptogenesis.

Excitation and Inhibition Balance Underlying Epileptiform Activity

OBJECTIVE

The phenomenon of postictal generalized EEG suppression state (PGES) - a period with suppressed activity following seizure termination and has been found to be associated with sudden unexpected death in epilepsy - remains poorly understood. This article aims to examine the how the balance of excitation and inhibition (E/I balance) affect the dynamics of seizure and PGES.

METHODS

A network of 1000 Izhikevich model neurons was developed and only the strengths of synaptic connections were adjusted to recreate the dynamics observed in recordings of seizure and PGES from human patients.

RESULTS

A rapid rise followed by a slow decay of dominant frequency was observed in iEEG recordings of ictal periods and reproduced in the simulated local field potential by changing the E/I balance of the model network. The rate of this dominant frequency evolution was quantified by a single measure, β, which was found to have a significant rank correlation with the duration of PGES in iEEG data and the rate of E/I balance shift in the model. Significance and Conclusion: (i) highlighting the importance of E/I balance in the dynamics of seizure and PGES; (ii) suggesting the measure, β, as a marker for PGES and the shift in E/I balance as a neural correlate for this marker.

Neuro-Glial Network Model Of Postictal Generalized EEG Suppression (PGES)

Over the past couple of decades, glial cells have been highlighted as active agents in hyperexcitability of neuronal networks, specifically playing key roles in seizure onset and termination. In particular, microglia have been suggested to have both neuroprotective and neurotoxic effects on the brain. Investigation into seizure termination is of particular interest, as it is sometimes followed by a postictal generalized EEG suppression (PGES) - a low activity state that is potentially associated with sudden unexpected death in epilepsy. In this study, we attempt to link glial effects - synaptic pruning and astrocytic potassium clearance - to the duration of spontaneous epileptiform discharges (SEDs) as well as interSED intervals (iSEDs). We build upon an earlier model of a neuroglial network by translating it into the cortical paradigm and including microglial units. Preliminary findings of our model demonstrated that the duration of SEDs is largely determined by the astrocytic potassium clearance, whereas iSEDs significantly increased with microglial-driven synaptic pruning. In our model, astrocytic potassium clearance itself did not bring a PGES-like state, whereas microglial effects did, which suggests a potential biomarker for PGES phenomena.

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.

Statistical Properties and Predictability of Extreme Epileptic Events

The use of extreme events theory for the analysis of spontaneous epileptic brain activity is a relevant multidisciplinary problem. It allows deeper understanding of pathological brain functioning and unraveling mechanisms underlying the epileptic seizure emergence along with its predictability. The latter is a desired goal in epileptology which might open the way for new therapies to control and prevent epileptic attacks. With this goal in mind, we applied the extreme event theory for studying statistical properties of electroencephalographic (EEG) recordings of WAG/Rij rats with genetic predisposition to absence epilepsy. Our approach allowed us to reveal extreme events inherent in this pathological spiking activity, highly pronounced in a particular frequency range. The return interval analysis showed that the epileptic seizures exhibit a highly-structural behavior during the active phase of the spiking activity. Obtained results evidenced a possibility for early (up to 7 s) prediction of epileptic seizures based on consideration of EEG statistical properties.

Phase Coherent Currents Underlying Neocortical Seizure-Like State Transitions

In the epileptic brain, phase amplitude cross-frequency coupling (CFC) features have been used to objectively classify seizure-related states, and the inter-seizure state has been demonstrated as being random, in contrast to the seizure state being predictable; however, the excitatory and inhibitory networks underlying their dynamics remain unclear. Therefore, the objectives of this study are to classify the dynamics of seizure sub-states labeling seizure-like event (SLE) onset and termination intervals using CFC features and to obtain their underlying excitatory/inhibitory cellular correlates. SLEs were induced in mouse neocortical brain slices using a low-magnesium perfusate, and were recorded in Layer II/III using simultaneous local field potential (LFP) and whole-cell voltage clamp electrodes. Classification of onset and termination of SLE transitions was investigated using CFC features in conjunction with an unsupervised two-state hidden Markov model (HMM). γ-Distributions of their durations indicated that both are predictable. Furthermore, omitting 4 Hz from the HMM classifier switched both SLE sub-states from statistically deterministic to random without changing the dynamics of the SLE state. These results were generalized to 4-aminopyridine (4-AP)-induced SLEs and human seizure traces. Only during these sub-states, both excitatory and inhibitory currents coupled with the field. Where excitatory currents phase locked to a broad range of frequencies between 1 and 12 Hz, inhibitory currents dominantly phase locked at 4 Hz. We conclude that inhibition underlies the predictability of neocortical CFC-defined SLE transition sub-states.

Loss of neuronal network resilience precedes seizures and determines the ictogenic nature of interictal synaptic perturbations

The mechanism of seizure emergence and the role of brief interictal epileptiform discharges (IEDs) in seizure generation are two of the most important unresolved issues in modern epilepsy research. We found that the transition to seizure is not a sudden phenomenon, but is instead a slow process that is characterized by the progressive loss of neuronal network resilience. From a dynamical perspective, the slow transition is governed by the principles of critical slowing, a robust natural phenomenon that is observable in systems characterized by transitions between dynamical regimes. In epilepsy, this process is modulated by synchronous synaptic input from IEDs. IEDs are external perturbations that produce phasic changes in the slow transition process and exert opposing effects on the dynamics of a seizure-generating network, causing either anti-seizure or pro-seizure effects. We found that the multifaceted nature of IEDs is defined by the dynamical state of the network at the moment of the discharge occurrence.

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.

Coupled Oscillators Model of Hyperexcitable Neuroglial Networks

Glial populations within neuronal networks of the brain have recently gained much interest in the context of hyperexcitability and epilepsy. In this paper, we present an oscillator-based neuroglial model capable of generating Spontaneous Electrical Discharges (SEDs) in hyperexcitable conditions. The network is composed of 16 coupled Cognitive Rhythm Generators (CRGs), which are oscillator-based mathematical constructs previously described by our research team. CRGs are well-suited for modeling assemblies of excitable cells, and in this network, each represents one of the following populations: excitatory pyramidal cells, inhibitory interneurons, astrocytes, and microglia. We investigated various pathways leading to hyperexcitability, and our results suggest an important role for astrocytes and microglia in the generation of SEDs of various durations. Analysis of the resultant SEDs revealed two underlying duration distributions with differing properties. Particularly, short and long SEDs are associated with deterministic and random underlying processes, respectively. The mesoscale of this model makes it well-suited for (a) the elucidation of glia-related hypotheses in hyperexcitable conditions, (b) use as a testing platform for neuromodulation purposes, and (c) a hardware implementation for closed-loop neuromodulation.

A forward-looking review of seizure prediction

PURPOSE OF REVIEW

Seizure prediction has made important advances over the last decade, with the recent demonstration that prospective seizure prediction is possible, though there remain significant obstacles to broader application. In this review, we will describe insights gained from long-term trials, with the aim of identifying research goals for the next decade.

RECENT FINDINGS

Unexpected results from these studies, including strong and highly individual relationships between spikes and seizures, diurnal patterns of seizure activity, and the coexistence of different seizure populations within individual patients exhibiting distinctive dynamics, have caused us to re-evaluate many prior assumptions in seizure prediction studies and suggest alternative strategies that could be employed in the search for algorithms providing greater clinical utility. Advances in analytical approaches, particularly deep-learning techniques, harbour great promise and in combination with less-invasive systems with sufficiently power-efficient computational capacity will bring broader clinical application within reach.

SUMMARY

We conclude the review with an exercise in wishful thinking, which asks what the ideal seizure prediction dataset would look like and how these data should be manipulated to maximize benefits for patients. The motivation for structuring the review in this way is to create a forward-looking, optimistic critique of the existing methodologies.

Characteristics of Epileptiform Discharge Duration and Interdischarge Interval in Genetic Generalized Epilepsies

We sought to investigate (1) the characteristics of epileptiform discharge (ED) duration and interdischarge interval (IDI) and (2) the influence of vigilance state on the ED duration and IDI in genetic generalized epilepsy (GGE). In a cohort of patients diagnosed with GGE, 24-h ambulatory EEG recordings were performed prospectively. We then tabulated durations, IDI, and vigilance state in relation to all EDs captured on EEGs. We used K-means cluster analysis and finite mixture modeling to quantify and characterize the groups of ED duration and IDI. To investigate the influence of sleep, we calculated the mean, median, and SEM in each population from all subjects for sleep state and wakefulness separately, followed by the Kruskal–Wallis test to compare the groups. We analyzed 4,679 EDs and corresponding IDI from 23 abnormal 24-h ambulatory EEGs. Our analysis defined two populations of ED durations and IDI: short and long. In all populations, both ED durations and IDI were significantly longer in wakefulness. Our results highlight different characteristics of ED populations in GGE and the influence by the sleep–wake cycle.

Low-to-High Cross-Frequency Coupling in the Electrical Rhythms as Biomarker for Hyperexcitable Neuroglial Networks of the Brain

OBJECTIVE

One of the features used in the study of hyperexcitablility is high-frequency oscillations (HFOs, >80 Hz). HFOs have been reported in the electrical rhythms of the brain's neuroglial networks under physiological and pathological conditions. Cross-frequency coupling (CFC) of HFOs with low-frequency rhythms was used to identify pathologic HFOs in the epileptogenic zones of epileptic patients and as a biomarker for the severity of seizure-like events in genetically modified rodent models. We describe a model to replicate reported CFC features extracted from recorded local field potentials (LFPs) representing network properties.

METHODS

This study deals with a four-unit neuroglial cellular network model where each unit incorporates pyramidal cells, interneurons, and astrocytes. Three different pathways of hyperexcitability generation-Na - ATPase pump, glial potassium clearance, and potassium afterhyperpolarization channel-were used to generate LFPs. Changes in excitability, average spontaneous electrical discharge (SED) duration, and CFC were then measured and analyzed.

RESULTS

Each parameter caused an increase in network excitability and the consequent lengthening of the SED duration. Short SEDs showed CFC between HFOs and theta oscillations (4-8 Hz), but in longer SEDs the low frequency changed to the delta range (1-4 Hz).

CONCLUSION

Longer duration SEDs exhibit CFC features similar to those reported by our team.

SIGNIFICANCE

First, Identifying the exponential relationship between network excitability and SED durations; second, highlighting the importance of glia in hyperexcitability (as they relate to extracellular potassium); and third, elucidation of the biophysical basis for CFC coupling features.

Dynamics of Epileptiform Discharges Induced by Transcranial Magnetic Stimulation in Genetic Generalized Epilepsy

Objective: In patients with Genetic Generalized Epilepsy (GGE), transcranial magnetic stimulation (TMS) can induce epileptiform discharges (EDs) of varying duration. We hypothesized that (a) the ED duration is determined by the dynamic states of critical network nodes (brain areas) at the early post-TMS period, and (b) brain connectivity changes before, during and after the ED, as well as within the ED. Methods: EEG recordings from two GGE patients were analyzed. For hypothesis (a), the characteristics of the brain dynamics at the early ED stage are measured with univariate and multivariate EEG measures and the dependence of the ED duration on these measures is evaluated. For hypothesis (b), effective connectivity measures are combined with network indices so as to quantify the brain network characteristics and identify changes in brain connectivity. Results: A number of measures combined with specific channels computed on the first EEG segment post-TMS correlate with the ED duration. In addition, brain connectivity is altered from pre-ED to ED and post-ED and statistically significant changes were also detected across stages within the ED. Conclusion: ED duration is not purely stochastic, but depends on the dynamics of the post-TMS brain state. The brain network dynamics is significantly altered in the course of EDs.

Sustained efficacy of closed loop electrical stimulation for long-term treatment of absence epilepsy in rats

Closed-loop brain stimulation is a promising alternative to treat drug-resistant epilepsies. In contrast to optogenetic interventions, transcranial electrical stimulation (TES) does not require cellular modification of neurons to be effective, and it is less invasive compared to deep brain stimulation. Furthermore, on-demand TES of targeted brain regions allows the potential for normal function of these networks during interictal periods, a possibility that is eliminated by resective surgical treatment approaches. To further explore the translation of closed-loop TES for treatment of epilepsy, we show here for the first time that unsupervised closed-loop TES in rats can consistently interrupt seizures for 6 weeks and has the potential to control seizure activity up to 4 months (longest periods examined). On-demand TES significantly reduced the time spent in seizure and the individual seizure duration, although significantly higher seizure rate was observed during the treatment. The 6 week long stimulation had no residual adverse effects on the electrophysiologic characteristics of the brain after the termination of the treatment and did not induce glial remodelling in the brain. Our findings demonstrate the safety and effectiveness of minimally invasive, potentially lifelong TES treatment of epilepsy either alone or as a complement to drug treatments.

Detection of nonstationary transition to synchronized states of a neural network using recurrence analyses

We study the stability of asymptotic states displayed by a complex neural network. We focus on the loss of stability of a stationary state of networks using recurrence quantifiers as tools to diagnose local and global stabilities as well as the multistability of a coupled neural network. Numerical simulations of a neural network composed of 1024 neurons in a small-world connection scheme are performed using the model of Braun et al. [Int. J. Bifurcation Chaos 08, 881 (1998)IJBEE40218-127410.1142/S0218127498000681], which is a modified model from the Hodgkin-Huxley model [J. Phys. 117, 500 (1952)]. To validate the analyses, the results are compared with those produced by Kuramoto's order parameter [Chemical Oscillations, Waves, and Turbulence (Springer-Verlag, Berlin Heidelberg, 1984)]. We show that recurrence tools making use of just integrated signals provided by the networks, such as local field potential (LFP) (LFP signals) or mean field values bring new results on the understanding of neural behavior occurring before the synchronization states. In particular we show the occurrence of different stationary and nonstationarity asymptotic states.

Dynamics of convulsive seizure termination and postictal generalized EEG suppression

It is not fully understood how seizures terminate and why some seizures are followed by a period of complete brain activity suppression, postictal generalized EEG suppression. This is clinically relevant as there is a potential association between postictal generalized EEG suppression, cardiorespiratory arrest and sudden death following a seizure. We combined human encephalographic seizure data with data of a computational model of seizures to elucidate the neuronal network dynamics underlying seizure termination and the postictal generalized EEG suppression state. A multi-unit computational neural mass model of epileptic seizure termination and postictal recovery was developed. The model provided three predictions that were validated in EEG recordings of 48 convulsive seizures from 48 subjects with refractory focal epilepsy (20 females, age range 15-61 years). The duration of ictal and postictal generalized EEG suppression periods in human EEG followed a gamma probability distribution indicative of a deterministic process (shape parameter 2.6 and 1.5, respectively) as predicted by the model. In the model and in humans, the time between two clonic bursts increased exponentially from the start of the clonic phase of the seizure. The terminal interclonic interval, calculated using the projected terminal value of the log-linear fit of the clonic frequency decrease was correlated with the presence and duration of postictal suppression. The projected terminal interclonic interval explained 41% of the variation in postictal generalized EEG suppression duration (P < 0.02). Conversely, postictal generalized EEG suppression duration explained 34% of the variation in the last interclonic interval duration. Our findings suggest that postictal generalized EEG suppression is a separate brain state and that seizure termination is a plastic and autonomous process, reflected in increased duration of interclonic intervals that determine the duration of postictal generalized EEG suppression.

Model-guided control of hippocampal discharges by local direct current stimulation

Neurostimulation is an emerging treatment for drug-resistant epilepsies when surgery is contraindicated. Recent clinical results demonstrate significant seizure frequency reduction in epileptic patients, however the mechanisms underlying this therapeutic effect are largely unknown. This study aimed at gaining insights into local direct current stimulation (LDCS) effects on hyperexcitable tissue, by i) analyzing the impact of electrical currents locally applied on epileptogenic brain regions, and ii) characterizing currents achieving an "anti-epileptic" effect (excitability reduction). First, a neural mass model of hippocampal circuits was extended to accurately reproduce the features of hippocampal paroxysmal discharges (HPD) observed in a mouse model of epilepsy. Second, model predictions regarding current intensity and stimulation polarity were confronted to in vivo mice recordings during LDCS (n = 8). The neural mass model was able to generate realistic hippocampal discharges. Simulation of LDCS in the model pointed at a significant decrease of simulated HPD (in duration and occurrence rate, not in amplitude) for cathodal stimulation, which was successfully verified experimentally in epileptic mice. Despite the simplicity of our stimulation protocol, these results contribute to a better understanding of clinical benefits observed in epileptic patients with implanted neurostimulators. Our results also provide further support for model-guided design of neuromodulation therapy.

Control of in vivo ictogenesis via endogenous synaptic pathways

The random nature of seizures poses difficult challenges for epilepsy research. There is great need for a reliable method to control the pathway to seizure onset, which would allow investigation of the mechanisms of ictogenesis and optimization of treatments. Our hypothesis is that increased random afferent synaptic activity (i.e. synaptic noise) within the epileptic focus is one endogenous method of ictogenesis. Building upon previous theoretical and in vitro work showing that synaptic noise can induce seizures, we developed a novel in vivo model of ictogenesis. By increasing the excitability of afferent connections to the hippocampus, we control the risk of temporal lobe seizures during a specific time period. The afferent synaptic activity in the hippocampus was modulated by focal microinjections of potassium chloride into the nucleus reuniens, during which the risk of seizure occurrence increased substantially. The induced seizures were qualitatively and quantitatively indistinguishable from spontaneous ones. This model thus allows direct control of the temporal lobe seizure threshold via endogenous pathways, providing a novel tool in which to investigate the mechanisms and biomarkers of ictogenesis, test for seizure threshold, and rapidly tune antiseizure treatments.

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.

Preventive and Abortive Strategies for Stimulation Based Control of Epilepsy: A Computational Model Study

Epilepsy is a condition in which periods of ongoing normal EEG activity alternate with periods of oscillatory behavior characteristic of epileptic seizures. The dynamics of the transitions between the two states are still unclear. Computational models provide a powerful tool to explore the underlying mechanisms of such transitions, with the purpose of eventually finding therapeutic interventions for this debilitating condition. In this study, the possibility to postpone seizures elicited by a decrease of inhibition is investigated by using external stimulation in a realistic bistable neuronal model consisting of two interconnected neuronal populations representing pyramidal cells and interneurons. In the simulations, seizures are induced by slowly decreasing the conductivity of GABA[Formula: see text] synaptic channels over time. Since the model is bistable, the system will change state from the initial steady state (SS) to the limit cycle (LS) state because of internal noise, when the inhibition falls below a certain threshold. Several state-independent stimulations paradigms are simulated. Their effectiveness is analyzed for various stimulation frequencies and intensities in combination with periodic and random stimulation sequences. The distributions of the time to first seizure in the presence of stimulation are compared with the situation without stimulation. In addition, stimulation protocols targeted to specific subsystems are applied with the objective of counteracting the baseline shift due to decreased inhibition in the system. Furthermore, an analytical model is used to investigate the effects of random noise. The relation between the strength of random noise stimulation, the control parameter of the system and the transitions between steady state and limit cycle are investigated. The study shows that it is possible to postpone epileptic activity by targeted stimulation in a realistic neuronal model featuring bistability and that it is possible to stop seizures by random noise in an analytical model.

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

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

SIGNIFICANCE STATEMENT

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

Estimation of brain network ictogenicity predicts outcome from epilepsy surgery

Surgery is a valuable option for pharmacologically intractable epilepsy. However, significant post-operative improvements are not always attained. This is due in part to our incomplete understanding of the seizure generating (ictogenic) capabilities of brain networks. Here we introduce an in silico, model-based framework to study the effects of surgery within ictogenic brain networks. We find that factors conventionally determining the region of tissue to resect, such as the location of focal brain lesions or the presence of epileptiform rhythms, do not necessarily predict the best resection strategy. We validate our framework by analysing electrocorticogram (ECoG) recordings from patients who have undergone epilepsy surgery. We find that when post-operative outcome is good, model predictions for optimal strategies align better with the actual surgery undertaken than when post-operative outcome is poor. Crucially, this allows the prediction of optimal surgical strategies and the provision of quantitative prognoses for patients undergoing epilepsy surgery.

Human focal seizures are characterized by populations of fixed duration and interval

OBJECTIVE

We report on a quantitative analysis of data from a study that acquired continuous long-term ambulatory human electroencephalography (EEG) data over extended periods. The objectives were to examine the seizure duration and interseizure interval (ISI), their relationship to each other, and the effect of these features on the clinical manifestation of events.

METHODS

Chronic ambulatory intracranial EEG data acquired for the purpose of seizure prediction were analyzed and annotated. A detection algorithm identified potential seizure activity, which was manually confirmed. Events were classified as clinically corroborated, electroencephalographically identical but not clinically corroborated, or subclinical. K-means cluster analysis supplemented by finite mixture modeling was used to locate groupings of seizure duration and ISI.

RESULTS

Quantitative analyses confirmed well-resolved groups of seizure duration and ISIs, which were either mono-modal or multimodal, and highly subject specific. Subjects with a single population of seizures were linked to improved seizure prediction outcomes. There was a complex relationship between clinically manifest seizures, seizure duration, and interval.

SIGNIFICANCE

These data represent the first opportunity to reliably investigate the statistics of seizure occurrence in a realistic, long-term setting. The presence of distinct duration groups implies that the evolution of seizures follows a predetermined course. Patterns of seizure activity showed considerable variation between individuals, but were highly predictable within individuals. This finding indicates seizure dynamics are characterized by subject-specific time scales; therefore, temporal distributions of seizures should also be interpreted on an individual level. Identification of duration and interval subgroups may provide a new avenue for improving seizure prediction.

A computational study of stimulus driven epileptic seizure abatement

Active brain stimulation to abate epileptic seizures has shown mixed success. In spike-wave (SW) seizures, where the seizure and background state were proposed to coexist, single-pulse stimulations have been suggested to be able to terminate the seizure prematurely. However, several factors can impact success in such a bistable setting. The factors contributing to this have not been fully investigated on a theoretical and mechanistic basis. Our aim is to elucidate mechanisms that influence the success of single-pulse stimulation in noise-induced SW seizures. In this work, we study a neural population model of SW seizures that allows the reconstruction of the basin of attraction of the background activity as a four dimensional geometric object. For the deterministic (noise-free) case, we show how the success of response to stimuli depends on the amplitude and phase of the SW cycle, in addition to the direction of the stimulus in state space. In the case of spontaneous noise-induced seizures, the basin becomes probabilistic introducing some degree of uncertainty to the stimulation outcome while maintaining qualitative features of the noise-free case. Additionally, due to the different time scales involved in SW generation, there is substantial variation between SW cycles, implying that there may not be a fixed set of optimal stimulation parameters for SW seizures. In contrast, the model suggests an adaptive approach to find optimal stimulation parameters patient-specifically, based on real-time estimation of the position in state space. We discuss how the modelling work can be exploited to rationally design a successful stimulation protocol for the abatement of SW seizures using real-time SW detection.

A critical role for network structure in seizure onset: a computational modeling approach

Recent clinical work has implicated network structure as critically important in the initiation of seizures in people with idiopathic generalized epilepsies. In line with this idea, functional networks derived from the electroencephalogram (EEG) at rest have been shown to be significantly different in people with generalized epilepsy compared to controls. In particular, the mean node degree of networks from the epilepsy cohort was found to be statistically significantly higher than those of controls. However, the mechanisms by which these network differences can support recurrent transitions into seizures remain unclear. In this study, we use a computational model of the transition into seizure dynamics to explore the dynamic consequences of these differences in functional networks. We demonstrate that networks with higher mean node degree are more prone to generating seizure dynamics in the model and therefore suggest a mechanism by which increased mean node degree of brain networks can cause heightened ictogenicity.

MULTIPLE OSCILLATORY STATES IN MODELS OF COLLECTIVE NEURONAL DYNAMICS

In our previous studies, we showed that the both realistic and analytical computational models of neural dynamics can display multiple sustained states (attractors) for the same values of model parameters. Some of these states can represent normal activity while other, of oscillatory nature, may represent epileptic types of activity. We also showed that a simplified, analytical model can mimic this type of behavior and can be used instead of the realistic model for large scale simulations. The primary objective of the present work is to further explore the phenomenon of multiple stable states, co-existing in the same operational model, or phase space, in systems consisting of large number of interconnected basic units. As a second goal, we aim to specify the optimal method for state control of the system based on inducing state transitions using appropriate external stimulus. We use here interconnected model units that represent the behavior of neuronal populations as an effective dynamic system. The model unit is an analytical model (S. Kalitzin et al., Epilepsy Behav. 22 (2011) S102–S109) and does not correspond directly to realistic neuronal processes (excitatory–inhibitory synaptic interactions, action potential generation). For certain parameter choices however it displays bistable dynamics imitating the behavior of realistic neural mass models. To analyze the collective behavior of the system we applied phase synchronization analysis (PSA), principal component analysis (PCA) and stability analysis using Lyapunov exponent (LE) estimation. We obtained a large variety of stable states with different dynamic characteristics, oscillatory modes and phase relations between the units. These states can be initiated by appropriate initial conditions; transitions between them can be induced stochastically by fluctuating variables (noise) or by specific inputs. We propose a method for optimal reactive control, allowing forced transitions from one state (attractor) into another.

On the nature of seizure dynamics

Seizures can occur spontaneously and in a recurrent manner, which defines epilepsy; or they can be induced in a normal brain under a variety of conditions in most neuronal networks and species from flies to humans. Such universality raises the possibility that invariant properties exist that characterize seizures under different physiological and pathological conditions. Here, we analysed seizure dynamics mathematically and established a taxonomy of seizures based on first principles. For the predominant seizure class we developed a generic model called Epileptor. As an experimental model system, we used ictal-like discharges induced in vitro in mouse hippocampi. We show that only five state variables linked by integral-differential equations are sufficient to describe the onset, time course and offset of ictal-like discharges as well as their recurrence. Two state variables are responsible for generating rapid discharges (fast time scale), two for spike and wave events (intermediate time scale) and one for the control of time course, including the alternation between 'normal' and ictal periods (slow time scale). We propose that normal and ictal activities coexist: a separatrix acts as a barrier (or seizure threshold) between these states. Seizure onset is reached upon the collision of normal brain trajectories with the separatrix. We show theoretically and experimentally how a system can be pushed toward seizure under a wide variety of conditions. Within our experimental model, the onset and offset of ictal-like discharges are well-defined mathematical events: a saddle-node and homoclinic bifurcation, respectively. These bifurcations necessitate a baseline shift at onset and a logarithmic scaling of interspike intervals at offset. These predictions were not only confirmed in our in vitro experiments, but also for focal seizures recorded in different syndromes, brain regions and species (humans and zebrafish). Finally, we identified several possible biophysical parameters contributing to the five state variables in our model system. We show that these parameters apply to specific experimental conditions and propose that there exists a wide array of possible biophysical mechanisms for seizure genesis, while preserving central invariant properties. Epileptor and the seizure taxonomy will guide future modeling and translational research by identifying universal rules governing the initiation and termination of seizures and predicting the conditions necessary for those transitions.

Is ictal cognitive dysfunction predictable?

OBJECTIVE

Accurate prediction of electrographic seizure onset may reduce injuries and improve quality of life in pharmaco-resistant epileptics. However, because sub-clinical, far out-number clinical seizures, indiscriminate issuance of warnings may have a paralyzing effect on these patients. This study investigates the predictability of ictal cognitive dysfunction.

METHODS

Latency and percentage of correct responses to a reaction time test triggered by automated seizure detections were compared to those obtained inter-ictally in 14 subjects undergoing surgery evaluation. Since accurate prediction of seizures is elusive, early detection was used, as it indirectly but reliably investigates for the existence of a cognitive pre-ictal state.

RESULTS

Significant differences between ictal and inter-ictal cognitive performance were not uncovered until late into the temporal evolution of "focal" seizures.

CONCLUSIONS

These observations suggest that cognitive dysfunction is unpredictable in seizures originating from discrete cortical regions, as the transition into unawareness seems abrupt.

SIGNIFICANCE

Prediction of electrographic seizure onsets with worthwhile accuracy would likely result in large numbers of daily warnings, the great majority for sub-clinical seizures. This outcome would considerably increase, without safety justification, patients' psychological burden inherent to each forecast, thus further diminishing quality of life.

DYNAMICS OF COLLECTIVE MULTI-STABILITY IN MODELS OF MULTI-UNIT NEURONAL SYSTEMS

In this study, we investigate the correspondence between dynamic patterns of behavior in two types of computational models of neuronal activity. The first model type is the realistic neuronal model; the second model type is the phenomenological or analytical model. In the simplest model set-up of two interconnected units, we define a parameter space for both types of systems where their behavior is similar. Next we expand the analytical model to two sets of 90 fully interconnected units with some overlap, which can display multi-stable behavior. This system can be in three classes of states: (i) a class consisting of a single resting state, where all units of a set are in steady state, (ii) a class consisting of multiple preserving states, where subsets of the units of a set participate in limit cycle, and (iii) a class consisting of a single saturated state, where all units of a set are recruited in a global limit cycle. In the third and final part of the work, we demonstrate that phase synchronization of units can be detected by a single output unit.

Towards dynamical network biomarkers in neuromodulation of episodic migraine

Computational methods have complemented experimental and clinical neurosciences and led to improvements in our understanding of the nervous systems in health and disease. In parallel, neuromodulation in form of electric and magnetic stimulation is gaining increasing acceptance in chronic and intractable diseases. In this paper, we firstly explore the relevant state of the art in fusion of both developments towards translational computational neuroscience. Then, we propose a strategy to employ the new theoretical concept of dynamical network biomarkers (DNB) in episodic manifestations of chronic disorders. In particular, as a first example, we introduce the use of computational models in migraine and illustrate on the basis of this example the potential of DNB as early-warning signals for neuromodulation in episodic migraine.

Mechanisms of intermittent state transitions in a coupled heterogeneous oscillator model of epilepsy

We investigate the dynamic mechanisms underlying intermittent state transitions in a recently proposed neural mass model of epilepsy. A low dimensional model is constructed, which preserves two key features of the neural mass model, namely (i) coupling between oscillators and (ii) heterogeneous proximity of these oscillators to a bifurcation between distinct limit cycles. We demonstrate that state transitions due to intermittency occur in the abstract model. This suggests that there is a general bifurcation mechanism responsible for this behaviour and that this is independent of the precise form of the evolution equations. Such abstractions of neural mass models allow a deeper insight into underlying dynamic and physiological mechanisms, and also allow the more efficient exploration of large scale brain dynamics in disease.

Proposing a two-level stochastic model for epileptic seizure genesis

By assuming the brain as a multi-stable system, different scenarios have been introduced for transition from normal to epileptic state. But, the path through which this transition occurs is under debate. In this paper a stochastic model for seizure genesis is presented that is consistent with all scenarios: a two-level spontaneous seizure generation model is proposed in which, in its first level the behavior of physiological parameters is modeled with a stochastic process. The focus is on some physiological parameters that are essential in simulating different activities of ElectroEncephaloGram (EEG), i.e., excitatory and inhibitory synaptic gains of neuronal populations. There are many depth-EEG models in which excitatory and inhibitory synaptic gains are the adjustable parameters. Using one of these models at the second level, our proposed seizure generator is complete. The suggested stochastic model of first level is a hidden Markov process whose transition matrices are obtained through analyzing the real parameter sequences of a seizure onset area. These real parameter sequences are estimated from real depth-EEG signals via applying a parameter identification algorithm. In this paper both short-term and long-term validations of the proposed model are done. The long-term synthetic depth-EEG signals simulated by this model can be taken as a suitable tool for comparing different seizure prediction algorithms.