Dynamics on networks: the role of local dynamics and global networks on the emergence of hypersynchronous neural activity

Computer-assisted analysis of routine EEG to identify hidden biomarkers of epilepsy: A systematic review

Background

Computational analysis of routine electroencephalogram (rEEG) could improve the accuracy of epilepsy diagnosis. We aim to systematically assess the diagnostic performances of computed biomarkers for epilepsy in individuals undergoing rEEG.

Methods

We searched MEDLINE, EMBASE, EBM reviews, IEEE Explore and the grey literature for studies published between January 1961 and December 2022. We included studies reporting a computational method to diagnose epilepsy based on rEEG without relying on the identification of interictal epileptiform discharges or seizures. Diagnosis of epilepsy as per a treating physician was the reference standard. We assessed the risk of bias using an adapted QUADAS-2 tool.

Results

We screened 10 166 studies, and 37 were included. The sample size ranged from 8 to 192 (mean=54). The computed biomarkers were based on linear (43%), non-linear (27%), connectivity (38%), and convolutional neural networks (10%) models. The risk of bias was high or unclear in all studies, more commonly from spectrum effect and data leakage. Diagnostic accuracy ranged between 64% and 100%. We observed high methodological heterogeneity, preventing pooling of accuracy measures.

Conclusion

The current literature provides insufficient evidence to reliably assess the diagnostic yield of computational analysis of rEEG.

Significance

We provide guidelines regarding patient selection, reference standard, algorithms, and performance validation.

The impact of paediatric epilepsy and co-occurring neurodevelopmental disorders on functional brain networks in wake and sleep

Epilepsy is one of the most common neurological disorders in children. Diagnosing epilepsy in children can be very challenging, especially as it often coexists with neurodevelopmental conditions like autism and ADHD. Functional brain networks obtained from neuroimaging and electrophysiological data in wakefulness and sleep have been shown to contain signatures of neurological disorders, and can potentially support the diagnosis and management of co-occurring neurodevelopmental conditions. In this work, we use electroencephalography (EEG) recordings from children, in restful wakefulness and sleep, to extract functional connectivity networks in different frequency bands. We explore the relationship of these networks with epilepsy diagnosis and with measures of neurodevelopmental traits, obtained from questionnaires used as screening tools for autism and ADHD. We explore differences in network markers between children with and without epilepsy in wake and sleep, and quantify the correlation between such markers and measures of neurodevelopmental traits. Our findings highlight the importance of considering the interplay between epilepsy and neurodevelopmental traits when exploring network markers of epilepsy.

Estimating the likelihood of epilepsy from clinically noncontributory electroencephalograms using computational analysis: A retrospective, multisite case-control study

OBJECTIVE

This study was undertaken to validate a set of candidate biomarkers of seizure susceptibility in a retrospective, multisite case-control study, and to determine the robustness of these biomarkers derived from routinely collected electroencephalography (EEG) within a large cohort (both epilepsy and common alternative conditions such as nonepileptic attack disorder).

METHODS

The database consisted of 814 EEG recordings from 648 subjects, collected from eight National Health Service sites across the UK. Clinically noncontributory EEG recordings were identified by an experienced clinical scientist (N = 281; 152 alternative conditions, 129 epilepsy). Eight computational markers (spectral [n = 2], network-based [n = 4], and model-based [n = 2]) were calculated within each recording. Ensemble-based classifiers were developed using a two-tier cross-validation approach. We used standard regression methods to assess whether potential confounding variables (e.g., age, gender, treatment status, comorbidity) impacted model performance.

RESULTS

We found levels of balanced accuracy of 68% across the cohort with clinically noncontributory normal EEGs (sensitivity =61%, specificity =75%, positive predictive value =55%, negative predictive value =79%, diagnostic odds ratio =4.64, area under receiver operated characteristics curve =.72). Group level analysis found no evidence suggesting any of the potential confounding variables significantly impacted the overall performance.

SIGNIFICANCE

These results provide evidence that the set of biomarkers could provide additional value to clinical decision-making, providing the foundation for a decision support tool that could reduce diagnostic delay and misdiagnosis rates. Future work should therefore assess the change in diagnostic yield and time to diagnosis when utilizing these biomarkers in carefully designed prospective studies.

Classification of musical intervals by spiking neural networks: Perfect student in solfége classes

We investigate a spike activity of a network of excitable FitzHugh-Nagumo neurons, which is under constant two-frequency auditory signals. The neurons are supplemented with linear frequency filters and nonlinear input signal converters. We show that it is possible to configure the network to recognize a specific frequency ratio (musical interval) by selecting the parameters of the neurons, input filters, and coupling between neurons. A set of appropriately configured subnetworks with different topologies and coupling strengths can serve as a classifier for musical intervals. We have found that the selective properties of the classifier are due to the presence of a specific topology of coupling between the neurons of the network.

Spike-and-wave discharges of absence seizures in a sleep waves-constrained corticothalamic model

AIMS

Recurrent network activity in corticothalamic circuits generates physiological and pathological EEG waves. Many computer models have simulated spike-and-wave discharges (SWDs), the EEG hallmark of absence seizures (ASs). However, these models either provided detailed simulated activity only in a selected territory (i.e., cortical or thalamic) or did not test whether their corticothalamic networks could reproduce the physiological activities that are generated by these circuits.

METHODS

Using a biophysical large-scale corticothalamic model that reproduces the full extent of EEG sleep waves, including sleep spindles, delta, and slow (<1 Hz) waves, here we investigated how single abnormalities in voltage- or transmitter-gated channels in the neocortex or thalamus led to SWDs.

RESULTS

We found that a selective increase in the tonic γ-aminobutyric acid type A receptor (GABA-A) inhibition of first-order thalamocortical (TC) neurons or a selective decrease in cortical phasic GABA-A inhibition is sufficient to generate ~4 Hz SWDs (as in humans) that invariably start in neocortical territories. Decreasing the leak conductance of higher-order TC neurons leads to ~7 Hz SWDs (as in rodent models) while maintaining sleep spindles at 7-14 Hz.

CONCLUSION

By challenging key features of current mechanistic views, this simulated ictal corticothalamic activity provides novel understanding of ASs and makes key testable predictions.

Machine-learning for the prediction of one-year seizure recurrence based on routine electroencephalography

Predicting seizure recurrence risk is critical to the diagnosis and management of epilepsy. Routine electroencephalography (EEG) is a cornerstone of the estimation of seizure recurrence risk. However, EEG interpretation relies on the visual identification of interictal epileptiform discharges (IEDs) by neurologists, with limited sensitivity. Automated processing of EEG could increase its diagnostic yield and accessibility. The main objective was to develop a prediction model based on automated EEG processing to predict one-year seizure recurrence in patients undergoing routine EEG. We retrospectively selected a consecutive cohort of 517 patients undergoing routine EEG at our institution (training set) and a separate, temporally shifted cohort of 261 patients (testing set). We developed an automated processing pipeline to extract linear and non-linear features from the EEGs. We trained machine learning algorithms on multichannel EEG segments to predict one-year seizure recurrence. We evaluated the impact of IEDs and clinical confounders on performances and validated the performances on the testing set. The receiver operating characteristic area-under-the-curve for seizure recurrence after EEG in the testing set was 0.63 (95% CI 0.55-0.71). Predictions were still significantly above chance in EEGs with no IEDs. Our findings suggest that there are changes other than IEDs in the EEG signal embodying seizure propensity.

A modification to the Kuramoto model to simulate epileptic seizures as synchronization

The Kuramoto model was developed to describe the coupling of oscillators, motivated by the natural synchronization phenomena. We are interested in modeling an epileptic seizure considering it as the synchronization of action potentials using and modifying this model. In this article, we propose to modify this model, changing the constant coupling force for a function with logistic growth to simulate the onset and epileptic seizure level in an adult male rat caused by the administration of lithium-pilocarpine. Later, we select some frequencies and their respective amplitude values using an algorithm based on the fast Fourier transform (FFT) from an electroencephalography signal when the rat is in basal conditions. Then, we take these values as the natural frequencies of the oscillators in the modified Kuramoto model, considering every oscillator as a single neuron to simulate the emergence of an epileptic seizure numerically by increasing the synchronization value in the coupling function. Finally, using Dynamic Time Warping algorithm, we compare the simulated signal by the Kuramoto model with an FFT approximation of the epileptic seizure.

The role of additive and diffusive coupling on the dynamics of neural populations

Dynamical models consisting of networks of neural masses commonly assume that the interactions between neural populations are via additive or diffusive coupling. When using the additive coupling, a population's activity is affected by the sum of the activities of neighbouring populations. In contrast, when using the diffusive coupling a neural population is affected by the sum of the differences between its activity and the activity of its neighbours. These two coupling functions have been used interchangeably for similar applications. In this study, we show that the choice of coupling can lead to strikingly different brain network dynamics. We focus on a phenomenological model of seizure transitions that has been used both with additive and diffusive coupling in the literature. We consider small networks with two and three nodes, as well as large random and scale-free networks with 64 nodes. We further assess resting-state functional networks inferred from magnetoencephalography (MEG) from people with juvenile myoclonic epilepsy (JME) and healthy controls. To characterize the seizure dynamics on these networks, we use the escape time, the brain network ictogenicity (BNI) and the node ictogenicity (NI), which are measures of the network's global and local ability to generate seizure activity. Our main result is that the level of ictogenicity of a network is strongly dependent on the coupling function. Overall, we show that networks with additive coupling have a higher propensity to generate seizures than those with diffusive coupling. We find that people with JME have higher additive BNI than controls, which is the hypothesized BNI deviation between groups, while the diffusive BNI provides opposite results. Moreover, we find that the nodes that are more likely to drive seizures in the additive coupling case are more likely to prevent seizures in the diffusive coupling case, and that these features correlate to the node's number of connections. Consequently, previous results in the literature involving such models to interrogate functional or structural brain networks could be highly dependent on the choice of coupling. Our results on the MEG functional networks and evidence from the literature suggest that the additive coupling may be a better modeling choice than the diffusive coupling, at least for BNI and NI studies. Thus, we highlight the need to motivate and validate the choice of coupling in future studies involving network models of brain activity.

Modulations of local synchrony over time lead to resting-state functional connectivity in a parsimonious large-scale brain model

Biophysical models of large-scale brain activity are a fundamental tool for understanding the mechanisms underlying the patterns observed with neuroimaging. These models combine a macroscopic description of the within- and between-ensemble dynamics of neurons within a single architecture. A challenge for these models is accounting for modulations of within-ensemble synchrony over time. Such modulations in local synchrony are fundamental for modeling behavioral tasks and resting-state activity. Another challenge comes from the difficulty in parametrizing large scale brain models which hinders researching principles related with between-ensembles differences. Here we derive a parsimonious large scale brain model that can describe fluctuations of local synchrony. Crucially, we do not reduce within-ensemble dynamics to macroscopic variables first, instead we consider within and between-ensemble interactions similarly while preserving their physiological differences. The dynamics of within-ensemble synchrony can be tuned with a parameter which manipulates local connectivity strength. We simulated resting-state static and time-resolved functional connectivity of alpha band envelopes in models with identical and dissimilar local connectivities. We show that functional connectivity emerges when there are high fluctuations of local and global synchrony simultaneously (i.e. metastable dynamics). We also show that for most ensembles, leaning towards local asynchrony or synchrony correlates with the functional connectivity with other ensembles, with the exception of some regions belonging to the default-mode network.

Quantitative Analysis of Visually Reviewed Normal Scalp EEG Predicts Seizure Freedom Following Anterior Temporal Lobectomy

Objective

Anterior temporal lobectomy (ATL) is a widely performed and successful intervention for drug‐resistant temporal lobe epilepsy (TLE). However, up to one third of patients experience seizure recurrence within 1 year after ATL. Despite the extensive literature on presurgical electroencephalography (EEG) and magnetic resonance imaging (MRI) abnormalities to prognosticate seizure freedom following ATL, the value of quantitative analysis of visually reviewed normal interictal EEG in such prognostication remains unclear. In this retrospective multicenter study, we investigate whether machine learning analysis of normal interictal scalp EEG studies can inform the prediction of postoperative seizure freedom outcomes in patients who have undergone ATL.

Methods

We analyzed normal presurgical scalp EEG recordings from 41 Mayo Clinic (MC) and 23 Cleveland Clinic (CC) patients. We used an unbiased automated algorithm to extract eyes closed awake epochs from scalp EEG studies that were free of any epileptiform activity and then extracted spectral EEG features representing (a) spectral power and (b) interhemispheric spectral coherence in frequencies between 1 and 25 Hz across several brain regions. We analyzed the differences between the seizure‐free and non–seizure‐free patients and employed a Naïve Bayes classifier using multiple spectral features to predict surgery outcomes. We trained the classifier using a leave‐one‐patient‐out cross‐validation scheme within the MC data set and then tested using the out‐of‐sample CC data set. Finally, we compared the predictive performance of normal scalp EEG‐derived features against MRI abnormalities.

Results

We found that several spectral power and coherence features showed significant differences correlated with surgical outcomes and that they were most pronounced in the 10–25 Hz range. The Naïve Bayes classification based on those features predicted 1‐year seizure freedom following ATL with area under the curve (AUC) values of 0.78 and 0.76 for the MC and CC data sets, respectively. Subsequent analyses revealed that (a) interhemispheric spectral coherence features in the 10–25 Hz range provided better predictability than other combinations and (b) normal scalp EEG‐derived features provided superior and potentially distinct predictive value when compared with MRI abnormalities (>10% higher F1 score).

Significance

These results support that quantitative analysis of even a normal presurgical scalp EEG may help prognosticate seizure freedom following ATL in patients with drug‐resistant TLE. Although the mechanism for this result is not known, the scalp EEG spectral and coherence properties predicting seizure freedom may represent activity arising from the neocortex or the networks responsible for temporal lobe seizure generation within vs outside the margins of an ATL.

Neurocraft: software for microscale brain network dynamics

The brain operates at millisecond timescales but despite of that, the study of its functional networks is approached with time invariant methods. Equally, for a variety of brain conditions treatment is delivered with fixed temporal protocols unable to monitor and follow the rapid progression and therefore the cycles of a disease. To facilitate the understanding of brain network dynamics we developed Neurocraft, a user friendly software suite. Neurocraft features a highly novel signal processing engine fit for tracking evolving network states with superior time and frequency resolution. A variety of analytics like dynamic connectivity maps, force-directed representations and propagation models, allow for the highly selective investigation of transient pathophysiological dynamics. In addition, machine-learning tools enable the unsupervised investigation and selection of key network features at individual and group-levels. For proof of concept, we compared six seizure-free and non seizure-free focal epilepsy patients after resective surgery using Neurocraft. The network features were calculated using 50 intracranial electrodes on average during at least 120 epileptiform discharges lasting less than one second, per patient. Powerful network differences were detected in the pre-operative data of the two patient groups (effect size = 1.27), suggesting the predictive value of dynamic network features. More than one million patients are treated with cardiac and neuro modulation devices that are unable to track the hourly or daily changes in a subject's disease. Decoding the dynamics of transition from normal to abnormal states may be crucial in the understanding, tracking and treatment of neurological conditions. Neurocraft provides a user-friendly platform for the research of microscale brain dynamics and a stepping stone for the personalised device-based adaptive neuromodulation in real-time.

A large-scale brain network mechanism for increased seizure propensity in Alzheimer's disease

People with Alzheimer's disease (AD) are 6-10 times more likely to develop seizures than the healthy aging population. Leading hypotheses largely consider hyperexcitability of local cortical tissue as primarily responsible for increased seizure prevalence in AD. However, in the general population of people with epilepsy, large-scale brain network organization additionally plays a role in determining seizure likelihood and phenotype. Here, we propose that alterations to large-scale brain network organization seen in AD may contribute to increased seizure likelihood. To test this hypothesis, we combine computational modelling with electrophysiological data using an approach that has proved informative in clinical epilepsy cohorts without AD. EEG was recorded from 21 people with probable AD and 26 healthy controls. At the time of EEG acquisition, all participants were free from seizures. Whole brain functional connectivity derived from source-reconstructed EEG recordings was used to build subject-specific brain network models of seizure transitions. As cortical tissue excitability was increased in the simulations, AD simulations were more likely to transition into seizures than simulations from healthy controls, suggesting an increased group-level probability of developing seizures at a future time for AD participants. We subsequently used the model to assess seizure propensity of different regions across the cortex. We found the most important regions for seizure generation were those typically burdened by amyloid-beta at the early stages of AD, as previously reported by in-vivo and post-mortem staging of amyloid plaques. Analysis of these spatial distributions also give potential insight into mechanisms of increased susceptibility to generalized (as opposed to focal) seizures in AD vs controls. This research suggests avenues for future studies testing patients with seizures, e.g. co-morbid AD/epilepsy patients, and comparisons with PET and MRI scans to relate regional seizure propensity with AD pathologies.

Resting-state EEG for the diagnosis of idiopathic epilepsy and psychogenic nonepileptic seizures: A systematic review

Quantitative markers extracted from resting-state electroencephalogram (EEG) reveal subtle neurophysiological dynamics which may provide useful information to support the diagnosis of seizure disorders. We performed a systematic review to summarize evidence on markers extracted from interictal, visually normal resting-state EEG in adults with idiopathic epilepsy or psychogenic nonepileptic seizures (PNES). Studies were selected from 5 databases and evaluated using the Quality Assessment of Diagnostic Accuracy Studies-2. 26 studies were identified, 19 focusing on people with epilepsy, 6 on people with PNES, and one comparing epilepsy and PNES directly. Results suggest that oscillations along the theta frequency (4-8 Hz) may have a relevant role in idiopathic epilepsy, whereas in PNES there was no evident trend. However, studies were subject to a number of methodological limitations potentially introducing bias. There was often a lack of appropriate reporting and high heterogeneity. Results were not appropriate for quantitative synthesis. We identify and discuss the challenges that must be addressed for valid resting-state EEG markers of epilepsy and PNES to be developed.

Characterizing the electrophysiological abnormalities in visually reviewed normal EEGs of drug-resistant focal epilepsy patients

Routine scalp EEG is essential in the clinical diagnosis and management of epilepsy. However, a normal scalp EEG (based on expert visual review) recorded from a patient with epilepsy can cause delays in diagnosis and clinical care delivery. Here, we investigated whether normal EEGs might contain subtle electrophysiological clues of epilepsy. Specifically, we investigated (i) whether there are indicators of abnormal brain electrophysiology in normal EEGs of epilepsy patients, and (ii) whether such abnormalities are modulated by the side of the brain generating seizures in focal epilepsy. We analysed awake scalp EEG recordings of age-matched groups of 144 healthy individuals and 48 individuals with drug-resistant focal epilepsy who had normal scalp EEGs. After preprocessing, using a bipolar montage of eight channels, we extracted the fraction of spectral power in the alpha band (8-13 Hz) relative to a wide band of 0.5-40 Hz within 10-s windows. We analysed the extracted features for (i) the extent to which people with drug-resistant focal epilepsy differed from healthy subjects, and (ii) whether differences within the drug-resistant focal epilepsy patients were related to the hemisphere generating seizures. We then used those differences to classify whether an EEG is likely to have been recorded from a person with drug-resistant focal epilepsy, and if so, the epileptogenic hemisphere. Furthermore, we tested the significance of these differences while controlling for confounders, such as acquisition system, age and medications. We found that the fraction of alpha power is generally reduced (i) in drug-resistant focal epilepsy compared to healthy controls, and (ii) in right-handed drug-resistant focal epilepsy subjects with left hemispheric seizures compared to those with right hemispheric seizures, and that the differences are most prominent in the frontal and temporal regions. The fraction of alpha power yielded area under curve values of 0.83 in distinguishing drug-resistant focal epilepsy from healthy and 0.77 in identifying the epileptic hemisphere in drug-resistant focal epilepsy patients. Furthermore, our results suggest that the differences in alpha power are greater when compared with differences attributable to acquisition system differences, age and medications. Our findings support that EEG-based measures of normal brain function, such as the normalized spectral power of alpha activity, may help identify patients with epilepsy even when an EEG does not contain any epileptiform activity, recorded seizures or other abnormalities. Although alpha abnormalities are unlikely to be disease-specific, we propose that such abnormalities may provide a higher pre-test probability for epilepsy when an individual being screened for epilepsy has a normal EEG on visual assessment.

A computational biomarker of juvenile myoclonic epilepsy from resting-state MEG

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Computational modelling is combined with MEG to differentiate people with juvenile myoclonic epilepsy from healthy controls.

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Brain network ictogenicity (BNI) was found higher in people with juvenile myoclonic epilepsy relative to healthy controls.

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BNI’s classification accuracy in our cohort was 73%.

Objective

For people with idiopathic generalized epilepsy, functional networks derived from their resting-state scalp electrophysiological recordings have shown an inherent higher propensity to generate seizures than those from healthy controls when assessed using the concept of brain network ictogenicity (BNI). Herein we tested whether the BNI framework is applicable to resting-state magnetoencephalography (MEG) from people with juvenile myoclonic epilepsy (JME).

Methods

The BNI framework consists in deriving a functional network from apparently normal brain activity, placing a mathematical model of ictogenicity into the network and then computing how often such network generates seizures in silico. We considered data from 26 people with JME and 26 healthy controls.

Results

We found that resting-state MEG functional networks from people with JME are characterized by a higher propensity to generate seizures (i.e., higher BNI) than those from healthy controls. We found a classification accuracy of 73%.

Conclusions

The BNI framework is applicable to MEG and was capable of differentiating people with epilepsy from healthy controls.

Significance

The BNI framework may be applied to resting-state MEG to aid in epilepsy diagnosis.

Interictal electroencephalographic functional network topology in drug-resistant and well-controlled idiopathic generalized epilepsy

OBJECTIVE

The study aim was to compare interictal encephalographic (EEG) functional network topology between people with well-controlled idiopathic generalized epilepsy (WC-IGE) and drug-resistant IGE (DR-IGE).

METHODS

Nineteen participants with WC-IGE, 18 with DR-IGE, and 20 controls underwent a resting state, 64-channel EEG. An artifact-free epoch was bandpass filtered into the frequency range of high and low extended alpha. Weighted functional connectivity matrices were calculated. Mean degree, degree distribution variance, characteristic path length (L), clustering coefficient, small world index (SWI), and betweenness centrality were measured. A Kruskal-Wallis H-test assessed effects across groups. Where significant differences were found, Bonferroni-corrected Mann-Whitney pairwise comparisons were calculated.

RESULTS

In the low alpha band (6-9 Hz), there was a significant difference in L at the three-group level (p < .0001). This was lower in controls than both WC-IGE and DR-IGE (p < .0001 for both), with no difference in L between WC-IGE and DR-IGE. Mean degree (p = .031), degree distribution variance (p = .032), and SWI (p = .023) differed across the three groups in the high alpha band (10-12 Hz). Mean degree and degree distribution variance were lower in WC-IGE than controls (p = .029 for both), and SWI was higher in WC-IGE compared with controls (p = .038), with no differences in other pairwise comparisons.

SIGNIFICANCE

IGE network topology is more regular in the low alpha frequency band, potentially reflecting a more vulnerable structure. WC-IGE network topology is different from controls in the high alpha band. This may reflect drug-induced network changes that have stabilized the WC-IGE network by rendering it less likely to synchronize. These results are of potential importance in advancing the understanding of mechanisms of epilepsy drug resistance and as a possible basis for a biomarker of DR-IGE.

Collective almost synchronization-based model to extract and predict features of EEG signals

Understanding the brain is important in the fields of science, medicine, and engineering. A promising approach to better understand the brain is through computing models. These models were adjusted to reproduce data collected from the brain. One of the most commonly used types of data in neuroscience comes from electroencephalography (EEG), which records the tiny voltages generated when neurons in the brain are activated. In this study, we propose a model based on complex networks of weakly connected dynamical systems (Hindmarsh-Rose neurons or Kuramoto oscillators), set to operate in a dynamic regime recognized as Collective Almost Synchronization (CAS). Our model not only successfully reproduces EEG data from both healthy and epileptic EEG signals, but it also predicts EEG features, the Hurst exponent, and the power spectrum. The proposed model is able to forecast EEG signals 5.76 s in the future. The average forecasting error was 9.22%. The random Kuramoto model produced the outstanding result for forecasting seizure EEG with an error of 11.21%.

Dynamical mesoscale model of absence seizures in genetic models

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

Domino-like transient dynamics at seizure onset in epilepsy

The International League Against Epilepsy (ILAE) groups seizures into "focal", "generalized" and "unknown" based on whether the seizure onset is confined to a brain region in one hemisphere, arises in several brain region simultaneously, or is not known, respectively. This separation fails to account for the rich diversity of clinically and experimentally observed spatiotemporal patterns of seizure onset and even less so for the properties of the brain networks generating them. We consider three different patterns of domino-like seizure onset in Idiopathic Generalized Epilepsy (IGE) and present a novel approach to classification of seizures. To understand how these patterns are generated on networks requires understanding of the relationship between intrinsic node dynamics and coupling between nodes in the presence of noise, which currently is unknown. We investigate this interplay here in the framework of domino-like recruitment across a network. In particular, we use a phenomenological model of seizure onset with heterogeneous coupling and node properties, and show that in combination they generate a range of domino-like onset patterns observed in the IGE seizures. We further explore the individual contribution of heterogeneous node dynamics and coupling by interpreting in-vitro experimental data in which the speed of onset can be chemically modulated. This work contributes to a better understanding of possible drivers for the spatiotemporal patterns observed at seizure onset and may ultimately contribute to a more personalized approach to classification of seizure types in clinical practice.

Experimental and Computational Study on Motor Control and Recovery After Stroke: Toward a Constructive Loop Between Experimental and Virtual Embodied Neuroscience

Being able to replicate real experiments with computational simulations is a unique opportunity to refine and validate models with experimental data and redesign the experiments based on simulations. However, since it is technically demanding to model all components of an experiment, traditional approaches to modeling reduce the experimental setups as much as possible. In this study, our goal is to replicate all the relevant features of an experiment on motor control and motor rehabilitation after stroke. To this aim, we propose an approach that allows continuous integration of new experimental data into a computational modeling framework. First, results show that we could reproduce experimental object displacement with high accuracy via the simulated embodiment in the virtual world by feeding a spinal cord model with experimental registration of the cortical activity. Second, by using computational models of multiple granularities, our preliminary results show the possibility of simulating several features of the brain after stroke, from the local alteration in neuronal activity to long-range connectivity remodeling. Finally, strategies are proposed to merge the two pipelines. We further suggest that additional models could be integrated into the framework thanks to the versatility of the proposed approach, thus allowing many researchers to achieve continuously improved experimental design.

Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review

Many biological and neural systems can be seen as networks of interacting periodic processes. Importantly, their functionality, i.e., whether these networks can perform their function or not, depends on the emerging collective dynamics of the network. Synchrony of oscillations is one of the most prominent examples of such collective behavior and has been associated both with function and dysfunction. Understanding how network structure and interactions, as well as the microscopic properties of individual units, shape the emerging collective dynamics is critical to find factors that lead to malfunction. However, many biological systems such as the brain consist of a large number of dynamical units. Hence, their analysis has either relied on simplified heuristic models on a coarse scale, or the analysis comes at a huge computational cost. Here we review recently introduced approaches, known as the Ott-Antonsen and Watanabe-Strogatz reductions, allowing one to simplify the analysis by bridging small and large scales. Thus, reduced model equations are obtained that exactly describe the collective dynamics for each subpopulation in the oscillator network via few collective variables only. The resulting equations are next-generation models: Rather than being heuristic, they exactly link microscopic and macroscopic descriptions and therefore accurately capture microscopic properties of the underlying system. At the same time, they are sufficiently simple to analyze without great computational effort. In the last decade, these reduction methods have become instrumental in understanding how network structure and interactions shape the collective dynamics and the emergence of synchrony. We review this progress based on concrete examples and outline possible limitations. Finally, we discuss how linking the reduced models with experimental data can guide the way towards the development of new treatment approaches, for example, for neurological disease.

Emergent Spaces for Coupled Oscillators

Systems of coupled dynamical units (e.g., oscillators or neurons) are known to exhibit complex, emergent behaviors that may be simplified through coarse-graining: a process in which one discovers coarse variables and derives equations for their evolution. Such coarse-graining procedures often require extensive experience and/or a deep understanding of the system dynamics. In this paper we present a systematic, data-driven approach to discovering “bespoke” coarse variables based on manifold learning algorithms. We illustrate this methodology with the classic Kuramoto phase oscillator model, and demonstrate how our manifold learning technique can successfully identify a coarse variable that is one-to-one with the established Kuramoto order parameter. We then introduce an extension of our coarse-graining methodology which enables us to learn evolution equations for the discovered coarse variables via an artificial neural network architecture templated on numerical time integrators (initial value solvers). This approach allows us to learn accurate approximations of time derivatives of state variables from sparse flow data, and hence discover useful approximate differential equation descriptions of their dynamic behavior. We demonstrate this capability by learning ODEs that agree with the known analytical expression for the Kuramoto order parameter dynamics at the continuum limit. We then show how this approach can also be used to learn the dynamics of coarse variables discovered through our manifold learning methodology. In both of these examples, we compare the results of our neural network based method to typical finite differences complemented with geometric harmonics. Finally, we present a series of computational examples illustrating how a variation of our manifold learning methodology can be used to discover sets of “effective” parameters, reduced parameter combinations, for multi-parameter models with complex coupling. We conclude with a discussion of possible extensions of this approach, including the possibility of obtaining data-driven effective partial differential equations for coarse-grained neuronal network behavior, as illustrated by the synchronization dynamics of Hodgkin–Huxley type neurons with a Chung-Lu network. Thus, we build an integrated suite of tools for obtaining data-driven coarse variables, data-driven effective parameters, and data-driven coarse-grained equations from detailed observations of networks of oscillators.

Dynamic network properties of the interictal brain determine whether seizures appear focal or generalised

Current explanatory concepts suggest seizures emerge from ongoing dynamics of brain networks. It is unclear how brain network properties determine focal or generalised seizure onset, or how network properties can be described in a clinically-useful manner. Understanding network properties would cast light on seizure-generating mechanisms and allow to quantify to which extent a seizure is focal or generalised. Functional brain networks were estimated in segments of scalp-EEG without interictal discharges (68 people with epilepsy, 38 controls). Simplified brain dynamics were simulated using a computer model. We introduce: Critical Coupling (C_c), the ability of a network to generate seizures; Onset Index (OI), the tendency of a region to generate seizures; and Participation Index (PI), the tendency of a region to become involved in seizures. C_c was lower in both patient groups compared with controls. OI and PI were more variable in focal-onset than generalised-onset cases. In focal cases, the regions with highest OI and PI corresponded to the side of seizure onset. Properties of interictal functional networks from scalp EEG can be estimated using a computer model and used to predict seizure likelihood and onset patterns. This may offer potential to enhance diagnosis through quantification of seizure type using inter-ictal recordings.

Electrophysiological properties and seizure networks in hypothalamic hamartoma

Objective

Little is known about the intrinsic electrophysiological properties of hypothalamic hamartoma (HH) in vivo and seizure network since only few cases using stereoelectroencephalography (SEEG) electrodes exploring both cortex and HH have been published. To elucidate these issues, we analyzed simultaneous SEEG recordings in HH and cortex systematically.

Methods

We retrospectively investigated data from 15 consecutive patients with SEEG electrodes into the HH for the treatment purpose of radiofrequency thermocoagulation treatment. Additional SEEG electrodes were placed into the cortex in 11 patients to assess extra‐HH involvement. Interictal discharges within the HH and anatomo‐electroclinical correlations during seizures of each patient were qualitatively and quantitatively analyzed.

Results

Overall, 77 electrodes with 719 contacts were implanted, and 33 spontaneous seizures were recorded during long‐term SEEG monitoring. Interictally, distinct electrophysiological patterns, including isolated intermittent spikes/sharp waves, burst spike and wave trains, paroxysmal fast discharges, periodic discharges, and high‐frequency oscillations, were identified within the HH. Notably, synchronized or independent interictal discharges in the cortex were observed. Regarding the ictal discharges, the electrical onset pattern within the HH always started with abrupt giant shifts superimposed on low‐voltage fast activity across patients. The gelastic seizure network mainly involved the HH, orbitofrontal areas, and cingulate gyrus. Seizures with automatisms and impaired awareness primarily propagated to mesial temporal lobes. Moreover, independent ictal discharges arising from the mesial temporal lobe were detected in three out of nine patients.

Interpretation

This study comprehensively reveals intrinsic electrophysiological patterns and epileptogenic networks in vivo, providing new insights into the mechanisms underlying cortical and subcortical epileptogenesis.

Beyond the Epileptic Focus: Functional Epileptic Networks in Focal Epilepsy

Focal epilepsy can be conceptualized as a network disorder, and the functional epileptic network can be described as a complex system of multiple brain areas that interact dynamically to generate epileptic activity. However, we still do not fully understand the functional architecture of epileptic networks. We studied a cohort of 21 patients with extratemporal focal epilepsy. We used independent component analysis of functional magnetic resonance imaging (fMRI) data. In order to identify the epilepsy-related components, we examined the general linear model-derived electroencephalography-fMRI (EEG–fMRI) time courses associated with interictal epileptic activity as intrinsic hemodynamic epileptic biomarkers. Independent component analysis revealed components related to the epileptic time courses in all 21 patients. Each epilepsy-related component described a network of spatially distributed brain areas that corresponded to the specific epileptic network in each patient. We also provided evidence for the interaction between the epileptic activity generated at the epileptic network and the physiological resting state networks. Our findings suggest that independent component analysis, guided by EEG–fMRI epileptic time courses, have the potential to define the functional architecture of the epileptic network in a noninvasive way. These data could be useful in planning invasive EEG electrode placement, guiding surgical resections, and more effective therapeutic interventions.

Computational modelling in source space from scalp EEG to inform presurgical evaluation of epilepsy

OBJECTIVE

The effectiveness of intracranial electroencephalography (iEEG) to inform epilepsy surgery depends on where iEEG electrodes are implanted. This decision is informed by noninvasive recording modalities such as scalp EEG. Herein we propose a framework to interrogate scalp EEG and determine epilepsy lateralization to aid in electrode implantation.

METHODS

We use eLORETA to map source activities from seizure epochs recorded from scalp EEG and consider 15 regions of interest (ROIs). Functional networks are then constructed using the phase-locking value and studied using a mathematical model. By removing different ROIs from the network and simulating their impact on the network's ability to generate seizures in silico, the framework provides predictions of epilepsy lateralization. We consider 15 individuals from the EPILEPSIAE database and study a total of 62 seizures. Results were assessed by taking into account actual intracranial implantations and surgical outcome.

RESULTS

The framework provided potentially useful information regarding epilepsy lateralization in 12 out of the 15 individuals (p=0.02, binomial test).

CONCLUSIONS

Our results show promise for the use of this framework to better interrogate scalp EEG to determine epilepsy lateralization.

SIGNIFICANCE

The framework may aid clinicians in the decision process to define where to implant electrodes for intracranial monitoring.

Background EEG Connectivity Captures the Time-Course of Epileptogenesis in a Mouse Model of Epilepsy

Large-scale brain networks are increasingly recognized as important for the generation of seizures in epilepsy. However, how a network evolves from a healthy state through the process of epileptogenesis remains unclear. To address this question, here, we study longitudinal epicranial background EEG recordings (30 electrodes, EEG free from epileptiform activity) of a mouse model of mesial temporal lobe epilepsy. We analyze functional connectivity networks and observe that over the time course of epileptogenesis the networks become increasingly asymmetric. Furthermore, computational modelling reveals that a set of nodes, located outside of the region of initial insult, emerges as particularly important for the network dynamics. These findings are consistent with experimental observations, thus demonstrating that ictogenic mechanisms can be revealed on the EEG, that computational models can be used to monitor unfolding epileptogenesis and that both the primary focus and epileptic network play a role in epileptogenesis.

Revealing epilepsy type using a computational analysis of interictal EEG

Seizure onset in epilepsy can usually be classified as focal or generalized, based on a combination of clinical phenomenology of the seizures, EEG recordings and MRI. This classification may be challenging when seizures and interictal epileptiform discharges are infrequent or discordant, and MRI does not reveal any apparent abnormalities. To address this challenge, we introduce the concept of Ictogenic Spread (IS) as a prediction of how pathological electrical activity associated with seizures will propagate throughout a brain network. This measure is defined using a person-specific computer representation of the functional network of the brain, constructed from interictal EEG, combined with a computer model of the transition from background to seizure-like activity within nodes of a distributed network. Applying this method to a dataset comprising scalp EEG from 38 people with epilepsy (17 with genetic generalized epilepsy (GGE), 21 with mesial temporal lobe epilepsy (mTLE)), we find that people with GGE display a higher IS in comparison to those with mTLE. We propose IS as a candidate computational biomarker to classify focal and generalized epilepsy using interictal EEG.

Dynamic brain network states in human generalized spike-wave discharges

Generalized spike-wave discharges in idiopathic generalized epilepsy are conventionally assumed to have abrupt onset and offset. However, in rodent models, discharges emerge during a dynamic evolution of brain network states, extending several seconds before and after the discharge. In human idiopathic generalized epilepsy, simultaneous EEG and functional MRI shows cortical regions may be active before discharges, and network connectivity around discharges may not be normal. Here, in human idiopathic generalized epilepsy, we investigated whether generalized spike-wave discharges emerge during a dynamic evolution of brain network states. Using EEG-functional MRI, we studied 43 patients and 34 healthy control subjects. We obtained 95 discharges from 20 patients. We compared data from patients with discharges with data from patients without discharges and healthy controls. Changes in MRI (blood oxygenation level-dependent) signal amplitude in discharge epochs were observed only at and after EEG onset, involving a sequence of parietal and frontal cortical regions then thalamus (P < 0.01, across all regions and measurement time points). Examining MRI signal phase synchrony as a measure of functional connectivity between each pair of 90 brain regions, we found significant connections (P < 0.01, across all connections and measurement time points) involving frontal, parietal and occipital cortex during discharges, and for 20 s after EEG offset. This network prominent during discharges showed significantly low synchrony (below 99% confidence interval for synchrony in this network in non-discharge epochs in patients) from 16 s to 10 s before discharges, then ramped up steeply to a significantly high level of synchrony 2 s before discharge onset. Significant connections were seen in a sensorimotor network in the minute before discharge onset. This network also showed elevated synchrony in patients without discharges compared to healthy controls (P = 0.004). During 6 s prior to discharges, additional significant connections to this sensorimotor network were observed, involving prefrontal and precuneus regions. In healthy subjects, significant connections involved a posterior cortical network. In patients with discharges, this posterior network showed significantly low synchrony during the minute prior to discharge onset. In patients without discharges, this network showed the same level of synchrony as in healthy controls. Our findings suggest persistently high sensorimotor network synchrony, coupled with transiently (at least 1 min) low posterior network synchrony, may be a state predisposing to generalized spike-wave discharge onset. Our findings also show that EEG onset and associated MRI signal amplitude change is embedded in a considerably longer period of evolving brain network states before and after discharge events.

Network Properties Revealed during Multi-Scale Calcium Imaging of Seizure Activity in Zebrafish

Seizures are characterized by hypersynchronization of neuronal networks. Understanding these networks could provide a critical window for therapeutic control of recurrent seizure activity, i.e., epilepsy. However, imaging seizure networks has largely been limited to microcircuits in vitro or small “windows” in vivo. Here, we combine fast confocal imaging of genetically encoded calcium indicator (GCaMP)-expressing larval zebrafish with local field potential (LFP) recordings to study epileptiform events at whole-brain and single-neuron levels in vivo. Using an acute seizure model (pentylenetetrazole, PTZ), we reliably observed recurrent electrographic ictal-like events associated with generalized activation of all major brain regions and uncovered a well-preserved anterior-to-posterior seizure propagation pattern. We also examined brain-wide network synchronization and spatiotemporal patterns of neuronal activity in the optic tectum microcircuit. Brain-wide and single-neuronal level analysis of PTZ-exposed and 4-aminopyridine (4-AP)-exposed zebrafish revealed distinct network dynamics associated with seizure and non-seizure hyperexcitable states, respectively. Neuronal ensembles, comprised of coactive neurons, were also uncovered during interictal-like periods. Taken together, these results demonstrate that macro- and micro-network calcium motifs in zebrafish may provide a greater understanding of epilepsy.

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

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

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

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

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

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

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Increased white matter integrity found in thalamo-cortical connections.

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Decreased white matter integrity found in cortico-cortical connections.

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

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

NMDA-receptor antibodies alter cortical microcircuit dynamics

Recently, autoantibodies against NMDA receptors (NMDARs) were identified as a major cause of autoimmune encephalitis. They cause abnormalities in brain function often associated with significant changes in patients’ brain dynamics. Here we use computational modeling to identify how NMDAR dysfunction causes abnormalities in brain dynamics using patient EEGs and local field potential recordings in a mouse model of NMDAR-Ab encephalitis. NMDAR autoantibodies cause a specific shift in excitatory coupling within cortical circuits that places the circuits closer to pathological transitions between dynamic brain states. Because of the proximity to these phase transitions, otherwise benign fluctuations in neuronal coupling cause abnormal EEG responses in the presence of the antibodies. Our modeling results thus explain fluctuating abnormalities in brain dynamics observed in patients.

NMDA-receptor antibodies (NMDAR-Abs) cause an autoimmune encephalitis with a diverse range of EEG abnormalities. NMDAR-Abs are believed to disrupt receptor function, but how blocking this excitatory synaptic receptor can lead to paroxysmal EEG abnormalities—or even seizures—is poorly understood. Here we show that NMDAR-Abs change intrinsic cortical connections and neuronal population dynamics to alter the spectral composition of spontaneous EEG activity and predispose brain dynamics to paroxysmal abnormalities. Based on local field potential recordings in a mouse model, we first validate a dynamic causal model of NMDAR-Ab effects on cortical microcircuitry. Using this model, we then identify the key synaptic parameters that best explain EEG paroxysms in pediatric patients with NMDAR-Ab encephalitis. Finally, we use the mouse model to show that NMDAR-Ab–related changes render microcircuitry critically susceptible to overt EEG paroxysms when these key parameters are changed, even though the same parameter fluctuations are tolerated in the in silico model of the control condition. These findings offer mechanistic insights into circuit-level dysfunction induced by NMDAR-Ab.

Chaos in Kuramoto oscillator networks

Kuramoto oscillators are widely used to explain collective phenomena in networks of coupled oscillatory units. We show that simple networks of two populations with a generic coupling scheme, where both coupling strengths and phase lags between and within populations are distinct, can exhibit chaotic dynamics as conjectured by Ott and Antonsen [Chaos 18, 037113 (2008)]. These chaotic mean-field dynamics arise universally across network size, from the continuum limit of infinitely many oscillators down to very small networks with just two oscillators per population. Hence, complicated dynamics are expected even in the simplest description of oscillator networks.

Topolnogical classifier for detecting the emergence of epileptic seizures

OBJECTIVE

An innovative method based on topological data analysis is introduced for classifying EEG recordings of patients affected by epilepsy. We construct a topological space from a collection of EEGs signals using Persistent Homology; then, we analyse the space by Persistent entropy, a global topological feature, in order to classify healthy and epileptic signals.

RESULTS

The performance of the resulting one-feature-based linear topological classifier is tested by analysing the Physionet dataset. The quality of classification is evaluated in terms of the Area Under Curve (AUC) of the receiver operating characteristic curve. It is shown that the linear topological classifier has an AUC equal to [Formula: see text] while the performance of a classifier based on Sample Entropy has an AUC equal to 62.0%.

Postoperative seizure outcome-guided machine learning for interictal electrocorticography in neocortical epilepsy

The objective of this study was to introduce a new machine learning guided by outcome of resective epilepsy surgery defined as the presence/absence of seizures to improve data mining for interictal pathological activities in neocortical epilepsy. Electrocorticographies for 39 patients with medically intractable neocortical epilepsy were analyzed. We separately analyzed 38 frequencies from 0.9 to 800 Hz including both high-frequency activities and low-frequency activities to select bands related to seizure outcome. An automatic detector using amplitude-duration-number thresholds was used. Interictal electrocorticography data sets of 8 min for each patient were selected. In the first training data set of 20 patients, the automatic detector was optimized to best differentiate the seizure-free group from not-seizure-free-group based on ranks of resection percentages of activities detected using a genetic algorithm. The optimization was validated in a different data set of 19 patients. There were 16 (41%) seizure-free patients. The mean follow-up duration was 21 ± 11 mo (range, 13-44 mo). After validation, frequencies significantly related to seizure outcome were 5.8, 8.4-25, 30, 36, 52, and 75 among low-frequency activities and 108 and 800 Hz among high-frequency activities. Resection for 5.8, 8.4-25, 108, and 800 Hz activities consistently improved seizure outcome. Resection effects of 17-36, 52, and 75 Hz activities on seizure outcome were variable according to thresholds. We developed and validated an automated detector for monitoring interictal pathological and inhibitory/physiological activities in neocortical epilepsy using a data-driven approach through outcome-guided machine learning. NEW & NOTEWORTHY Outcome-guided machine learning based on seizure outcome was used to improve detections for interictal electrocorticographic low- and high-frequency activities. This method resulted in better separation of seizure outcome groups than others reported in the literature. The automatic detector can be trained without human intervention and no prior information. It is based only on objective seizure outcome data without relying on an expert's manual annotations. Using the method, we could find and characterize pathological and inhibitory activities.

Elevated Ictal Brain Network Ictogenicity Enables Prediction of Optimal Seizure Control

Recent studies have shown that mathematical models can be used to analyze brain networks by quantifying how likely they are to generate seizures. In particular, we have introduced the quantity termed brain network ictogenicity (BNI), which was demonstrated to have the capability of differentiating between functional connectivity (FC) of healthy individuals and those with epilepsy. Furthermore, BNI has also been used to quantify and predict the outcome of epilepsy surgery based on FC extracted from pre-operative ictal intracranial electroencephalography (iEEG). This modeling framework is based on the assumption that the inferred FC provides an appropriate representation of an ictogenic network, i.e., a brain network responsible for the generation of seizures. However, FC networks have been shown to change their topology depending on the state of the brain. For example, topologies during seizure are different to those pre- and post-seizure. We therefore sought to understand how these changes affect BNI. We studied peri-ictal iEEG recordings from a cohort of 16 epilepsy patients who underwent surgery and found that, on average, ictal FC yield higher BNI relative to pre- and post-ictal FC. However, elevated ictal BNI was not observed in every individual, rather it was typically observed in those who had good post-operative seizure control. We therefore hypothesize that elevated ictal BNI is indicative of an ictogenic network being appropriately represented in the FC. We evidence this by demonstrating superior model predictions for post-operative seizure control in patients with elevated ictal BNI.

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

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

Electroencephalography in the Diagnosis of Genetic Generalized Epilepsy Syndromes

Genetic generalized epilepsy (GGE) consists of several syndromes diagnosed and classified on the basis of clinical features and electroencephalographic (EEG) abnormalities. The main EEG feature of GGE is bilateral, synchronous, symmetric, and generalized spike-wave complex. Other classic EEG abnormalities are polyspikes, epileptiform K-complexes and sleep spindles, polyspike-wave discharges, occipital intermittent rhythmic delta activity, eye-closure sensitivity, fixation-off sensitivity, and photoparoxysmal response. However, admixed with typical changes, atypical epileptiform discharges are also commonly seen in GGE. There are circadian variations of generalized epileptiform discharges. Sleep, sleep deprivation, hyperventilation, intermittent photic stimulation, eye closure, and fixation-off are often used as activation techniques to increase the diagnostic yield of EEG recordings. Reflex seizure-related EEG abnormalities can be elicited by the use of triggers such as cognitive tasks and pattern stimulation during the EEG recording in selected patients. Distinct electrographic abnormalities to help classification can be identified among different electroclinical syndromes.

Stochastic Kuramoto oscillators with discrete phase states

We present a generalization of the Kuramoto phase oscillator model in which phases advance in discrete phase increments through Poisson processes, rendering both intrinsic oscillations and coupling inherently stochastic. We study the effects of phase discretization on the synchronization and precision properties of the coupled system both analytically and numerically. Remarkably, many key observables such as the steady-state synchrony and the quality of oscillations show distinct extrema while converging to the classical Kuramoto model in the limit of a continuous phase. The phase-discretized model provides a general framework for coupled oscillations in a Markov chain setting.

An optimal strategy for epilepsy surgery: Disruption of the rich-club?

Surgery is a therapeutic option for people with epilepsy whose seizures are not controlled by anti-epilepsy drugs. In pre-surgical planning, an array of data modalities, often including intra-cranial EEG, is used in an attempt to map regions of the brain thought to be crucial for the generation of seizures. These regions are then resected with the hope that the individual is rendered seizure free as a consequence. However, post-operative seizure freedom is currently sub-optimal, suggesting that the pre-surgical assessment may be improved by taking advantage of a mechanistic understanding of seizure generation in large brain networks. Herein we use mathematical models to uncover the relative contribution of regions of the brain to seizure generation and consequently which brain regions should be considered for resection. A critical advantage of this modeling approach is that the effect of different surgical strategies can be predicted and quantitatively compared in advance of surgery. Herein we seek to understand seizure generation in networks with different topologies and study how the removal of different nodes in these networks reduces the occurrence of seizures. Since this a computationally demanding problem, a first step for this aim is to facilitate tractability of this approach for large networks. To do this, we demonstrate that predictions arising from a neural mass model are preserved in a lower dimensional, canonical model that is quicker to simulate. We then use this simpler model to study the emergence of seizures in artificial networks with different topologies, and calculate which nodes should be removed to render the network seizure free. We find that for scale-free and rich-club networks there exist specific nodes that are critical for seizure generation and should therefore be removed, whereas for small-world networks the strategy should instead focus on removing sufficient brain tissue. We demonstrate the validity of our approach by analysing intra-cranial EEG recordings from a database comprising 16 patients who have undergone epilepsy surgery, revealing rich-club structures within the obtained functional networks. We show that the postsurgical outcome for these patients was better when a greater proportion of the rich club was removed, in agreement with our theoretical predictions.

Evolving Network Model That Almost Regenerates Epileptic Data

In many realistic networks, the edges representing the interactions between nodes are time varying. Evidence is growing that the complex network that models the dynamics of the human brain has time-varying interconnections, that is, the network is evolving. Based on this evidence, we construct a patient- and data-specific evolving network model (comprising discrete-time dynamical systems) in which epileptic seizures or their terminations in the brain are also determined by the nature of the time-varying interconnections between the nodes. A novel and unique feature of our methodology is that the evolving network model remembers the data from which it was conceived from, in the sense that it evolves to almost regenerate the patient data even on presenting an arbitrary initial condition to it. We illustrate a potential utility of our methodology by constructing an evolving network from clinical data that aids in identifying an approximate seizure focus; nodes in such a theoretically determined seizure focus are outgoing hubs that apparently act as spreaders of seizures. We also point out the efficacy of removal of such spreaders in limiting seizures.

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.

Quantitative evaluation of simulated functional brain networks in graph theoretical analysis

There is increasing interest in the potential of whole-brain computational models to provide mechanistic insights into resting-state brain networks. It is therefore important to determine the degree to which computational models reproduce the topological features of empirical functional brain networks. We used empirical connectivity data derived from diffusion spectrum and resting-state functional magnetic resonance imaging data from healthy individuals. Empirical and simulated functional networks, constrained by structural connectivity, were defined based on 66 brain anatomical regions (nodes). Simulated functional data were generated using the Kuramoto model in which each anatomical region acts as a phase oscillator. Network topology was studied using graph theory in the empirical and simulated data. The difference (relative error) between graph theory measures derived from empirical and simulated data was then estimated. We found that simulated data can be used with confidence to model graph measures of global network organization at different dynamic states and highlight the sensitive dependence of the solutions obtained in simulated data on the specified connection densities. This study provides a method for the quantitative evaluation and external validation of graph theory metrics derived from simulated data that can be used to inform future study designs.

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We tested the convergence of simulated and empirical brain network topology.

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Simulated functional data were based on the Kuramoto model.

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Network topology was defined using graph theory metrics.

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Graph theory metrics of global network topology showed greater convergence.

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The solutions obtained in the simulated data depended on connection density.

A dynamical framework to relate perceptual variability with multisensory information processing

Multisensory processing involves participation of individual sensory streams, e.g., vision, audition to facilitate perception of environmental stimuli. An experimental realization of the underlying complexity is captured by the “McGurk-effect”- incongruent auditory and visual vocalization stimuli eliciting perception of illusory speech sounds. Further studies have established that time-delay between onset of auditory and visual signals (AV lag) and perturbations in the unisensory streams are key variables that modulate perception. However, as of now only few quantitative theoretical frameworks have been proposed to understand the interplay among these psychophysical variables or the neural systems level interactions that govern perceptual variability. Here, we propose a dynamic systems model consisting of the basic ingredients of any multisensory processing, two unisensory and one multisensory sub-system (nodes) as reported by several researchers. The nodes are connected such that biophysically inspired coupling parameters and time delays become key parameters of this network. We observed that zero AV lag results in maximum synchronization of constituent nodes and the degree of synchronization decreases when we have non-zero lags. The attractor states of this network can thus be interpreted as the facilitator for stabilizing specific perceptual experience. Thereby, the dynamic model presents a quantitative framework for understanding multisensory information processing.

A computational biomarker of idiopathic generalized epilepsy from resting state EEG

Epilepsy is one of the most common serious neurologic conditions. It is characterized by the tendency to have recurrent seizures, which arise against a backdrop of apparently normal brain activity. At present, clinical diagnosis relies on the following: (1) case history, which can be unreliable; (2) observation of transient abnormal activity during electroencephalography (EEG), which may not be present during clinical evaluation; and (3) if diagnostic uncertainty occurs, undertaking prolonged monitoring in an attempt to observe EEG abnormalities, which is costly. Herein, we describe the discovery and validation of an epilepsy biomarker based on computational analysis of a short segment of resting-state (interictal) EEG. Our method utilizes a computer model of dynamic networks, where the network is inferred from the extent of synchrony between EEG channels (functional networks) and the normalized power spectrum of the clinical data. We optimize model parameters using a leave-one-out classification on a dataset comprising 30 people with idiopathic generalized epilepsy (IGE) and 38 normal controls. Applying this scheme to all 68 subjects we find 100% specificity at 56.7% sensitivity, and 100% sensitivity at 65.8% specificity. We believe this biomarker could readily provide additional support to the diagnostic process.