Treatment effects in epilepsy: a mathematical framework for understanding response over time.

Epilepsy is a neurological disorder characterized by recurrent seizures, affecting over 65 million people worldwide. Treatment typically commences with the use of anti-seizure medications, including both mono- and poly-therapy. Should these fail, more invasive therapies such as surgery, electrical stimulation and focal drug delivery are often considered in an attempt to render the person seizure free. Although a significant portion ultimately benefit from these treatment options, treatment responses often fluctuate over time. The physiological mechanisms underlying these temporal variations are poorly understood, making prognosis a significant challenge when treating epilepsy. Here we use a dynamic network model of seizure transition to understand how seizure propensity may vary over time as a consequence of changes in excitability. Through computer simulations, we explore the relationship between the impact of treatment on dynamic network properties and their vulnerability over time that permit a return to states of high seizure propensity. For small networks we show vulnerability can be fully characterised by the size of the first transitive component (FTC). For larger networks, we find measures of network efficiency, incoherence and heterogeneity (degree variance) correlate with robustness of networks to increasing excitability. These results provide a set of potential prognostic markers for therapeutic interventions in epilepsy. Such markers could be used to support the development of personalized treatment strategies, ultimately contributing to understanding of long-term seizure freedom.

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.

Circadian distribution of epileptiform discharges in epilepsy: Candidate mechanisms of variability.

Epilepsy is a serious neurological disorder characterised by a tendency to have recurrent, spontaneous, seizures. Classically, seizures are assumed to occur at random. However, recent research has uncovered underlying rhythms both in seizures and in key signatures of epilepsy-so-called interictal epileptiform activity-with timescales that vary from hours and days through to months. Understanding the physiological mechanisms that determine these rhythmic patterns of epileptiform discharges remains an open question. Many people with epilepsy identify precipitants of their seizures, the most common of which include stress, sleep deprivation and fatigue. To quantify the impact of these physiological factors, we analysed 24-hour EEG recordings from a cohort of 107 people with idiopathic generalized epilepsy. We found two subgroups with distinct distributions of epileptiform discharges: one with highest incidence during sleep and the other during day-time. We interrogated these data using a mathematical model that describes the transitions between background and epileptiform activity in large-scale brain networks. This model was extended to include a time-dependent forcing term, where the excitability of nodes within the network could be modulated by other factors. We calibrated this forcing term using independently-collected human cortisol (the primary stress-responsive hormone characterised by circadian and ultradian patterns of secretion) data and sleep-staged EEG from healthy human participants. We found that either the dynamics of cortisol or sleep stage transition, or a combination of both, could explain most of the observed distributions of epileptiform discharges. Our findings provide conceptual evidence for the existence of underlying physiological drivers of rhythms of epileptiform discharges. These findings should motivate future research to explore these mechanisms in carefully designed experiments using animal models or people with epilepsy.

Classification of human chronotype based on fMRI network-based statistics.

Chronotype-the relationship between the internal circadian physiology of an individual and the external 24-h light-dark cycle-is increasingly implicated in mental health and cognition. Individuals presenting with a late chronotype have an increased likelihood of developing depression, and can display reduced cognitive performance during the societal 9-5 day. However, the interplay between physiological rhythms and the brain networks that underpin cognition and mental health is not well-understood. To address this issue, we use rs-fMRI collected from 16 people with an early chronotype and 22 people with a late chronotype over three scanning sessions. We develop a classification framework utilizing the Network Based-Statistic methodology, to understand if differentiable information about chronotype is embedded in functional brain networks and how this changes throughout the day. We find evidence of subnetworks throughout the day that differ between extreme chronotypes such that high accuracy can occur, describe rigorous threshold criteria for achieving 97.3% accuracy in the Evening and investigate how the same conditions hinder accuracy for other scanning sessions. Revealing differences in functional brain networks based on extreme chronotype suggests future avenues of research that may ultimately better characterize the relationship between internal physiology, external perturbations, brain networks, and disease.

Virtual intracranial EEG signals reconstructed from MEG with potential for epilepsy surgery.

Modelling the interactions that arise from neural dynamics in seizure genesis is challenging but important in the effort to improve the success of epilepsy surgery. Dynamical network models developed from physiological evidence offer insights into rapidly evolving brain networks in the epileptic seizure. A limitation of previous studies in this field is the dependence on invasive cortical recordings with constrained spatial sampling of brain regions that might be involved in seizure dynamics. Here, we propose virtual intracranial electroencephalography (ViEEG), which combines non-invasive ictal magnetoencephalographic imaging (MEG), dynamical network models and a virtual resection technique. In this proof-of-concept study, we show that ViEEG signals reconstructed from MEG alone preserve critical temporospatial characteristics for dynamical approaches to identify brain areas involved in seizure generation. We show the non-invasive ViEEG approach may have some advantage over intracranial electroencephalography (iEEG). Future work may be designed to test the potential of the virtual iEEG approach for use in surgical management of epilepsy.

Analysis of wearable time series data in endocrine and metabolic research.

Many hormones in the body oscillate with different frequencies and amplitudes, creating a dynamic environment that is essential to maintain health. In humans, disruptions to these rhythms are strongly associated with increased morbidity and mortality. While mathematical models can help us understand rhythm misalignment, translating this insight into personalised healthcare technologies requires solving additional challenges. Here, we discuss how combining minimally invasive, high-frequency biosampling technologies with wearable devices can assist the development of hormonal surrogates. We review bespoke algorithms that can help analyse multidimensional, noisy, time series data and identify wearable signals that could constitute clinical proxies of endocrine rhythms. These techniques can support the development of computational biomarkers to support the diagnosis and management of endocrine and metabolic conditions.

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

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.

Dynamic Hormone Control of Stress and Fertility.

Neuroendocrine axes display a remarkable diversity of dynamic signaling processes relaying information between the brain, endocrine glands, and peripheral target tissues. These dynamic processes include oscillations, elastic responses to perturbations, and plastic long term changes observed from the cellular to the systems level. While small transient dynamic changes can be considered physiological, larger and longer disruptions are common in pathological scenarios involving more than one neuroendocrine axes, suggesting that a robust control of hormone dynamics would require the coordination of multiple neuroendocrine clocks. The idea of apparently different axes being in fact exquisitely intertwined through neuroendocrine signals can be investigated in the regulation of stress and fertility. The stress response and the reproductive cycle are controlled by the Hypothalamic-Pituitary-Adrenal (HPA) axis and the Hypothalamic-Pituitary-Gonadal (HPG) axis, respectively. Despite the evidence surrounding the effects of stress on fertility, as well as of the reproductive cycle on stress hormone dynamics, there is a limited understanding on how perturbations in one neuroendocrine axis propagate to the other. We hypothesize that the links between stress and fertility can be better understood by considering the HPA and HPG axes as coupled systems. In this manuscript, we investigate neuroendocrine rhythms associated to the stress response and reproduction by mathematically modeling the HPA and HPG axes as a network of interlocked oscillators. We postulate a network architecture based on physiological data and use the model to predict responses to stress perturbations under different hormonal contexts: normal physiological, gonadectomy, hormone replacement with estradiol or corticosterone (CORT), and high excess CORT (hiCORT) similar to hypercortisolism in humans. We validate our model predictions against experiments in rodents, and show how the dynamic responses of these endocrine axes are consistent with our postulated network architecture. Importantly, our model also predicts the conditions that ensure robustness of fertility to stress perturbations, and how chronodisruptions in glucocorticoid hormones can affect the reproductive axis' ability to withstand stress. This insight is key to understand how chronodisruption leads to disease, and to design interventions to restore normal rhythmicity and health.

Epilepsy surgery: Evaluating robustness using dynamic network models.

Epilepsy is one of the most common neurological conditions affecting over 65 million people worldwide. Over one third of people with epilepsy are considered refractory: they do not respond to drug treatments. For this significant cohort of people, surgery is a potentially transformative treatment. However, only a small minority of people with refractory epilepsy are considered suitable for surgery, and long-term seizure freedom is only achieved in half the cases. Recently, several computational approaches have been proposed to support presurgical planning. Typically, these approaches use a dynamic network model to explore the potential impact of surgical resection in silico. The network component of the model is informed by clinical imaging data and is considered static thereafter. This assumption critically overlooks the plasticity of the brain and, therefore, how continued evolution of the brain network post-surgery may impact upon the success of a resection in the longer term. In this work, we use a simplified dynamic network model, which describes transitions to seizures, to systematically explore how the network structure influences seizure propensity, both before and after virtual resections. We illustrate key results in small networks, before extending our findings to larger networks. We demonstrate how the evolution of brain networks post resection can result in a return to increased seizure propensity. Our results effectively determine the robustness of a given resection to possible network reconfigurations and so provide a potential strategy for optimizing long-term seizure freedom.

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.

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 (Cc), 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. Cc 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.

The Role of Excitability and Network Structure in the Emergence of Focal and Generalized Seizures.

Epileptic seizures are generally classified as either focal or generalized. It had been traditionally assumed that focal seizures imply localized brain abnormalities, whereas generalized seizures involve widespread brain pathologies. However, recent evidence suggests that large-scale brain networks are involved in the generation of focal seizures, and generalized seizures can originate in localized brain regions. Herein we study how network structure and tissue heterogeneities underpin the emergence of focal and widespread seizure dynamics. Mathematical modeling of seizure emergence in brain networks enables the clarification of the characteristics responsible for focal and generalized seizures. We consider neural mass network dynamics of seizure generation in exemplar synthetic networks and we measure the variance in ictogenicity across the network. Ictogenicity is defined as the involvement of network nodes in seizure activity, and its variance is used to quantify whether seizure patterns are focal or widespread across the network. We address both the influence of network structure and different excitability distributions across the network on the ictogenic variance. We find that this variance depends on both network structure and excitability distribution. High variance, i.e., localized seizure activity, is observed in networks highly heterogeneous with regard to the distribution of connections or excitabilities. However, networks that are both heterogeneous in their structure and excitability can underlie the emergence of generalized seizures, depending on the interplay between structure and excitability. Thus, our results imply that the emergence of focal and generalized seizures is underpinned by an interplay between network structure and excitability distribution.

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.

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.

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.

The role that choice of model plays in predictions for epilepsy surgery.

Mathematical modelling has been widely used to predict the effects of perturbations to brain networks. An important example is epilepsy surgery, where the perturbation in question is the removal of brain tissue in order to render the patient free of seizures. Different dynamical models have been proposed to represent transitions to ictal states in this context. However, our choice of which mathematical model to use to address this question relies on making assumptions regarding the mechanism that defines the transition from background to the seizure state. Since these mechanisms are unknown, it is important to understand how predictions from alternative dynamical descriptions compare. Herein we evaluate to what extent three different dynamical models provide consistent predictions for the effect of removing nodes from networks. We show that for small, directed, connected networks the three considered models provide consistent predictions. For larger networks, predictions are shown to be less consistent. However consistency is higher in networks that have sufficiently large differences in ictogenicity between nodes. We further demonstrate that heterogeneity in ictogenicity across nodes correlates with variability in the number of connections for each node.

A Model-Based Assessment of the Seizure Onset Zone Predictive Power to Inform the Epileptogenic Zone.

Epilepsy surgery is a clinical procedure that aims to remove the brain tissue responsible for the emergence of seizures, the epileptogenic zone (EZ). It is preceded by an evaluation to determine the brain tissue that must be resected. The identification of the seizure onset zone (SOZ) from intracranial EEG recordings stands as one of the key proxies for the EZ. In this study we used computational models of epilepsy to assess to what extent the SOZ may or may not represent the EZ. We considered a set of different synthetic networks (e.g., regular, small-world, random, and scale-free networks) to represent large-scale brain networks and a phenomenological network model of seizure generation. In the model, the SOZ was inferred from the seizure likelihood (SL), a measure of the propensity of single nodes to produce epileptiform dynamics, whilst a surgery corresponded to the removal of nodes and connections from the network. We used the concept of node ictogenicity (NI) to quantify the effectiveness of each node removal on reducing the network's propensity to generate seizures. This framework enabled us to systematically compare the SOZ and the seizure control achieved by each considered surgery. Specifically, we compared the distributions of SL and NI across different networks. We found that SL and NI were concordant when all nodes were similarly ictogenic, whereas when there was a small fraction of nodes with high NI, the SL was not specific at identifying these nodes. We further considered networks with heterogeneous node excitabilities, i.e., nodes with different susceptibilities of being engaged in seizure activity, to understand how such heterogeneity may affect the relationship between SL and NI. We found that while SL and NI are concordant when there is a small fraction of hyper-excitable nodes in a network that is otherwise homogeneous, they do diverge if the network is heterogeneous, such as in scale-free networks. We observe that SL is highly dependent on node excitabilities, whilst the effect of surgical resections as revealed by NI is mostly determined by network structure. Together our results suggest that the SOZ is not always a good marker of the EZ.

Sex-associated differences in excitability within the bed nucleus of the stria terminalis are reflective of cell-type.

The bed nucleus of the stria terminalis (BNST) is a sexually dimorphic brain region which plays a key role in stress, anxiety, and anxiety-related disorders. Human females have an increased susceptibility to anxiety-related disorders, however the physiological basis of this is not fully understood. Here we examined the effect of the oestrous cycle and sex on the electrophysiological properties of Type I and Type II cells in the anterolateral area of the BNST (BNSTALG) in unstressed animals. There was no significant effect of oestrous cycle on any of the parameters examined in either cell type. Compared to males, the female cohort had lower capacitance in Type I cells while having a higher capacitance in Type II cells. Type II cells also displayed decreased excitability in the female cohort. In order to confirm the effect of these populations on stress and anxiety, a correlation with behaviour on the elevated zero maze was carried out. We observed that increased excitability in Type II neurons correlated with a decrease in anxiety-like behaviour. These sex-specific differences in excitability may contribute to altered susceptibility to anxiety-related disorders.

Evolving dynamic networks: An underlying mechanism of drug resistance in epilepsy?

At least one-third of all people with epilepsy have seizures that remain poorly controlled despite an increasing number of available anti-epileptic drugs (AEDs). Often, there is an initial good response to a newly introduced AED, which may last up to months, eventually followed by the return of seizures thought to be due to the development of tolerance. We introduce a framework within which the interplay between AED response and brain networks can be explored to understand the development of tolerance. We use a computer model for seizure generation in the context of dynamic networks, which allows us to generate an 'in silico' electroencephalogram (EEG). This allows us to study the effect of changes in excitability network structure and intrinsic model properties on the overall seizure likelihood. Within this framework, tolerance to AEDs - return of seizure-like activity - may occur in 3 different scenarios: 1) the efficacy of the drug diminishes while the brain network remains relatively constant; 2) the efficacy of the drug remains constant, but connections between brain regions change; 3) the efficacy of the drug remains constant, but the intrinsic excitability within brain regions varies dynamically. We argue that these latter scenarios may contribute to a deeper understanding of how drug resistance to AEDs may occur.

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.