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.

A Computational Biomarker of Photosensitive Epilepsy from Interictal EEG.

People with photosensitive epilepsy (PSE) are prone to seizures elicited by visual stimuli. The possibility of inducing epileptiform activity in a reliable way makes PSE a useful model to understand epilepsy, with potential applications for the development of new diagnostic methods and new treatments for epilepsy. A relationship has been demonstrated between PSE and both occipital and more widespread cortical hyperexcitability using various types of stimulation. Here we aimed to test whether hyperexcitability could be inferred from resting interictal electroencephalographic (EEG) data without stimulation. We considered a cohort of 46 individuals with idiopathic generalized epilepsy who underwent EEG during intermittent photic stimulation: 26 had a photoparoxysmal response (PPR), the PPR group, and 20 did not, the non-PPR group. For each individual, we computed functional networks from the resting EEG data before stimulation. We then placed a computer model of ictogenicity into the networks and simulated the propensity of the network to generate seizures in silico [the brain network ictogenicity (BNI)]. Furthermore, we computed the node ictogenicity (NI), a measure of how much each brain region contributes to the overall ictogenic propensity. We used the BNI and NI as proxies for testing widespread and occipital hyperexcitability, respectively. We found that the BNI was not higher in the PPR group relative to the non-PPR group. However, we observed that the (right) occipital NI was significantly higher in the PPR group relative to the non-PPR group. Other regions did not have significant differences in NI values between groups.

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.

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.

Recurrence quantification analysis of dynamic brain networks.

Evidence suggests that brain network dynamics are a key determinant of brain function and dysfunction. Here we propose a new framework to assess the dynamics of brain networks based on recurrence analysis. Our framework uses recurrence plots and recurrence quantification analysis to characterize dynamic networks. For resting-state magnetoencephalographic dynamic functional networks (dFNs), we have found that functional networks recur more quickly in people with epilepsy than in healthy controls. This suggests that recurrence of dFNs may be used as a biomarker of epilepsy. For stereo electroencephalography data, we have found that dFNs involved in epileptic seizures emerge before seizure onset, and recurrence analysis allows us to detect seizures. We further observe distinct dFNs before and after seizures, which may inform neurostimulation strategies to prevent seizures. Our framework can also be used for understanding dFNs in healthy brain function and in other neurological disorders besides epilepsy.

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.

Quantification and Selection of Ictogenic Zones in Epilepsy Surgery.

Network models of brain dynamics provide valuable insight into the healthy functioning of the brain and how this breaks down in disease. A pertinent example is the use of network models to understand seizure generation (ictogenesis) in epilepsy. Recently, computational models have emerged to aid our understanding of seizures and to predict the outcome of surgical perturbations to brain networks. Such approaches provide the opportunity to quantify the effect of removing regions of tissue from brain networks and thereby search for the optimal resection strategy. Here, we use computational models to elucidate how sets of nodes contribute to the ictogenicity of networks. In small networks we fully elucidate the ictogenicity of all possible sets of nodes and demonstrate that the distribution of ictogenicity across sets depends on network topology. However, the full elucidation is a combinatorial problem that becomes intractable for large networks. Therefore, we combine computational models with a genetic algorithm to search for minimal sets of nodes that contribute significantly to ictogenesis. We demonstrate the potential applicability of these methods in practice by identifying optimal sets of nodes to resect in networks derived from 20 individuals who underwent resective surgery for epilepsy. We show that they have the potential to aid epilepsy surgery by suggesting alternative resection sites as well as facilitating the avoidance of brain regions that should not be resected.

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.

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.

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.

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.