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Dynamic functional connectivity (dFC) analysis of resting-state fMRI data is commonly performed by calculating sliding-window correlations (SWC), followed by k-means clustering in order to assign each window to a given state. Studies using synthetic data have shown that k-means performance is highly dependent on sliding window parameters and signal-to-noise ratio. Additionally, sources of heterogeneity between subjects may affect the accuracy of group-level clustering, thus affecting measurements of dFC state temporal properties such as dwell time and fractional occupancy. This may result in spurious conclusions regarding differences between groups (e.g. when comparing a clinical population to healthy controls). Therefore, is it important to quantify the ability of k-means to estimate dFC state temporal properties when applied to cohorts of multiple subjects, and to explore ways in which clustering performance can be maximised.Here, we explore the use of dimensionality reduction methods prior to clustering in order to map high-dimensional data to a lower dimensional space, providing salient features to the subsequent clustering step. We assess the use of deep autoencoders for feature selection prior to applying k-means clustering to the encoded data. We compare this deep clustering method to feature selection using principle component analysis (PCA), uniform manifold approximation and projection (UMAP), as well as applying k-means to the original feature space using either L1 or L2 distance. We provide extensive quantitative evaluation of clustering performance using synthetic datasets, representing data from multiple heterogeneous subjects. In synthetic data we find that deep clustering gives the best performance, while other approaches are often insufficient to capture temporal properties of dFC states. We then demonstrate the application of each method to real-world data from human subjects and show that the choice of feature selection method has a significant effect on group-level measurements of state temporal properties. We therefore advocate for the use of deep clustering as a precursor to clustering in dFC.

Highlights • Cases were children cooled for neonatal encephalopathy, without cerebral palsy. • Controls were matched for age, sex and socioeconomic status. • In cases, tract-level fractional anisotropy correlated with motor performance. • Graph-theoretic properties of structural networks correlated with motor performance. • Connections to frontal lobe regions were associated with motor performance., Therapeutic hypothermia reduces the incidence of severe motor disability, such as cerebral palsy, following neonatal hypoxic-ischaemic encephalopathy. However, cooled children without cerebral palsy at school-age demonstrate motor deficits and altered white matter connectivity. In this study, we used diffusion-weighted imaging to investigate the relationship between white matter connectivity and motor performance, measured using the Movement Assessment Battery for Children-2, in children aged 6–8 years treated with therapeutic hypothermia for neonatal hypoxic-ischaemic encephalopathy at birth, who did not develop cerebral palsy (cases), and matched typically developing controls. Correlations between total motor scores and diffusion properties in major white matter tracts were assessed in 33 cases and 36 controls. In cases, significant correlations (FDR-corrected P

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., Author summary People with Alzheimer’s disease (AD) are more likely to develop seizures than cognitively healthy people. In this study, we aimed to understand whether whole-brain network structure is related to this increased seizure likelihood. We used electroencephalography (EEG) to estimate brain networks from people with AD and healthy controls. We subsequently inserted these networks into a model brain and simulated disease progression by increasing the excitability of brain tissue. We found the simulated AD brains were more likely to develop seizures than the simulated control brains. No participants had seizures when we collected data, so our results suggest an increased probability of developing seizures at a future time for AD participants. Therefore functional brain network structure may play a role in increased seizure likelihood in AD. We also used the model to examine which brain regions were most important for generating seizures, and found that the seizure-generating regions corresponded to those typically affected in early AD. Our results also provide a potential explanation for why people with AD are more likely to have generalized seizures (i.e. seizures involving the whole brain, as opposed to ‘focal’ seizures which only involve certain areas) than the general population with epilepsy.

Graphical abstract, Highlights • We studied brain structure in case children cooled for neonatal encephalopathy. • Cases did not have cerebral palsy and were matched with controls. • Cases had reduced fractional anisotropy in several white matter tracts. • Several whole-brain structural connectivity network metrics correlated with IQ. • We identified subnetworks associated with case status, IQ and processing speed., Therapeutic hypothermia following neonatal encephalopathy due to birth asphyxia reduces death and cerebral palsy. However, school-age children without cerebral palsy treated with therapeutic hypothermia for neonatal encephalopathy still have reduced performance on cognitive and motor tests, attention difficulties, slower reaction times and reduced visuo-spatial processing abilities compared to typically developing controls. We acquired diffusion-weighted imaging data from school-age children without cerebral palsy treated with therapeutic hypothermia for neonatal encephalopathy at birth, and a matched control group. Voxelwise analysis (33 cases, 36 controls) confirmed reduced fractional anisotropy in widespread areas of white matter in cases, particularly in the fornix, corpus callosum, anterior and posterior limbs of the internal capsule bilaterally and cingulum bilaterally. In structural brain networks constructed using probabilistic tractography (22 cases, 32 controls), graph-theoretic measures of strength, local and global efficiency, clustering coefficient and characteristic path length were found to correlate with IQ in cases but not controls. Network-based statistic analysis implicated brain regions involved in visuo-spatial processing and attention, aligning with previous behavioural findings. These included the precuneus, thalamus, left superior parietal gyrus and left inferior temporal gyrus. Our findings demonstrate that, despite the manifest successes of therapeutic hypothermia, brain development is impaired in these children.

Highlights • Computational modelling is combined with scalp EEG to assess epilepsy lateralization. • Our approach proved useful in informing lateralization in 12 out of 15 individuals studied. • The framework proposed may be used to aid deciding where to implant intracranial electrodes., 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.

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.

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.

OBJECTIVES: Functional and structural disconnection of the brain is a prevailing hypothesis to explain cognitive impairment in Alzheimer's Disease (AD). We aim to understand the link between alterations to networks and cognitive impairment using functional connectivity analysis and modelling.METHODS: EEG was recorded from 21 AD patients and 26 controls, mapped into source space using eLORETA, and functional connectivity was calculated using phase locking factor. The mini-mental state exam (MMSE) was used to assess cognitive impairment. A computational model was used to uncover mechanisms of altered functional connectivity.RESULTS: Small-worldness (SW) of functional networks decreased in AD and was positively correlated with MMSE score and the language sub-score. Reduced SW was a result of increased path lengths, predominantly localized to the temporal lobes. Combining observed differences in local oscillation frequency with reduced temporal lobe effective connectivity in the model could account for observed functional network differences.CONCLUSIONS: Temporal lobe disconnection plays a key role in cognitive impairment in AD.SIGNIFICANCE: We combine electrophysiology, neuropsychological scores, and computational modelling to provide novel insight into the relationships between the disconnection hypothesis and cognitive decline in AD.

Neural mass models (NMMs) are increasingly used to uncover the large-scale mechanisms of brain rhythms in health and disease. The dynamics of these models is dependent upon the choice of parameters, and therefore it is crucial to be able to understand how dynamics change when parameters are varied. Despite being considered low dimensional in comparison to micro-scale, neuronal network models, with regards to understanding the relationship between parameters and dynamics, NMMs are still prohibitively high dimensional for classical approaches such as numerical continuation. Therefore, we need alternative methods to characterise dynamics of NMMs in high dimensional parameter spaces. Here, we introduce a statistical framework that enables the efficient exploration of the relationship between model parameters and selected features of the simulated, emergent model dynamics of NMMs. We combine the classical machine learning approaches of trees and random forests to enable studying the effect that varying multiple parameters has on the dynamics of a model. The method proceeds by using simulations to transform the mathematical model into a database. This database is then used to partition parameter space with respect to dynamic features of interest, using random forests. This allows us to rapidly explore dynamics in high dimensional parameter space, capture the approximate location of qualitative transitions in dynamics and assess the relative importance of all parameters in the model in all dimensions simultaneously. We apply this method to a commonly used NMM in the context of transitions to seizure dynamics. We find that the inhibitory sub-system is most crucial for the generation of seizure dynamics, confirm and expand previous findings regarding the ratio of excitation and inhibition, and demonstrate that previously overlooked parameters can have a significant impact on model dynamics. We advocate the use of this method in future to constrain high dimensional parameter spaces enabling more efficient, person-specific, model calibration., Author summary Understanding the workings of the healthy brain and the disruptions that lead to disease remains a grand challenge for neuroscience. Given the complexity of the brain, mathematical models are becoming increasingly important to elucidate these fundamental mechanisms. However, as our fundamental understanding evolves, so models grow in complexity. If the model has only one or two parameters, formal analysis is possible, however understanding changes in system behaviour becomes increasingly difficult as the number of model parameters increases. In this article we introduce a method to overcome this challenge and use it to better elucidate the contribution of different mechanisms to the emergence of brain rhythms. Our method uses machine learning approaches to classify the dynamics of the model under different parameters and to calculate their variability. This allows us to determine which parameters are critically important for the emergence of specific dynamics. Applying this method to a classical model of epilepsy, we find new explanations for the generation of seizures. This method can readily be used in other application areas of computational biology.

Objective To show that time-irreversible EEG signals recorded with intracranial electrodes during seizures can serve as markers of the epileptogenic zone. Methods We use the recently developed method of mapping time series into directed horizontal graphs (dHVG). Each node of the dHVG represents a time point in the original intracranial EEG (iEEG) signal. Statistically significant differences between the distributions of the nodes’ number of input and output connections are used to detect time-irreversible iEEG signals. Results In 31 of 32 seizure recordings we found time-irreversible iEEG signals. The maximally time-irreversible signals always occurred during seizures, with highest probability in the middle of the first seizure half. These signals spanned a large range of frequencies and amplitudes but were all characterized by saw-tooth like shaped components. Brain regions removed from patients who became post-surgically seizure-free generated significantly larger time-irreversibilities than regions removed from patients who still had seizures after surgery. Conclusions Our results corroborate that ictal time-irreversible iEEG signals can indeed serve as markers of the epileptogenic zone and can be efficiently detected and quantified in a time-resolved manner by dHVG based methods. Significance Ictal time-irreversible EEG signals can help to improve pre-surgical evaluation in patients suffering from pharmaco-resistant epilepsies.

Epileptic seizures are associated with a dysregulation of electrical brain activity on many different spatial scales. To better understand the dynamics of epileptic seizures, that is, how the seizures initiate, propagate, and terminate, it is important to consider changes of electrical brain activity on different spatial scales. Herein we set out to analyze periictal electrical brain activity on comparatively small and large spatial scales by assessing changes in single intracranial electroencephalography (EEG) signals and of averaged interdependences of pairs of EEG signals.

Stimulation of human epileptic tissue can induce rhythmic, self-terminating responses on the EEG or ECoG. These responses play a potentially important role in localising tissue involved in the generation of seizure activity, yet the underlying mechanisms are unknown. However, in vitro evidence suggests that self-terminating oscillations in nervous tissue are underpinned by non-trivial spatio-temporal dynamics in an excitable medium. In this study, we investigate this hypothesis in spatial extensions to a neural mass model for epileptiform dynamics. We demonstrate that spatial extensions to this model in one and two dimensions display propagating travelling waves but also more complex transient dynamics in response to local perturbations. The neural mass formulation with local excitatory and inhibitory circuits, allows the direct incorporation of spatially distributed, functional heterogeneities into the model. We show that such heterogeneities can lead to prolonged reverberating responses to a single pulse perturbation, depending upon the location at which the stimulus is delivered. This leads to the hypothesis that prolonged rhythmic responses to local stimulation in epileptogenic tissue result from repeated self-excitation of regions of tissue with diminished inhibitory capabilities. Combined with previous models of the dynamics of focal seizures this macroscopic framework is a first step towards an explicit spatial formulation of the concept of the epileptogenic zone. Ultimately, an improved understanding of the pathophysiologic mechanisms of the epileptogenic zone will help to improve diagnostic and therapeutic measures for treating epilepsy. © 2011 Elsevier Inc.

Generalised epileptic seizures are frequently accompanied by sudden, reversible transitions from low amplitude, irregular background activity to high amplitude, regular spike-wave discharges (SWD) in the EEG. The underlying mechanisms responsible for SWD generation and for the apparently spontaneous transitions to SWD and back again are still not fully understood. Specifically, the role of spatial cortico-cortical interactions in ictogenesis is not well studied. We present a macroscopic, neural mass model of a cortical column which includes two distinct time scales of inhibition. This model can produce both an oscillatory background and a pathological SWD rhythm. We demonstrate that coupling two of these cortical columns can lead to a bistability between out-of-phase, low amplitude background dynamics and in-phase, high amplitude SWD activity. Stimuli can cause state-dependent transitions from background into SWD. In an extended local area of cortex, spatial heterogeneities in a model parameter can lead to spontaneous reversible transitions from a desynchronised background to synchronous SWD due to intermittency. The deterministic model is therefore capable of producing absence seizure-like events without any time dependent adjustment of model parameters. The emergence of such mechanisms due to spatial coupling demonstrates the importance of spatial interactions in modelling ictal dynamics, and in the study of ictogenesis. © 2011 Elsevier Inc.

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

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

Epileptic seizures are due to the pathological collective activity of large cellular assemblies. A better understanding of this collective activity is integral to the development of novel diagnostic and therapeutic procedures. In contrast to reductionist analyses, which focus solely on small-scale characteristics of ictogenesis, here we follow a systems-level approach, which combines both small-scale and larger-scale analyses. Peri-ictal dynamics of epileptic networks are assessed by studying correlation within and between different spatial scales of intracranial electroencephalographic recordings (iEEG) of a heterogeneous group of patients suffering from pharmaco-resistant epilepsy. Epileptiform activity as recorded by a single iEEG electrode is determined objectively by the signal derivative and then subjected to a multivariate analysis of correlation between all iEEG channels. We find that during seizure, synchrony increases on the smallest and largest spatial scales probed by iEEG. In addition, a dynamic reorganization of spatial correlation is observed on intermediate scales, which persists after seizure termination. It is proposed that this reorganization may indicate a balancing mechanism that decreases high local correlation. Our findings are consistent with the hypothesis that during epileptic seizures hypercorrelated and therefore functionally segregated brain areas are re-integrated into more collective brain dynamics. In addition, except for a special sub-group, a highly significant association is found between the location of ictal iEEG activity and the location of areas of relative decrease of localised EEG correlation. The latter could serve as a clinically important quantitative marker of the seizure onset zone (SOZ).

Summary 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.