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Therapeutic hypothermia improves outcomes following neonatal hypoxic-ischaemic encephalopathy (HIE), reducing cases of death and severe disability such as cerebral palsy compared to normothermia management. However, when cooled children reach early school-age they have cognitive and motor impairments which are associated with underlying alterations to brain structure and white matter connectivity. It is unknown whether these differences in structural connectivity cause differences in functional connectivity between cooled children and healthy controls. Resting-state fMRI has been used to characterise static and dynamic functional connectivity in children, both with typical development and those with neurodevelopmental disorders. Previous studies of restingstate brain networks in children with HIE have focussed on the neonatal period. In this study, we used resting-state fMRI to investigate static and dynamic functional connectivity in children aged 6-8 years who were cooled for neonatal HIE without cerebral palsy (n = 22, median age [IQR] 7.08 [6.85-7.52] years), and healthy controls matched for age, sex and socioeconomic status (n = 20, median age [IQR] 6.75 [6.48-7.25] years). Using group independent component analysis, we identified 33 intrinsic connectivity networks consistent with those previously reported in children and adults. There were no case-control differences in the spatial maps of these intrinsic connectivity networks. We constructed subject-specific static functional connectivity networks by measuring pairwise Pearson correlations between component time courses, and found no case-control differences in functional connectivity after FDR correction. To study the time-varying organisation of resting-state networks, we used sliding-window correlations and deep clustering to investigate dynamic functional connectivity characteristics. We found k = 4 repetitively occurring functional connectivity states, which exhibited no case-control differences in dwell time, fractional occupancy, or state functional connectivity matrices. These results show that the spatiotemporal characteristics of resting-state brain networks in cooled children without severe disability are comparable to those in healthy controls at early school-age, despite underlying differences in brain structure and white matter connectivity. To our knowledge, this is the first study to investigate resting-state functional connectivity in children with HIE beyond the neonatal period, and the first to investigate dynamic functional connectivity in any children with HIE.

BACKGROUND AND PURPOSE Functional brain imaging using genetically encoded Ca2+ sensors in larval zebrafish is being developed for studying seizures and epilepsy as a more ethical alternative to rodent models. Despite this, few data have been generated on pharmacological mechanisms of action other than GABAA antagonism. Assessing larval responsiveness across multiple mechanisms is vital to test the translational power of this approach, as well as assessing its validity for detecting unwanted drug-induced seizures and testing antiepileptic drug efficacy. EXPERIMENTAL APPROACH Using light-sheet imaging, we systematically analysed the responsiveness of 4 days post fertilisation (dpf; which are not considered protected under European animal experiment legislation) transgenic larval zebrafish to treatment with 57 compounds spanning more than 12 drug classes with a link to seizure generation in mammals, alongside eight compounds with no such link. KEY RESULTS We show 4dpf zebrafish are responsive to a wide range of mechanisms implicated in seizure generation, with cerebellar circuitry activated regardless of the initiating pharmacology. Analysis of functional connectivity revealed compounds targeting cholinergic and monoaminergic reuptake, in particular, showed phenotypic consistency broadly mapping onto what is known about neurotransmitter-specific circuitry in the larval zebrafish brain. Many seizure-associated compounds also exhibited altered whole brain functional connectivity compared with controls. CONCLUSIONS AND IMPLICATIONS This work represents a significant step forward in understanding the translational power of 4dpf larval zebrafish for use in neuropharmacological studies and for studying the events driving transition from small-scale pharmacological activation of local circuits, to the large network-wide abnormal synchronous activity associated with seizures.

Despite impressive scientific advances in understanding the structure and function of the human brain, big challenges remain. A deep understanding of healthy and aberrant brain activity at a wide range of temporal and spatial scales is needed. Here we discuss, from an interdisciplinary network perspective, the advancements in physical and mathematical modeling as well as in data analysis techniques that, in our opinion, have potential to further advance our understanding of brain structure and function.

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.

We introduce harmonic cross-correlation decomposition (HCD) as a tool to detect and visualize features in the frequency structure of multivariate time series. HCD decomposes multivariate time series into spatiotemporal harmonic modes with the leading modes representing dominant oscillatory patterns in the data. HCD is closely related to data-adaptive harmonic decomposition (DAHD) [Chekroun and Kondrashov, Chaos 27, 093110 (2017)10.1063/1.4989400] in that it performs an eigendecomposition of a grand matrix containing lagged cross-correlations. As for DAHD, each HCD mode is uniquely associated with a Fourier frequency, which allows for the definition of multidimensional power and phase spectra. Unlike in DAHD, however, HCD does not exhibit a systematic dependency on the ordering of the channels within the grand matrix. Further, HCD phase spectra can be related to the phase relations in the data in an intuitive way. We compare HCD with DAHD and multivariate singular spectrum analysis, a third related correlation-based decomposition, and we give illustrative applications to a simple traveling wave, as well as to simulations of three coupled Stuart-Landau oscillators and to human EEG recordings.

Therapeutic hypothermia reduces the incidence of severe motor disability, such as cerebral palsy, following neonatal hypoxic-ischemic 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 school-age children treated with therapeutic hypothermia for neonatal hypoxic ischaemic encephalopathy at birth, who did not develop cerebral palsy (cases), and matched controls. Analysis of tract-level microstructure (33 cases, 36 controls) revealed correlations between total motor scores and fractional anisotropy, in cases but not controls, in the anterior thalamic radiation bilaterally, the inferior fronto-occipital fasciculus bilaterally and both the hippocampal and cingulate gyrus parts of the left cingulum. Analysis of structural brain networks (22 cases, 32 controls), in which edges were determined by probabilistic tractography and weighted by fractional anisotropy, revealed correlations between total motor scores and several whole-brain network metrics in cases but not controls. We then investigated edge-level association with motor function using the network-based statistic. This revealed subnetworks which exhibited group differences in the association between motor outcome and edge weights, for total motor scores as well as for balance and manual dexterity domain scores. All three of these subnetworks comprised numerous frontal lobe regions known to be associated with motor function, including the superior frontal gyrus and middle frontal gyrus. These findings demonstrate an association between impaired motor function and brain organisation in case children.

Neonatal encephalopathy leads to high risk of death and neurodevelopmental impairment, including cerebral palsy. Treatment with therapeutic hypothermia offers improved outcome. However, recent studies have shown that school-age children treated with therapeutic hypothermia for neonatal encephalopathy have reduced performance on cognitive and motor tests, attention difficulties, slower reaction times and reduced visuo-spatial processing abilities compared to typically developing controls, despite ruling out a diagnosis of cerebral palsy and having developmental scores around the normative mean at 18 months. We hypothesised that alterations in white matter microstructure and disruption to brain connectivity might underlie these symptoms. In this case-control study, we used diffusion-weighted imaging to investigate white matter microstructure and whole-brain structural connectivity in school-age children without cerebral palsy treated with therapeutic hypothermia for neonatal encephalopathy at birth, compared to controls matched for age, sex and socio-economic status.At the whole-brain level, tract-based spatial statistics of 33 cases (median age 6.9 years; range 6.0-7.9) and 36 controls confirmed reduced fractional anisotropy in cases in widespread areas of white matter (p < 0.05), particularly in the fornix, corpus callosum, anterior and posterior limbs of the internal capsule bilaterally, and the cingulum bilaterally. By parcellating the brain and performing probabilistic tractography, we then extracted structural brain networks, weighted by fractional anisotropy, for 22 cases (median age 7.0 years; range 6.0-7.8) and 32 controls. Network properties related to network integration and segregation were found to correlate with cognitive scores in cases but not controls. Network-based statistic analysis revealed weakened connectivity in cases (p = 0.0304) for a subnetwork involving the precuneus, thalamus, left superior parietal gyrus and left inferior temporal gyrus. Subnetworks were also found in which the dependence of cognitive outcome on connectivity was higher in cases than in controls, for both full-scale IQ (p = 0.0132) and processing speed (p = 0.0122), possibly reflecting delayed or disrupted white matter maturation. These analyses implicated numerous brain regions involved in visuo-spatial processing and attention, aligning with previous behavioural findings. Additionally, many of these regions have been highlighted as major hubs in the human connectome, which are thought to be vulnerable to damage due to their high metabolic rate.Our findings demonstrate that, despite the successes of therapeutic hypothermia, there remain aspects of brain structure which are impacted by neonatal encephalopathy. Therefore, these children may benefit from targeted therapeutic intervention.

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.

Psoriasis is a chronic inflammatory skin disease clinically characterized by the appearance of red colored, well-demarcated plaques with thickened skin and with silvery scales. Recent studies have established the involvement of a complex signalling network of interactions between cytokines, immune cells and skin cells called keratinocytes. Keratinocytes form the cells of the outermost layer of the skin (epidermis). Visible plaques in psoriasis are developed due to the fast proliferation and unusual differentiation of keratinocyte cells. Despite that, the exact mechanism of the appearance of these plaques in the cytokine-immune cell network is not clear. A mathematical model embodying interactions between key immune cells believed to be involved in psoriasis, keratinocytes and relevant cytokines has been developed. The complex network formed of these interactions poses several challenges. Here, we choose to study subnetworks of this complex network and initially focus on interactions involving \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {TNF}_{\alpha }$$\end{document}TNFα, IL-23/IL-17, and IL-15. These are chosen based on known evidence of their therapeutic efficacy. In addition, we explore the role of IL-15 in the pathogenesis of psoriasis and its potential as a future drug target for a novel treatment option. We perform steady state analyses for these subnetworks and demonstrate that the interactions between cells, driven by cytokines could cause the emergence of a psoriasis state (hyper-proliferation of keratinocytes) when levels of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {TNF}_{\alpha }$$\end{document}TNFα, IL-23/IL-17 or IL-15 are increased. The model results explain and support the clinical potentiality of anti-cytokine treatments. Interestingly, our results suggest different dynamic scenarios underpin the pathogenesis of psoriasis, depending upon the dominant cytokines of subnetworks. We observed that the increase in the level of IL-23/IL-17 and IL-15 could lead to psoriasis via a bistable route, whereas an increase in the level of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {TNF}_{\alpha }$$\end{document}TNFα would lead to a monotonic and gradual disease progression. Further, we demonstrate how this insight, bistability, could be exploited to improve the current therapies and develop novel treatment strategies for psoriasis.

In many real-world applications, we are interested in approximating black-box, costly functions as accurately as possible with the smallest number of function evaluations. A complex computer code is an example of such a function. In this work, a Gaussian process (GP) emulator is used to approximate the output of complex computer code. We consider the problem of extending an initial experiment (set of model runs) sequentially to improve the emulator. A sequential sampling approach based on leave-one-out (LOO) cross-validation is proposed that can be easily extended to a batch mode. This is a desirable property since it saves the user time when parallel computing is available. After fitting a GP to training data points, the expected squared LOO (ES-LOO) error is calculated at each design point. ES-LOO is used as a measure to identify important data points. More precisely, when this quantity is large at a point it means that the quality of prediction depends a great deal on that point and adding more samples nearby could improve the accuracy of the GP. As a result, it is reasonable to select the next sample where ES-LOO is maximised. However, ES-LOO is only known at the experimental design and needs to be estimated at unobserved points. To do this, a second GP is fitted to the ES-LOO errors and where the maximum of the modified expected improvement (EI) criterion occurs is chosen as the next sample. EI is a popular acquisition function in Bayesian optimisation and is used to trade-off between local/global search. However, it has a tendency towards exploitation, meaning that its maximum is close to the (current) "best" sample. To avoid clustering, a modified version of EI, called pseudo expected improvement, is employed which is more explorative than EI yet allows us to discover unexplored regions. Our results show that the proposed sampling method is promising.

Visual Abstract, 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.

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.

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.

The entorhinal cortex (EC) is one of the first areas to be disrupted in neurodegenerative diseases such as Alzheimer's disease and frontotemporal dementia. The responsiveness of individual neurons to electrical and environmental stimuli varies along the dorsal–ventral axis of the medial EC (mEC) in a manner that suggests this topographical organization plays a key role in neural encoding of geometric space. We examined the cellular properties of layer II mEC stellate neurons (mEC-SCs) in rTg4510 mice, a rodent model of neurodegeneration. Dorsoventral gradients in certain intrinsic membrane properties, such as membrane capacitance and afterhyperpolarizations, were flattened in rTg4510 mEC-SCs, while other cellular gradients [e.g., input resistance (Ri), action potential properties] remained intact. Specifically, the intrinsic properties of rTg4510 mEC-SCs in dorsal aspects of the mEC were preferentially affected, such that action potential firing patterns in dorsal mEC-SCs were altered, while those in ventral mEC-SCs were unaffected. We also found that neuronal oscillations in the gamma frequency band (30–80 Hz) were preferentially disrupted in the dorsal mEC of rTg4510 slices, while those in ventral regions were comparatively preserved. These alterations corresponded to a flattened dorsoventral gradient in theta-gamma cross-frequency coupling of local field potentials recorded from the mEC of freely moving rTg4510 mice. These differences were not paralleled by changes to the dorsoventral gradient in parvalbumin staining or neurodegeneration. We propose that the selective disruption to dorsal mECs, and the resultant flattening of certain dorsoventral gradients, may contribute to disturbances in spatial information processing observed in this model of dementia.SIGNIFICANCE STATEMENTThe medial entorhinal cortex (mEC) plays a key role in spatial memory and is one of the first areas to express the pathological features of dementia. Neurons of the mEC are anatomically arranged to express functional dorsoventral gradients in a variety of neuronal properties, including grid cell firing field spacing, which is thought to encode geometric scale. We have investigated the effects of tau pathology on functional dorsoventral gradients in the mEC. Using electrophysiological approaches, we have shown that, in a transgenic mouse model of dementia, the functional properties of the dorsal mEC are preferentially disrupted, resulting in a flattening of some dorsoventral gradients. Our data suggest that neural signals arising in the mEC will have a reduced spatial content in dementia.

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 seizure activity manifests as complex spatio-temporal dynamics on the clinically relevant macroscopic scale. These dynamics are known to arise from spatially heterogeneous tissue, but the relationship between specific spatial abnormalities and epileptic rhythm generation is not well understood. We formulate a simplified macroscopic modelling framework with which to study the role of spatial heterogeneity in the generation of epileptiform spatio-temporal rhythms. We characterize the overall model dynamics in terms of spontaneous activity and excitability and demonstrate normal and abnormal spreading of activity. We introduce a means to systematically investigate the topology of abnormal sub-networks and explore its impact on spontaneous and stimulus-evoked rhythmic dynamics. This computationally efficient framework complements results from detailed biophysical models, and allows the testing of specific hypotheses about epileptic dynamics on the macroscopic scale.