BACKGROUND: Schizophrenia manifests as a constellation of both psychotic symptoms (eg. hallucinations, delusions) and so-called negative symptoms. The latter includes anhedonia, avolition, amotivation and they are the strongest predictors of disability. Resting state fMRI (rsfMRI) has demonstrated that the brain is organized into low-dimensional number (7-17) brain networks and this allowed visualization of the relationship between symptom severity and large-scale brain network organization. Traditional rsfMRI analyses have assumed that the spatial organization of these networks are spatially invariant between individuals. This dogma has recently been overturned with the observation that the spatial organization of these brain networks shows significant variation between individuals. We sought to determine if previously observed relationships between symptom severity and network connectivity are actually due to individual differences in spatial organization. METHODS: 44 participants diagnosed with schizophrenia underwent rsfMRI scans and clinical assessment. A multivariate pattern analysis was used to examine how each participant’s whole brain functional connectivity correlates with ‘negative’ symptom severity. RESULTS: Brain connectivity to a region of the right dorso-lateral pre-frontal cortex (r DLPFC) correlates with symptom severity. The result is explained by the individual differences in the topographic distribution of two brain networks: the default mode network (DMN) and the task positive network (TPN). Both networks demonstrate strong (r~0.49) and significant (p<0.001) relationships between topography and symptom severity. For individuals with low symptom severity, this critical region is a part of the DMN. In highly symptomatic individuals, this region is a part of the TPN. CONCLUSIONS: Previously overlooked individual variation in brain organization is tightly linked to individual variation in schizophrenia symptom severity. The recognition of critical links between network topology and pathological symptomology may serve as a guide for future interventions aimed at establishing causal relationships between certain critical regions of the brain and cognitive and behavioral phenotypes. Thus, fMRI and network topology may be translated to a clinical setting as a viable, individual-centered treatment option. / 2020-06-17T00:00:00Z

Human structural and functional brain architecture is increasingly studied by applying the mathematical framework of complex networks to data from magnetic resonance imaging. Connections (edges) in such brain networks are commonly constructed using correlations of features between pairs of brain regions, such as regional morphology (across participants) or neurophysiological time series (within participants). Subsequent analyses frequently focus on summary network statistics calculated using the strongest correlations, but often neglect potential underlying shifts within the correlation distribution. This thesis presents methods for the construction and analysis of correlation-derived structural and functional brain networks, focusing on the implications of changes within the correlation distribution. First, schizophrenia is considered as an example disease which is known to present a reduction in mean correlation between regional neurophysiological time series. Previous studies reported increased network randomisation in schizophrenia, but these results may have been driven by inclusion of a greater number of noisy edges in patients’ networks, based on retention of a fixed proportion of the strongest edges during network thresholding. Here, a novel probabilistic thresholding procedure is applied, based on the realisation that the strongest edges are not necessarily most likely to be true following adjustment of edge probabilities for effects of participant in-scanner motion. Probabilistically thresholded functional networks show decreased randomness, and increased consistency across participants. Further, applying probabilistic thresholding eliminates increased network randomisation in schizophrenia, supporting the hypothesis that previously reported group differences originated in the application of standard thresholding approaches to patient networks with decreased functional correlations. Subsequently, healthy adolescent development is studied, to help understand the frequent emergence of psychiatric disorders in this period. Importantly, both structural and functional brain networks undergo maturational shifts in correlation distribution over adolescence. Due to reliance of structural correlation networks on a group of subjects, previous studies of adolescent structural network development divided groups into discrete age-bins. Here, a novel sliding-window method is used to describe adolescent development of structural correlation networks in a continuous manner. Moreover, networks are probabilistically thresholded by retaining edges that are most consistent across bootstrapped samples of participants, leading to clearer maturational trajectories. These structural networks show non-linear trajectories of adolescent development driven by changes in association cortical areas, compatible with a developmental process of pruning combined with consolidation of surviving connections. Robustness of the results is demonstrated using extensive sensitivity analyses. Finally, adolescent developmental changes in functional network architecture are described, focusing on the characterisation of unthresholded (fully weighted) networks. The distribution of functional correlations presents a non-uniform shift over adolescence. Initially strong cortical connections to primary sensorimotor areas further strengthen into adulthood, whereas association cortical and subcortical edges undergo a subtler reorganisation of functional connectivity. Furthermore, individual subcortical regions show distinct maturational profiles. Patterning of maturation according to known functional systems is affirmed by partitioning regions developing at similar rates into maturational modules. Taken together, this thesis comprises novel methods for the characterisation of disease-related and normative developmental changes in structural and functional correlation brain networks. These methods are generalizable to a wide range of scenarios, beyond the specific disease and developmental age-ranges presented herein.

Le concept de réseaux - l'idée que deux ou plusieurs nœuds distribués peuvent interagir pour produire un phénomène - a longtemps été utilisé dans la recherche et le traitement de l'épilepsie. En effet, même dans les épilepsies considérées comme «focales», les perspectives cliniques et théoriques soulignent l'importance des questions suivantes, à savoir : 1) comment pouvons-nous localiser, partitionner et caractériser les réseaux impliqués dans l'épilepsie et 2) dans quelle mesure ces réseaux interagissent avec le réseau cérébral à grande échelle? Récemment, la notion de réseaux pathologiques dans l'épilepsie a été renforcée par l’apport de la neuroimagerie, avec en particulier le paradigme 'd'état de repos' qui reconnaît l'information inhérente à l'activité spontanée du cerveau, en plus de celle liée aux événements transitoires exogènes et paroxystiques endogènes.En tirant partie de ces techniques, ce travail fournit de nouveaux concepts sur 1) les relations multimodales et le couplage entre l’hémodynamique et la connectivité fonctionnelle électro physiologique aussi bien dans les cortex épileptiques que non affectés, 2) les processus pathologiques affectant l’homéostasie ionique et les dysfonctionnements neuronaux dans les réseaux épileptiques, 3) les interactions au niveau de groupe entre les réseaux épileptiques et les propriétés topologiques du cerveau, et 4) comment les interactions entre la pathologie épileptique et des propriétés uniques du réseau cérébral peuvent contribuer à produire des effets cliniques au niveau du réseau. / The concept of networks – the idea that two or more distributed nodes may interact to produce a phenomenon – has long been of utility in research into and the treatment of epilepsy. Indeed, even in epilepsies deemed ‘focal’, clinical and theoretical insights underline the importance of the questions 1) how can we localize, partition and characterize networks involved in epilepsy, and 2) to what extent do such networks interact with the brain network at large? Recently, the notion of pathological network effects in epilepsy has been reinvigorated with input from neuroimaging, especially a ‘resting-state’ paradigm that recognizes the systemic information inherent in the ongoing activity of the brain in addition to that provided when it is disturbed by transient exogenous events and endogenous paroxysms. By leveraging these techniques, this work provides novel insights into 1) the multimodal relationships and coupling between haemodynamic- and electrophysiologically-defined functional connectivity, both in epileptic and unaffected cortices 2) pathological processes affecting ionic homeostasis and neural dysfunction in epileptic networks 3) group-level interactions between epileptic networks and brain network topological properties and 4) how interactions between epileptic pathology and unique brain network properties may contribute to produce to clinical effects at the network level. This work opens up new perspectives on the understanding of network effects in epilepsy, sources of variance in their analysis, the biological processes occurring in parallel and contributing to them and their role in an individualized understanding of pathology.

In recent years, deep learning has made a significant impact in various fields – helping to push the state-of-the-art forward in many application domains. Convolutional Neural Networks (CNN) have been applied successfully to tasks such as visual object detection, image super-resolution, and video action recognition while Long Short-term Memory (LSTM) and Transformer networks have been used to solve a variety of challenging tasks in natural language processing. However, these popular deep learning architectures (i.e., CNNs, LSTMs, and Transformers) can only handle data that can be represented as grids or sequences. Due to this limitation, many existing deep learning approaches do not generalize to problem domains where the data is represented as graphs – social networks in social network analysis or molecular graphs in chemoinformatics, for instance. The goal of this thesis is to help bridge the gap by studying deep learning solutions that can handle graph data naturally. In particular, we explore deep learning-based approaches in the following areas. 1. Graph Attention. In the real-world, graphs can be both large – with many complex patterns – and noisy which can pose a problem for effective graph mining. An effective way to deal with this issue is to use an attention-based deep learning model. An attention mechanism allows the model to focus on task-relevant parts of the graph which helps the model make better decisions. We introduce a model for graph classification which uses an attention-guided walk to bias exploration towards more task-relevant parts of the graph. For the task of node classification, we study a different model – one with an attention mechanism which allows each node to select the most task-relevant neighborhood to integrate information from. 2. Graph Representation Learning. Graph representation learning seeks to learn a mapping that embeds nodes, and even entire graphs, as points in a low-dimensional continuous space. The function is optimized such that the geometric distance between objects in the embedding space reflect some sort of similarity based on the structure of the original graph(s). We study the problem of learning time-respecting embeddings for nodes in a dynamic network. 3. Brain Network Discovery. One of the fundamental tasks in functional brain analysis is the task of brain network discovery. The brain is a complex structure which is made up of various brain regions, many of which interact with each other. The objective of brain network discovery is two-fold. First, we wish to partition voxels – from a functional Magnetic Resonance Imaging scan – into functionally and spatially cohesive regions (i.e., nodes). Second, we want to identify the relationships (i.e., edges) between the discovered regions. We introduce a deep learning model which learns to construct a group-cohesive partition of voxels from the scans of multiple individuals in the same group. We then introduce a second model which can recover a hierarchical set of brain regions, allowing us to examine the functional organization of the brain at different levels of granularity. Finally, we propose a model for the problem of unified and group-contrasting edge discovery which aims to discover discriminative brain networks that can help us to better distinguish between samples from different classes.

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In recent years, deep learning has made a significant impact in various fields – helping to push the state-of-the-art forward in many application domains. Convolutional Neural Networks (CNN) have been applied successfully to tasks such as visual object detection, image super-resolution, and video action recognition while Long Short-term Memory (LSTM) and Transformer networks have been used to solve a variety of challenging tasks in natural language processing. However, these popular deep learning architectures (i.e., CNNs, LSTMs, and Transformers) can only handle data that can be represented as grids or sequences. Due to this limitation, many existing deep learning approaches do not generalize to problem domains where the data is represented as graphs – social networks in social network analysis or molecular graphs in chemoinformatics, for instance. The goal of this thesis is to help bridge the gap by studying deep learning solutions that can handle graph data naturally. In particular, we explore deep learning-based approaches in the following areas. 1. Graph Attention. In the real-world, graphs can be both large – with many complex patterns – and noisy which can pose a problem for effective graph mining. An effective way to deal with this issue is to use an attention-based deep learning model. An attention mechanism allows the model to focus on task-relevant parts of the graph which helps the model make better decisions. We introduce a model for graph classification which uses an attention-guided walk to bias exploration towards more task-relevant parts of the graph. For the task of node classification, we study a different model – one with an attention mechanism which allows each node to select the most task-relevant neighborhood to integrate information from. 2. Graph Representation Learning. Graph representation learning seeks to learn a mapping that embeds nodes, and even entire graphs, as points in a low-dimensional continuous space. The function is optimized such that the geometric distance between objects in the embedding space reflect some sort of similarity based on the structure of the original graph(s). We study the problem of learning time-respecting embeddings for nodes in a dynamic network. 3. Brain Network Discovery. One of the fundamental tasks in functional brain analysis is the task of brain network discovery. The brain is a complex structure which is made up of various brain regions, many of which interact with each other. The objective of brain network discovery is two-fold. First, we wish to partition voxels – from a functional Magnetic Resonance Imaging scan – into functionally and spatially cohesive regions (i.e., nodes). Second, we want to identify the relationships (i.e., edges) between the discovered regions. We introduce a deep learning model which learns to construct a group-cohesive partition of voxels from the scans of multiple individuals in the same group. We then introduce a second model which can recover a hierarchical set of brain regions, allowing us to examine the functional organization of the brain at different levels of granularity. Finally, we propose a model for the problem of unified and group-contrasting edge discovery which aims to discover discriminative brain networks that can help us to better distinguish between samples from different classes.

We present a rigorous yet accessible introduction to structures on finite sets foundational for a formal study of complex networks. This includes a thorough treatment of binary relations, distance spaces, their properties and similarities. Correspondences between relations and graphs are given and a brief introduction to graph theory is followed by a more detailed study of cohesiveness and centrality. We show how graph degeneracy is equivalent to the concept of k-cores, which give a measure of the cohesiveness or interconnectedness of a subgraph. We then further extend this to d-cores of directed graphs. After a brief introduction to topology, focusing on topological spaces from distances, we present a historical discussion on the early developments of algebraic topology. This is followed by a more formal introduction to simplicial homology where we define the homology groups. In the context of algebraic topology, the d-cores of a digraph give rise to a partially ordered set of subgraphs, leading to a set of filtrations that is two-dimensional in nature. Directed clique complexes of digraphs are defined in order to encode the directionality of complete subdigraphs. Finally, we apply these methods to the neuronal network of C.elegans. Persistent homology with respect to directed core filtrations as well as robustness of homology to targeted edge percolations in different directed cores is analyzed. Much importance is placed on intuition and on unifying methods of such dispersed disciplines as sociology and network neuroscience, by rooting them in pure mathematics. / Vi presenterar en rigorös men lättillgänglig introduktion till de abstrakta strukturer på ändliga mängder som är grundläggande för en formell studie av komplexa nätverk. Detta inkluderar en grundlig redogörelse av binära relationer och distansrum, deras egenskaper samt likheter. Korrespondenser mellan olika typer av relationer och grafer förklaras och en kort introduktion till grafteori följs av en mer detaljerad studie av sammanhållning och centralitet. Vi visar hur begreppet 'degeneracy' är ekvivalent med begreppet k-kärnor (eng: k-cores), vilket ger ett mått på sammanhållningen hos en delgraf. Vi utökar sedan detta till konceptet d-kärnor (eng: d-cores) för riktade grafer. Efter en kort introduktion till topologi med fokus på topologiska rum från distansrum, så presenterar vi en historisk diskussion kring den tidiga utvecklingen av algebraisk topologi. Detta följs av en mer formell introduktion till homologi, där vi bl.a. definierar homologigrupperna. Vi definierar sedan så kallade riktade klick-komplex som simplistiska komplex (eng: simplicial complexes) från riktade grafer, där d-kärnorna av en riktad graf då ger upphov till filtrerade komplex i två parametrar. Persistent homologi med avseende på dessa riktade kärnfiltreringar såväl som robusthet mot kantpercolationer i olika kärnor analyseras sedan för det neurala nätverket hos C.Elegans. Stor vikt läggs vid intuition och förståelse, samt vid att förena metodiker för så spridda discipliner som sociologi och neurovetenskap.

Le cerveau humain est un réseau «large-échelle» formé de régions corticales distribuées et fonctionnellement interconnectées. Le traitement de l'information par le cerveau est un processus dynamique mettant en jeu une réorganisation rapide des réseaux cérébraux fonctionnels, sur une échelle de temps très courte (inférieure à la seconde). Dans le champ des neurosciences cognitives, deux grandes questions restent ouvertes concernant ces réseaux. D'une part, est-il possible de suivre leur dynamique spatio-temporelle avec une résolution temporelle nettement supérieure à celle de l'IRM fonctionnelle? D'autre part, est-il possible de mettre en évidence des différences significatives dans ces réseaux lorsque le cerveau traite des stimuli (visuels, par exemple) ayant des caractéristiques différentes. Ces deux questions ont guidé les développements méthodologiques élaborés dans cette thèse. En effet, de nouvelles méthodes basées sur l'électroencéphalographie sont proposées. Ces méthodes permettent, d'une part de suivre la reconfiguration dynamique des réseaux cérébraux fonctionnels à une échelle de temps inférieure à la seconde. Elles permettent, d'autre part, de comparer deux réseaux cérébraux activés dans des conditions spécifiques. Nous proposons donc un nouvel algorithme bénéficiant de l'excellente résolution temporelle de l'EEG afin de suivre la reconfiguration rapide des réseaux fonctionnels cérébraux à l'échelle de la milliseconde. L'objectif principal de cet algorithme est de segmenter les réseaux cérébraux en un ensemble d' «états de connectivité fonctionnelle» à l'aide d'une approche de type « clustering ». L'algorithme est basé sur celui des K-means et a été appliqué sur les graphes de connectivité obtenus à partir de l'estimation des valeurs de connectivité fonctionnelle entre les régions d'intérêt considérées. La seconde question abordée dans ce travail relève de la mesure de similarité entre graphes. Ainsi, afin de comparer des réseaux de connectivité fonctionnelle, nous avons développé un algorithme (SimNet) capable de quantifier la similarité entre deux réseaux dont les nœuds sont définis spatialement. Cet algorithme met en correspondance les deux graphes en « déformant » le premier pour le rendre identique au second sur une contrainte de coût minimal associée à la déformation (insertion, suppression, substitution de nœuds et d’arêtes). Il procède selon deux étapes, la première consistant à calculer une distance sur les nœuds et la seconde une distance sur les arrêtes. Cet algorithme fournit un indice de similarité normalisé: 0 pour aucune similarité et 1 pour deux réseaux identiques. Il a été évalué sur des graphes simulés puis comparé à des algorithmes existants. Il montre de meilleures performances pour détecter la variation spatiale entre les graphes. Il a également été appliqué sur des données réelles afin de comparer différents réseaux cérébraux. Les résultats ont montré des performances élevées pour comparer deux réseaux cérébraux réels obtenus à partir l'EEG à haute résolution spatiale, au cours d'une tâche cognitive consistant à nommer des éléments de deux catégories différentes (objets vs animaux). / The human brain is a "large-scale" network consisting of distributed and functionally interconnected regions. The information processing in the brain is a dynamic process that involves a fast reorganization of functional brain networks in a very short time scale (less than one second). In the field of cognitive neuroscience, two big questions remain about these networks. Firstly, is it possible to follow the spatiotemporal dynamics of the brain networks with a temporal resolution significantly higher than the functional MRI? Secondly, is it possible to detect a significant difference between these networks when the brain processes stimuli (visual, for example) with different characteristics? These two questions are the main motivations of this thesis. Indeed, we proposed new methods based on dense electroencephalography. These methods allow: i) to follow the dynamic reconfiguration of brain functional networks at millisecond time scale and ii) to compare two activated brain networks under specific conditions. We propose a new algorithm benefiting from the excellent temporal resolution of EEG to track the fast reconfiguration of the functional brain networks at millisecond time scale. The main objective of this algorithm is to segment the brain networks into a set of "functional connectivity states" using a network-clustering approach. The algorithm is based on K-means and was applied on the connectivity graphs obtained by estimation the functional connectivity values between the considered regions of interest. The second challenge addressed in this work falls within the measure of similarity between graphs. Thus, to compare functional connectivity networks, we developed an algorithm (SimNet) that able to quantify the similarity between two networks whose node coordinates is known. This algorithm maps one graph to the other using different operations (insertion, deletion, substitution of nodes and edges). The algorithm is based on two main parts, the first one is based on calculating the nodes distance and the second one is to calculate the edges distance. This algorithm provides a normalized similarity index: 0 for no similarity and 1 for two identical networks. SimNet was evaluated with simulated graphs and was compared with previously-published graph similarity algorithms. It shows high performance to detect the similarity variation between graphs involving a shifting of the location of nodes. It was also applied on real data to compare different brain networks. Results showed high performance in the comparison of real brain networks obtained from dense EEG during a cognitive task consisting in naming items of two different categories (objects vs. animals).

It is estimated that about 35-40% of adults in the U.S. suffer from insufficient sleep. Chronic sleep deprivation has become a prevalent phenomenon because of contemporary lifestyle and work-related factors. Sleep deprivation can reduce the capabilities and efficiency of attentional performance by impairing perception, increasing effort to maintain concentration, as well as introducing vision disturbance. Thus, it is important to understand the neural mechanisms behind how chronic sleep deprivation impairs sustained attention. In recent years, more attention has been paid to the study of the integration between anatomically distributed and functionally connected brain regions. Functional connectivity has been widely used to characterize brain functional integration, which measures the statistical dependency between neurophysiological events of the human brain. Further, evidence from recent studies has shown the non-stationary nature of brain functional connectivity, which may reveal more information about the human brain. Thus, the objective of this thesis is to investigate the effects of chronic sleep deprivation on sustained attention from the perspective of dynamic functional connectivity. A modified spatial cueing paradigm was used to assess human sustained attention in rested wakefulness and chronic sleep deprivation conditions. Partial least squares approach was applied to distinguish brain functional connectivity for the experimental conditions. With the integration of a sliding-window approach, dynamic patterns of brain functional connectivity were identified in two experimental conditions. The brain was modeled as a series of dynamic functional networks in each experimental condition. Graph theoretic analysis was performed to investigate the dynamic properties of brain functional networks, using network measures of clustering coefficient and characteristics path length. In the chronic sleep deprivation condition, a compensation mechanism between highly clustered organization and ineffective adaptability of brain functional networks was observed. Specifically, a highly clustered organization of brain functional networks was illustrated with a large clustering coefficient. This organization suggested that brain utilizes more connections to maintain attention in the chronic sleep deprivation condition. A smaller impact of clustering coefficient variation on characteristics path lengths indicated an ineffective adaptability of brain functional networks in the chronic sleep deprivation condition. In the rested wakefulness condition, brain functional networks showed the small-world topology in general, with the average small-world topology index larger than one. Small-world topology was identified as an optimal network structure with the balance between local information processing and global integration. Given the fluctuating values of the index over time, small-world brain networks were observed in most cases, indicating an effective adaptability of the human brain to maintain the dominance of small-world networks in the rested wakefulness condition. On the contrary, given that the average small-world topology index was smaller than one, brain functional networks generally exhibited random network structure. From the perspective of dynamic functional networks, even though there were few cases showing small-world brain networks, brain functional networks failed to maintain the dominance of small-world topology in the chronic sleep deprivation condition. In conclusion, to the best of our knowledge this thesis was the first to investigate the effects of chronic sleep deprivation on sustained attention from the perspective of dynamic brain functional connectivity. A compensation mechanism between highly clustered organization and ineffective adaptability of brain functional networks was observed in the chronic sleep deprivation condition. Furthermore, chronic sleep deprivation impaired sustained attention by reducing the effectiveness of brain functional networks' adaptability, resulting in the disrupted dominance of small-world brain networks.

Les crises épileptiques sont des épisodes paroxysmiques d'activité cérébrale hypersynchrone. Ce travail de thèse s'attache à examiner les mécanismes de propagation des crises d'épilepsie sur une échelle temporelle lente et une grande échelle spatiale dans le cerveau humain et à les appliquer au contexte clinique. Chez les patients souffrant d'épilepsie partielle réfractaire, les crises débutent dans certaines régions localisées du cerveau, dénommées zone épileptogène, avant de recruter des régions distantes. Le succès de l'ablation chirurgicale de la zone epileptogène dépend principalement de sa délimitation adéquate, un problème souvent épineux en pratique clinique. À cela s'ajoute notre compréhension parcellaire des mécanismes à l'origine des crises et de leur propagation. Nous utilisons un modèle mathématique de masse neuronale reproduisant le décours temporel de l'activité moyenne critique et intercritique d'une région cérébrale, guidé de manière autonome par une variable permittive lente. Nous introduisons tout d'abord un couplage permittif lent entre ces masses neuronales, afin de révéler l'importance de la variété lente dans le recrutement des régions cérébrales dans la crise. Nous présentons ensuite un pipeline de traitement des données structurelles et de diffusion IRM pour reconstruire automatiquement le cerveau virtuel d'un patient. Nous utilisons ensuite une analyse de stabilité linéaire et la connectivité large-échelle pour prédire la zone de propagation. Nous appliquons notre méthode à un jeu de données de 15 patients épileptiques et démontrons l'importance du connectome pour prédire la direction de propagation des crises. / Epileptic seizures are paroxysmal hypersynchronizations of brain activity, spanning several temporal and spatial scales. In the present thesis, we investigate the mechanisms of epileptic seizure propagation on a slow temporal and large spatial scale in the human brain and apply them to a clinical context. For patients with partial refractory epilepsy, seizures arise from a localized region of the brain, the so-called epileptogenic zone, before recruiting distant regions. Success of the resective surgery of the epileptogenic zone depends on its correct delineation, which is often difficult in clinical practice. Furthermore, the mechanisms of seizure onset and recruitment are still largely unknown. We use a mathematical neural mass model to reproduce the time course of interictal and ictal mean activity of a brain region, in which the switching between these states is guided by an autonomous slow permittivity variable. We first introduce a slow permittivity coupling function between these neural masses, hypothesizing the importance of the slow manifold in the recruitment of brain regions into the seizure. Before exploring large-scale networks of such coupled systems, we present a processing pipeline for automatic reconstruction of a patient's virtual brain, including surface and connectivity (i.e., connectome), using structural and diffusion MRI, and tractography methods. Using linear stability analysis and large-scale connectivity, we predict the propagation zone. We apply our method to a dataset of 15 epileptic patients and establish the importance of the connectome in determining large-scale propagation of epileptic seizures.