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Directed functional connectivity in patients with focal epilepsy using high density scalp EEG

LUIS COITO, Ana Luisa

Abstract

There is increasing evidence that epileptic activity involves widespread brain networks rather than single sources. Using high-density Electroencephalography (EEG), Electrical Source Imaging (ESI) and Granger-causality measures, we investigated whole-brain directed functional connectivity in left and right Temporal lobe Epilepsy (LTLE and RTLE, respectively), during interictal spikes and spike-free epochs, and in healthy subjects. This allowed us to identify the main drivers and connectivity patterns of interictal epileptic activity in TLE, and of the resting-state in both TLE and healthy subjects. We further found that LTLE and RTLE had different interictal network patterns, and that resting-state outflows were decreased and had a different pattern in TLE vs healthy controls. Our studies show that whole-brain EEG-based directed functional connectivity analysis is a very promising tool to investigate how brain regions driver others during epileptic and non-epileptic activity. This could importantly contribute for epilepsy presurgical planning, especially in patients whose focus is not clear by other already available [...]

LUIS COITO, Ana Luisa. Directed functional connectivity in patients with focal epilepsy using high density scalp EEG. Thèse de doctorat : Univ. Genève et Lausanne, 2016, no.

Neur. 173

URN : urn:nbn:ch:unige-881438

DOI : 10.13097/archive-ouverte/unige:88143

Available at:

http://archive-ouverte.unige.ch/unige:88143

Disclaimer: layout of this document may differ from the published version.

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DOCTORAT EN NEUROSCIENCES des Universités de Genève

et de Lausanne

UNIVERSITÉ DE GENÈVE FACULTÉ DES SCIENCES Professeur Christoph Michel, directeur de thèse

Professeur Serge Vulliémoz, co-directeur de thèse

TITRE DE LA THÈSE

DIRECTED FUNCTIONAL CONNECTIVITY IN PATIENTS WITH FOCAL EPILEPSY USING HIGH-DENSITY SCALP EEG

THÈSE Présentée à la Faculté des Sciences de l’Université de Genève

pour obtenir le grade de Docteure en Neurosciences

par

Ana Luisa LUIS COITO

du Portugal

Thèse N° 173 Genève

Editeur ou imprimeur : Université de Genève 2016

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"It is essential to understand our brains in some detail if we are to assess correctly our place in this vast and complicated universe we see all around us."

Francis Crick

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Acknowledgements

First of all, I am very grateful to my supervisors Professors Serge Vulliémoz, Christoph Michel and Gijs Plomp for their support, supervision, and help during these years. It has been a great pleasure for me to work with you all. Thank you so much Serge for your teachings and guidance, and for always finding time in spite of your busy clinical work. I have undoubtedly learnt a lot with you about EEG and epilepsy. I am also very thankful to Christoph for accepting and allowing me to do my PhD in his lab, and for all the valuable comments and remarks on my work. I am very grateful to Gijs for his supervision and valuable discussions about brain connectivity methodology.

I am very thankful to Professors Fernando Lopes da Silva, Fabrice Wendling, Adrian Guggisberg and Dimitri van de Ville for accepting to review and be part of my thesis committee.

I owe a sincere thanks to Prof. Lopes da Silva for our inspiring conversation 4 years ago in Instituto Superior Técnico, where, knowing that I really wanted to work with EEG and epilepsy, he recommended me to apply to the lab of Prof. Christoph Michel.

I would like to thank all the collaborators of this work. A special thanks to Prof. Margitta Seeck for receiving me so well in the Epilepsy Unit of the University Hospital of Geneva and for all her valuable comments and advices. I am thankful to Pieter van Mierlo from Ghent University for our many discussions about connectivity, for the advices and always useful comments, and for reading the introduction of this manuscript. I am also very grateful to Thibault Verhoeven, from Ghent University, for applying machine learning techniques to our connectivity data to automatically diagnose and lateralise temporal lobe epilepsy. I thank also Eugenio Abela and Prof. Roland Wiest, from Bern University, as well as Yvonne Höller, Aljoscha Thomschewski and Prof. Eugen Trinka, from Salzburg University, for providing us some clinical data.

Je voudrais aussi remercier tous meus collègues et amis du Functional Brain Mapping Lab pour le soutien, aide, conversations et amusement pendant ces années. Thank you Giannarita Iannotti for the good moments, trips, fun, support, friendship, yoga...I am glad that beyond colleagues, we became good friends and that we could share the time of our PhD together. Mélanie Genetti, thank you for our many inspiring conversations and wise advices. Francesca Pittau, thank you for our many nice professional and non- professional conversations and for your contribution for my deeper understanding of the clinical aspects of epilepsy. Laurent Spinelli thank you for reading the introduction of this manuscript and for the useful comments on it, and also thank you for all your technical help and for all our conversations. Thank you Vincent Rochas, Markus Gschwind, Sara Baldini, and all those with whom I have shared the office on the fourth floor during these years, for all your support. A special thanks to Frederic Grouiller for providing his scripts for preprocessing of structural MRI images. I am also very thankful to all the other FBM lab members, who in one way or another, have all helped and contributed for my work.

Ich will Sebastian für all seine Unterstützung danken und dafür, dass er immer da ist. Ich möchte auch Marietta und Rudi für all ihre Unterstützung, Hilfe und Freundlichkeit danken.

Last but not least (como se costuma dizer, os últimos são os primeiros), quero agradecer aos meus pais Filomena e Alberto por todo o apoio, compreensão e educação que me têm dado e que sempre vão dar.

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Summary

There is increasing evidence that epileptic activity involves widespread brain networks rather than isolated single sources. A better understanding about the organization and dynamics of these brain networks is crucial for understanding the onset and spread of epileptic activity and cognitive impairments in epilepsy patients. Furthermore, it could add an important diagnostic and prognostic value, particularly for patients who do not respond to antiepileptic drug treatment and are candidates for a surgical resection of the epileptogenic zone.

Mesial temporal Lobe Epilepsy (TLE) is the most frequent type of pharmaco-resistant epilepsy and it is characterized by recurrent focal seizures arising from mediotemporal structures. The most common treatment for these patients is neurosurgery to remove the cortical zone responsible for the initiation of the epileptic seizures. There is also strong evidence that left and right TLE (LTLE and RTLE, respectively) are distinct entities, with different cognitive and structural impairments.

EEG measures directly and with a high temporal resolution neuronal electrical activity, which turns it very suitable to study dynamic brain processes, such as epileptic activity. However, EEG does not indicate the location of the active neuronal populations at a given moment, because measurements at the scalp reflect the summed neuro-electrical currents generated within the brain. Electric Source Imaging (ESI) can be used to reconstruct the source activity that underlies a given distribution of scalp potentials recorded at a given time point. Clinical studies have shown that ESI reliably estimates the localization of the seizure onset zone and the epileptogenic zone. Moreover, studies have shown that brain connectivity should be investigated at the level of source signals rather than scalp electrodes.

Brain interactions in TLE can be studied using the concept of brain connectivity. Specifically, functional connectivity measures the statistical dependencies between different neuronal signals. Directed functional connectivity investigates directional relationships between brain regions, i.e., the causal influence that one brain region exerts onto another. It can be investigated using data-driven techniques based on the concept of Granger-causality, such as Partial Directed Coherence (PDC).

The aim of this project was to assess the directed functional connectivity changes in patients with LTLE and RTLE in order to improve the characterization of epileptic networks, and with that, to provide a better management and planning of epilepsy surgery candidates, and also, to possibly find new biomarkers for early diagnosis of epilepsy.

First of all, we developed a methodological pipeline to investigate whole-brain directed functional connectivity between brain areas using source signals derived from high-density EEG. This analysis includes: ESI using individual head models, parcellation of the grey matter in 82 regions, fixation of the dipole orientation for each region, computation of the spectral power in the source space, and Granger-causal modeling (weighted Partial Directed Coherence) computation.

We then applied this approach to study brain networks organisation in TLE patients. First, we investigated the whole-brain dynamic pattern of interictal directed functional connectivity in LTLE and RTLE. We identified the main drivers and the network patterns of interictal epileptic activity in LTLE and RTLE. We further found that LTLE and RTLE have different network patterns: RTLE patients showed

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stronger connectivity targeting the contralateral hemisphere in comparison with LTLE patients, consistent with differences in neuropsychological impairments between the groups. This study offered an improved characterization of the dynamic behaviour of interictal spike networks.

However, interictal spikes are not always visible during scalp EEG recordings. But even though, seizure relapse and behavioural impairments can be observed. Therefore, a better characterisation of abnormal networks in the absence of interictal spikes could have an important diagnostic and prognostic value. In our second clinical study, we investigated whether resting-state directed functional connectivity was altered in EEG epochs free of interictal spikes in LTLE and RTLE when compared to healthy controls. We found that resting-state outflows are decreased in TLE patients even in the absence of interictal spikes and that these alterations are correlated with clinical and behavioural parameters. We further found that patients and healthy controls had a different network pattern. These resting-state network alterations in the absence of interictal spikes strengthens the view of chronic and progressive network changes in TLE, and could constitute an important biomarker of TLE. In a follow-up study, we used these outflow values as features for a classification system (using Random Forests) and were able to obtain an accuracy of 90% for both diagnosing TLE (classifier: TLE vs healthy controls) and lateralizing TLE (classifier: LTLE vs RTLE). This demonstrates the potential of resting-state EEG-based directed functional connectivity for automatically diagnose and lateralize TLE.

We then applied the same framework to study resting-state whole-brain EEG-based directed functional connectivity in healthy subjects as compared to surrogate data. We reliably identified the main driving regions of the resting brain, which were consistent with the Default-Mode-Network spatial features, and our results pointed to the posterior cingulate cortex as the main driver of information flow in the brain at rest.

Finally, we started analysing the intracranial correlates of scalp connectivity by using simultaneous recordings of intracranial EEG and high-density scalp EEG. In one TLE patient, we found that both source activity and connectivity patterns estimated from scalp signals resembled the ones estimated from intracranial signals. We are currently performing the same analysis for a larger cohort of patients. This study could further confirm the reliability of non-invasive analyses based on scalp EEG to study the epileptogenic zone and epileptic networks.

Our studies show that whole-brain EEG-based directed functional connectivity analysis is a very promising tool to investigate connectivity patterns and how brain regions driver others during epileptic and non-epileptic activity. This could, therefore, constitute an important contribution for epilepsy presurgical planning, especially in patients in which the focus is not clear by other already available neuroimaging tools.

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Résumé

Il y a de plus en plus de preuves que l'activité épileptique implique des réseaux cérébraux étendus plutôt qu’une source unique isolée. Une meilleure compréhension de l'organisation et de la dynamique de ces réseaux cérébraux est cruciale pour la compréhension du début et de la propagation de l'activité épileptique et des troubles cognitifs chez les patients épileptiques. De plus, ceci pourrait avoir une valeur diagnostique et pronostique importante, en particulier pour les patients qui ne répondent pas au traitement antiépileptique médicamenteux et qui sont candidats à une résection chirurgicale de la zone épileptogène.

L'épilepsie du lobe temporal mésial (TLE) est le type le plus fréquent de l'épilepsie pharmaco-résistante et elle se caractérise par des crises focales récurrentes découlant de structures mesiotemporales. Le traitement le plus commun pour ces patients est la neurochirurgie pour enlever la zone corticale responsable pour l'initiation des crises épileptiques. Il y a aussi des preuves solides que l'épilepsie du lobe temporal gauche et droite (LTLE et RTLE, respectivement) sont des entités distinctes, avec différentes déficiences cognitives et structurelles.

L'Électroencéphalographie (EEG) mesure directement l'activité neuronale électrique avec une résolution temporelle élevée, et l'EEG est donc très approprié pour étudier les processus dynamiques du cerveau, telles que l'activité épileptique. Cependant, l'EEG ne précise pas la localisation des populations de neurones actifs à un certain moment parce que les mesures au scalp reflètent la somme des courants neuro-électriques produits dans le cerveau. L’imagerie de source électrique (Electrical Source Imaging, ESI) peut être utilisée pour reconstituer l'activité des sources qui sont responsables d’une certaine distribution des potentiels électriques enregistrés sur le scalp à un certain instant. Des études cliniques ont montré que l'ESI estime de manière fiable la localisation de la zone de début de crise et la zone épileptogènique. En outre, des études ont montré que la connectivité du cerveau devrait être étudiée au niveau des signaux de source plutôt que des électrodes du scalp.

Les interactions entre régions neuronales chez les patients avec TLE peuvent être étudiées en utilisant le concept de la connectivité cérébrale. Plus précisément, la connectivité fonctionnelle mesure les dépendances statistiques entre différents signaux neuronaux. La connectivité fonctionnelle directe étudie les relations directionnelles entre régions cérébrales, soit l'influence causale qu'une région du cerveau exerce sur un autre.

Elle peut être étudiée en utilisant des techniques basées sur le concept de causalité de Granger, tels que

“Partial Directed Coherence (PDC)”.

Le but de ce projet était d'évaluer les changements de connectivité fonctionnelle directionnelle chez les patients avec LTLE et RTLE afin d'améliorer la caractérisation des réseaux épileptiques et de fournir une meilleure gestion et planification des candidats à la chirurgie de l'épilepsie. Ceci pourrait aussi permettre de trouver de nouveaux biomarqueurs pour la détection de l'épilepsie.

Tout d'abord, nous avons développé une approche méthodologique pour étudier la connectivité fonctionnelle directionnelle entre toutes les régions du cerveau en utilisant des signaux de source provenant de l'EEG de haute densité. Cette analyse comprend: ESI en utilisant des modèles de tête individuels, division de la matière grise en 82 régions, fixation de l'orientation des dipôles pour chaque région, calcul de la puissance spectrale dans l'espace source, et calcul de la causalité de Granger (weighted Partial Directed

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Coherence).

Ensuite, nous avons appliqué cette approche pour étudier l'organisation des réseaux cérébraux chez les patients avec TLE. Tout d'abord, nous avons étudié les changements dynamiques dans le cerveau entier pendant les pointes interictales en utilisant la connectivité fonctionnelle directionnelle chez les patients avec LTLE et RTLE. Nous avons identifié les principales régions émettrices d’information et les caractéristiques du réseau de l'activité épileptique interictale chez les patients avec LTLE et RTLE. Nous avons en outre constaté que différents réseaux sont impliqués dans LTLE et RTLE: les patients avec RTLE ont montré une connectivité plus forte vers l'hémisphère contralatéral en comparaison avec les patients LTLE, ce qui concorde avec les différences de déficit neuropsychologiques entre les groupes. Cette étude a offert une meilleure caractérisation du comportement dynamique des réseaux impliqués dans les pointes interictales.

Cependant, les pointes intercritiques ne sont pas toujours visibles pendant les enregistrements EEG de scalp. Pourtant, la récidive de crises et les troubles cognitifs peuvent être observés en dépit de leur absence.

Par conséquent, une meilleure caractérisation des réseaux anormaux en l'absence de décharges épileptiformes interictales (IEDs) pourrait avoir une valeur diagnostique et pronostique importante. Dans notre deuxième étude clinique, nous avons examiné si la connectivité fonctionnelle directionnelle était modifiée lorsque l'EEG au repos ne montre pas des pointes interictales chez LTLE et RTLE par rapport aux contrôles sains.

Nous avons constaté que la connectivité au repos est diminuée chez les patients avec TLE même en absence d'IEDs, et que ces modifications sont corrélées avec certains paramètres cliniques et comportementaux. Nous avons en outre constaté que les patients et les contrôles sains avaient une configuration de réseau différente.

Ces altérations du réseau au repos en l'absence de pointes interictales renforcent le point de vue que des changements chroniques et progressifs des réseaux neuronaux sont présents chez TLE, et pourraient constituer un biomarqueur important de TLE. Dans une étude suivante, nous avons utilisé ces valeurs de connectivité comme information pour un système de classification (algorithme de “Random Forests”) et nous avons obtenu une précision de 90% pour diagnostiquer TLE (classificateur: TLE vs témoins en bonne santé) ainsi que latéralisé TLE (classificateur: LTLE vs RTLE). Cela démontre le potentiel de la connectivité fonctionnelle directionnelle basée sur l’'EEG de repos pour diagnostiquer automatiquement et latéraliser les patients avec TLE.

Enfin, nous avons utilisé la même stratégie pour étudier la connectivité fonctionnelle directionnelle du cerveau entier en utilisant l'EEG au repos chez des sujets sains par rapport à des données de surrogate. Nous avons identifié les principales régions sources du cerveau au repos, qui étaient concordantes avec les caractéristiques spatiales du réseau du mode par défault (Default Mode Network), et nos résultats ont identifié le cortex cingulaire postérieur comme la principale source de transfert d'information dans le cerveau au repos.

Nos études montrent que l'analyse de la connectivité fonctionnelle directionnelle basée sur l'EEG au niveau du cerveau entier est un outil très prometteur pour étudier les modèles de connectivité et la façon dont les régions du cerveau influence les autres lors de l'activité épileptique et non-épileptique. Cela pourrait donc constituer une contribution importante pour la planification préopératoire l'épilepsie, en particulier chez les patients dont le foyer n’est pas clairement identifié par d'autres outils de neuroimagerie déjà disponibles.

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Table of Contents

Acknowledgements ... 5

Summary... 7

Résumé ... 9

Table of Contents ... 11

Chapter 1 - Introduction ... 14

1 Context ... 14

2 Epilepsy ... 15

2.1 Definition of epilepsy, causes, prevalence, incidence and morbidity ... 15

2.2 Definition of Seizures & Interictal epileptiform Discharges ... 16

2.3 Pharmaco-Resistance, Temporal Lobe Epilepsy and Epilepsy Surgery ... 16

2.4 Definition of symptomatogenic zone, irritative zone, seizure onset zone, epileptogenic zone, epileptogenic lesion, eloquent cortex ... 17

2.5 Presurgical evaluation... 18

2.5.1 Long-term scalp video-EEG ... 18

2.5.2 Structural MRI ... 18

2.5.3 Functional Imaging ... 18

2.5.4 Neuropsychological and Psychiatric assessment ... 19

2.5.5 Intracranial EEG ... 19

3 EEG and Electrical source imaging (ESI) ... 21

3.1 EEG ... 21

3.1.1 Origin of the EEG ... 21

3.1.2 EEG acquisition and scalp field maps ... 23

3.1.3 EEG rhythms ... 24

3.1.4 Detection of epileptic activity ... 25

3.2 Electrical Source Imaging (ESI) ... 26

3.2.1 The Forward model ... 27

3.2.2 The Inverse Problem ... 29

3.2.2.1 Dipole Models ... 30

3.2.2.2 Distributed Source Models: Minimum norm estimates, LORETA and LAURA ... 30

3.2.2.3 Other approaches: Beamformers and Bayesian approaches ... 32

3.2.3 ESI validation in focal epilepsy ... 33

2.3 A brief word on Magnetoencephalography (MEG) ... 34

4 Brain Connectivity ... 36

4.1 Linear Measures of Functional Connectivity ... 37

4.1.1 Correlation and cross-correlation ... 37

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4.1.2 Coherency, Magnitude Squared Coherence, Phase of the Coherency, Imaginary Coherence

and Partial Coherence ... 38

4.1.3 Granger-causality and Autoregressive Modelling ... 39

4.1.3.1 Granger-causality Index ... 42

4.1.3.2 Directed Coherence ... 43

4.1.3.3 Directed Transfer Function ... 43

4.1.3.4 Partial Directed Coherence ... 43

4.2 Nonlinear measures of functional connectivity ... 45

4.2.1 Phase-synchronisation measures: Phase-locking value and Phase-lag Index ... 45

4.2.2 Information-based Measures ... 46

4.2.3 Nonlinear correlation coefficient ... 47

4.3 Graph Theory ... 48

4.4 Functional connectivity using intracranial EEG vs scalp EEG vs ESI ... 49

5 Connectivity in the Healthy Brain and in Focal Epilepsy ... 50

5.1 Physiological Resting State Networks and Epilepsy ... 50

5.2 Electrophysiological-based functional connectivity in focal epilepsy ... 51

5.2.1 Seizure studies ... 52

5.2.2 Interictal studies ... 54

6 Aim of the Project ... 57

Chapter 2 - Results ... 58

Study 1 ... 58

Directed functional brain connectivity based on EEG source imaging: methodology and application to temporal lobe epilepsy ... 58

Study 2 ... 59

Dynamic directed interictal connectivity in left and right temporal lobe epilepsy ... 59

Study 3 ... 60

Altered directed connectivity in temporal lobe epilepsy in the absence of interictal spikes: a high density EEG study ... 60

Automated classification and lateralisation of TLE patients based on high density EEG and directed functional connectivity ... Error! Bookmark not defined. Study 4 ... 62

Electrophysiological directed functional connectivity of the resting human brain ... 62

Study 5 ... 63

Simultaneous intracranial – scalp EEG reveals concordant directed connectivity in epileptic spikes ... 63

Chapter 3 - Discussion ... 66

1. Studying whole-brain directed functional connectivity with scalp EEG signals and methodological considerations ... 66

2. Directed functional connectivity during and without interictal spikes in left and right TLE patients using high-density scalp EEG ... 69

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2.1. Dynamic connectivity during interictal spikes ... 70

2.2. Network changes in TLE: increased or decreased functional connectivity? ... 70

2.3. Altered network pattern in TLE ... 71

2.4. LTLE versus RTLE ... 72

2.5. Intracranial correlates of scalp EEG-based functional connectivity ... 72

3. Directed functional connectivity in the healthy resting human brain ... 73

4. Limitations ... 74

5. Future Perspectives ... 74

Conclusions ... 75

References ... 76

Articles ... 86

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Chapter 1 - Introduction

1 Context

Epilepsy is one of the most common chronic neurological disorders. It is a complex dynamic disease [1]

characterized by recurrent unprovoked seizures caused by an abnormal electrical activity. Around 30% of the patients with epilepsy are refractory to anti-epileptic drugs [2]. Medial temporal Lobe Epilepsy (TLE) is the most frequent type of pharmaco-resistant epilepsy [3] and it is characterized by recurrent focal seizures arising from mediotemporal structures. Depending on the hemisphere where the epileptogenic zone is located, TLE can be further divided in left TLE (LTLE) and right TLE (RTLE). These have been shown to have significant differences regarding memory processes [4], psychosocial functioning [5], or contralateral medial temporal damage [6]. Thus, it is important to differentiate these two entities for a correct diagnosis and clinical management of these patients.

Some of these patients are submitted to neurosurgery in order to remove the cortical zone responsible for the initiation of the epileptic seizures, in order to achieve seizure freedom. However, sometimes, despite an accurate location of this zone during presurgical evaluation, patients are still not seizure free after surgery.

This is because epilepsy involves hyperexcitable neuronal networks rather than single sources [7, 8].

Therefore, a better understanding about the interactions between brain regions is crucial for understanding this disorder and could provide an important diagnostic and prognostic value, particularly for patients who do not respond to antiepileptic drug treatment and are candidates for a surgical resection of the epileptogenic zone. These interactions can be studied used the concept of brain connectivity. Specifically, functional connectivity measures the statistical dependencies between different signals and it can reveal the directionality of the connection or not, depending on the method used. Directed functional connectivity investigates directional relationships between brain regions, i.e., the causal influence that one brain region exerts onto another, and it can be investigated using data-driven techniques based on the concept of Granger- causality [9].

Electroencephalography (EEG) offers a direct measure of neuronal electrical activity at a high temporal resolution (millisecond range), which is well suited to investigate dynamic brain processes [10], that can be then studied using Granger-causality approaches. However, the measured EEG potential does not unambiguously indicate the location of the active neuronal populations at a given moment, because measurements at the scalp reflect the summed neuro-electrical currents generated within the brain. Electric Source Imaging (ESI) is then used to reconstruct the source activity that underlies the distribution of scalp potentials recorded at a given time point [11]. Clinical studies have used ESI to reliably estimate the localization of the seizure onset zone and the epileptogenic zone [12-14]. Moreover, studies have shown that brain connectivity should be examined at the level of source signals rather than scalp electrodes [15, 16] to minimize problems that are inherent to connectivity analysis using scalp signals, which can lead to spurious connections and limited interpretability of scalp EEG connectivity results [16].

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The study of directed functional connectivity based on ESI can be particularly important in epilepsy, in which EEG is the best marker of pathological brain activity. Indeed, studies in TLE reported altered functional connectivity between brain regions using invasive and non-invasive electrophysiology, functional MRI and isotopic imaging [17-23], and structural connectivity abnormalities (cortical thickness, diffusion tractography) [24] which expanded beyond the affected temporal lobe, ipsi- and contra-laterally. Interictal spikes can transiently worsen these deficits [25], so describing large-scale brain interactions non-invasively with high temporal resolution is important for understanding the epileptic network dynamics in order to capture the time-varying pattern of interictal connectivity. This is an important issue given that spikes are transient highly non-stationary events with fast propagation and their contribution to cognitive impairment is poorly understood.

However, patients with TLE often suffer from cognitive deficits even when no spike is detected in the scalp EEG. The characterization of brain network dysfunction even in the absence of visible scalp epileptic activity could be very important to improve diagnostic accuracy and treatment in these patients.

In this project, we studied the directed functional connectivity changes in patients with TLE using ESI signals. In the following introductory sections, we will detail the background for the understanding of our work. In section 1, we introduce epilepsy, with special focus on TLE, pharmaco-resistance and the presurgical evaluation tools. In section 2, we provide further details on EEG and the principles of ESI. In section 3, we describe the concept of brain connectivity and how to estimate it, with special focus on algorithms currently used to estimate functional connectivity. In section 4, we describe the specific application of these algorithms to study drug-resistant epilepsy. Finally, in section 5, we state the aims of this PhD project.

2 Epilepsy

2.1 Definition of epilepsy, causes, prevalence, incidence and morbidity

Epilepsy is one of the most common chronic neurological disorders and it is characterized by recurrent unprovoked seizures caused by an excessive electrical activity that involves hyperexcitable neuronal networks. According to the definition of epilepsy by the World Health Organization “Epilepsy is a chronic disorder characterized by recurrent seizures, which may vary from a brief lapse of attention or muscle jerks, to severe and prolonged convulsions. The seizures are caused by sudden, usually brief, excessive electrical discharges in a group of brain cells (neurons). In most cases, epilepsy can be successfully treated with anti- epileptic drugs.” [26]. Epilepsy is diagnosed when a patient has 1) at least two unprovoked seizures that are more than 24h apart or 2) one unprovoked seizure and a high recurrence risk over the following 10 years [27]. In most cases, the etiology of epilepsy is unknown. However, many factors can cause this disorder, including genetic factors, head trauma, tumors, stroke, dementia, meningitis, prenatal injury, oxygen deprivation, etc. The process from this initial precipitating insult to the first spontaneous seizure is called epileptogenesis. The International League Against Epilepsy (ILAE) has recently proposed a new

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classification of epilepsy based on the etiology: genetic, structural, metabolic, immune, infections or unknown.

Epilepsy affects around 50 million people worldwide (i.e. around 0.7% of the population), although the incidence is higher in low and middle income countries (between 0.7 and 1.4% of the population) [26].

Epilepsy incidence is also higher in infants and in elderly: in the former due to abnormal brain development, metabolic disorders or perinatal insults, and in the latter due to brain lesions such as stroke, tumor or trauma.

Epilepsy is associated with physical (such as fractures and bruising from injuries related to seizures), neurological, cognitive, psychiatric (anxiety and depression) and socio-professional co-morbidities.

Moreover, the mortality of epileptic patients is three times higher than the general population, especially in the first 15 years following diagnosis and in the low and middle income countries [26].

2.2 Definition of Seizures & Interictal epileptiform Discharges

The epileptic activity is normally subdivided in ictal periods (seizures), postictal (after a seizure) and interictal periods (in between seizures). We describe below in further detail seizures and interictal activity.

According to the ILAE, "an epileptic seizure is a transient occurrence of signs and/or symptoms due to abnormal excessive or synchronous neuronal activity in the brain" [28]. Epileptic seizures can be characterized by several clinical manifestations, including sensory, motor, neuro-vegetative, cognitive or psychic signs and symptoms. They can consist, for instance, of a lapse of attention (loss of awareness or consciousness), muscle jerks, or severe and long convulsions. Seizures can occur with a frequency from less than one per year to several per day [26].

Epileptic seizures are subdivided in two main types: generalized and focal. Generalized seizures are defined by the ILAE as originating in a brain area and "rapidly engaging bilaterally distributed networks"

[29]. The location and lateralization of the onset of each seizure might change from seizure to seizure. Focal seizures are defined as "originating within networks limited to one hemisphere. They may be discretely localized or more widely distributed" [29]. The onset of each seizure belonging to the same type is consistent in all seizures of the same type, however there might be different seizure types in the same patient. As also noted by the ILAE, “the preferential propagation patterns are to the contralateral hemisphere", however other networks can be engaged [29]. The type of focal seizures gives the name to the underlying epilepsy syndrome (also called, in this, case focal epilepsy), depending on which hemisphere and brain lobe is involved: left/right temporal, frontal, occipital or parietal lobe epilepsy. The clinical manifestation of seizures has many forms depending on which brain areas are affected.

Beyond seizures, epileptic activity can be manifested by the occurrence of abnormal brain activity during interictal periods, that are commonly called interictal epileptiform discharges (IEDs). Epilepsy patients often have also cognitive deficits, which are present during these interictal periods with or without IEDs [30].

2.3 Pharmaco-Resistance, Temporal Lobe Epilepsy and Epilepsy Surgery

About 30% of epilepsy patients do not respond to anti-epileptic drugs [2], i.e., they continue to have seizures despite a well conducted anti-epileptic drug treatment with at least two drugs during at least two years. In this case, the patients are said to be pharmaco-resistant. In most patients, these drug-resistant

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epilepsies are focal, i.e. the seizures are generated in an abnormally excitable brain region (epileptogenic zone).

Medial Temporal Lobe Epilepsy (TLE) is a type of focal epilepsy and is the most frequent type of pharmaco-resistant epilepsy in adults [3]. TLE is characterized by recurrent focal seizures arising from mediotemporal structures (hippocampus, amygdala, entorhinal cortex) and its most frequent structural pathology is unilateral Hippocampal Sclerosis (HS) [31]. Seizures often start with an epigastric sensation, and emotional or other psychic auras, impaired consciousness and autonomic behaviours are also common.

In some of these patients, the treatment option is epilepsy surgery, in which the cortical zone responsible for the initiation of seizures (epileptogenic zone) is aimed to be removed with the ultimate goal of achieving seizure freedom, while preserving the eloquent cortex. Therefore, the accurate location of the cortical areas that should be removed by surgery is crucial. This is investigated for each individual patient during presurgical evaluation. TLE is often successfully treated by surgery, however long-term relapses in up to 58% of cases have been reported [32], suggesting insufficient network disruption.

2.4 Definition of symptomatogenic zone, irritative zone, seizure onset zone, epileptogenic zone, epileptogenic lesion, eloquent cortex

In the context of focal epileptic activity, the following terminology is commonly used: symptomatogenic zone, irritative zone, ictal onset zone, epileptogenic zone, epileptogenic lesion, eloquent cortex [33].

The symptomatogenic zone is the cortical area that produces the initial ictal symptoms when activated by an epileptiform discharge. It is defined by the analysis of patient’s seizure history or ictal video-EEG recordings.

The irritative zone is the cortical area that generates IEDs seen with scalp or intracranial EEG, magnetoencephalography (MEG) or simultaneous EEG and functional magnetic resonance imaging (fMRI).

The seizure onset zone is the region where clinical seizures are generated. It is commonly estimated by scalp or intracranial EEG.

The epileptogenic zone is the brain region necessary to generate seizures and that needs to be surgically removed to obtain seizure freedom. Thus, it is contained in the seizure onset zone. It is inferred by a combination of all the above zones estimated during presurgical evaluation and confirmed a posteriori if the patient is seizure-free after surgery. Non-invasive mutilmodal concordance is important to estimate accurately the epileptogenic zone. However, intracranial EEG is needed when there is an ambiguity about the focus, its extent or overlap with the eloquent cortex.

The epileptogenic lesion consists in the structural brain abnormalities with the potential of generating interictal and ictal epileptic activity. It is identified by structural MRI or by post-operative histological examination.

The eloquent cortex is the cortical area that is identified as crucial for neurological or cognitive functions (i.e. motor, sensory, visual, language cortex) and thus, it should be preserved by epilepsy surgery. It is commonly detected using electrical stimulation of the cortex during invasive EEG recordings, evoked potentials and fMRI.

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2.5 Presurgical evaluation

In the presurgical evaluation, several non-invasive and invasive techniques are used and the results later combined in order to identify the epileptogenic zone and its overlap with the eloquent cortex. These techniques include long-term scalp video-EEG, structural imaging, functional imaging, intracranial EEG and neuropsychological and psychiatric assessment.

2.5.1 Long-term scalp video-EEG

Long-term scalp video-EEG recordings are performed during several days and aim to capture seizures and interictal epileptiform activity, and are, thus, crucial in presurgical evaluation. The video is important to identify specific movements or behaviours during the seizures (semiology) to define the symptomatic zone.

In section 2, we will describe in further detail the origin, acquisition and the detection of epileptic activity with EEG.

2.5.2 Structural MRI

Structural and functional imaging have also to be performed in order to find concordant areas of tissue damage/dysfunction and further estimate the brain regions that need to be surgically removed.

Structural MRI can be acquired with different contrasts in order to highlight different type of tissues.

Namely, T1-weighted images are used to provide a very good contrast between grey and white matter:

because white matter contains fat, it will be brighter. T1-weighted images are used to identify some brain abnormalities such as hippocampus sclerosis, atrophy, focal cortical dysplasia and lesions. In T2-weighted images, the fluids are brighter, which is good to visualize edema.

2.5.3 Functional Imaging

Functional Imaging techniques include Positron Emission Tomography (PET), Single Photon Emission Computed Tomography (SPECT) and functional MRI (fMRI) which are all used to help localize the epileptogenic zone.

PET and SPECT are based on the intravenous injection of radioactive tracers. In PET, pairs of gamma rays are emitted indirectly by a positron-emitting tracer. The commonly used tracer is 18F- fluorodeoxyglucose (FDG), an analogue of glucose, which will then show which tissues are hyper or hypometabolic (higher or lower glucose consumption). (FDG)-PET is useful to detect a focal interictal hypometabolism which sometimes extend beyond visible MRI lesions. It can be particularly important in patients with no MRI lesion. In SPECT, 3D images of the cerebral blood flow are created by the amount of tracer uptake in the brain. This is particularly important in focal epilepsy because a decreased cerebral blood flow during interictal periods on a focal area is indicative of the epileptogenic zone and a hyperperfusion during ictal periods indicates sites of epileptic activity and seizure spread [34]. The difference between ictal and interictal SPECT is known as SISCOM [35].

fMRI uses blood-oxygenation level-dependent (BOLD) contrast to indirectly investigate neuronal activity through the measure of neuronal oxygen consumption and focal perfusion (hemodynamic) changes.

BOLD signal increases correspond to increases in neuronal activity compared to a chosen baseline of brain

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activity. fMRI is commonly used to identify the eloquent cortex (map language areas and the sensory-motor cortex).

2.5.4 Neuropsychological and Psychiatric assessment

Neuropsychological assessment is performed in order to evaluate specific cognitive impairments related to epilepsy, which could be indicative of a lateralised or bilateral dysfunction. Namely, a language or verbal memory impairment suggests the involvement of the language dominant hemisphere (normally, the left) [36]

while a visuo-spatial memory impairment suggests the involvement of the other hemisphere (normally, the right) [37]. The assessment can also indicate the involvement of frontal and/or temporal regions, adding thus concordance or not to the other imaging techniques [38]. Moreover, neuropsychological evaluation is also crucial to estimate the risk of post-operative cognitive disability, namely in TLE where the temporal lobe is aimed to be resected [39].

Psychiatric assessment is also very relevant since psychiatric comorbidities and epilepsy often coexist, in particular TLE [40, 41]. Indeed, patients with epilepsy also suffer from affective disorders, obsessive- compulsive disorders and psychoses, which put them at higher risk for post-operative worsening of the condition [40, 42, 43]. Namely, it is known that 1 in 3 patients with epilepsy suffer from psychiatric comorbidities while only 1 in 6 in people without epilepsy [44]. However, it is also known that people with primary depressive disorders have also a higher risk of developing epilepsy [41]. It is, however, currently unclear whether epilepsy is a risk factor for psychiatric comorbidities or vice-versa.

2.5.5 Intracranial EEG

When all the non-invasive techniques mentioned above do not show concordant results, the patient is commonly referred to invasive EEG monitoring in order to have a more direct measure of the brain electrical activity and to assess deep regions whose activity is more difficultly seen at scalp EEG.

Intracranial EEG recordings implies a brain surgery to place the electrodes in or on the brain, and thus carries many risks, and should only be performed in cases in which there is a clear hypothesis regarding the location of the epileptogenic zone. These are two types of intracranial EEG recordings: the stereotactic EEG (SEEG) in which depth electrodes are implanted in the brain, and the subdural EEG or electrocorticogram (ECoG) in which electrodes in grids and/or strips are placed under the duramatter over the brain surface. The number of electrodes to be placed in the brain is limited and thus, the choice of the location of these electrodes should be carefully investigated. If the electrodes are not recording the actual seizure onset zone, the intracranial EEG can show instead only regions to where the ictal activity spread and not the initial onset.

The intracranial EEG records the local field potentials created by a group of neurons in the proximity of the electrode. The recorded signals normally have high signal-to-noise ratio because they are recorded directly from the cortex without attenuation by the skull.

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Figure 1 – Illustrative representation of (A) ECoG and (B) SEEG.

Other methods are starting being commonly used in presurgical evaluation, namely Electrical Source Imaging (which will be detailed in the next section), MEG and magnetic Source Imaging (MSI), and simultaneous EEG and functional MRI (EEG-fMRI) (especially useful to detect BOLD changes associated with IEDs and map the irritative zone).

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3 EEG and Electrical source imaging (ESI)

Electroencephography (EEG) is a technique to measure the electrical brain activity. It consists in a graphic representation of the electrical potential difference between two recorded brain sites plotted over time. EEG is possible due to the current flow through the tissues between the sources and the recording scalp electrode, also known as volume conduction. EEG measures directly the neuronal activity at a high temporal resolution which is well suited to investigate dynamic brain processes [10]. It is the main diagnostic tool for epilepsy and it also offers a huge potential to investigate epileptic networks.

This section describes the origin of the EEG signals, EEG acquisition and scalp field maps (topographies), the different EEG rhythms, how to detect epileptic activity in EEG signals and introduces Electrical Source Imaging (ESI).

3.1 EEG

3.1.1 Origin of the EEG

The cortex is organized in cortical columns with different layers and some of which contain pyramidal cells aligned perpendicularly to the cortical surface. This organization is characterized by synaptic connections between neurons of different layers and structures.

Neurons generate electrical currents when activated, which are due to ionic currents at the level of the cellular membranes. There are two types of neuronal potentials: the fast action potentials at the level of the axon, and the slower postsynaptic potentials at the level of the dendrites or soma of the neuron. Action potentials consists in a fast depolarisation of the neuronal membrane (the intracellular potential changes from negative to positive due to the flow of Na+ inwards) followed by a flow of K+ outwards (repolarisation) and then a rapid return to the resting intracellular negativity. An impulse is then generated which propagates along the neuron, generating local currents outside of the cell which facilitate the propagation of the signal along the neuron. However, these currents are too small to be detected by EEG and the axons are arranged randomly so many of the currents cancel each other out. When the action potential arrives to the axon terminal, neurotransmitters are released into the synaptic cleft, and then bind to the receptors of a postsynaptic neuron, creating a postsynaptic potential, which is caused by ionic channels in the membrane that open up. Depending on the type of neurotransmitter, its receptor and interactions with specific ionic channels, the postsynaptic potential can be excitatory or inhibitory: the membrane of the postsynaptic cell becomes depolarised (thus, more likely to generate an action potential) or hyperpolarised (less likely to generate an action potential). If the postsynaptic potential is excitatory, at the level of the synapse there is a flow of Na+ or Ca2+ into the neuron, while if it is inhibitory, there is a transference of Cl- inwards or K+ outwards. In the former case, the influx of cations from the extracellular space into the neuron creates a negatively charged local extracellular space (sink).At the distal part of the neuron, there is an outflow of cations from the intracellular to the extracellular space (passive current), which then becomes positively charged (source). In the case of the inhibitory postsynaptic potentials, there is an extracellular source at the level of the soma and a passive sink at the basal and apical dendrites. Therefore, the postsynaptic activity at the soma-dendritic membrane causes a sink-source configuration in the extracellular space around the

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neuron, which forms a current dipole between the apical and distal part of the neuron (Figure 2). The neuron can be then approximated as a microscopic electrical dipole perpendicular to the cortical surface [10, 45-47].

However, the current dipole of a single neuron is very small, so individually, they are undetectable by the EEG. Indeed, the activity of a large number of neurons with parallel orientation needs to be synchronised in order to have a measurable electrical field in the scalp. The dendritic trees of pyramidal neurons are parallel to each other and perpendicular to the cortical surface, and thus, are believed to be the main generators of the EEG signal. In order to have a measurable electrical field at the surface about 40-200 mm2 of cortex has to be synchronously activated [48]. When the pyramidal neurons are activated by a postsynaptic potential, the longitudinal components of the intra and extracellular currents sum up while the transverse components cancel out. This results in a current along the neurons main axis.

EEG records, thus, the sum of excitatory or inhibitory postsynaptic potentials of a large population of synchronized pyramidal cells that are oriented perpendicularly to the cortical surface (Figure 2) [45].

Therefore, due to the brain geometry, the electrical activity measured by the EEG is mainly generated in the gyrus parallel to the surface, while the sulcal activity is usually unseen by the EEG. The postsynaptic potential should consist of the same type, i.e. excitatory or inhibitory.

The measured EEG signal is influenced by 1) the electrical conductive properties of the tissues between the electrical generators (sources) and the EEG electrode (for instance, the brain parenchyma, the duramatter, the cerebroencephalic fluid, the skull and the scalp) as well as the impendances between the head and the electrode; 2) the orientation of the cortical sources to the recording electrode; 3) the conductive properties of the recording electrode (e.g. size, material, resistance).

Figure 2 – Illustrative representation of a pyramidal cell excitatory postsynaptic potential.

Simultaneous intracranial and scalp recordings have shown that synchronous cortical activity over at least 6-10 cm2 of cortex is necessary for the detection of pathological events in scalp EEG [49].

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3.1.2 EEG acquisition and scalp field maps

EEG captures the time-varying potentials at certain electrodes placed on the scalp at certain predefined standard positions. An internationally accepted standard is the 10-20 system, in which the electrodes are placed proportionately (10% and 20% spacing) between certain bone landmarks (normally, inion, nasion and preauricular points) in a way that the entire brain is equally covered (Figure 3). The amount and exact placement of the electrodes depend on the application. In the clinical EEG, normally 21-32 electrodes are placed on the scalp using a conductive gel to reduce the scalp-electrode impedance. Impedances should be kept as low as possible (typically <20kΩ is recommend). By convention, the electrodes over the left side of the head are attributed an odd number and those on the right side of the head an even number. The letters of the electrode placement reflect the relative position over the head: Fp (frontopolar), F (frontal), C (central), P (parietal), T (temporal), O (occipital) and A (auricular) and Z stands for midline. The electrodes are then connected to an amplifier and the output reveals a variation in voltage over time: the EEG signal.

EEG is commonly recorded with a sampling frequency between 250 and 2000 Hz, and thus, it has a temporal resolution in the millisecond range. This high temporal resolution of the EEG turns it very suitable to study dynamic and fast-occurring processes in the brain, such as IEDs (more on this in section 2.1.4). The spatial sampling of the EEG depends on the number of electrodes. When the number of recorded electrodes is equal or superior to 64 channels, it is called high-density EEG recording.

EEG consists of a two-dimensional (2D) array with one of the dimensions being the number of time samples and the other the number of electrodes. For each time point, EEG potentials can also be represented as scalp field maps, also called topographies (Figure 3) [50].

The potentials at each EEG electrode are always recorded against a reference. Thus, the recorded EEG potentials represent always the difference between the potential at the electrodes and the potential at the reference. Therefore, the recorded values at the reference electrode are always zero. A common used reference is Cz (thus, the center of the head). If another reference is chosen computationally, the new values at each electrode correspond to the voltage difference between the recorded voltage and the voltage at the new reference. A common used reference here is the average reference, which is the average of the potentials in all electrodes, for each time point. However, it is important to point out that the relative potential differences between electrodes remain the same since the same value is being subtracted from the original measurements for each time point, and thus, although EEG values change, scalp topographies are not affected by the change of reference (the isopotential lines remain the same just their labelling changes) [11, 50]. It has been recommended thus, that the distribution of the scalp field rather than the scalp potential values are used for analyses so that data interpretation is independent from the choice of the reference.

Indeed, it has been recognized that scalp potential maps and whole-head sampling with a higher number of electrodes provide more information about the localisation and orientation of intracranial sources than do the sole interpretation of EEG values and a restricted number of electrodes [11, 51].

In order to visualize the EEG traces, there are several montages that can be used, such as the bipolar montage (potential difference between adjacent electrodes), the double-banana or the triple banana. Figure 3 shows an example of triple banana montage.

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In order to quantify the strength of a scalp potential field map, for each time point, the Global Field Power (GFP) can be computed. It includes the differences between all possible pairs of electrodes and thus, it is reference independent. It is defined by the sum of all squared potential differences at each time point:

N t t u t

GFP

N

i

i

1

))2

( ) ( ( )

(

 (1)

where ui is the potential at electrode i, μ is the average potential of all electrodes and N is the number of electrodes.

Figure 3 - (A) The 10-20 system (adapted from [52]). (B) Triple banana montage. (C) EEG visualised with this montage. (C) Scalp topographic map correspondent to the time point indicated with the red marker in (C)

. 3.1.3 EEG rhythms

The synchronised activity of a population of pyramidal neurons allows the EEG to record oscillations that have a certain amplitude and frequency, depending on the age, awake/sleep state and on the presence of neuronal dysfunctions. These EEG rhythms are generally divided according to the observed frequency content in mainly 5 rhythms or frequency bands [45]: 1) delta: the frequency of the signal is below 4 Hz. The EEG signals have large amplitude. It is the predominant physiological rhythm in adults during deep sleep.

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When present in an awake adult it may indicate a brain disorder. 2) theta: frequencies range between 4 and 7 Hz. It is present during certain sleep stages. 3) alpha: frequencies range between 8 and 12 Hz. It is the most predominant rhythm is resting-state EEG in adults, i.e., subjects that are awake with eyes-closed and not performing any particular task. This rhythm is normally localized in the occipital lobe. 4) beta: frequencies range between 13 and 30 Hz. It normally occurs when subjects are with eyes-open during alertness but also with eyes-closed during drowsiness. 5) gamma: frequencies are higher than 30 Hz. It is related to active information processing. In general, when the cortex processes information, neuronal activity is fast but also somehow unsynchronized, which results in an EEG amplitude relatively small. Physiological and pathological high frequency oscillations (HFOs) have also been described [53]. They have a frequency range between 200 and 500 Hz. HFOs can be observed in human intracranial recordings and are supposed to reflect fields of hypersynchronized action potentials [54]. However, HFOs are only rarely recorded with scalp EEG [55] and high sampling rates are required. HFOs are outside the scope of this project and we here focus mainly on the theta, alpha and beta frequency bands.

3.1.4 Detection of epileptic activity

EEG is the most important tool for detecting epileptic activity, and thus, diagnosing epilepsy.

During ictal periods (seizures), the EEG shows a synchronous activity manifested by periodic waves with higher amplitude than the interictal periods (without interictal events).

IEDs are non-physiological transient waves that are clearly distinguished from background activity. IEDs can occur isolated or in brief bursts. In general, isolated, independent spikes do not generate clinical symptoms. When the bursts last for several seconds, they likely represent electrical seizures rather than IEDs. IEDs can be subdivided into sharp waves (duration of 70-200 miliseconds (ms)), spikes (duration of 20-70 ms), spike-and-slow-wave complexes (spike followed by a slow wave) and polyspike-and-slow-wave- complexes (two or more spikes associated with one or more slow wave).

An example of an IED is shown is Figure 4.

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Figure 4 - (A) Example of a medial temporal lobe spike (spike peak indicated with a pink maker) and (B) topographic maps in the period within the red box represented in (A) (please note that not all maps occurring during this

period are represented).

Since, in some cases, seizures do not occur very often and thus, might not be detected during the patient's stay at the hospital, the detection of IEDs is the main diagnosis tool. Although the importance of these interictal spikes for epileptogenesis and seizure generation has been debated, they have always been very important in clinics for the diagnosis and localization of the epileptic foci. The emergence of spikes precedes the first seizure in animal models of epilepsy and may guide the development of aberrant neuronal circuits and the initiation of spontaneous seizures [56]. There is also evidence of IEDs related cognitive impairments in epilepsy, notably regarding memory maintenance and retrieval in the hippocampus of TLE patients [25].

3.2 Electrical Source Imaging (ESI)

In spite of the high temporal resolution of the EEG, it does not indicate per se the location of the active neuronal populations at a given moment, because as introduced in section 2.1.1., measurements at the scalp reflect the summed neuro-electrical currents generated within the brain. Electrical Source Imaging (ESI) is

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thus used to reconstruct the source activity that underlies a given distribution of scalp potentials recorded at each time point. Another advantage of ESI, like topographic analysis, and in opposition to the EEG waveform analyses, is that it is reference-free [11]. It does require, however, that the whole scalp is equally covered [11, 51].

ESI involves the computation of the forward model and the solution of the inverse problem. In the forward model, the scalp potentials are estimated for any given electrical source distribution based on a head volume conductor model (head model). In the inverse problem, given the recorded scalp potentials, the source parameters are estimated based on the solution of the forward problem. Below, we provide an overview of the forward and inverse models. For comprehensive reviews on ESI as well as the advantages and drawbacks of the different algorithms, we refer the reader to [11, 48, 57].

3.2.1 The Forward model

The forward problem describes how electrical currents in the brain produce the measured scalp potentials. The forward problem depends on the use of an appropriate head model, which takes into account the position of the solution points (sources), the position of the scalp electrodes, the head geometry, and the head tissues conductivity. These geometrical and electromagnetic properties, that relate scalp potentials and current source densities, are expressed in the forward operator, also known as lead field matrix, after solving the Maxwell's equations. This lead field matrix is multiplied by the estimated current source densities to produce the scalp potentials (forward solution):

c J K

 .

 (2)

where

(

1

,

2

..., )

NE

 is the vector of scalp potentials seen at NE number of EEG electrodes, )

1..

( NS

J J

J is a vector containing the current source densities at NS number of sources (contains information about dipole orientation and strength), c is a vector containing the channel noise and K is the lead field matrix, expressed by:

T N N T

N T N

T N T

T

T N T

T

S E E

E

S S

k k

k

k k

k

k k

k K

, 2

, 1 ,

2 2

, 2 1 , 2

, 1 2

, 1 1 , 1

(3)

where ke,sis the 3D lead field vector [50].

The scalp potential at electrode e is expressed as a linear combination of the contribution of all possible sources:

c j k j

k j

keT T eT T eTN NT

e ,1 1 ,2 2 ... , S S

 (4)

Each source contributes to the potential at e according to the lead field, which in turn depends on the distance between the source and the electrode and on the head model (geometry and conductivity profile).

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