Santiago Ramón

This thesis focuses on two studies investigating the resting-state EEG functional connectivity (i) in patients with benign childhood epilepsy with centrotemporal spikes (BCECTS) and (ii) in preterm and full-term neonates during quite sleep (QS) and active sleep (AS).

In the first part of the thesis, we investigated changes in brain functional connectivity in BECTS patients compared to healthy controls in various frequency bands under the eyes-closed resting condition. The differences in EEG functional and effective connectivity patterns between BCECTS patients and healthy controls were studied in both the sensor and source spaces. The graph theory metrics were also used to characterize functional segregation and integration in BCECTS brain networks in comparison to healthy controls. The first part of the study showed that the EEG resting state network of BCECTS patients was disrupted in the presence and absence of interictal epileptic discharges (IEDs). Patients displayed significantly higher θ power in the scalp EEG across the whole brain regions and lower spectral power in the alpha band especially at the occipital regions in the presence of IEDs. We also observed decreased source activities at the frontal and occipital regions and bilateral increased source activities at the temporal regions in BCECTS patients compared to controls. Our functional connectivity study showed that BCECTS was associated with functionally altered resting state that probably arises from disrupted functional organization of resting-state brain networks on a frequency dependent manner. Our results showed that the BCECTS brain networks were more ordered especially in lower frequency bands in the presence of IEDs and less ordered in the absence of IEDs in comparison to healthy controls. We further investigated the effective connectivity in BCECTS patients to identify major drivers of the epileptic activity. We found that the post and precentral regions with supplementary motor areas were the major drivers in the ipsilateral hemisphere of the epileptic foci. The causal influence from the central to ipsilateral frontal regions and contralateral hemisphere might explain cognitive deficits in children with BCECTS.

In the second part of the thesis, we investigated EEG functional connectivity in preterm babies using high density EEG data and graph metrics during quite sleep. Continuous evolution of cerebral structures during early brain maturation imposes rapid spatial and temporal changes in neonatal EEG patterns. There are different endogenous brain activities such as theta temporal bursts which can serve as biomarkers for neurodevelopment in preterm neonates. We investigated the impact of theta temporal activities on EEG functional connectivity patterns. For normal brain activities with/without theta temporal burst activity, preterm babies presented higher functional connection densities at the frontal and posterior regions compared to other regions. This finding suggests that these regions may functionally develop earlier than other brain regions. The comparison between normal and theta temporal activities revealed higher activity at each of the temporal region. Theta temporal activity in the preterm increased functional connectivity restricted to temporal regions.

In the last part of the thesis, we investigated functional connectivity during QS and AS sleep conditions in full-term neonates. Stronger source activities were observed at the frontal region during AS while the QS condition was characterized with increased source activities at the temporal and posterior regions. Similarly, higher functional connection densities were found at the frontal, temporal and posterior regions during both QS and AS. In both conditions, the clustering coefficient at the central region was lower compared to other regions. The increased source activity at the frontal and posterior regions might support the evidence that these regions develop earlier than other brain regions.

Throughout this thesis, we presented clear and robust approaches for assessing brain functional connectivity patterns in epileptic patients as well as in healthy preterm and full-term neonates. Our findings open new avenues to better understanding complex interactions between brain functional networks involved in epileptic activity. In neonates, our results also demonstrated that the functional connectivity analysis can be efficiently used to study the effect of EEG transients and sleep stages on the functional organization of the brain networks during the early periods of neurodevelopment.

iii

Résumé

Cette thèse porte sur deux aspects de la connectivité fonctionnelle cérébrale en EEG chez l'enfant à l'état de repos : (i) chez les enfants présentant une Epilepsie Bénigne à Pointes Centro-Temporales ou EPCT et (ii) chez les nouveau-nés à terme et prématuré pendant le sommeil.

Dans la première étude, nous avons examiné les modifications de la connectivité fonctionnelle cérébrale liées à l'épilepsie en comparant les résultats chez les patients EPCT par rapport aux témoins sains. Ceci a été réalisé dans différentes bandes de fréquences à l'état de repos, les yeux fermés. Les différences de connectivité fonctionnelle mais aussi effective ont été étudiées dans l'espace capteur et dans l'espace source. La théorie des graphs a été appliquée afin de caractériser la ségrégation et l'intégration fonctionnelle des réseaux cérébraux chez les patients EPCT et les sujets sains.

La première partie de l'étude a montré que les réseaux à l'état de repos des patients EPCT étaient perturbés par la présence de pointes épileptiques intercritiques (IIS). La puissance EEG dans la bande θ était significativement plus élevée sur l'ensemble du scalp lors de la présence des pointes épileptiques alors que la puissance de la bande alpha était diminuée notamment dans les régions occipitales. Dans l'espace source nous avons aussi observé une diminution de l'activité cérébrale dans les régions frontales et occipitales et une augmentation dans les régions temporales bilatérales chez les patients EPCT comparés aux sujets sains.

Notre étude de connectivité fonctionnelle a montré que les patients EPCT présentaient une altération du réseau cérébral au repos qui pouvait être mise en relation avec une perturbation des réseaux dit de repos selon la gamme de fréquence analysée. Nos résultats ont montré que les réseaux cérébraux chez les patients EPCT étaient plus ordonnés en particulier dans les bandes de fréquences basses et notamment en présence des pointes épileptiques intercritiques. Nous avons examiné la connectivité effective chez les patients EPCT afin d'identifier les principaux drivers de l'activité épileptique. Nous avons montré que les régions les plus impliquées dans l'émergence des pointes épileptiques étaient les régions précentrales dont les aires motrices supplémentaires de l'hémisphère ipslatéral au foyer épileptique. L'influence causale de la région centrale vers la région frontale ipsilatérale et controlatérale pourrait être impliquée dans les déficits cognitifs observés chez l'enfant présentant une Epilepsie Bénigne à Pointes Centro-Temporales Dans la seconde étude, nous avons étudié la connectivité fonctionnelle cérébrale chez les nouveau-nés prématurés, dans le sommeil calme, à l'aide de l'EEG haute densité et en utilisant les outils de la théorie des graphs. L'évolution constante des structures cérébrales au cours de la maturation cérébrale précoce impose des changements rapides spatiaux et temporels des patterns de l'EEG néonatal. Il existe différents types de neurobiomarqueurs développementaux endogènes de l'activité cérébrale néonatale parmi lesquels les activités théta temporales. Nous avons étudié l'impact des activités thêta temporales sur la connectivité fonctionnelle à cette période du développement. Avec ou sans activité théta temporale, la densité de la connectivité fonctionnelle est plus élevée dans les régions frontales et occipitales suggérant l'existence d'un gradient de maturation. La présence des activités théta temporales induit une augmentation de la connectivité fonctionnelle restreinte aux régions temporales ipsilaterales.

Chez les nouveau-nés nés à terme, nous avons étudié la connectivité fonctionnelle au cours du sommeil calme et du sommeil agité. L'activité de source était plus importante dans les régions frontales au cours du sommeil agité alors qu'elle était plus importante dans les régions temporales et postérieures dans le sommeil calme. De la même manière la densité de connectivité fonctionnelle est plus élevée dans les régions frontales, temporales et postérieures dans le sommeil agité et le sommeil calme. Dans ces deux conditions, le coefficient de clustering était moins important dans la région centrale que dans les autres régions. L'augmentation de l'activité de source dans les régions frontales et postérieures pourrait constituer un autre argument concernant le développement précoce de ces régions.

xii Table 5.1: Characteristics of controls and patients' groups ……………………………73 Worldwide, about 65 million people are affected by epilepsy, a chronic neurological disease characterized by sudden bursts of abnormal neuronal activities in the brain, manifesting as seizures. Significant progress has been made towards understanding basic mechanisms of epilepsy especially in young children. There are many age-specific clinical and electroencephalographic features of epilepsy that are not clearly understood yet. Functional connectivity analyses can provide fundamental insights into complex interactions and functional organization of the brain networks under normal and pathological conditions. Functional connections between brain networks can occur between spatially close or remote areas to effectively perform information segregation and integration. The functional connectivity analysis in patients with epilepsy helps neurologists to better understand the pathophysiological impact of altered neurophysiology on the brain function especially during critical periods of neurodevelopment.

List of figures

In adults, the brain neural networks are connected with firmer intricate connections between various brain regions. The infant brain, however, contains less intricate, loose networks with relatively less functional connections between different regions. This suggests that functional brain networks sustaining advanced behavior are immature in infants. During the maturation process, a gradual reorganization of cortical regions between birth and adulthood occurs and large-scale cortical networks develop from a ''local and segregated'' to a ''distributed and integrated'' organization.

In neonates, the functional organization of the brain networks is not clearly understood yet. The functional analysis in neonates will expand our understanding of the sequential steps in the brain maturation and may help to investigate disturbances in the maturation process of the brain in preterm and full-term babies.

In this thesis we focus on two studies investigating the resting-state EEG functional connectivity in children with benign childhood epilepsy with centrotemporal spikes (BCECTS) and in preterm and full-term neonates.

Purpose of the Thesis

The main aim of this thesis is to investigate the functional plasticity in development in neonates and the effect of pathology such as epilepsy in young children during the course of development. Therefore, the thesis was subdivided into two parts

In the first part of the thesis, we investigated changes in brain functional connectivity patterns in BCECTS patients compared to healthy controls in various frequency bands under the eyes-closed resting condition. The differences in EEG functional and effective connectivity patterns between BCECTS patients and healthy controls were studied in both the sensor and source spaces. . The objectives of this study were:

 To investigate the changes in the EEG resting-state spectral power and spatial distribution of EEG cortical sources in different frequency bands in BCECTS patients in comparison to healthy controls.  To characterize the brain functional connectivity patterns in BCECTS patients with different graph theory metrics commonly used to explore local and global topologies of the brain networks in terms of functional integration and segregation.  To investigate the impact of interictal epileptic discharges on the functional connectivity patterns in BCECTS patients.  To identify time-varying changes in functional connectivity as well as the brain regions involved in the generation and propagation of interictal epileptic discharges.

In the second part of the thesis, we assessed functional connectivity patterns of the brain networks in healthy preterm and full-term neonates with high density EEG data during quiet and active sleep periods. The purposes of this study were:  To investigate the brain functional organization in preterm and full-term neonates.  To investigate the impact of endogenous brain activities like theta temporal activity on the brain functional connectivity patterns in neonates.  To characterize the functional connectivity patterns of the neonatal brain networks with different network metrics.  To investigate the brain functional organization in healthy full-term neonates during quiet and active sleep periods.

Thesis Outline

Chapter 1 introduces the motivation and purposes of the thesis. The rest of the thesis is organized as follows.

Chapter 2 provides an introduction to the brain anatomy and functional maturation during infancy and adulthood. A short background on the generation and recording of EEG in neonates and adult is also provided. The last part of Chapter 2 presents an overview on epileptic activity with particular attention to the benign childhood epilepsy.

Chapter 3 reports a short review on brain connectivity analyses including structural, functional and effective connectivity. Special attention is paid to the functional connectivity analysis and graph theory metrics with mathematical details.

In chapter 4, we use the approach presented in Chapter 3 to investigate the differences in brain functional connectivity patterns between BCECTS patients and healthy controls under the resting state condition.

Chapter 5 investigates the functional connectivity patterns using the seed-based functional analysis and explores the temporal dynamics of the brain functional connectivity during interictal epileptic discharges in BCECTS patients.

Chapter 6 is devoted to the brain functional connectivity analysis in preterm and full-term neonates using high density EEG. The specific features of neonatal EEG activities such as theta temporal burst activity (TTA) and different sleep stages including quiet and active sleep are taken into considerations.

Chapter 7 gives the concluding remarks and future research directions.

Chapter 2

EEG and Epilepsy

Introduction

The temporal dynamics of the brain is determined by successions of spatiotemporal transient patterns of activities integrated by the brain's anatomical structure including principally connections with highly adaptable nature. The temporal coherence is achieved by the synchronization of neural networks operating in harmony in distinct frequency bands. The brain functioning can be explained at the level of the neural networks interconnected in an intricate pattern. In this view, the brain can be regarded as an ensemble of connected dynamical systems relating the inputs and outputs of its constituent parts. To capture the temporal evolution of brain activities, one needs a tool to monitor it over time. This chapter describes briefly brain anatomy and functions, EEG genesis and measurement, and basic EEG rhythms during the resting state in adults, young children and neonates. A short overview of epilepsy including pediatric epilepsy is also given, with particular attention to the benign childhood epilepsy.

Human brain

The brain tissue consists of billions of neurons. It is divided into gray and white matters. Grey matter consists of cell bodies and few myelinated axons, while white matter consists of very few cell bodies and is principally composed of long-range myelinated axon tracts [START_REF] Stiles | The Basics of Brain Development[END_REF]. The brain is protected by the skull and dura matter, arachnoid and pia matter. The space between the pia matter and the arachnoid is filled with cerebrospinal fluid (CSF) (Figure 2.1) [START_REF] Silverthorn | Human Physiology: An Integrated Approach[END_REF]. The CSF protects the brain against the bone and serves as a medium for the transportation of the brain nutrients and water to the white and gray matters. In large scale, the brain is divided into the cerebellum at the bottom of the brain and the cerebrum at the upper part of the brain usually referred to as the cerebral cortex. The cerebrum is divided into right and left hemispheres including frontal, temporal, parietal and occipital lobes (Figure 2.3). Brain is protected by the skull, scalp and CSF with the pia matter and arachnoid membrane (adapted from [START_REF] Silverthorn | Human Physiology: An Integrated Approach[END_REF])

Brain structural maturation

The human brain structure matures rapidly form early fetal period within which the brain has a smooth, "lissencephalic" structure and it gradually develops the characteristic mature pattern of gyral and sulcal folding (Figure 2.2). The formation of gyri and sulci follows an orderly sequence as the age increases [START_REF] Stiles | The Basics of Brain Development[END_REF]. Another important characteristic feature of the brain development is the longitudinal fissure that separates the two cerebral hemispheres. Some part of the brain is developed at the early age such as cingulate, parietooccipital and calcarine (14-16 weeks); central and superior temporal regions (20-24 weeks); and superior frontal, precentral, inferior frontal and postcentral regions (25-26 weeks). Secondary sulci emerge between 30-35 weeks. The formation of tertiary sulci begins during 36 weeks and extends into the postnatal period (Figure 2.2) (O' Leary et al., 2007;[START_REF] Stiles | The Basics of Brain Development[END_REF][START_REF] Van Essen | Surface-Based and Probabilistic Atlases of Primate Cerebral Cortex[END_REF].

Although, the development and migration of neurons are largely prenatal events, the proliferation and migration of glial progenitors continues for an extended period after birth, and the differentiation and maturation of these cells continue throughout the childhood period. In the postnatal period, neurogenesis continues to only a very limited degree [START_REF] O'leary | Area patterning of the mammalian cortex[END_REF][START_REF] Stiles | The Basics of Brain Development[END_REF]. However, in some brain region like hippocampus, cortex and striatum, new neurons continue to develop where they migrate from the subgranular layer to the nearby granular layer. These exceptional forms of neurogenesis appear to continue throughout adult life but produce only a small percentage of the neuronal population.

Functional maturation

The neonatal brain maturation is functionally characterized by specific features which serve as biomarkers for the functional development of the brain [START_REF] André | Electroencephalography in premature and full-term infants. Developmental features and glossary[END_REF]. Although, most of the primary sensory systems are already functionally established at birth but the long range functional connectivity is limited in infants under the age of 2 years old [START_REF] Fransson | Resting-state networks in the infant brain[END_REF][START_REF] Stiles | The Basics of Brain Development[END_REF]. The functional brain development in neonates is concomitant with the sequential functional maturation of different cortical regions. New cognitive functions during infancy and childhood might be the result of emerging patterns of interactions between different regions [START_REF] Johnson | Functional brain development in humans[END_REF]. Meanwhile, the mature brain in adults is physically delineated as the cerebral cortex. The cerebral cortex serves as a central processing center integrating sensory information and making decisions for many types of motor output. The cerebral cortex is divided into several brain regions. The functional regions of the cerebral cortex do not necessarily correspond to the anatomical lobes of the brain. However, the frontal lobe (Figure 2.3) is known for thinking, executing functions, planning and behavioral controls [START_REF] Silverthorn | Human Physiology: An Integrated Approach[END_REF][START_REF] Stiles | The Basics of Brain Development[END_REF]. The motor cortex is responsible for the motor coordination and movement while the parietal lobe is involved in the perception, sensing, and simple cognitive task. The occipital lobe is involved in visual processing and the temporal lobe in language processing and memoryfunctions . The functional specialization is not symmetrical across the cerebral cortex. For instance, language and verbal skills tend to be concentrated on the left side of the brain, with spatial skills centered on the right side [START_REF] Knecht | Handedness and hemispheric language dominance in healthy humans[END_REF][START_REF] Springer | Left brain, right brain: Perspectives from cognitive neuroscience[END_REF].

Figure 2.3: The cerebral cortex is specialized into functional areas such as sensory, motor and association areas that integrate information (adapted from [START_REF] Silverthorn | Human Physiology: An Integrated Approach[END_REF]).

Electroencephalography

Generators of EEG

EEG is the electrical activity of the brain, most specifically it is the sum of extracellular current flows from large group of neurons [START_REF] Holmes | Basic Neurophysiology and the Cortical Basis of EEG[END_REF]. EEG arises from synchronized synaptic activity of populations of cortical neurons called pyramidal cells (Figure 2.4). The pyramidal neurons are organized in such a way that the neighboring dendritic trees are in parallel to each other and almost orthogonal to the cortical surface. The pyramidal neurons are believed to be the main generator of EEG. For more information on the generation of EEG, the readers are referred to the following reviews [START_REF] Holmes | Basic Neurophysiology and the Cortical Basis of EEG[END_REF][START_REF] Jackson | The neurophysiological bases of EEG and EEG measurement: A review for the rest of us[END_REF][START_REF] Silva | EEG: Origin and Measurement[END_REF]. The high temporal resolution of EEG makes it an excellent tool to study the neuronal activity of different brain regions over time.

EEG recordings

EEG recordings are performed by placing electrodes in predefined standard positions on the head. An international standard EEG electrode configuration is shown in Figure 2.5. EEG can be recorded between pairs of active electrodes (bipolar montage) or respective to passive or active reference electrode (monopolar montage). The positions of the electrodes are based on the anatomical landmarks such as inion and nasion. The number of electrodes and their exact positions depend on the application. In clinical practice, usually 20 to 32 electrodes are used. For research purposes, it is usually required to increase the spatial resolution by increasing the number of electrodes [START_REF] Lantz | Epileptic source localization with high density EEG: how many electrodes are needed?[END_REF][START_REF] Sohrabpour | Effect of EEG electrode number on epileptic source localization in pediatric patients[END_REF][START_REF] Song | EEG source localization: Sensor density and head surface coverage[END_REF]. EEG is mostly recorded on the scalp surface with subjects relaxed or involved in the experimental tasks. One important problem of scalp EEG is the artifact due to head movement, eye blinking, muscle activity and electronic interferences. Due to low amplitude of EEG in the order of 100μV, artifacts can contaminate the recordings and produce false results if not properly minimized or rejected.

Neonatal EEG is usually recorded with 8 surface electrodes positioned according to the international 10/20 system, which is adapted to the newborn head (Figure 2.6). Additional electrodes are also added for monitoring electrocardiography(ECG), respiration and electromyography (EMG). In addition, video-EEG is usually performed to record the activity and response of neonates [START_REF] Lamblin | EEG in the neonatal unit[END_REF][START_REF] Walls-Esquivel | Electroencephalography (EEG) recording techniques and artefact detection in early premature babies[END_REF]. There is growing interest to increase the number of electrodes due to the spatial specificity of the neonatal EEG [START_REF] Odabaee | Spatial patterning of the neonatal EEG suggests a need for a high number of electrodes[END_REF].

EEG brain activity

Resting state EEG

Resting state is the dynamic substrate of the present momentary state of the brain, and determines the fate of incoming information. At rest, the brain goes through all working modes such as sensory, attention, executive, control and language. Some brain regions are activated or deactivated at rest, usually studied with the functional magnetic resonance imaging (fMRI) [START_REF] Biswal | Resting state fMRI: A personal history[END_REF].

Resting state EEG is used to monitor brain activity in the absence of task or brain stimulation [START_REF] Olejniczak | Neurophysiologic basis of EEG[END_REF]. It can be used to identify abnormalities by comparing different neurological disorders and event related potentials such as visual stimuli or motor responses to resting state activity. The most common way of characterizing resting EEG is by breaking down oscillatory patterns into different frequency bands. Power spectral analysis is the most common method used to quantify the resting state EEG in different frequency bands. The functional connectivity analysis can also be used to assess interaction between brain regions [START_REF] Coben | EEG power and coherence in autistic spectrum disorder[END_REF][START_REF] Murias | Resting State Cortical Connectivity Reflected in EEG Coherence in Individuals With Autism[END_REF][START_REF] Sponheim | Clinical and biological concomitants of resting state EEG power abnormalities in schizophrenia[END_REF].

The mature brain EEG activity is studied based on the different EEG rhythms or brain oscillations according to the frequency contents. The EEG rhythms may be related to the normal brain functions, functional states and pathological conditions (Başar et al., 2013;Başar and Güntekin, 2013;[START_REF] Klimesch | EEG alpha and theta oscillations reflect cognitive and memory performance: a review and analysis[END_REF][START_REF] Michel | Electrical Neuroimaging[END_REF]. As shown in Figure 2.7, EEG rhythms can be classified into:

ECG EMG

Respiratory recording

Delta rhythm (less than 4Hz): This rhythm is observed in deep sleep stages with large amplitude and its presence in awake adult may indicate brain disorders.

Theta rhythm (4 to 8Hz): Theta rhythm plays an important role in neurodevelopment during childhood, and found in drowsiness and some certain sleep stages. High theta activity in awake young children and adults is related with brain disorders.

Alpha rhythm (8 to 13Hz): It appears spontaneously in relaxed and awake adult with eyes closed and is most pronounced at the occipital regions of the brain. It also relates to cognitive process in normal brain function.

Beta rhythm (13 to 30Hz): It is best defined at the central and frontal brain regions and related to alertness and thinking.

Gamma rhythm (above 30 Hz):

With very low amplitude it is related to higher cognitive thinking and information processing in the brain. [START_REF] André | Electroencephalography in premature and full-term infants. Developmental features and glossary[END_REF]. The brain changes are resulted fromthe dendritic development, glial proliferations, synaptogenesis and myelination [START_REF] Zhang | Relationship between brain activity and voiding patterns in healthy preterm neonates[END_REF]. The development underlying rapid sequences of EEG changes are often used to predict and determine the healthy state of newborns. EEG has been proven to be an efficient tool for the assessment of cerebral functions in neonates [START_REF] Lamblin | Electroencephalography of the premature and term newborn. Maturational aspects and glossary[END_REF][START_REF] Vecchierini | EEG patterns in 10 extreme premature neonates with normal neurological outcome: qualitative and quantitative data[END_REF].

 (0.5 -4Hz)  (4 -8Hz)  (9 -13Hz)  (13 -30Hz)  (30 -70Hz) 2s
Preterm neonates born below 32 wGA are characterized by long discontinuity interrupted by bursts of EEG activity (Figure 2.8a). The interburst interval is significantly reduced with increasing with increasing age [START_REF] Vanhatalo | Development of neonatal EEG activity: from phenomenology to physiology[END_REF][START_REF] Wallois | Synopsis of maturation of specific features in EEG of premature neonates[END_REF]. The EEG bursts are of high amplitude with dominant frequencies in lower frequency bands (δ and θ bands). The amplitude of bursts decreases with increasing age. The duration of interburst is also used to estimate the brain maturity in neonates. In preterm neonates, the theta temporal burst (Figure 2.8b),used as biomarker for the brain maturation, appears at the temporal region. In preterm neonates of 32 to 36 wGA thedelta brushes as another biomarker appear at the occipital and temporal regions [START_REF] André | Electroencephalography in premature and full-term infants. Developmental features and glossary[END_REF][START_REF] Wallois | Synopsis of maturation of specific features in EEG of premature neonates[END_REF]. The delta brushes are characterized by low amplitude fast activites superimposed on slow waves of high amplitude. Healthy full-term neonates above 37 wGA are characterized with biphasic frontal sharp transients especially during quite sleep [START_REF] Torres | The normal EEG of the human newborn[END_REF]. See Figure 2.9 for the synopsis of maturation in neonates [START_REF] Wallois | Synopsis of maturation of specific features in EEG of premature neonates[END_REF]. In turn, quite sleep is associated with the absence of rapid eye movement, fewer body movement, higher muscle tones, decreased variability of respiratory rates and high amplitude continuous EEG with less discontinues EEG pattern [START_REF] André | Electroencephalography in premature and full-term infants. Developmental features and glossary[END_REF][START_REF] Mizrahi | Atlas of neonatal electroencephalography[END_REF][START_REF] Scher | Neonatal EEG/sleep state analyses: a complex phenotype of developmental neural plasticity[END_REF].

Epilepsy activity in EEG

Epilepsy is a brain disorder that affects about 0.5 to 1% of the world population. It is characterized by the recurrent, excessive and uncontrolled abnormal brain activity. Epilepsy can begin at any age, but is more common in children compared to adults. The prevalence of epilepsy generally depends on the gender, age and geographical population. Many factors are responsible for the epilepsy such as genetic, low oxygen during birth, head injuries that occur during birth or from accidents during youth or adulthood, brain tumors, infections such as meningitis or encephalitis, damage to the brain and abnormal levels of substances [START_REF] Banerjee | The descriptive epidemiology of epilepsy-A review[END_REF]Lars Forsgren et al., 2005;L. Forsgren et al., 2005).

Epileptic seizure is abnormal hypersynchronous neuronal activities of the brain. The clinical manifestation of seizures has many forms depending on which brain regions are involved in epileptic activity. Although the underlying causes of epilepsy are still unknown, certain factors are known to provoke seizures in people with epilepsy. Missing medication doses, heavy alcohol use, cocaine or other drug, and lack of sleep can provoke seizures in epileptic patients [START_REF] Bonney | Review of seizure outcomes after surgical resection of dysembryoplastic neuroepithelial tumors[END_REF][START_REF] Semah | Is the underlying cause of epilepsy a major prognostic factor for recurrence?[END_REF]. There are many classifications of epilepsy but depending on the etiology of epilepsy, it can be classified to either partial or generalized epilepsies. Partial epilepsies have focal origin which can be simple without losing consciousness and complex involving losing consciousness. The simple partial epilepsy is characterized by focal motor movements, sensory symptoms or autonomic symptoms [START_REF] Rheims | Greater Response to Placebo in Children Than in Adults: A Systematic Review and Meta-Analysis in Drug-Resistant Partial Epilepsy[END_REF]. This type of epilepsy can be further classified into temporal, frontal, occipital or temporal lobe epilepsy depending on the source of seizure. Different physical sensation and motor automatisms are associated with complex partial epilepsy. The partial epilepsy can evolve to generalized epilepsy if not properly taking care of. The generalized epilepsy involves the whole brain and may last longer in order of 20 seconds. Example of generalized epilepsy is absence epilepsy that consists of sudden lapse of consciousness with the impairment of mental functions [START_REF] Scheffer | Generalized epilepsy with febrile seizures plus. A genetic disorder with heterogeneous clinical phenotypes[END_REF][START_REF] Singh | Generalized epilepsy with febrile seizures plus: A common childhood-onset genetic epilepsy syndrome[END_REF].

One of the important applications of the EEG is to study epilepsy. The appearance of higher amplitude waves during ictal period compared to interictal periods and several other paroxysms are general landmark of epilepsy. These features help to identify, classify and localize seizures. Epileptic components and waves vary especially in frequency range, duration and topography [START_REF] Banerjee | The descriptive epidemiology of epilepsy-A review[END_REF]. Manifestation of epileptic activity can also be obtained during interictal epileptic discharges (IEDs), which are the spike and sharp waves, either of which can occur with or without a subsequent slow wave. IEDs can occur separately in brief burst that look like seizure activity. However, the introduction of video-EEG recording has been an important milestone helping to identify specific movements and behavior of patients during seizures.

Benign childhood epilepsy

Benign childhood epilepsy (BCE) affects 10 to 20% of children with epilepsy (Camfield et al., 2014;Chrysostomos P. Panayiotopoulos, 1999). Characteristically, the seizures begin between 2 and 16 years of age. Benign childhood epilepsy is considered a benign form of childhood epilepsy that occurs in children who show normal mental development. The risk of cognitive impairment has been shown to be higher by comparing the test performance of children with BCE with that of the healthy age-matched children [START_REF] Danielsson | Cognitive deficits in children with benign rolandic epilepsy of childhood or rolandic discharges: a study of children between 4 and 7 years of age with and without seizures compared with healthy controls[END_REF][START_REF] Datta | Cognitive impairment and cortical reorganization in children with benign epilepsy with centrotemporal spikes[END_REF]. Unlike adult epilepsy such as temporal lobe epilepsy, brain imaging has shown that brain structural of BCE patients is usually normal [START_REF] Fountain | Evidence for Functional Impairment But Not Structural Disease in Benign Rolandic Epilepsy[END_REF].

The most common BCE is benign childhood epilepsy with central temporal spikes (BCECTS) and often called rolandic epilepsy or Panayiotopoulos syndrome (Chrysostomos P. Panayiotopoulos, 1999;C. P. Panayiotopoulos, 1999). The common seizure begins in sleep and is very simple and partial. Secondary generalized type of epilepsy is not that common. The occurrence of BCECTS involves unilateral sensory-motor symptoms, speech arrest and hypersalivation.

The most useful diagnostic tool for BCE is EEG. The appearance of infrequent seizures or generalized burst in EEG with bi or triphasic spike activity in rolandic areas is highly suggestive of benign childhood epilepsy. It can occur at either left or right hemisphere of the brain region or at both. With high density EEG (Figure 2.10), it is mainly localized in the high central (C3 and C4) or low central (C5 and C6) supra-sylvian regions. Further analyses including normal neurological examination and spike source imaging showing an anterior-posterior dipole orientation confirm the possibility of BCECTS [START_REF] Camfield | Epileptic Syndromes in Childhood: Clinical Features, Outcomes, and Treatment[END_REF][START_REF] Panayiotopoulos | The Epilepsies: Seizures, Syndromes and Management[END_REF]. However, brain imaging is not always required except in some difficult cases.

Chapter 3

Brain connectivity analysis

Introduction

The brain is a highly distributed complex system in which a very large number of processes are simultaneously processed in parallel. The brain complexity can be defined based on its neuronal populations, which at a macroscopic scale operate on random and regular regimes. The complex architecture of the brain involves neuronal networks which are highly specialized in multiple parallel operations linked together to give rise to coherent perception and action. The anatomical and functional inter-neuronal connectivity of brain networks can occur between spatially close or remote areas, the former having a relatively high probability of occurrence. The functional connectivity between brain networks are organized for effective information processing including segregation and integration. In particular, both segregation and integration of information have to be dealt within a single architecture of brain networks. At a microscopic scale, the brain consists of electrical circuits formed by the interconnection of billions of elementary processing units (neurons and glia) [START_REF] Bear | Neuroscience: Exploring the Brain[END_REF].

In adults, the brain neural networks are connected with firmer intricate connections between various brain regions. However, due to higher efficiency the connections in gray matter are significantly reduced. The adult brains have been shown to follow a web-like mesh of many different interconnecting links involving all the regions. In adults, there are brain regions showing a disproportionally high degree of anatomical connectivity (so called ''cortical hubs'') to control the flow of information [START_REF] Gong | Establishment and characterization of a cell based artificial antigen-presenting cell for expansion and activation of CD8+ T cells ex vivo[END_REF][START_REF] Hagmann | Mapping the Structural Core of Human Cerebral Cortex[END_REF], such as: aspects of selfreferential thinking [START_REF] Gusnard | Medial prefrontal cortex and self-referential mental activity: relation to a default mode of brain function[END_REF], episodic memory retrieval [START_REF] Kim | Widespread transcription at neuronal activity-regulated enhancers[END_REF], prospective thought [START_REF] Addis | Remembering the past and imagining the future: common and distinct neural substrates during event construction and elaboration[END_REF], decision making, and in goal-oriented attentional tasks [START_REF] Corbetta | Control of goal-directed and stimulus-driven attention in the brain[END_REF]. These adult hub-related networks largely overlap with the default mode network and the fronto-parietal attention network (task-positive network) [START_REF] Buckner | Cortical Hubs Revealed by Intrinsic Functional Connectivity: Mapping, Assessment of Stability, and Relation to Alzheimer's Disease[END_REF]. Thus, the organization of adult hub-related networks sustains the complexity of the brain functionality [START_REF] Heuvel | Rich-Club Organization of the Human Connectome[END_REF].

The infant brain contains less intricate, loose networks with relatively less functional connections between different regions. The functional connectivity associated with cortical hubs in the infant brain largely overlaps with primary sensorimotor, auditory, and visual systems [START_REF] Fransson | Spontaneous Brain Activity in the Newborn Brain During Natural Sleep-An fMRI Study in Infants Born at Full Term[END_REF][START_REF] Fransson | Resting-state networks in the infant brain[END_REF]. The information flow through infant cortical hubs is dominated by processes related to rather reflexive (perception-action) behavior. This suggests that functional brain networks sustaining advanced behavior are immature in infants. During the maturation process, a gradual reorganization of hub network connectivity between birth and adulthood occurs and large-scale cortical networks develop from a ''local and segregated'' to a ''distributed and integrated'' organization [START_REF] Fair | Functional brain networks develop from a "local to distributed" organization[END_REF][START_REF] Power | The Development of Human Functional Brain Networks[END_REF][START_REF] Supekar | Development of Large-Scale Functional Brain Networks in Children[END_REF].

At birth, the neural networks are partially developed. In the first 6 years, the networks expand and the brain grows rapidly to allow new skills to be learned. The development of the immature brain is concomitant with certain morphological aspects of the developing brain and EEG results. These aspects are closely associated with the gestational age. Disturbance in the process of maturation for the infant babies of more than 26 weeks is likely to generate structural modification of the brain such as atrophy, gliosis and/or cavitation. Early detection of neurodevelopmental abnormalities would help to diagnose and treat affected babies. Full-term and premature neonates are at high risk of brain damage and life-long cognitive disability. According to different studies [START_REF] Marlow | Neurologic and Developmental Disability at Six Years of Age after Extremely Preterm Birth[END_REF][START_REF] Monset-Couchard | Catch-Up Growth in 166 Small-for-Gestational Age Premature Infants Weighing Less than 1,000 g at Birth[END_REF], about 6.2% of new-born infants in France are premature and from 36 to 60% of the premature infants of less than 30 weeks have neurological dysfunctions such as motor, cognitive and sensory deficits and learning disorders.

This chapter describes connectivity methods with particular attention to the functional and effective connectivity measures used in this thesis. The graph theoretical measures are also reviewed. The chapter starts with a short review on analytical signals required for the computation of functional connectivity and EEG source imaging.

Brain connectivity

Brain networks communicate to execute a particular function or task. The intercommunication phenomenon in the brain is termed brain connectivity. Brain connectivity reveals pathways or how information is exchanged between the brain regions [START_REF] Breakspear | Neuronal Dynamics and Brain Connectivity[END_REF]. Brain connectivity measures are bivariate, i.e., they involve the interactions between two brain regions or scalp electrodes.

There are three modes of brain connectivity-structural, functional and effective [START_REF] Friston | Models of Brain Function in Neuroimaging[END_REF][START_REF] Horwitz | The elusive concept of brain connectivity[END_REF]. Structural or anatomical connectivity refers to a network of structural (synaptic) connections linking sets of neurons or neuronal elements. Functional connectivity is fundamentally a statistical concept that estimates the temporal correlation between two signals over time. In general, functional connectivity captures deviations from statistical independence between distributed and often spatially remote neuronal units. Effective connectivity investigates the directional effect of one neural element over another. The difference between the three modes of connectivity is shown in Figure 3.1.

Structural connectivity

Structural connectivity is the anatomical connections between brain regions. This type of connection includes fiber pathways between the brain regions which can be assessed by the propagation of water molecules. The common imaging technique used is diffusion weighted imaging (DWI) which can be applied in several directions to examine the diffusion of water molecules in the brain [START_REF] Johansen-Berg | Using Diffusion Imaging to Study Human Connectional Anatomy[END_REF]. Diffusion tensor imaging (DTI) [START_REF] Shenton | A review of magnetic resonance imaging and diffusion tensor imaging findings in mild traumatic brain injury[END_REF] is another non-invasive method for characterizing the microstructural organization of the brain tissues in vivo. This method generates maps that visualize different aspects of the tissue microstructure (mean diffusivity, tissue anisotropy and dominant fiber orientation).

Functional connectivity

Functional connectivity is defined as statistical dependencies between brain regions [START_REF] Friston | Functional and effective connectivity in neuroimaging: A synthesis[END_REF]. Functional connectivity in neuroimaging is always estimated from fMRI and EEG/MEG time series. Functional connectivity is symmetric, implying that connectivity from x to y is similar to connectivity for y to x. There are many functional connectivity measures and descriptions. In this thesis we will focus on the power-based, phase-based and information-based functional connectivity measures. Before quantifying the functional connectivity between measurement sites or sources, their signals are transformed to the complex-value analytical signals. In addition, the source analysis is required for the transformation of EEG sensors signals to source signals.

Frequency-domain signals

Frequency-domain signal is a complex-valued variable usually obtained from the fast Fourier transform of the signal. The Fourier transform of a time-series, x, is obtained by the dot product of the signal and sine waves of different frequencies:

𝑋(𝑓) = ∑ 𝑥 𝑘 𝑒 -𝑖2𝜋𝑓(𝑘-1) 𝑁 𝑁 𝑘=1 (3.1) Structural Functional Effective
where N refers to the number of data points in vector, x, and X(f) is the complex-series signal at frequency f. The number of unique frequencies extracted from a times-series of length N is N/2+1 based on the Nyquist theorem.

The short-time fast Fourier transform (FFT) is an extension of the Fourier transform. The Fourier transform assumes the EEG signal to be stationary and obscures time-frequency changes in EEG data. The short-time FFT is computed by first segmenting (with Hann or Gaussian windows) the data to minimized edge artifacts from contaminating the time-frequency results [START_REF] Cohen | Analyzing Neural Time Series Data: Theory and Practice[END_REF]. However, the disadvantage of this method is that tapering attenuates the signals.

The attenuation of signals in the short-time FFT method is corrected by an improved method, called Multitaper method. It is designed to increase the signal to noise ratio of the signal by applying multiple tapers with several different temporal characteristics [START_REF] Bronez | On the performance advantage of multitaper spectral analysis[END_REF]. The multitaper method introduces some frequency smoothing depending on the number of tapers. This method is beneficial when one deals with noisy or few single trial EEG signals. It is also well suited for high frequency analysis with very good anti-frequency leakage [START_REF] Van Vugt | Comparison of spectral analysis methods for characterizing brain oscillations[END_REF].

Another method usually used to obtain frequency-domain signals is the wavelet analysis like Complex Morlet Wavelet (CMW) which involves many technical details on controlling the frequency smoothing such as number of cycles, minimum and maximum frequencies, and frequency resolution [START_REF] Tallon-Baudry | Stimulus specificity of phaselocked and non-phase-locked 40 Hz visual responses in human[END_REF]. The wavelet methods are well suited for localizing frequency information in time. CMW is defined as:

𝑤(𝑡, 𝑓) = (𝜎 𝑡 √𝜋) - 1 2 𝑒 - 𝑡 2 2𝜎 𝑡 2 𝑒 -𝑖2𝜋𝑓𝑡 (3.2)
where f is the center frequency and σt is the temporal standard deviation. The time-frequency analytical signal X (t,f) of a signal x(t) is then computed by convolving x(t) and w(t,f):

𝑋(𝑡, 𝑓) = 𝑥(𝑡) * 𝑤(𝑡, 𝑓) (3.3)
The spectral bandwidth is controlled by the ratio of f to σf to obtain desired frequency ranges.

The Hilbert transform is another time-frequency decomposition method which allows more control over frequency characteristics, a major advantage over the wavelet method [START_REF] Cohen | Analyzing Neural Time Series Data: Theory and Practice[END_REF][START_REF] Freeman | Hilbert transform for brain waves[END_REF]. The signal is first band-filtered within a desire frequency range. The Hilbert transformation is then applied to extract the frequency-domain signal X (t, f) as: 𝑋(𝑡, 𝑓) = 𝑥(𝑡, 𝑓) + 𝑖𝑥 𝐻 (𝑡, 𝑓) (3.4)

Where xH (t, f) is the Hilbert transform of the input signal x (t,f).

These methods are commonly used in EEG data analysis and can give similar results with minimal differences [START_REF] Akin | Comparison of Wavelet Transform and FFT Methods in the Analysis of EEG Signals[END_REF][START_REF] Van Quyen | Comparison of Hilbert transform and wavelet methods for the analysis of neuronal synchrony[END_REF][START_REF] Van Vugt | Comparison of spectral analysis methods for characterizing brain oscillations[END_REF]. Other timefrequency decomposition methods are S-transform, an adaptation of short-time FFT, matching pursuit, Hilbert-Huang, P-episode and many more.

Power spectral density

Power spectral density function (PSD) is obtained from the analytical signals:

PSD(f) = X(f) * X * (𝑓) 𝑁 (3.5) Where ) ( * f X
is the complex conjugate of X(f) and N is the number of data points. The power decreases with increasing frequency [START_REF] Freeman | Origin, structure, and role of background EEG activity. Part 4: Neural frame simulation[END_REF][START_REF] Kiebel | Parametric analysis of oscillatory activity as measured with EEG/MEG[END_REF]. Power spectral analysis is used in EEG analysis to evaluate classical EEG frequency bands relevant to physiological rhythms.

Usually, EEG powers are normalized for statistical analysis and comparisons between different conditions. Normalization is done with reference to a baseline or to a maximum value. The common normalization is based on decibel conversion, percentage or unit conversion and ztransform.

The functional connectivity in the source space requires EEG source imaging by transforming EEG signal in the sensor space to source activities in the source space.

EEG source imaging EEG Source Imaging (ESI) is the modeling of the electrical source distributions associated with the brain activation from noninvasive EEG/MEG recording (He et al., 2011;[START_REF] Michel | Localization of the sources of EEG delta, theta, alpha and beta frequency bands using the FFT dipole approximation[END_REF]. ESI comprises forward and inverse problems (Figure 3.2):

Forward problem

The forward problem estimates the scalp potentials based on the head volume conductor [START_REF] Hallez | Review on solving the forward problem in EEG source analysis[END_REF]. The accurate modeling of the head volume conductors is very important for accurate imaging of the brain sources. The head model provides the description of the geometry and electrical properties of each tissues type (gray, white matter, CSF, skull and scalp). Simple spherical head model is built from the concentric spheres. The realistic head models are built from the structural MRI and computed tomography (CT) of the brain model by the boundary element method (BEM) [START_REF] Fuchs | A standardized boundary element method volume conductor model[END_REF], finite difference method (FDM) [START_REF] Hallez | A finite difference method with reciprocity used to incorporate anisotropy in electroencephalogram dipole source localization[END_REF] and finite element method (FEM) [START_REF] Wolters | A parallel algebraic multigrid solver for finite element method based source localization in the human brain[END_REF]. BEM usually assumes three homogenous layers (brain, skull and scalp) (Figure 3.2). BEM is computationally efficient unlike FEM and FDM that divide the head into small elements for each of which the geometry and conductivity can be defined separately. FEM and FDM allow incorporation of tissues anisotropy [START_REF] Hallez | Incorporation of anisotropic conductivities in EEG source analysis[END_REF][START_REF] Wolters | Influence of tissue conductivity anisotropy on EEG/MEG field and return current computation in a realistic head model: a simulation and visualization study using highresolution finite element modeling[END_REF] but complexity of the model construction make them computationally very expensive. The scalp potentials, V with the current sources dipole at position r = [x y z] and dipole moment D = [ Dx Dy Dz] are related by:

𝑉 = 𝐿(𝑟)𝐷 (3.6)
where L is the transfer or leadfield matrix that describes the relationship between dipole, D and the scalp potentials, V. The leadfield matrix consists of head geometry and tissues conductivity. [START_REF] Hallez | Review on solving the forward problem in EEG source analysis[END_REF] provide a detailed review on forward modeling.

Inverse problem

The inverse problem estimates the source distribution with the leadfield matrix and scalp potentials measured with electrodes [START_REF] Grech | Review on solving the inverse problem in EEG source analysis[END_REF]. The inverse problems are either based on dipoles source model or imaging method. In dipole source modeling, the aim is to estimate one or more dipole sources while minimizing the relative residual energy (RRE) [START_REF] Grech | Review on solving the inverse problem in EEG source analysis[END_REF][START_REF] Mosher | EEG source localization and imaging using multiple signal classification approaches[END_REF][START_REF] Mosher | Multiple dipole modeling and localization from spatio-temporal MEG data[END_REF]. This is done by assuming a predetermined number of dipoles as equivalent to the generator of the EEG. The dipole locations and moments are then estimated through optimization. Dipole source localization has been found to be useful in localizing epileptic activity with a reasonably good source detection rate. RRE is mathematically defined as:

𝑅𝑅𝐸 = ‖𝑉 -𝐿𝐷‖ ‖𝑉‖ (3.7)
Where V is scalp potentials, D is the dipole with its orientation and position and L is the leadfield matrix.

The second technique for the inverse problem is the imaging method. Unlike the dipole method, the imaging method is underdetermined, that is, the number of parameters to be estimated is larger than the number of scalp potentials. Imaging methods are based on the distributed source models with a fixed dipole position in each brain voxel. Underdetermined problems in imaging method are solved by the regularization of the parameters. This has led to development of various imaging methods generally based on the equation 3.8 to estimate the current density, D [START_REF] Grech | Review on solving the inverse problem in EEG source analysis[END_REF][START_REF] Michel | Electrical Neuroimaging[END_REF]:

𝐷 = 𝐴 -1 𝐿 𝑇 (𝐿𝐴 -1 𝐿 𝑇 + 𝜆𝐵 -1 ) -1 𝑉 (3.8)
Where L and V are the leadfield matrix and scalp potentials, respectively,  is the regularization parameter, the choice of A and B determines the type of the method being used such as minimum norm estimate [START_REF] Gramfort | Mixed-norm estimates for the M/EEG inverse problem using accelerated gradient methods[END_REF], linear beamfomer [START_REF] Drongelen | A spatial filtering technique to detect and localize multiple sources in the brain[END_REF][START_REF] Gross | Dynamic imaging of coherent sources: Studying neural interactions in the human brain[END_REF], low resolution electromagnetic tomography (LORETA) [START_REF] Pascual-Marqui | Standardized low-resolution brain electromagnetic tomography (sLORETA): technical details[END_REF], and many more.

Time and frequency domain source analysis

The EEG/MEG high temporal resolution is considered as the most important advantage of this type of imaging modality over other techniques like fMRI. In studies on event related potential (ERP) or epilepsy EEG source analysis in the time domain is usually performed on the 'events' selected by searching for electrodes with potential peaks [START_REF] Michel | Localization of the sources of EEG delta, theta, alpha and beta frequency bands using the FFT dipole approximation[END_REF][START_REF] Pascual-Marqui | Standardized low-resolution brain electromagnetic tomography (sLORETA): technical details[END_REF]. Alternatively, source localization methods can be applied to each time point and the temporal dynamics can directly be studied in the source space. This is usually used for the connectivity analysis in the source space.

The EEG high temporal resolution allows studying the behavior of sources in different frequencies by applying frequency transformation algorithms, source localization and connectivity in the frequency domain [START_REF] Gross | Dynamic imaging of coherent sources: Studying neural interactions in the human brain[END_REF][START_REF] Michel | Localization of the sources of EEG delta, theta, alpha and beta frequency bands using the FFT dipole approximation[END_REF]. This is preferable for many researchers that are interested in connectivity analysis and localization of sources for different frequency bands. Source analysis in the frequency domain is preceded by the analysis of analytical signals over a certain time epoch or segment as described earlier.

Power-based functional connectivity analysis

The functional connectivity can be evaluated in the time or frequency domain using linear dependence measures such as linear cross-correlation or coherence functions.

The Pearson correlation coefficient is a commonly used correlation method, defined as the covariance of two signals x and y, scaled by their variances:

𝑟(𝑥, 𝑦) = ∑ (𝑥 𝑡 -𝜇 𝑥 )(𝑦 𝑡 -𝜇 𝑦 ) 𝑁 𝑡=1 √∑ (𝑥 𝑡 -𝜇 𝑥 ) 2 𝑁 𝑡=1 ∑ (𝑦 𝑡 -𝜇 𝑦 ) 2 𝑁 𝑡=1 (3.9)
where N is the number of data points, x and y are mean values of the signals x and y, respectively. The resulting correlation value lies between -1 and 1 with 1 implying highest positive correlation.

The spectral coherence is similar to the correlation coefficient but in the frequency domain. The spectral coherence incorporates power information (both amplitude and phase). It is defined as follows:

𝐶 𝑥𝑦 (𝑓) = |𝑆 𝑥𝑦 (𝑓)| 2 𝑆 𝑥𝑥 (𝑓)𝑆 𝑦𝑦 (𝑓) (3.10)
where Sxy is the cross-spectral density of analytical signals X and Y, and Sxx and Syy are the auto-spectral density of X and Y, respectively. C lies between 0 and 1 with 1 implying highest coherence at frequency f. The spectral coherence incorporates power information and the results are likely to be influenced by cross-spectral of the two signals. However, it has been suggested to neglect the real component of the cross-spectrum [START_REF] Nolte | Identifying true brain interaction from EEG data using the imaginary part of coherency[END_REF] because it is highly affected by volumeconduction artifacts in EEG.

Phase-based functional connectivity analysis

There are several phase-based functional connectivity analyses relying on the distribution of phase differences between different electrodes. A common method to measure the strength of phase synchronization between different brain regions is the phase locking value (PLV) defined as [START_REF] Lachaux | Studying single-trials of phase synchronous activity in the brain[END_REF]:

𝑃𝐿𝑉 𝑥𝑦 (𝑓) = 1 𝑁 |∑ 𝑒 𝑖(∅ 𝑥 -∅ 𝑦 ) 𝑁 𝑡=1 | (3.11)
Where x and y are phase angles of the signals x and y, respectively, and N is the number of data points. The phase angles are usually obtained from the frequency-domain signals. The PLV values also range between 0 and 1.

Another method usually used for phase synchronization analysis is the phase lag index (PLI) [START_REF] Stam | Phase lag index: Assessment of functional connectivity from multi channel EEG and MEG with diminished bias from common sources[END_REF]. It was introduced to obtain reliable estimates of phase synchronization that are invariant against the presence of common sources (volume conduction and active reference electrodes in the case of EEG sensors). PLI is defined as:

𝑃𝐿𝐼 𝑥𝑦 (𝑓) = | 1 𝑁 ∑ 𝑠𝑔𝑛 (𝑖𝑚𝑎𝑔(𝑆 𝑥𝑦 )) 𝑁 𝑡=1 | (3.12)
Where imag(S) is the imaginary part of the cross-spectral density and sgn indicates sign (-1 for negative values, +1 for positive values and 0 for zero values). PLI is less sensitive to noise and volume conduction but is hindered by the discontinuity as small perturbations turn phase lags into leads and vice versa. As an extension of PLI, the weighted phase lag index (wPLI) [START_REF] Vinck | An improved index of phase-synchronization for electrophysiological data in the presence of volume-conduction, noise and sample-size bias[END_REF] was introduced as :

𝑤𝑃𝐿𝐼 𝑥𝑦 (𝑓) = 1 𝑁 ∑ |𝑖𝑚𝑎𝑔(𝑆 𝑥𝑦 )|𝑠𝑔𝑛(𝑖𝑚𝑎𝑔(𝑆 𝑥𝑦 ) ) 𝑁 𝑡=1 1 𝑁 ∑ |𝑖𝑚𝑎𝑔(𝑆 𝑥𝑦 )| 𝑁 𝑡=1
(3.13)

Information-based functional connectivity analysis

The information-based connectivity analysis involves both linear and non-linear statistical dependencies between two time series [START_REF] Hurtado | Statistical Method for Detection of Phase-Locking Episodes in Neural Oscillations[END_REF][START_REF] Jeong | Mutual information analysis of the EEG in patients with Alzheimer's disease[END_REF]. This technique is based on the concept of entropy that measures the probability of variable. The Shannon entropy (Hx) of a signal x is defined as: M and N correspond to the number of bins for signals x and y, respectively.

𝐻(𝑋) = -∑

Effective connectivity

The objective of effective connectivity analyses is to estimate causal dependencies between brain regions [START_REF] Friston | Functional and effective connectivity in neuroimaging: A synthesis[END_REF]. Unlike functional connectivity measures, effective connectivity indicates the direction of information flow between different brain regions [START_REF] Friston | Functional and effective connectivity in neuroimaging: A synthesis[END_REF]. The directional interaction can be estimated by model-based techniques such as dynamic causal modelling [START_REF] Friston | Dynamic causal modelling[END_REF], structural equation modeling [START_REF] Ullman | Structural Equation Modeling[END_REF], or Granger causality [START_REF] Hesse | The use of time-variant EEG Granger causality for inspecting directed interdependencies of neural assemblies[END_REF].

The effective connectivity analysis requires autoregressive modelling and model parameter estimation to estimate effective connections between brain regions.

Autoregressive modeling

Autoregressive (AR) modeling attempts to estimate future values of a signal based on a weighted sum of its past values. For a signal of length n, a multivariate autoregressive (MVAR) [START_REF] Ding | Short-window spectral analysis of cortical event-related potentials by adaptive multivariate autoregressive modeling: data preprocessing, model validation, and variability assessment[END_REF] model is represented by: 𝑋(𝑛) = ∑ 𝐴(𝑚)𝑋(𝑛 -𝑚) + 𝐸(𝑛)

(3.17

) 𝑝 𝑚=1
where E(n) is the matrix containing uncorrelated white noise at time n, p is the model order, and A(m) is a n by n coefficient matrix for delay m.

Model selection

The most common approach for model order (p) selection involves first setting a set of model orders and then finding one that minimizes one or more information criteria evaluated over the model order range [START_REF] Lütkepohl | New Introduction to Multiple Time Series Analysis[END_REF]. Two commonly used information criteria are the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC).

The AIC and BIC for MVAR are defined as follows: Where (p) is the covariance matrix of the residuals, T is the number of data points, p is the model number, and k is the number signals. Each of these criteria needs to be minimized to find the optimal model order. Other criteria include the Final Prediction Error (FPE) and Hanna-Quinn Criterion (HQC).

Effective connectivity measures

The power spectral density S of a chosen and validated model is calculated from the coefficients and residuals of MVAR:

𝑆(𝑓) = 𝐻(𝑓)𝐻 * (𝑓) (3.20)
where H(f) (= A -1 (f)) is the transfer matrix of the MVAR model of dimensions K by K. Hij is the information flow from xj to xi at frequency f. Common effective connectivity measures are: Partial coherence [START_REF] Brillinger | Time Series[END_REF])

𝑃𝐶𝑂𝐻 𝑖𝑗 = |𝑆 𝑖𝑗 (𝑓)| 2 𝑆 𝑖𝑖 (𝑓)𝑆 𝑗𝑗 (𝑓) (3.21)
Partial directed coherence [START_REF] Baccalá | Partial directed coherence: a new concept in neural structure determination[END_REF])

𝑃𝐷𝐶 𝑖𝑗 = |𝐴 𝑖𝑗 (𝑓)| 2 ∑ |𝐴 𝑖𝑗 (𝑓)| 2 𝑘 𝑗=1 (3.22)
Direct transfer function [START_REF] Kamiński | Evaluating causal relations in neural systems: Granger causality, directed transfer function and statistical assessment of significance[END_REF])

𝐷𝑇𝐹 𝑖𝑗 = |𝐻 𝑖𝑗 (𝑓)| 2 ∑ |𝐻 𝑖𝑗 (𝑓)| 2 𝑘 𝑗=1
(3.23)

Graph network analysis

Introduction

Graph theory is a mathematical framework developed to study physical, biological and information systems. There are increased interests in application of graph theory to study functional and structural brain networks [START_REF] He | Graph theoretical modeling of brain connectivity[END_REF][START_REF] Sporns | Networks of the Brain[END_REF], and to expand our knowledge on the human brain diseases, ageing and higher cognitive functions [START_REF] Bullmore | Brain Graphs: Graphical Models of the Human Brain Connectome[END_REF][START_REF] Deuker | Reproducibility of graph metrics of human brain functional networks[END_REF][START_REF] Netoff | Epilepsy in small-world networks[END_REF][START_REF] Stam | Modern network science of neurological disorders[END_REF].

All networks consist of two basic components: nodes and pairwise edges (links) between the nodes [START_REF] Bullmore | Complex brain networks: graph theoretical analysis of structural and functional systems[END_REF]. Nodes in the brain networks are usually represented by the brain regions or electrodes positions for scalp EEG. Nodes are sometimes determined by the functional activity and parcellation of the surface of the cortex or the entire brain (Figure 3.3). The parcellation is sometime done by using brain atlases constructed with the anatomical features of the brain [START_REF] Deco | Great Expectations: Using Whole-Brain Computational Connectomics for Understanding Neuropsychiatric Disorders[END_REF][START_REF] Stanley | Defining nodes in complex brain networks[END_REF]. Functional or effective coupling between electrodes or brain regions indicate edges or links. All networks are represented by their connectivity (adjacency) matrices. Rows and columns in these matrices denote nodes while the entries denote edges.

Graph theoretical measures

There are many network metrics [START_REF] Rubinov | Complex network measures of brain connectivity: uses and interpretations[END_REF]. Before the computation of networks metrics, the graph is first thresholded (Figure 3.4) and converted to a binary form denoting absence or presence of connections. The network measures can also be applied to the weighted matrices consist of information about the connection strength [START_REF] Fallani | Graph analysis of functional brain networks: practical issues in translational neuroscience[END_REF][START_REF] Rubinov | Complex network measures of brain connectivity: uses and interpretations[END_REF]. The threshold is required to increase the signal to noise ratio by pruning out weak and nonsignificant representing spurious connections.

There are many ways to threshold a graph. The common method is to choose a common arbitrary value for all subjects or conditions in an experiment. Another option is to specify the number of connections (connection density) and keep the strongest connections while setting the rest to zero. Other thresholding methods is by generating surrogate data for the statistical assessment of the functional measures, especially for the short signals [START_REF] Drakesmith | Overcoming the effects of false positives and threshold bias in graph theoretical analyses of neuroimaging data[END_REF][START_REF] Langer | The problem of thresholding in small-world network analysis[END_REF]. Sometimes, thresholds are chosen based on the distribution of the connectivity matrices. Depending on the subject distribution, thresholds will change, this is why it is important to take the topology of the connectivity matrix into consideration [START_REF] Fallani | Graph analysis of functional brain networks: practical issues in translational neuroscience[END_REF].

After thresholding, the networks are binarized by setting the suprathreshold values to 1 and the subthreshold values to 0 before the computation of the network metrics. There are many network measures particularly for characterizing the brain functional network topology. The brain network measures are always classified based on the neurobiological interpretations such as network centrality, functional segregation, functional integration, small-world networks, networks motifs and many others. In the following, we pay special attention to the network metrics used throughout the thesis.

Network centrality

Centrality is the most important property of brain networks. It assesses the importance of individual nodes or brain regions by measuring how often a particular node interacts with many other nodes in the network (Figure 3.5). The most common measure of centrality is degree which is the number of connections of a node links to the rest of the network. Degree, k of node i, is mathematically defined as: Where a is the adjacency matrix of dimensions N by N.

Another important centrality measure is the Betweenness Centrality (BC) [START_REF] Freeman | Centrality in social networks conceptual clarification[END_REF] which measures the fraction of all shortest paths that pass through a given node. It also detects important anatomical and functional connections, and is defined as:

𝐵𝐶 𝑖 = 1 (𝑁 -1)(𝑁 -2) ∑ 𝑃 ℎ𝑗 (𝑖) 𝑃 ℎ𝑗 (3.25) ℎ,𝑗,ℎ≠𝑗,ℎ≠𝑖,𝑗≠𝑖
Phj is the total number of shortest paths between h and j, and Phj(i) is the number of shortest paths that pass through node i with N total nodes. Other centrality measures include closeness centrality, modularity and participation coefficient [START_REF] Rubinov | Complex network measures of brain connectivity: uses and interpretations[END_REF].

Functional segregation

Functional segregation of the brain networks reflects the existence of specialized brain regions as modules organized in distinct populations [START_REF] Tononi | A measure for brain complexity: relating functional segregation and integration in the nervous system[END_REF]. Functional segregation measures the presence of clusters or modules within the network (Figure 3.6). The common functional

High degree

High betweeness segregation measure is the clustering coefficient which measures the fraction of triangles around individual nodes [START_REF] Watts | Collective dynamics of "small-world[END_REF]. It is defined mathematically as:

𝐶 𝑖 = 2𝑡 𝑖 𝑘 𝑖 (𝑘 𝑖 -1) (3.26)
Where where ki and ti is the degree and number of triangles around ith node, and t is defined as:

𝑡 𝑖 = 1 2 ∑ 𝑎 𝑖𝑗 𝑎 𝑖ℎ 𝑎 𝑗ℎ (3. 𝑗,ℎ 𝜖 𝑁 27)
where a is adjacency matrix. An alternative to the clustering coefficient is the local efficiency (LE) which quantify how well information is exchanged between neighboring nodes [START_REF] Latora | Efficient Behavior of Small-World Networks[END_REF]. It is defined mathematically as:

𝐿𝐸 𝑖 = ∑ 𝑎 𝑖𝑗 𝑎 𝑖ℎ [𝑑 𝑗ℎ (𝑁 𝑖 )] -1 𝑗,ℎ∈𝑁,𝑗≠𝑖 𝑘 𝑖 (𝑘 𝑖 -1) (3.28)
Where aij and aih is the connection status (0 or 1) between the nodes i and j, and i and h, respectively, , and djh(Ni) is the sum of shortest paths between nodes j and h that contains the neighbors of node i.

Functional integration

Functional integration measures the ease of information transfer or communication between brain regions [START_REF] Tononi | A measure for brain complexity: relating functional segregation and integration in the nervous system[END_REF]. The communication between brain networks is measured by the paths connecting them (Figure 3.6). The characteristic path length (L) is the most commonly used 1 2 measure of functional integration. L is the path between brain regions [START_REF] Watts | Collective dynamics of "small-world[END_REF].

It is defined mathematically as:

𝐿 𝑖 = ∑ 𝑑 𝑖𝑗 𝑁 𝑗=1,𝑗≠𝑖 𝑁 -1 (3.29)
Where dij is the shortest absolute distance between the nodes i and j. The inverse of average characteristic path length is known as the global efficiency (E) which is defined as:

𝐸 = 1 𝑁 ∑ ∑ 𝑑 𝑖𝑗 -1 𝑗𝜖𝑁,𝑗≠𝑖 𝑁 -1 𝑖𝜖𝑁 (3.30)

Small-world networks

The brain is a very complex network that supports spatio-temporal information processing. A normal brain network combines functionally segregated modules with robust functional integrating links. This kind of network is called a small-world network (SWN) supporting optimal functional integration and segregation [START_REF] Bassett | Small-world brain networks[END_REF][START_REF] Sporns | The small world of the cerebral cortex[END_REF]. This network structure is highly clustered (high clustering coefficient) with shorter path length (or higher efficiency) (Figure 3.7) between brain regions compared to ordered (high C and long L) or random networks (low C and short L) [START_REF] Watts | Collective dynamics of "small-world[END_REF]. A formal test to investigate whether a network behaves like a small-world network is to evaluate the ratio of the normalized clustering coefficient(C) to the characteristic path length (L):

𝑆𝑊𝑁 = ( 𝐶 𝐶 𝑟𝑎𝑛𝑑 ) ( 𝐿 𝐿 𝑟𝑎𝑛𝑑 ) (3.31)
Where C and Crand are the clustering coefficients, and L and Lrand are the characteristic path lengths of the tested network and a random network, respectively. If the SWN value is greater than 1, the network exhibits properties similar to small-world networks. However, the SWN is influenced by several factors such as connectivity methods, the network size (SWN increases with increasing the number of nodes), thresholding and other parameters.

Other network categories include network motifs, network resilience and many others. The readers are referred to these papers [START_REF] Rubinov | Complex network measures of brain connectivity: uses and interpretations[END_REF][START_REF] Sporns | Networks of the Brain[END_REF][START_REF] Telesford | The brain as a complex system: using network science as a tool for understanding the brain[END_REF] for more information. The relationship between epilepsy and cognitive and neuropsychological impairments in children has been observed for a very long time [START_REF] Datta | Cognitive impairment and cortical reorganization in children with benign epilepsy with centrotemporal spikes[END_REF][START_REF] Fonseca | Epileptiform EEG discharges in benign childhood epilepsy with centrotemporal spikes: reactivity and transitory cognitive impairment[END_REF][START_REF] Holmes | Role of interictal epileptiform abnormalities in cognitive impairment[END_REF][START_REF] Jambaqué | Verbal and visual memory impairment in childrem with epilepsy[END_REF]. Despite the large number of studies on this topic, the proper effects of epileptic activity on the cognitive functioning and development are not yet clearly defined. Many studies are carried out with patients with different focal sources of epilepsy, age, frequent of seizure and epileptic syndromes. Cognitive and behavioral deficits observed in epileptic children are sometimes regarded as the result of complex interactions between biological, psychological and social factors [START_REF] Ay | Neuropsychologic impairment in children with rolandic epilepsy[END_REF][START_REF] Shields | Benign epilepsy with centrotemporal spikes[END_REF].

Benign childhood epilepsy with centrotemporal spike (BCECTS) is one of the most common idiopathic epilepsy with prevalence between 10 to 20% in children with epilepsy under the age of 16 [START_REF] Panayiotopoulos | Benign childhood focal epilepsies: assessment of established and newly recognized syndromes[END_REF]. BCECTS is characterized by seizures typically originated in the centroptemporal region with autonomic manifestations in the face, mouth and throat [START_REF] Loiseau | Benign Childhood Partial Seizures and Related Epileptic Syndromes[END_REF]. The majority of seizures occur during sleep or at the sleep onset (Camfield and Camfield, 2014;[START_REF] Shields | Benign epilepsy with centrotemporal spikes[END_REF]. Unlike other types of epilepsy like temporal lobe epilepsy [START_REF] Taylor | Structural connectivity changes in temporal lobe epilepsy: Spatial features contribute more than topological measures[END_REF], benign childhood epilepsy is known to be unaffected by the structural abnormality [START_REF] Hughes | Benign epilepsy of childhood with centrotemporal spikes (BECTS): to treat or not to treat, that is the question[END_REF]. However, epilepsy activity can cause different malfunctions between subcortical and cortical regions that may lead to changes in resting state EEG activity.

In this chapter we investigate differences in resting-state brain activity between BCECTS patients and healthy controls under the eyes-closed condition in the presence and absence of centrotemporal spike (CTS) or interictal epileptic discharges (IEDs). For this purpose, we studied changes in the EEG spectral power and functional connectivity in both sensor and source spaces. Graph theory metrics were also used to characterize functional connectivity between BCECTS brain networks in comparison to healthy controls.

EEG spectral power and source analysis

Spectral power analysis is one of the standard methods used for the quantification of EEG. The spectral power density (power spectrum) reflects the distribution of signal power over frequency. Spectral power features in different frequency bands may share different physiological properties (Başar et al., 2013;[START_REF] Klimesch | EEG alpha oscillations: the inhibition-timing hypothesis[END_REF].

There are several studies using spectral power and source analyses of scalp EEG in benign childhood epilepsy (BCE) [START_REF] Béla | Valproate selectively reduces EEG activity in anterior parts of the cortex in patients with idiopathic generalized epilepsy. A low resolution electromagnetic tomography (LORETA) study[END_REF][START_REF] Besenyei | EEG background activity is abnormal in the temporal and inferior parietal cortex in benign rolandic epilepsy of childhood: a LORETA study[END_REF][START_REF] Clemens | Pathological theta oscillations in idiopathic generalised epilepsy[END_REF][START_REF] Clemens | Theta EEG source localization using LORETA in partial epilepsy patients with and without medication[END_REF][START_REF] Kikumoto | EEG and seizure exacerbation induced by carbamazepine in Panayiotopoulos syndrome[END_REF]. All reported high power spectral mostly at the epileptic region. Most of these studies were done on the diverse groups of patients with different epileptic foci and age group.

In the first study, we recruited twenty-one patients with BCECTS with an average age of 9.84 ± 1.75 years old and twelve healthy controls with the same age range for the EEG resting-state analysis. High density EEG data were recorded under the eye closed condition lasting at least 14 minutes for each subject. A homogenous group of twelve patients was selected based on the source location of interictal epileptic discharges (IEDs). High density EEG data were preprocessed to remove artifacts. The artifact-free segments were then segmented into non-overlapping epochs for each subject. Two conditions were considered for the epileptic patients, EEG segments with and without IEDs. Absolute and relative spectral power and source activities were computed for these conditions in five different frequency bands (δ, θ, α, β1 and β2) in both sensor and source spaces. The changes in EEG spectral power were statistically compared between patients and controls with nonparametric statistical tests.

Our results showed that the EEG resting state networks of BCECTS patients were functionally disrupted in the presence and absence of centrotemporal spikes. The major findings were dysfunction at the centrotemporal region, cortical source suppression at the frontal and occipital regions in patients. Patients were also characterized with high θ power in scalp EEG across the brain and lower spectral power in the α band especially at the occipital regions in the presence of IEDs. More details can be found in the following paper 1 . One of the major problems with the EEG spectral power analysis in the sensor space was the volume conduction effect. Also, scalp EEG reference may introduce spurious synchrony [START_REF] Nunez | EEG coherency: I: statistics, reference electrode, volume conduction, Laplacians, cortical imaging, and interpretation at multiple scales[END_REF] making the sensor-space analysis and interpretation more difficult. This problem still persists in the source space [START_REF] Van Den Broek | Volume conduction effects in EEG and MEG[END_REF]. On the other hand, spectral power analysis in the source and sensor spaces are univariate analyses that only show changes in brain activity at the single-channel or voxel level.

The interaction between brain regions are analyzed by bivariate and multivariate functional connectivity analyses. Functional connectivity refers to the functional relationship between spatially separated brain regions and has been applied to several studies including epilepsy [START_REF] Centeno | Network connectivity in epilepsy: resting state fMRI and EEG-fMRI contributions[END_REF]. The characterization of the dynamics of cortical networks in EEG and Electrocorticography (ECoG) in epileptic patients during the resting state has demonstrated disruptions in global and regional brain networks (Douw et al., 2010a(Douw et al., , 2010b;;[START_REF] Quraan | Altered Resting State Brain Dynamics in Temporal Lobe Epilepsy Can Be Observed in Spectral Power, Functional Connectivity and Graph Theory Metrics[END_REF]. The functional connectivity of human brain networks is often characterized with the graph theory [START_REF] Rubinov | Complex network measures of brain connectivity: uses and interpretations[END_REF]. A large number of graph theory metrics has been used in epilepsy studies such as degree, or other metrics used for characterizing functional segregation, integration and modularity of the brain networks [START_REF] Fallani | Graph analysis of functional brain networks: practical issues in translational neuroscience[END_REF][START_REF] Stam | Modern network science of neurological disorders[END_REF].

EEG functional connectivity and graph theory

Introduction

In the previous studies, the functional connectivity analysis was performed to explore functional alteration of the brain networks in BCECTS patients in comparison to healthy controls. This was done using EEG segments with/without interictal discharges in the sensor and source spaces to investigate the impact of interictal epileptic discharges on functional interactions between brain networks in BCECTS patients. In the first study, phase locking value (PLV) [START_REF] Lachaux | Measuring phase synchrony in brain signals[END_REF] was applied to the scalp EEG to estimate functional connectivity. The functional connectivity in the second study was estimated by the lagged phase synchronization [START_REF] Pascual-Marqui | Instantaneous and lagged measurements of linear and nonlinear dependence between groups of multivariate time series: frequency decomposition[END_REF] in the source space with 84 brain regions defined by the Brodmann atlas [START_REF] Brodmann | Vergleichende Lokalisationslehre der Großhirnrinde[END_REF]. LPS has been shown to be less sensitive to non-physiological signals and volume conduction artifacts [START_REF] Pascual-Marqui | Assessing interactions in the brain with exact low-resolution electromagnetic tomography[END_REF].

Both PLV and LPS measured phase synchronization by computing relative phase difference between two electrodes or brain regions. However, PLV like spectral coherence measure zero-lag connectivity and are developed based on scalp electrodes and therefore sensitive to volume conduction. PLV is one of the common functional connectivity measures used extensively for the correlation between EEG electrodes. Unlike PLV, LPS is non-zero lag connectivity and was developed and implemented in eLORETA [START_REF] Pascual-Marqui | Assessing interactions in the brain with exact low-resolution electromagnetic tomography[END_REF] academic software that was used for this study. LPS removes confounding effect of instantaneous dependencies by removing zero-lag contribution due to volume conduction and low spatial resolution which makes LPS adequate measure of electrophysiological connectivity.

The functional connectivity in both sensor and source spaces were characterized with graph metrics. The network centrality was measured by the degree, functional segregation by clustering coefficient and functional integration by characteristic path length or global efficiency. The was aimed to investigate both local and global connectivity in epileptic patients in comparison to healthy controls.

In the sensor space, patients were characterized with higher connection density at the epileptic zone in all frequency bands. Lower connection density was also observed at the frontal and posterior region with or without IEDs. The BCECTS brain network showed deviations from small-word features in comparison to the healthy controls in a frequency dependent manner. The BCECTS brain networks were more functionally ordered in the presence of IEDs compared to healthy controls. However, in the absence of IEDs, BCECTS brain networks were less ordered compared to the healthy controls in all frequency bands (see the following paper for more details)2 .

Volume conduction artifacts may confound the results of EEG functional connectivity in sensor space. In source space, we used the Lagged Phase Synchronization (LPS) which is generally believed to be less sensitive to volume conduction compared to other zero-lagged functional connectivity metric like the classical coherence and PLV. LPS was computed between 84 Region of Interests (ROIs) defined by the Brodmann atlas as implemented in eLORETA software. Compared to controls, patients (without IEDs) showed higher θ-α and lower β LPS. Patients also displayed higher integration and lower segregation in the θ and α bands compared to healthy controls. They also exhibited higher local functional connectivity at the epileptogenic network including motor areas, central region and temporal regions of the ipsilateral hemisphere to the epileptic zone. The contralateral frontal region in patients was also found to exhibit lower local connectivity. All of these findings support the evidence of alteration of resting state functional connectivity in BCECTS patients in different frequency bands. More information can be found in the following article.

All of these studies further supported the evidence that EEG resting-state functional connectivity in BCECTS patients was altered in a frequency dependent manner. In the next chapter, we focus on the direction of information flow between different brain regions in BCECTS patients.

Chapter 5 EEG resting state functional connectivity analysis in children with benign epilepsy with centrotemporal spikes, Part II

Introduction

In the previous chapter, we investigated frequency-dependent alterations in BCECTS functional brain network topology in BCECTS patients. Some regions especially the epileptic zone showed activation in the presence or absence of interictal epileptic discharges (IEDs). Despite the fact that BCECTS is focal, we found that epileptic brain reorganized because of lower activity at other regions especially frontal and posterior regions due to presence of IEDs at the centrotemporal region.

The lower activity at the frontal and posterior regions can be categorized as the primary effect of IEDs. However, in order to investigate the secondary effect of IEDs, we computed functional connectivity from the epileptic zone and its primary effect regions (frontal and posterior) to all other regions. This was done with the seed-based functional connectivity analysis. The BCECTS patients with and without IEDS functional connectivity patterns were compared to the healthy controls. The seed points were selected based on the results of our previous studies. In the second part of this chapter, the dynamic of directed interictal connectivity associated with IEDs was studied. This was done to investigate major drivers in BCECTS brain networks and effective connective pattern during IEDs.

Resting-state Functional Source connectivity

Large-Scale Network Dysfunction in Benign Childhood Epilepsy: A Resting-State Functional Source Connectivity Study

In the first part of this chapter, we investigated the impact of IEDs on the resting-state source functional connectivity (FC) pattern in BCECTS patients in comparison to the healthy controls. The FC in large-scale source space was computed by the Imaginary Coherence (IC) which has been demonstrated to be insensitive to the volume conduction [START_REF] Nolte | Identifying true brain interaction from EEG data using the imaginary part of coherency[END_REF] and reflected true measure for studying brain connectivity in resting state EEG data. Some regions of interests (ROIs) were selected as seed points including the epileptic zone (right central), left central, prefrontal cortex and occipital regions. These regions were found to be activated/deactivated in our previous studies. The FC patterns from these regions to other regions were studied under three conditions (controls, with and without IEDs in patients). The functional connectivity topology was characterized with two main graph metrics, betweenness and local efficiency. These two graph metrics were selected in order to investigated regions that involve as a central communicator between regions and as well as efficiency of the local between neighbor brain regions.

Through the resting-state source functional connectivity analysis, we found that the central regions including supplementary motor areas showed activation in the presence of IEDs. Higher FC patterns were also observed in the ipsilateral superior frontal region of the epileptic zone in these patients (see the following study for more details).

Introduction

Benign childhood epilepsy with centrotemporal spikes (BCECTS) is an idiopathic epilepsy syndrome usually affecting the young children under the age of 16 [START_REF] Panayiotopoulos | Benign childhood focal epilepsies: assessment of established and newly recognized syndromes[END_REF]. BCECTS is characterized by the occurrence of biphasic sharp waves discharges arising from the precentral and postcentral gryi in the suprasylvian region with motor, sensory and autonomic manifestations in the face, mouth and throat [START_REF] Bourel-Ponchel | Exploration de l'unité neurovasculaire dans l'épilepsie de l'enfant : approche multimodale haute densité couplant l'EEG à l'imagerie optique fonctionnelle[END_REF]. Though the benign epilepsy is not associated with large structural changes [START_REF] Camfield | Epileptic Syndromes in Childhood: Clinical Features, Outcomes, and Treatment[END_REF], there are several reports of cognitive disturbances in BCECTS (Camfield and Camfield, 2014) such as memory, language, attention and auditory impairments in BCECTS children.

In BCECTS patients, beside microstructural changes within and around the epileptic zone [START_REF] Ciumas | White matter development in children with benign childhood epilepsy with centro-temporal spikes[END_REF] studies using EEG (Adebimpe et al., 2015a;[START_REF] Yeom | Changes in current-source density of interictal spikes in benign epilepsy of childhood with centrotemporal spikes following treatment with oxcarbazepine[END_REF] have reported abnormal distribution of spectral power and current source density especially within the epileptogenic zone but also in more distant areas including the language and speech networks [START_REF] Besenyei | EEG background activity is abnormal in the temporal and inferior parietal cortex in benign rolandic epilepsy of childhood: a LORETA study[END_REF]. Over the past decade, the fMRI and EEG studies on the brain resting-state functional connectivity have reported altered functional interactions between brain networks in BCECTS and other types of epilepsy [START_REF] Centeno | Network connectivity in epilepsy: resting state fMRI and EEG-fMRI contributions[END_REF][START_REF] Tracy | Resting-state functional connectivity in epilepsy: growing relevance for clinical decision making[END_REF]. In BCECTS patients the functional alterations and reorganization of the brain networks have been observed not only in the epileptic zone but also in other distant neuronal networks areas (Adebimpe et al., 2015b) . However, little is known about the alteration of resting state brain networks in BCECTS.

In recent years, large scale functional connectivity analysis using high-density EEG data have gained attention in healthy subjects [START_REF] Deco | Great Expectations: Using Whole-Brain Computational Connectomics for Understanding Neuropsychiatric Disorders[END_REF] and in patients suffering from various diseases [START_REF] Prinz | Understanding epilepsy through network modeling[END_REF][START_REF] Stam | Graph theoretical analysis of magnetoencephalographic functional connectivity in Alzheimer's disease[END_REF][START_REF] Zhang | Epileptic discharges specifically affect intrinsic connectivity networks during absence seizures[END_REF]. In the present study, we performed seed-based functional connectivity analysis in BCECTS patients using high-density EEG data with or without interictal spikes in comparison to healthy controls. To assess spatial functional network interactions in different frequency bands, we reconstructed cortical source activities from high-density EEG recordings using a linear spatial filter [START_REF] Gross | Dynamic imaging of coherent sources: Studying neural interactions in the human brain[END_REF] [START_REF] Travis | A self-referential default brain state: patterns of coherence, power, and eLORETA sources during eyes-closed rest and Transcendental Meditation practice[END_REF]. Functional connectivity was computed by the imaginary coherence which has been shown to be insensitive to volume conduction artifacts [START_REF] Nolte | Identifying true brain interaction from EEG data using the imaginary part of coherency[END_REF]. We investigated voxelwise whole-brain functional connectivity with a priori restriction to specific regions of interests (sROIs) based on our previous results obtained using the EEG power spectral analysis and functional connectivity in sensor and source spaces [START_REF] Adebimpe | EEG Resting State Functional Connectivity Analysis in Children with Benign Epilepsy with Centrotemporal Spikes[END_REF](Adebimpe et al., , 2015a(Adebimpe et al., , 2015b)). We also used the network metrics from the graph theory to measure the flow of information and local efficiency in the brain networks. Our study was designed to investigate: (i) the functional connections from the origin of the epileptic zone to other brain regions, and (ii) the impact of interictal discharges on the BCECTS functional connectivity topology.

Materials and methods

Subjects

The EEG data were collected from twelve healthy controls (9.13 ± 1.50 years) and twenty-one children (9.73 ± 0.95 years) with BCECTS. The study was conducted in accordance with Amiens University Hospital's ethics committee (CPP Nord-Ouest No: 2011-A00782-39) and informed consent was obtained from each subject's parents. Healthy subjects had no history of neurological disorders. All patients showed no structural brain abnormalities on MRI.

High resolution EEG recording

EEG was recorded with an EEG system (ANT, Netherlands) using 64 electrodes placed on the scalp according to the international 10-10 systems. The EEG signals were recorded with a sampling frequency of 1024Hz. Linked-ear reference electrodes were used for data collection. All the subjects were fully awake with eyes closed. On average, 13 minutes of EEG were recorded for each subject.

Patient group

To better define the homogeneity of the patients, we first identified the location of interictal sources for each patient, using the spatiotemporal dipole modeling method (Advanced Source Analysis Software, Enschede, The Netherlands) [START_REF] Scherg | Two bilateral sources of the late AEP as identified by a spatio-temporal dipole model[END_REF] and the eLORETA [START_REF] Pascual-Marqui | Standardized low-resolution brain electromagnetic tomography (sLORETA): technical details[END_REF] source localization method as implemented in the Fieldtrip [START_REF] Oostenveld | FieldTrip: Open Source Software for Advanced Analysis of MEG, EEG, and Invasive Electrophysiological Data[END_REF]. Eleven of the twenty-one patients (9.25 ± 2.43 years) with only right centrotemporal spikes (CTS) were included in the epileptic group. Table 5.1 lists the characteristics of patients and controls and a summary of their EEG

Pre-processing and artefa ct rejection

The EEG data were band-pass filtered between 0.5-40 Hz with a 4 th order Butterworth filter and re-referenced to an average reference. The EEG recordings were then normalized by the Z-score transformation and thresholded using a threshold set to the mean of the z-score amplitude distribution for each channel, as implemented in Fieldtrip software3 [START_REF] Oostenveld | FieldTrip: Open Source Software for Advanced Analysis of MEG, EEG, and Invasive Electrophysiological Data[END_REF], to identify and reject ocular, movement and muscular artifacts.

The artifact-free EEG portions of the recordings were then segmented into 2-second nonoverlapping epochs. Five segments were randomly selected for each of the control subjects (CON). Two conditions were defined for the epileptic group: 5 segments with interictal spikes (with spikes condition -WSC) and 5 spike-free segments (with no spikes condition -NSC), all randomly selected. On average, WSC segments contained 7 interictal spikes.

Forward model

We used the Montreal Neurological Institute (MNI) brain MRI template for the construction of head model for lead field calculation using the Boundary Element Method (BEM) [START_REF] Oostendorp | Source parameter estimation in inhomogeneous volume conductors of arbitrary shape[END_REF]. The MNI template was segmented by SPM8 (Ashburner et al., 2012, p. 8) into scalp, skull and brain compartments with conductivity values of 0.33 S/m, 0.0041 S/m and 0.33 S/m, respectively. The lead fields were calculated using FieldTrip [START_REF] Oostenveld | FieldTrip: Open Source Software for Advanced Analysis of MEG, EEG, and Invasive Electrophysiological Data[END_REF] for 2726 source locations inside the brain. The electrodes were aligned to the head geometry using the fiducial points. The lead field, L(k), at each source location, k, was a 63 x 3 matrix, describing the contribution of source k to the sensors in 3 directions in the Cartesian space where 63 was the number of sensors in our study.

Source analysis

We used the beamforming method [START_REF] Gross | Dynamic imaging of coherent sources: Studying neural interactions in the human brain[END_REF] to create spatial filters in order to estimate the spectral amplitude and phase of neuronal signals at source level. The three orthogonal (one for each direction) spatial filters, A, were computed for each source location k:

𝐴(𝑘, 𝑝) = [𝐿 𝑇 (𝑘) * 𝐶(𝑝, 𝑝) -1 * 𝐿(𝑘)] -1 * 𝐿 𝑇 (𝑘) * 𝐶(𝑝, 𝑝) -1
(5.1)

Where L(k) is the lead field matrix at each source location with three orthogonal dipoles of all the sensors, C is the covariance matrix obtained from the sensor data, and p is the number of EEG channel. T indicates matrix transpose.

The eigenvalue decomposition method [START_REF] Sekihara | Asymptotic SNR of scalar and vector minimum-variance beamformers for neuromagnetic source reconstruction[END_REF] was used to determine the dominant dipole orientation and to obtain high SNR for reconstructed source activities. This is done by weightening the filters with the first eigenvectors v (i.e, the eigenvector with the largest eigenvalue of the real part of the covariance matrix at source location, k):

𝑣(𝑘, 𝑝) = [𝑣1, 𝑣2 , 𝑣3] = 𝑠𝑣𝑑(𝐴(𝑘, 𝑝) * 𝐶 * 𝐴(𝑘, 𝑝) * 𝑇 ) (5.2)
Where v1, v2 and v3 are spatial filters in x, y and z directions respectively. We linearly combined the three filters to a single filter pointing in the dominant dipole orientation:

𝐹(𝑘, 𝑝) = [𝑣1, 𝑣2 , 𝑣3] * [𝐴 1 (𝑘, 𝑝)𝐴 2 (𝑘, 𝑓) 𝐴 3 (𝑘, 𝑝)] (5.3)
Finally, the source signal was obtained by multiplying the spatial filter with the raw EEG data in the sensors space: 𝑆 𝑠𝑜𝑢𝑟𝑐𝑒 (𝑘, 𝑡) = 𝐹(𝑘, 𝑝) * 𝑆 𝑠𝑒𝑛𝑠𝑜𝑟 (𝑝, 𝑡)

(5.4)

Functional connectivity analysis

We computed the spectral estimates of source signals by using the multi-taper Fourier transform [START_REF] Mitra | Analysis of dynamic brain imaging data[END_REF] with a frequency resolution of 0.5Hz for five frequency bands -δ (0.5-3.5 Hz), θ (4-8 Hz), α (8.5-13 Hz), β1 (13.5-20 Hz) and β2 (20.5-30 Hz). The multi-taper frequency method is similar to the classical Fourier transform but with a very good anti-frequency leakage property [START_REF] Van Vugt | Comparison of spectral analysis methods for characterizing brain oscillations[END_REF].

Functional interaction between sources was quantified by the imaginary coherence (IC).

The computation of IC is straightforward and computationally inexpensive even for analyzing large number of connections among numerous voxels. The IC is calculated as follows:

𝑋 = 𝑋 1 * 𝑋 2 * (5.5) 𝐼𝐶 = 𝑖𝑚𝑎𝑔 { 𝐸{𝑋} √𝐸{|𝑋 1 | 2 }𝐸{|𝑋 2 | 2 } } (5.6)
Where X is the cross-spectrum of sources X1 and X2, and X2 * is the complex conjugate of X2. The results were 2726 by 2726 adjacent functional connectivity matrices.

We defined three regions of interest (ROIs) based on our previous studies, the epileptic zone (right central region area), the left frontal region and the right occipital region (Adebimpe et al., 2015b(Adebimpe et al., , 2015c) ) . The ROIs were defined based on the automated anatomical labeling (AAL) (Tzourio-Mazoyer et al., 2002). We computed the mean absolute IC between the sources in each ROI and all other voxels.

Graph theoretical analysis

To further quantify basic properties of local connectivity, we computed betweenness and efficiency [START_REF] Bullmore | Complex brain networks: graph theoretical analysis of structural and functional systems[END_REF] for each subject and frequency band. Before computation of these metrics, we set the threshold of functional connectivity matrix to one standard deviation above median connectivity values to obtain networks with fully connected nodes.

The betweenness centrality measures the fraction of shortest paths in the network that pass through a given node and is defined as:

𝐵 𝑖 = 1 (𝑁 -1)(𝑁 -2) ∑ 𝑃 ℎ𝑗 (𝑖) 𝑃 ℎ𝑗 ℎ,𝑗,ℎ≠𝑗,ℎ≠𝑖,𝑗≠𝑖 (5.7)
Where Bi is the betweenness of node i, Phj is the total number of shortest paths between h and j and Phj(i) is the number of shortest paths that pass through node i.

The local efficiency of a particular node is similar to clustering coefficient that measure functional segregation:

𝐿𝐸 𝑖 = ∑ 𝑎 𝑖𝑗 𝑎 𝑖ℎ [𝑑 𝑗ℎ (𝑁 𝑖 )] -1 𝑗,ℎ∈𝑁,𝑗≠𝑖 𝑘 𝑖 (𝑘 𝑖 -1) (5.8)
Where LEi is the local efficiency at node i, aij and aih are the connection status ( 0 or 1) between nodes i and j, and between i and h, respectively, and djh(Ni) is the sum of shortest paths between nodes j and h that contain the neighbors of node i.

Statistical analyses

We compared the voxel-by-voxel IC values between the three groups for all the frequency bands. This was done by nonparametric paired t-tests with multiple comparisons [START_REF] Maris | Nonparametric statistical testing of EEG-and MEG-data[END_REF] by randomly permuting source locations across the subjects (1000 resamples). The statistically significant (p<0.01) t-values were projected onto the MNI template surface with the BrainNet Viewer [START_REF] Xia | BrainNet Viewer: A Network Visualization Tool for Human Brain Connectomics[END_REF].

Results

Interictal spikes induced high activity at the centrotemporal region

We assessed the whole-brain source connectivity with the seed point located at the right central region (epileptogenic source) as shown in Figure 5.1. Both patients group showed increased functional connectivity from the right central to the left central region especially in the θ band. Meanwhile, patients with spike (WSC) exhibited stronger functional connectivity at the right central, parietal, supplementary motor area (SMA), bilateral rolandic region in the δ and β bands. Both epileptic conditions (with and without spikes) displayed significantly stronger functional connections from right central zone to the right frontal region in the δ band. We exploited the difference between the three groups for all the frequency bands. For each pair of groups as shown in Figure 5.1 WSC, compared to the other two conditions, had higher IC values at the epileptic region, right temporal, right frontal, parietal, occipital, frontal superior and prefrontal cortex in the δ band. In the presence of IEDs (WSC), higher IC values were observed at the left central region in the θ band. Meanwhile, decreased functional connectivity was observed in the prefrontal cortex in WSC compared to CON; and in the left central and right temporal regions compared to NSC in the α band. In the β band, WSC showed higher IC values at the right central, right rolandic, right temporal, and SMA regions, in comparison to the other conditions. Compared to controls, patients under NSC showed stronger functional connections at the supplementary motor area in the β2 band.

Decreased functional connections in patients in the left central regions Figure 5.2 shows lower functional connectivity in patients with the seed points at the left central regions. In all the group, there were direct functional connections between the left and right central regions especially in the δ and θ bands. Higher functional connectivity in healthy controls was found in the β1 band between the left and right central regions. Patients with IEDs exhibited higher functional connectivity from the left central to left temporal and rolandic regions in the δ, θ, α and β1 bands. Comparison between epileptic patients under WSC and controls revealed significantly stronger functional connections at the left temporal region in the δ, θ and α bands. Also, higher functional connectivity was observed at the frontal superior and SMA regions in WSC compared to CON in the β2 bands. Comparison between WSC and CON showed weaker functional connectivity at the right parietal and bilateral prefrontal cortex in the θ band; in the left parietal region in the α band; and in the bilateral prefrontal cortex, left temporal and left occipital regions in the β1 band. In the absence of spike (NSC compared to CON), there was reduced functional connectivity in the left prefrontal cortex in the θ band; in SMA, bilateral temporal regions, bilateral central regions, the bilateral prefrontal cortices and the right frontal superior region in the β2 bands.

Disrupted functional connectivity in patients' frontal region

With the seed points at the left prefrontal cortex as shown in Figure 5.3, patients showed higher FC under WSC in the α band. Higher FC at the bilateral prefrontal cortex, occipital, parietal and frontal superior regions in β1 band was observed in CON. In the absence of IEDS in epileptic patients, we observed higher FC from left to right prefrontal cortex in δ, and β bands. Comparison of WSC to control shows higher FC at the left superior frontal region in θ band; bilateral central regions, SMA and occipital in α band but lower FC in bilateral parietal, bilateral frontal superior, right rolandic and right temporal regions in β 1 bands. Reduced FC was also observed in patients without spike in comparison to CON at the parietal, bilateral rolandic regions, prefrontal cortex and occipital regions in β1 band. Comparison between both epileptic conditions shows higher FC at the parietals in α band of WSC and lower FC at the occipital region of the WSC compared to NSC in β 1 band.

Interictal spike reduced functional connectivity from occipital to other regions

We observed lower FC in patients with IEDS condition (WSC) compared to other groups as shown in Figure 5.4. In healthy controls, group statistical significance showed increased FC from the occipital to the right frontal and central regions in θ band and β2 bands. WSC revealed high FC at the right temporal in δ band; right central and temporal regions in θ, α and β1 bands. Comparison of WSC to CON revealed lower FC from the occipital to the left parietal regions in θ, α and β2 band; left occipital regions in α and β1 bands. There was higher FC in the absence of spike at the right frontal superior and rolandic regions in δ band; right rolandic and temporal region in α band. Meanwhile, lower FC at the parietal and occipital regions in β1 band in NSC compared to CON was observed. Comparison between epileptic patient conditions shows lower FC in δ band at the right occipital and temporal and frontal regions in WSC and bilateral central region and left prefrontal cortex in θ band. In β1 band, there was lower FC at the right frontal superior region, closer to the epileptic zone, of WSC compare to NSC.

Graph measures indicate disrupted connectivity pattern in patients

The spatial differences of betweenness and local efficiency between patients and control revealed different patterns of connectivity as a function of frequency bands as shown in Figures 5.5 and 5.6 respectively. Betweenness shows the how the brain region functionally interacts with other by measure the fractions of shortest paths that pass through a given brain region. Meanwhile, the local efficiency of network or particular brain region measures how efficiently it exchanges information between the other regions.

The higher betweenness (Figure 5.5) was observed at the right central in WSC compared to both other conditions in θ band, likewise at the right superior frontal of patients with spike in α and β1 bands. However, lower betweenness was found at the left occipital junction, left frontal region in α and β1 bands. In comparison of NSC to CON, NSC had higher betweenness at the bilateral occipital junction, and lower at the SMA and parietal regions in θ band. There was lower betweenness at the left prefrontal cortex in NSC compared to controls, left occipital junction in β1 band. Comparison of both epileptic conditions showed higher betweenness at bilateral rolandic regions in δ band and right central region in θ band in WSC. Meanwhile, in β1 band, WSC had higher and lower betweenness at the right and left occipital regions respectively in comparison NSC. Higher local efficiency (Figure 5.6) at occipital regions of WSC compared to CON in δ and β1 bands was observed. Also, WSC had higher local efficiency at the left temporal regions compared to CON in β bands. In the absence of IEDS, there was lower local efficiency at the right superior frontal region in θ bands; higher local efficiency at left centrotemporal region in α and β1 bands. Comparison between epileptic conditions showed decreased local efficiency at the left frontal and parietal in δ bands, left central in θ band; parietal, left and right frontal regions in α band in WSC. In β bands, higher local efficiency at the left occipital region in WSC compared to NSC in β 1 band and right superior frontal region in β2 band were observed.

Discussion

In this study we investigated functional connectivity in BCECTS patients in comparison to healthy controls. We presented a clear and robust method for assessing significant functional connectivity differences between patients and healthy subjects. We estimated the imaginary coherence at the source level [START_REF] Nolte | Identifying true brain interaction from EEG data using the imaginary part of coherency[END_REF] and we demonstrated alterations in the brain functional network organization of patients. We found that interictal spike activity affected the functional connectivity between the epileptic zone and the ipsilateral frontal, frontocentral, central and temporal areas and the contralateral central, precentral and frontal areas. We also observed a significant increase in IC values between the prefrontal cortex and the epileptic zone in the beta1 band. The sensorimotor regions showed higher betweenness and lower efficiency values in patients in the theta band. Hence, these findings imply that the brain functional networks in BCECTS patients are not only disrupted but also reorganized depending on the frequency band.

Epileptogenic network abnormalities in BCECTS patients

The epileptogenic networks refer to the areas involved in the generation and spread of epileptic activity. These networks may vary across different types of epilepsy. In BCECTS, it covers the sensorimotor networks and central region. The sensorimotor components consist of precentral, central and supplementary motor area [START_REF] Rosazza | Resting-state brain networks: literature review and clinical applications[END_REF]. In our study, we found that these regions were significantly activated in BCECTS patients in the presence or absence of interictal epileptic spikes especially in the δ and θ bands. In line with previous studies, we found that the patients' central regions, extended to the supplementary motor area, were highly activated [START_REF] Boor | Combined spike-related functional MRI and multiple source analysis in the non-invasive spike localization of benign rolandic epilepsy[END_REF][START_REF] Tang | Altered Regional Homogeneity in Rolandic Epilepsy: A Resting-State fMRI Study[END_REF]. The activations of these regions were concomitant with higher betweenness values in the θ band and lower local efficiency values in the frontal superior, fontal mid gyrus and supplementary motor regions. The involvement of these regions could result in jerking of the mouth, face and hand, kind of semiology of benign childhood epilepsy [START_REF] Moeller | EEG-fMRI in atypical benign partial epilepsy[END_REF]. However, the increased functional connectivity was restricted to the homolateral hemisphere of the epileptic zone in the β band. This observation could be supported by increases in spectral power around the epileptic zone (Adebimpe et al., 2015a;[START_REF] Bourel-Ponchel | Exploration de l'unité neurovasculaire dans l'épilepsie de l'enfant : approche multimodale haute densité couplant l'EEG à l'imagerie optique fonctionnelle[END_REF]. Even in the absence of interictal spikes, we found highly significant changes in IC values at the epileptic zone extending to the frontal regions in higher frequency bands. This might suggest that the abnormal brain function does not only occur during interictal discharges but also exists throughout interictal periods. Meanwhile, increased local efficiency in these patients in the absence of spikes at the left central and frontal region in the α and β1 band can be viewed as the brain functional reorganization due to epileptic activity in the opposite region.

The frontal cortices also showed involvement in the functional reorganization of the brain functional networks in BCECTS patients. This is supported by lower and higher local efficiency at the frontal region in low and high frequency band, respectively. The frontal lobe is known to play a major role in the processing and execution of higher cognitive skills and behaviors [START_REF] Stuss | Functions of the frontal lobes: relation to executive functions[END_REF]. Children with benign epilepsy have been found to be suffering from cognitive deficit and mental activity [START_REF] Verrotti | Memory impairment and Benign Epilepsy with centrotemporal spike (BECTS): a growing suspicion[END_REF]. One of the distinct features of the benign childhood epilepsy is the absence of large brain structural changes. The structural changes are most common in other types of epilepsy such as temporal lobe epilepsy [START_REF] Theiler | Testing for nonlinearity in time series: the method of surrogate data[END_REF]. However, some studies [START_REF] Kanemura | Growth disturbance of frontal lobe in BCECTS presenting with frontal dysfunction[END_REF] have reported serial changes in the frontal lobe growth in longitudinal MRI studies and microstructural changes of white matter (S. E. Kim et al., 2014) at the epileptic zones and also in the frontal lobe especially in the superior frontal and right inferior gyrus in BCECTS patients. These little structural changes might be correlated with the cognitive and behavior deficiency in BCECTS patients. Therefore, the changes in functional connectivity patterns between the prefrontal cortex and bilateral central regions might be related to the reported serial growth disturbance and alteration of brain tissues at the frontal region together with experience of motor and cognitive dysfunctions in these patients.

Is DMN impaired in BCECTS patients?

In our study, we found that the pattern of significant functional connectivity did not only depend on the frequency band but also on the seed points (ROIs). Decreased functional connectivity between the prefrontal cortex and the parietal region in BCECTS patients especially in the beta1 band might indicate impairment of the default mode network (DMN) as reported in several fMRI studies [START_REF] Ibrahim | Impaired development of intrinsic connectivity networks in children with medically intractable localization-related epilepsy[END_REF][START_REF] Xiao | Altered attention networks in benign childhood epilepsy with centrotemporal spikes (BECTS): A resting-state fMRI study[END_REF] and EEG functional connectivity study [START_REF] Canuet | Resting-State EEG Source Localization and Functional Connectivity in Schizophrenia-Like Psychosis of Epilepsy[END_REF]. This claim is further supported by our results which showed decreased betweenness in the parietal, precuneus, temporal and frontal regions in the β bands. The DMN has been associated to various brain functional activities including cognitive processes and is solicited during attention. The observed decreased functional connectivity and betweenness at these regions may support the idea that epileptic activity might lead to attention and learning deficits in children with epilepsy (E.-H. Kim et al., 2014). In addition, BCECTS children responding to antiepileptic drugs were found to be more attentive, in correlation with the decrease in amplitude of the spike waves [START_REF] Kaufmann | Attention-deficit disorders and epilepsy in childhood: incidence, causative relations and treatment possibilities[END_REF][START_REF] Schneebaum-Sender | Does a normalizing electroencephalogram in benign childhood epilepsy with centrotemporal spikes abort attention deficit hyperactivity disorder?[END_REF]. We also found that the presence of interictal spikes in EEG signals resulted in significant decreases in IC values between the prefrontal cortex to the parietal and precuneus regions and also decreased the flow of information between these regions. The involvement of DMN might be a core neurobiological feature in benign epilepsy and deserves further attention.

Interictal discharges affect temporal connectivity

Interictal discharges in the right centrotemporal area influenced ipsi and contralateral functional connectivity patterns in temporal areas. The functional connectivity analysis using the ROIs seed points at the right central regions indicated increased functional connectivity in the right homolateral temporal region in the delta and theta bands. The increased functional connectivity between the epileptic zone and the ipsilateral temporal region implied that the interictal discharges affected the temporal region. This was also evident from decreased betweenness values in BCECTS patients (especially under WSC) in lower frequency bands. Both the central region and superior temporal gyrus are part of auditory components [START_REF] Rosazza | Resting-state brain networks: literature review and clinical applications[END_REF] that are responsible for language and speech processing. Unbalanced auditory processing in both hemisphere could be responsible for phonological and language processing deficits in these patients [START_REF] Amaral | Temporal auditory processing and phonological awareness in children with benign epilepsy with centrotemporal spikes[END_REF]. The reduced IC in the left hemisphere is also supported by several studies [START_REF] Overvliet | Early onset of cortical thinning in children with rolandic epilepsy[END_REF] which found reduced cortical thickness predominantly in language mediating brain regions of the left hemisphere in patients compared to controls.

Decreased occipital functional activity in BCECTS patients

With the seed point located at the occipital cortex, the functional connectivity analysis showed significantly decreased connectivity between the occipital regions and postcentral and frontal regions in different frequency bands especially in low frequency bands. The decreased betweenness at the occipital region in the theta and alpha bands in BCECTS patients under WSC and NSC suggest lower functional connectivity in this region. This finding is in agreement with the results of our previous studies (Adebimpe et al., 2015a) which suggest that the functional connectivity pattern in the occipital cortex in BCECTS patients was modified due to interictal epileptic discharges. Several studies [START_REF] Deltour | Children with benign epilepsy with centrotemporal spikes (BECTS) show impaired attentional control: evidence from an attentional capture paradigm[END_REF][START_REF] Filippini | Comparing cortical auditory processing in children with typical and atypical benign epilepsy with centrotemporal spikes: Electrophysiologic evidence of the role of non-rapid eye movement sleep abnormalities[END_REF] reported a poor performance in visual assessment and visual spatial coordination in BCECTS children. This is in line with our findings that indicate lower local efficiency in the occipital cortex for these patients in the alpha band.

This study presented a clear and robust method for assessing resting-state EEG source functional connectivity patterns and demonstrated alterations of functional connectivity pattern in BCECTS patients. Although our previous studies have shown the strong impact of interictal epileptic discharges on the brain functional organization in BCECTS patients, dynamic directed interictal connectivity techniques provide important information on the driver-response interactions between the brain regions in BCECTS patients.

Dynamic directed interictal connectivity

Dynamic directed interictal connectivity in benign childhood epilepsy with centrotemporal spikes: A high density EEG study

This section investigates the dynamic directed interictal functional connectivity pattern associated with interictal epileptic spikes. The EEG source activity was recounsstructed ad reduced to 90 ROIs. The partial directed coherence (PDC) was used to compute the effective connectivity between brain regions. PDC has been shown to be insensitive to volume conduction artifacts. The outflow of the connectivity matrix was then investigated to identify major drivers between the brain regions involved in the propagation and generation of the epileptic activity. Overall, we found that central, rolandic, supplementary motor areas and superior frontal regions of the ipsilateral hemisphere to the epileptic zone were the major drivers among all the brain networks in BCECTS patients.

Introduction

Epilepsy is a neurological disorder characterized by recurrent unprovoked abnormal neuronal discharges. Interictal epileptic discharges (IEDs) involve complex interaction across several brain regions. The dynamics of brain networks during IEDS is the key to understanding pathological mechanism associated with IEDS.

Benign epilepsy with centrotemporal spikes (BCECTS) is the most common idiopathic epileptic syndrome with a prevalence of 8-20% of epileptic children [START_REF] Holmes | Benign focal epilepsies of childhood[END_REF]Panayiotopoulos, 1999;[START_REF] Wirrell | Benign epilepsy of childhood with centrotemporal spikes[END_REF]. In BCECTS, the interictal epileptic discharges(IEDS) arise principally from centrotemporal regions, but the functional connectivity analysis has shown that the brain functional networks in BCECTS patients are highly impacted by the IEDS which involve not only the epileptogenic region but also other distant brain regions (Adebimpe et al., 2015b;[START_REF] Kramer | Epilepsy as a disorder of cortical network organization[END_REF][START_REF] Laufs | Functional imaging of seizures and epilepsy: evolution from zones to networks[END_REF].

In general, functional connectivity measures are used to investigate non-directional statistical dependency between different brain regions. Effective connectivity is, however, directed and usually used to explore the causal influence from one region to another. Concerning epilepsy, the main question is to understand the mechanism of initiation and propagation of IEDs. There are many measures such as Partial Directed Coherence(PDC) [START_REF] Baccalá | Partial directed coherence: a new concept in neural structure determination[END_REF] and Directed Transfer Function (DTF) [START_REF] Kamiński | Evaluating causal relations in neural systems: Granger causality, directed transfer function and statistical assessment of significance[END_REF] which have been used to study the generation and propagation of IEDS in animal models and human subjects [START_REF] Gong | Effective Connectivity of Hippocampal Neural Network and Its Alteration in Mg2+-Free Epilepsy Model[END_REF][START_REF] Jenssen | Focal seizure propagation in the intracranial EEG[END_REF][START_REF] Van Mierlo | Ictal-onset localization through connectivity analysis of intracranial EEG signals in patients with refractory epilepsy[END_REF][START_REF] Wilke | Neocortical seizure foci localization by means of a directed transfer function method[END_REF]. The time-varying pattern of the effective connectivity associated with IEDS in scalp EEG remains a critical key to address the initiation and propagation of IEDS in epileptic patients.

In this paper, we used PDC [START_REF] Baccalá | Partial directed coherence: a new concept in neural structure determination[END_REF], an effective connectivity estimator in the frequency domain based on the multivariate autoregressive (MVAR) modeling for investigating causal interactions between EEG source signals. We aimed to investigate the connectivity patterns associated with IEDs and to explore the brain regions involved in the generation and propagation of epileptic activity. Moreover, we used PDC to investigate the major drivers that draw the brain networks into IEDs.

Materials and methods

Patients

Sixteen BCECTS patients (Table 5.2) were included in this study with right (12) and left (4) epileptic foci. The patients in each group had unilateral epileptic foci with interictal dipolar sources located (Figure 5.7)within centrotemporal regions and oriented from anterior to posterior [START_REF] Camfield | Epileptic Syndromes in Childhood: Clinical Features, Outcomes, and Treatment[END_REF].The study was conducted at the Amiens University Hospital, and approved by the university hospital ethics committee with the reference number: CPP Nord-Ouest No: 2011-A00782-39.

EEG data acquisition and preprocessing

EEG data were recorded from each individual using a high-density EEG recording system (ANT, Netherlands) with a sampling rate of 256 Hz and 64 channels positioned according to the international 10-10 system. Forehead ground and linked-ear reference electrodes were used for data collection. On average 14 minutes of eyes-closed resting state EEG data were recorded from each patient. During recording, the patients were in a supine position in a quiet dark room. The EEG data were re-referenced to a common average reference and filtered between 0.5 to 40 Hz to remove possible high frequency noise. Two experienced neurophysiologists visually inspected the EEG data to identify centrotemporal spikes. Twenty single spike segments were selected for each patient for connectivity analysis. The selected EEG spikes were free from major artifacts with at least 15 seconds intervals between segments to avoid any spike overlapping. To identify EEG segments with ocular and movement artifacts, the EEG recordings were first normalized by the Zscore transformation and then preprocessed semi-automatically using the thresholding method implemented in the Fieldtrip software [START_REF] Oostenveld | FieldTrip: Open Source Software for Advanced Analysis of MEG, EEG, and Invasive Electrophysiological Data[END_REF]"tutorial," n.d.). For each segment, EEG channels that exceeded a predefined threshold were marked and visually inspected by the experts. The threshold was set to the mean plus one standard deviation of the z-score amplitude distribution for each channel.

EEG source imaging

We used the Montreal Neurological Institute (MNI) brain MRI template [START_REF] Fonov | Unbiased nonlinear average age-appropriate brain templates from birth to adulthood[END_REF] for the construction of a head model required for leadfield calculation using the Boundary Element Method (BEM) [START_REF] Oostendorp | Source parameter estimation in inhomogeneous volume conductors of arbitrary shape[END_REF]. The MNI template was segmented by SPM8 into 3 homogeneous conductive compartments including scalp, skull and brain with conductivity values of 0.33 S/m, 0.0041 S/m and 0.33 S/m, respectively. The lead-fields were calculated using FieldTrip [START_REF] Oostenveld | FieldTrip: Open Source Software for Advanced Analysis of MEG, EEG, and Invasive Electrophysiological Data[END_REF] with a spatial resolution of 7.5 mm. In total, 4734 source locations were generated inside the brain. The electrodes were aligned to the head geometry using the fiducial points from each subject.

The eLORETA (Pascual-Marqui, 2007) inverse solution was used to calculate three dimensional current density distributions. The inverse solution was first applied to the average interictal spikes of each patient to localize the spike activity. The results were grand averaged (Figure 1) after normalization for each group (with right and left foci). For each spike segment, the inverse solution was used to obtain the source activities which were then projected by the eigen decomposition method [START_REF] Sekihara | Asymptotic SNR of scalar and vector minimum-variance beamformers for neuromagnetic source reconstruction[END_REF]. The distributed source activities were reduced to 90 regions of interest (ROIs) by using the automated anatomic labeling (AAL) atlas (Tzourio-Mazoyer et al., 2002). The closest distributed source activity to each ROI centroid was selected as the source activity of the ROI (Figure 5.8).

Dynamic partial directed coherence

We used the normalized Partial Directed Coherence (PDC) [START_REF] Baccalá | Partial directed coherence: a new concept in neural structure determination[END_REF] to determine the causal inference between the multivariate autoregressive (MVAR) model [START_REF] Pereda | Nonlinear multivariate analysis of neurophysiological signals[END_REF] of the ROIs source activity as implemented in the SIFT toolbox [START_REF] Delorme | and ERICA: New Tools for Advanced EEG Processing[END_REF]. The time-varying normalized PDC estimates directed interactions from the estimated MVAR with an appropriate model order (average of 15 was used for all the patients). This was estimated with sliding window of 500 milliseconds in a time step of 30 millisecodns. The appropriate model order was estimated with the Akaike information criterion (AIC) and estimation theory [START_REF] Schlögl | Analyzing event-related EEG data with multivariate autoregressive parameters[END_REF]. The estimation theory states that the ratio of 𝑁 * 𝑛 𝐶 * 𝑝 must be of order of 10 or larger where N is the number of data points, n is the number of data segments, C is the number of signals (ROIs) and p is the model order. However, we ran statistical tests to check the stability and consistency in order to validate the model. PDC was estimated in time and frequency domain but only the θ band was considered for analysis. Since the power in this frequency band was maximum (Figure 5.9), therefore, the information transfer was supposed to be most relevant at the maximum power frequency [START_REF] Van Mierlo | Accurate epileptogenic focus localization through time-variant functional connectivity analysis of intracranial electroencephalographic signals[END_REF].

Outflow and Laterality

We computed the outflow which is the summed connectivity strengths over outgoing edges. This is computed by summing outflows from each ROI to all other ROIs at a given time instant. The ROI with high summed outflow strongly drives the activity of other regions. The outflow of each region at each time instant was statistically compared to the temporal average of the baseline before the rise of the spike activity with a nonparametric permutation test (Kruskal-Wallis, p<0.05) and 1000 permutations.

The laterality was determined from the summed outflow across the rising phase of the spike to represent the network involved in the generation of the spike.

The laterality index, L, was computed to assess the hemispheric or regional dominance as follows:

𝐿 = ∑ 𝑂 𝑅 -𝑂 𝐿 𝑂 𝑅 + 𝑂 𝐿 (5.9)
Where OR and OL represent the summed outflow from the right and left brain region to all other regions, respectively.

For the laterality, nonparametric tests (Kruskal-Wallis, p<0.05) with 1000 permutations were used for statistical comparison to the baseline. All analyses were performed in Matlab and EEGLAB toolbox [START_REF] Delorme | EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis[END_REF] and statistics in the BrainNet viewer [START_REF] Xia | BrainNet Viewer: A Network Visualization Tool for Human Brain Connectomics[END_REF] was used for 3D representation and some Figures were plotted with the modified code of the e-connectome software (He et al., 2011).

Results

Electrical source activity

Figure 5.10 shows the electrical source activity reconstructed with the ROIs. In patients with right epileptic foci, we found stronger activities at the ipsilateral hemisphere to the epileptic zone at the right postcentral, inferior parietal and rolandic regions. This was extended to the frontal region at the orbital frontal and superior temporal region. Similarly, in patients with left foci, ROIs with stronger activity were localized at the left precentral and postcentral regions including rolandic regions. Frontal regions, very close to epileptic foci also showed strong activity at the left inferior frontal region.

Outflow density

The summed outflow (Figure 5.11) showed a dominance in the ipsilateral hemisphere to the epileptic focus in both patient groups with right and left epileptic foci. In the patient group with right epileptic focus, the key drivers with highest summed outflow included the right precentral and postcentral regions which were the main spike generation zones. Other regions including the right rolandic and supramarginal regions were also involved, although with lower summed outflow. In the patients with right epileptic foci, the superior and mid frontal regions were also involved and even reached their maximum summed outflow before the central regions. In these patients, the average summed outflow during the rise of flow (surface MRI) showed the right dominance with highest outflow at the central regions.

In the patients with left epileptic focus, just like the other group, the major key drivers included precentral and postcentral regions. It also included the inferior frontal operculum regions. In this group, fewer ROIs showed significant changes compared to the baseline probably due to the low sample size. Network pattern and laterality index Figure 5.12 shows the network patterns for both groups of patients. The strongest connections were found in the ipsilateral hemisphere to the epileptic focus from pre-and post-central regions and the supplementary area to the frontal regions. There were also functional connections with weaker strength to distant regions in the contralateral hemisphere. In the patient group with left epileptic focus, the major drivers were found at the left rolandic region. Few connections to the other brain region were observed for this group.

Both the patient groups exhibited laterality toward the ipsilateral hemisphere to the epileptic focus (R: 0.38 ± 0.09, L: -0.49±0.20). However, patients with right epileptic foci exhibited more laterality toward the right hemisphere in comparison to the baseline (χ 2 =5.47, p=0.019).

Discussion

Our results show the presence of abnormal functional network pattern occurring during the interictal epileptic discharges (IEDs) in BCECTS patients. The causal inference between the brain regions were identified by combining the EEG source imaging and the time-varying effective connectivity method. Both the patient's groups with epileptic foci at the right and left hemisphere showed stronger directional connections to the frontal regions and weaker connectivity to the distant regions in the contralateral hemisphere. We also demonstrated the dynamic changes in interactions between the brain networks before, during and after IEDs. Our results are consistent with the findings reported in our previous studies [START_REF] Adebimpe | EEG Resting State Functional Connectivity Analysis in Children with Benign Epilepsy with Centrotemporal Spikes[END_REF](Adebimpe et al., , 2015b(Adebimpe et al., , 2015c) in which we compared EEG segments with and without IEDs using the source imaging and functional connectivity analysis. The main advantage of PDC as an effective connectivity measure over the phase synchronization or coherence methods is that it allows detecting the direction of interaction between brain regions. All of these analyses provide a meaningful tool to evaluate the epileptic networks, their alteration caused by IEDs, and their possible impact on cognitive deficits reported in the children with BCECTS [START_REF] Danielsson | Cognitive deficits in children with benign rolandic epilepsy of childhood or rolandic discharges: a study of children between 4 and 7 years of age with and without seizures compared with healthy controls[END_REF][START_REF] Datta | Cognitive impairment and cortical reorganization in children with benign epilepsy with centrotemporal spikes[END_REF].

A B

The EEG source activity analysis revealed stronger activity at the central regions including the rolandic region in the epileptic zone. It also showed that the ipsilateral temporal and frontal regions were also involved in epileptic activity, however, with weaker strength. The stronger activity at the central and frontal regions of the ipsilateral hemisphere to the epileptic zone suggested a fronto-central network activation during the IEDs.

The main driver in the epileptic networks was found in the central regions (post and precentral) including rolandic regions. However, some of other key drivers were also observed outside the epileptic focus with weaker strength especially at the frontal regions, including parietal and temporal regions. We also found the involvement of the frontal regions in spike activity in both the patient groups, especially the frontal superior and mid regions (for patients with right epileptic foci) which reached their maximum summed outflow even before the precentral and postcentral ROIs. This finding suggests that the frontal regions are the secondary driver of the epileptic activity. The involvement of the frontal and central or fronto-central networks in the epileptic activity may suggest that interictal activity might impact the functionality of the attention networks [START_REF] Kaufmann | Attention-deficit disorders and epilepsy in childhood: incidence, causative relations and treatment possibilities[END_REF] in BCECTS patients. The ipsilateral frontal cortex showed increased functional connectivity driven by the right or left (pre and post, including central motor) central gyrus, respectively. The frontal cortex has been known to be involved in monitoring, behavioral adjustments and learning [START_REF] Rushworth | Functional organization of the medial frontal cortex[END_REF][START_REF] Rushworth | Frontal Cortex and Reward-Guided Learning and Decision-Making[END_REF] all of which are important in complex cognitive tasks such as language. The frontal cortex has been shown to be correlated with the attention and cognitive deficits [START_REF] Dunn | Focusing on ADHD and attention in children with epilepsy[END_REF][START_REF] Lopes | Intellectual functioning in children with epilepsy: Frontal lobe epilepsy, childhood absence epilepsy and benign epilepsy with centro-temporal spikes[END_REF][START_REF] Riva | Intellectual and language findings and their relationship to EEG characteristics in benign childhood epilepsy with centrotemporal spikes[END_REF]. The functional involvement of the frontal cortex in epileptic activity may reflect the fontal region growth disturbance [START_REF] Kanemura | Growth disturbance of frontal lobe in BCECTS presenting with frontal dysfunction[END_REF] caused by epileptic activity in BCECT patients. This finding is in line with those resulting from several studies performed with fMRI and MEG/EEG indicting the role of frontal cortex in the initiation and propagation of IEDs [START_REF] Panzica | Identification of the Epileptogenic Zone from Stereo-EEG Signals: A Connectivity-Graph Theory Approach[END_REF][START_REF] Rotondi | Altered EEG resting-state effective connectivity in drug-naïve childhood absence epilepsy[END_REF][START_REF] Wu | Local Activity and Causal Connectivity in Children with Benign Epilepsy with Centrotemporal Spikes[END_REF][START_REF] Yang | Altered restingstate connectivity during interictal generalized spike-wave discharges in drug-naïve childhood absence epilepsy[END_REF]. The evidence of involvement of the fronto-central regions may also be in agreement with results reported in other methods concerning clinical diagnosis of BCECTS with the tangential dipole orienting from central to frontal regions or vice versa [START_REF] Baumgartner | The Functional Organization of the Interictal Spike Complex in Benign Rolandic Epilepsy[END_REF][START_REF] Camfield | Epileptic Syndromes in Childhood: Clinical Features, Outcomes, and Treatment[END_REF] and our previous studies [START_REF] Adebimpe | EEG Resting State Functional Connectivity Analysis in Children with Benign Epilepsy with Centrotemporal Spikes[END_REF](Adebimpe et al., , 2015b(Adebimpe et al., , 2015c) ) reporting high/low activity at the ipsilateral central/frontal regions, respectively.

The existence of other drivers outside the epileptic focus especially at the supramarginal and parietal regions as well as the causal influence from the superior motor and post/pre central regions of the ipsilateral hemisphere to the epileptic foci to the contralateral hemisphere and extra-temporal regions support the evidence that the impairment of BCECTS brain networks might not be restricted to the epileptogenic focus. We also observed connections with weaker strength from the epileptic foci to the contralateral hemisphere compared to the ipsilateral frontal regions. This could represent the reorganization of the brain network during IEDs serving as the compensatory mechanism [START_REF] Bettus | Decreased basal fMRI functional connectivity in epileptogenic networks and contralateral compensatory mechanisms[END_REF][START_REF] Datta | Cognitive impairment and cortical reorganization in children with benign epilepsy with centrotemporal spikes[END_REF]. Laterality toward the epileptic foci also confirmed the reorganization of functional network organization due to epileptic discharges. The laterality toward the epileptic foci might have influence on the cognitive ability, language processing and verbal memory in BCECTS patients [START_REF] Li | Lateralization of epileptic foci through causal analysis of scalp-EEG interictal spike activity[END_REF][START_REF] Piccirilli | Language lateralization in children with benign partial epilepsy[END_REF][START_REF] Sveller | Relationship between language lateralization and handedness in left-hemispheric partial epilepsy[END_REF]. The causal influence from the ipsilateral supplementary motor areas to the bilateral frontal regions indicates the involvement of motor region as well. This might explain the high prevalence of language impairment in children with rolandic epilepsy as previously reported [START_REF] Overvliet | Correlation between language impairment and problems in motor development in children with rolandic epilepsy[END_REF][START_REF] Wolff | Benign Partial Epilepsy in Childhood: Selective Cognitive Deficits Are Related to the Location of Focal Spikes Determined by Combined EEG/MEG[END_REF]. Interestingly, many of the patients with BCECTS have a language-related learning disorder and not a general learning disorder. It is also reported that there is correlations [START_REF] Besseling | Aberrant functional connectivity between motor and language networks in rolandic epilepsy[END_REF][START_REF] Overvliet | Correlation between language impairment and problems in motor development in children with rolandic epilepsy[END_REF] between problems with motor development and language impairment in children with BCECTS, probably due to the casual influence from the motor region to other brain regions.

In this study, the PDC was only estimated in the θ band, the frequency range with maximum spectral power, mainly because it is generally believed that frequency with higher spectral power has potential for driving brain networks. Higher frequencies above 80Hz regarded as high frequencies oscillation (HFO) [START_REF] Kobayashi | High-frequency oscillations in idiopathic partial epilepsy of childhood[END_REF] might be involved in the generation and propagation of spike. This is subjected for future study because HFO is needed to be recorded with higher sampling rates than the one used in the current study. Our study is limited with small sample size especially for the patient group with left epileptic foci (4 subjects), though, the group was almost homogenous in terms of age range and source localization of IEDs.

In conclusion, we identified the causal connectivity patterns in BCECTS patients and the major drivers of the epileptic activity. The post and precentral regions with the supplementary motor areas were the major drivers in the ipsilateral hemisphere to the epileptic foci. The causal influence from the central to the ipsilateral frontal region and the contralateral hemisphere suggest that the BCECTS brain networks are functionally altered during IEDs. This could explain the negative impact of epileptic activity on the cognitive ability of the children with BCECTS.

Chapter 6

Functional Development in Neonates

Introduction

The adult brain is composed of networks with complex interactions. Several studies with the graph theory or network science have expanded our knowledge on the brain functional connectome in adults [START_REF] Bassett | Small-world brain networks[END_REF][START_REF] Bassett | Understanding complexity in the human brain[END_REF][START_REF] Sporns | Connectivity and complexity: the relationship between neuroanatomy and brain dynamics[END_REF]. In turn, little is known about the brain functional connectome in neonates. There have been predictions that the human brain functional connectivity evolves from birth (with local connections) to adulthood (with distributed topology) [START_REF] Fair | Functional brain networks develop from a "local to distributed" organization[END_REF]. Several fMRI studies in neonates have shown the presence of cortical hubs in the posterior, frontal and sensorimotor regions [START_REF] Ball | Rich-club organization of the newborn human brain[END_REF][START_REF] Fransson | Resting-state networks in the infant brain[END_REF]. The early brain activity especially in preterm is quite different from the mature brain. Neonatal brain activity is characterized with the occurrence of specific electrophysiological features such as theta temporal bursts in preterm and frontal transients in fullterm neonates with relative period of discontinuity which serve as a biomarker for brain maturation and development [START_REF] André | Electroencephalography in premature and full-term infants. Developmental features and glossary[END_REF][START_REF] Wallois | Synopsis of maturation of specific features in EEG of premature neonates[END_REF]. All these features can be observed only with EEG in neonates. Recent studies [START_REF] González | Assessment of electroencephalographic functional connectivity in term and preterm neonates[END_REF][START_REF] Meijer | Functional connectivity in preterm infants derived from EEG coherence analysis[END_REF][START_REF] Omidvarnia | Functional bimodality in the brain networks of preterm and term human newborns[END_REF][START_REF] Tokariev | Functional Brain Connectivity Develops Rapidly Around Term Age and Changes Between Vigilance States in the Human Newborn[END_REF] with EEG in neonates have attempted to explore functional connectivity in neonates. All of these studies were done using sparse electrodes. However, functional studies in neonates require a high number of electrodes due to the spatial specificity of EEG [START_REF] Odabaee | Spatial patterning of the neonatal EEG suggests a need for a high number of electrodes[END_REF]. In addition, most of the specific neonatal features including sleep stages have not been taken into consideration in functional studies. These features might have impact on the brain development.

In this chapter, functional brain connectivity patterns in preterm and full-term neonates were studied using high density EEG data (64 channels). The specific features of neonates such as the theta temporal burst activity and both quiet and active sleep stages were taken into considerations.

EEG functional connectivity in preterm neonates

EEG functional connectivity in preterm neonates modulated by endogenous activity

Introduction

Early preterm birth can highly affect the brain development at later infancy. Preterm babies are at high risk of neurodevelopmental disabilities and health impairments [START_REF] Drassinower | Prolonged latency of preterm premature rupture of membranes and risk of cerebral palsy[END_REF][START_REF] Karolis | Reinforcement of the Brain's Rich-Club Architecture Following Early Neurodevelopmental Disruption Caused by Very Preterm Birth[END_REF][START_REF] Périvier | Neonatal EEG and neurodevelopmental outcome in preterm infants born before 32 weeks[END_REF][START_REF] Rose | Brain microstructural development at near-term age in very-low-birth-weight preterm infants: an atlas-based diffusion imaging study[END_REF] due to the immaturity of the brain neural networks at birth. The development of the immature brain is concomitant with rapid alterations in functional connectivity patterns of the brain networks after birth [START_REF] Grieve | EEG functional connectivity in term age extremely low birth weight infants[END_REF]. The appearance or disappearance of specific cerebral transient events in neonates is related to the temporary involvement of the cerebral neural networks. There is increasing interest in understanding the neurodevelopmental dynamic of the preterm brain networks and their functional connectome. [START_REF] Doria | Emergence of resting state networks in the preterm human brain[END_REF][START_REF] Fransson | The functional architecture of the infant brain as revealed by resting-state fMRI[END_REF][START_REF] Fransson | Resting-state networks in the infant brain[END_REF][START_REF] Omidvarnia | Structural damage in early preterm brain changes the electric resting state networks[END_REF] The brain neuronal activities in preterm infants is strongly different from those observed in full-term neonates, young children and adults [START_REF] André | Electroencephalography in premature and full-term infants. Developmental features and glossary[END_REF]. The preterm EEG is characterized by its discontinuity with the occurrence of short burst of activity of high amplitude with dominant low frequencies [START_REF] André | Electroencephalography in premature and full-term infants. Developmental features and glossary[END_REF][START_REF] Vecchierini | Normal EEG of premature infants born between 24 and 30 weeks gestational age: terminology, definitions and maturation aspects[END_REF]. During the maturation process, the dynamics of preterm brain networks is characterized by the occurrence of specific features considered as biomarkers. The absence or a delay in the occurrence of these biomarkers during the neurodevelopmental process suggests a poor functional prognosis [START_REF] Vecchierini | EEG patterns in 10 extreme premature neonates with normal neurological outcome: qualitative and quantitative data[END_REF][START_REF] Wallois | Synopsis of maturation of specific features in EEG of premature neonates[END_REF]. The appearance of cortical bursts in early preterm has been found to be correlated with the mental development [START_REF] Iyer | Cortical burst dynamics predict clinical outcome early in extremely preterm infants[END_REF][START_REF] Vecchierini | EEG patterns in 10 extreme premature neonates with normal neurological outcome: qualitative and quantitative data[END_REF]. Other biomarkers include frontal sharp waves [24-28 wGA], Theta Temporal Activities in coalescence with Slow Waves (TTA-SW) [25-30wGA], delta brushes [30-36wGA] and frontal transients [36-42wGA] [START_REF] André | Electroencephalography in premature and full-term infants. Developmental features and glossary[END_REF][START_REF] Selton | Normal EEG in very premature infants: reference criteria[END_REF][START_REF] Vanhatalo | Development of neonatal EEG activity: from phenomenology to physiology[END_REF][START_REF] Wallois | Synopsis of maturation of specific features in EEG of premature neonates[END_REF]. The inter-hemispheric synchronization also evolves in the course of neurodevelopment. The functional interactions in premature infants follow a temporally variable complex pattern. In the very premature babies before 32wGA, short bursts of activity are highly synchronized across hemispheres. For a short period of time between 32 to 36wGA, the two hemispheres are out synchronization then they become resynchronized after 36 wGA.

The TTA-SWs are one of the earliest neurodevelopmental biomarkers of the brain maturation process in preterm babies. It has been shown that the TTA-SW is not sensory driven and that their generators are located bilaterally along the Superior Temporal Sulci (STS) (Routier et al., 2016). The generators of the TTA-SW are located in deeper structures at 26wGA than at 30 wGA probably within the subplate (Routier et al., 2016). Because of the small parcellation of the brain in preterm babies, the EEG patterns are region specific [START_REF] Odabaee | Spatial patterning of the neonatal EEG suggests a need for a high number of electrodes[END_REF].

Few studies have been conducted to investigate functional connectivity patterns in premature infants. A resting-state functional connectivity study with fMRI [START_REF] Fransson | The functional architecture of the infant brain as revealed by resting-state fMRI[END_REF][START_REF] Omidvarnia | Functional bimodality in the brain networks of preterm and term human newborns[END_REF] has shown cortical hubs and their associated cortical networks largely confined to primary sensory and motor brain regions in the infant brain. Due to its poor temporal resolution, fMRI cannot be used to investigate the dynamic of the functional connectivity in the immature neonatal brain especially during short bursts of activities. Using low density EEG data, Omidvarnia et al., [START_REF] Omidvarnia | Functional bimodality in the brain networks of preterm and term human newborns[END_REF] have investigated EEG functional connectivity patterns at the frontal and posterior regions in full term neonates and during EEG bursts of activity in preterm neonates.

In this study, we aimed to investigate the functional organization of the brain networks and the impact of the TTA-SW on the functional connectivity organization in the very preterm neonates during the quite sleep. To investigate the brain functional connectivity topology, we used graph metrics to characterized the functional connectivity using high density EEG data in this age group. To specifically characterize the connectivity pattern of TTA-SW and its impact on overall functional connectivity, we compared the graph metrics during bursts of activity with and without TTA-SW.

Materials and Methods

Figure 6.1 shows the block diagram of the processing pipeline.

Subjects and EEG recordings

High density EEG (HD-EEG) data recorded from 12 healthy preterm neonates (31.26 ± 0.18weeks, Gestational age, GA) were included in this study from the clinical database of the pediatric functional exploration of the nervous system service in Amiens University Hospital, France. The inclusion criteria were the absence of neurological disorders and illness. The HD-EEG data were recorded in the neonatal intensive care unit of the university hospital of Amiens, France. The data had been recorded for clinical routine use during quite sleep (QS) using ANT's EEG acquisition system (ANT, Netherlands) with a sampling rate of 1024Hz and a high density EEG cap (Medelopt™, France) adapted for preterm neonates with 64 channels positioned according to the international 10-10 standard system. EEG data of premature neonates are characterized by a discontinuous pattern alternating with short-lasting periods of cerebral activities mostly consisting of irregular intermingled θ-δ activities (Figure 6.2 (A)). Based on these characteristics, two electrophysiology experts selected twelve six-second artifact free EEG segments with theta temporal activity (TTA) followed by a slow wave (Figure 6.2 (B)) separately for each subject. EEG data preprocessing EEG data were first band-pass filtered between 0.5 and 40 Hz to exclude very low frequency activities as well as high frequency noise. The EEG trials were then re-referenced using a Laplacian montage ( current source density, CSD) [START_REF] Perrin | Spherical splines for scalp potential and current density mapping[END_REF] to effectively minimize volume conduction effects. CSD has been shown to have optimal source separation and performance required for functional connectivity analysis [START_REF] Srinivasan | EEG and MEG coherence: measures of functional connectivity at distinct spatial scales of neocortical dynamics[END_REF]. Considering missing or bad channels, 59 electrodes were considered for all the neonates for further analysis.

Frequency-domain signal

(A) (B)
The frequency-domain signal was computed using the Morlet wavelet, which is localized in both time and frequency and useful for processing nonstationary signals. However, Morlet wavelet, w (t,f ) is defined as:

𝑤(𝑡, 𝑓) = (𝜎 𝑡 √𝜋) - 1 2 𝑒 - 𝑡 2 2𝜎 𝑡 2 𝑒 -𝑖2𝜋𝑓𝑡 (6. 1)
Here, f is the center frequency and σt is the temporal standard deviation. The time-frequency complex signal Z (t,f) of a signal z(t) was computed by convolving it with w(t,f):

𝑍(𝑡, 𝑓) = 𝑧(𝑡) * 𝑤(𝑡, 𝑓) (6.2)
We choose the spectral bandwidth for each frequency band by controlling the center frequency f and its ratio to the standard deviation (σf). Two frequency bands ( 1 -4 Hz) with f= 2.5Hz and f/σf =3 and (4.17 -7.83 Hz) with f=6Hz and f/σf=6 were selected for connectivity analysis.

Synchronization index

The synchronization index was used to evaluate coupling between pairs of EEG channels over time. This was applied to 6-second EEG of 12 segments for each patient in order to investigates the dynamic synchronization within and between temporal regions only. Synchronization index computation is based on the statistical phase locking of the distribution of phase differences between pairs of EEG channels based on the normalized Shannon entropy [START_REF] Hurtado | Statistical Method for Detection of Phase-Locking Episodes in Neural Oscillations[END_REF]. The phase of the signal was obtained from the complex signal as obtained from equation 6.2. Therefore, the synchronization index, e(t) is defined as:

𝑒(𝑡) = -∑ 𝑝 𝑗 𝑁 𝑖=1 log 𝑝 𝑗 (6.3)
Where pj is the relative frequency of phase difference within the ith bin. e varies between 0 and E=logN where N is the number of bins and this was obtained with sliding windows of 200 milliseconds in a step of 20 milliseconds. In this study, we used 72 bins (5 o spaced). The synchronization index was normalized at each time point:

𝑞(𝑡) = 𝐸 -𝑒(𝑡) 𝐸 (6.4)

Functional connectivity analysis

To investigate the functional connectivity patterns for each condition, Phase Locking Value (PLV) was computed between all pairs of EEG channels [START_REF] Lachaux | Measuring phase synchrony in brain signals[END_REF][START_REF] Mormann | Mean phase coherence as a measure for phase synchronization and its application to the EEG of epilepsy patients[END_REF].

The PLV was computed for 3-second EEG data of 12 segments for both TTA-WS segment and normal activity (NAT). The PLV between electrodes X and Y is computed as:

𝑃𝐿𝑉(𝑥, 𝑦) = 1 𝑁 |∑ 𝑒 𝑖(𝜑 𝑥 (𝑡)-𝜑 𝑦 (𝑡)) 𝑁 𝑡=1 | (6.5)
Where φx and φy are the instantaneous phases computed from the frequency-domain signals of X and Y. The PLV ranged from 0 to 1, with 0 and 1 indicating no connection and maximum connection between any given pair of signals, respectively. The end-result of computing the PLV for all pairs of channels was a square connectivity matrix of size 59 (number of EEG channels). In the connectivity matrices, each entry Nx,y(= Ny,x) contained the PLV for channels X and Y.

Single-and group-level statistical analysis

To evaluate the significance in PLV, we generated 200 time-shifted surrogate signals sharing statistical characteristics of the original data [START_REF] Theiler | Testing for nonlinearity in time series: the method of surrogate data[END_REF]. The PLV between the first signal and all the time-shifted versions of the second signal yielded a null distribution for statistical testing. The significance was defined by the difference between the original and the mean of the surrogate values of statistics, divided by the standard deviation of the surrogate values:

𝑍 = 𝑃𝐿𝑉 -𝜇 𝑠𝑢𝑟𝑟𝑜𝑔𝑎𝑡𝑒 𝜎 𝑠𝑢𝑟𝑟𝑜𝑔𝑎𝑡𝑒 (6.6 )
We used a criterion of 5%, which implies that the proportion of surrogate values higher than the original PLV (between x and y) must be less than 5% (95% significance level). This procedure was performed for each individual connectivity matrix (Figure 1). The error rate in multiple comparisons was also corrected by controlling the false discovery rate [START_REF] Nichols | Multiple testing corrections, nonparametric methods, and random field theory[END_REF]) at 5% significance level for the grand averaging over individual connectivity matrices. Statistical comparisons between the TTA and normal activity (NAT) segments were done using the pairwise nonparametric permutation test with correction for multiple comparisons [START_REF] Maris | Nonparametric statistical testing of EEG-and MEG-data[END_REF] with 1000 permutations and the false discovery rate controlled at 5% significance level.

Graph theoretical measures

To compute graph metrics, the functional connectivity matrices were first thresholded and binarized the functional connectivity matrices. The matrices were thresholded by applying false discovery rate, q=0.01which controls the expected proportion of false positives among suprathreshold correlations. This was done to prune out the weaker correlation between the EEG channels.

The following graph metrics [START_REF] Rubinov | Complex network measures of brain connectivity: uses and interpretations[END_REF] were computed after the thresholding: Degree: Degree is the most common measures of centrality with straight forward neurobiological interpretation. A node with high degree implies more interaction with many nodes in the network.

Global Efficiency: Global efficiency measures the functional integration by computing the path between two vertices as the inverse of the shortest distance between the vertices.

Clustering coefficient: Clustering coefficient computes the functional segregation by measuring the presence of clusters or modules in functional networks.

Local Efficiency:

The local efficiency of a particular node is similar to clustering coefficient. This was added in order to estimate the efficiency of local connectivity within neighbors.

The details of the mathematical descriptions of these metrics are provided in the appendix.

The above graph metrics were selected in order to characterized the distribution of connection density (degree) in preterm neonates, global connectivity processing (global efficiency) and local connectivity and efficiency (clustering coefficient and local efficiency) of neighbor's nodes.

Nonparametric permutation testing was used for all graph metrics with correction for multiple comparisons including post hoc tests. A total of 1,000 permutations were used to determine the significance level for each test.

All computations and statistical analyses were performed in Matlab with custom scripts and open source toolboxes: EEGLAB (for 3D topological plots, http://sccn.ucsd.edu/eeglab/), and the brain connectivity toolbox (for graph parameter computations, https://sites.google.com/site/bctnet/).

Results

Synchronization between channels

As shown in Figure 6.3, the synchronization results indicated that the synchronizations level between the bilateral temporal regions (T7-T8 and P7-P8) were very weak compared to the synchronization within each temporal region (P8-T8 and P7-TP7). Though slightly increased due to the occurrence of TTA, the synchronization level still remained weak between and within the right and left temporal regions (around 2000 ms). The increase (started around 2000 ms as shown in Figure 3B) in the synchronization index within each temporal region (P8-T8 and P7-TP7) highlighted the impact of TTA on the synchronization level which lasted longer over the right hemisphere (P8-T8) compared to left hemisphere (P7-TP7). Figures 6.4 and 6.5 show the spatial topology of the pair-wire functional connectivity patterns for NAT and TTA. As shown, the functional connections were only densely packed at bilateral frontal and posterior regions. No long-distance functional connections with significant strength were observed between the both hemispheres as well as between anterior and posterior regions in the preterm brain networks. Regardless of the presence of TTA (TTA vs NAT) the spatial topology of the functional connections remained densely local at the bilateral frontal and posterior regions. In order to better investigate the impact of TTA on the brain functional organization, we compared the spatial distribution of degree between the TTA and NTA segments. The connection density was higher due to the presence of TTA in the θ band, though functional connections were restricted to the temporal regions. In the δ band, the occurrence of TTA spuriously lowered (p<0.01) the functional connectivity level between the temporal and parietal regions in the left hemisphere.

Topological organization of functional connectome

Spatial topology and network metrics

The spatial topology of the functional connectivity pattern indicated dense functional connections at the frontal and posterior regions. We further characterized the functional connectivity pattern to investigation the spatial distribution of local connectivity (Figure 6. The global network metrics (Figure 6.7) were higher for TTA compared to NAT except for the clustering coefficient in the δ band where TTA was significantly lower. F, T, C, and P represent frontal, temporal, central and posterior regions, respectively, as shown in Table 6.2.

Discussion

In order to assess the spatial functional organization of the premature's brain we analyzed the synchronization and functional connectivity of the brain networks using high density EEG in preterm neonates. The synchronization level between brain regions during TTA were assessed by the synchronization index in two frequency bands (δ and θ). The pairwise correlation between all the channels was also computed by the phase locking value (PLV). We further computed three graph metrics-degree, clustering coefficient and efficiency to characterize the functional connectivity pattern of the preterm brain networks. Our results showed that functional connectivity in the healthy preterm infants were local with very weak direct long-range functional connections between the hemispheres and between anterior to posterior areas. Moreover, the functional connectivity analysis of the theta temporal activity (TTA), as a specific biomarker at this period of neurodevelopment, showed restricted high connectivity density within the left and right temporal regions.

The functional connectivity analysis of resting state fMRI data has shown dense functional connectivity patterns at the frontal and posterior regions in preterm neonates [START_REF] Ball | Rich-club organization of the newborn human brain[END_REF][START_REF] Fransson | The functional architecture of the infant brain as revealed by resting-state fMRI[END_REF][START_REF] Heuvel | The Neonatal Connectome During Preterm Brain Development[END_REF][START_REF] Smyser | Functional connectivity MRI in infants: exploration of the functional organization of the developing brain[END_REF]. Using high-density EEG, we found locally dense functional connectivity in the bilateral frontal and posterior regions with very weak long-range functional connectivity between the hemispheres. Our findings support the hypothesis that the frontal and the posterior regions are at least partly functionally developed before the term birth [START_REF] Pandit | Whole-brain mapping of structural connectivity in infants reveals altered connection strength associated with growth and preterm birth[END_REF][START_REF] Teffer | Developmental changes in the spatial organization of neurons in the neocortex of humans and common chimpanzees[END_REF]. The existence of the rich-club structural connectivity predominantly in frontal and parietal regions has been reported in preterm neonates between 30 and 40 week using the diffusion magnetic resonance imaging [START_REF] Ball | Rich-club organization of the newborn human brain[END_REF]. The absence of inter-hemispheric asynchrony of EEG burst activity has also been reported in preterms of 28-32 wGA [START_REF] Wallois | Synopsis of maturation of specific features in EEG of premature neonates[END_REF]. This is likely due to the immaturity of transcallosal connection at this early stage of development [START_REF] Anderson | Detection of impaired growth of the corpus callosum in premature infants[END_REF][START_REF] Anderson | Growth rate of corpus callosum in very premature infants[END_REF][START_REF] Rose | Brain microstructural development at near-term age in very-low-birth-weight preterm infants: an atlas-based diffusion imaging study[END_REF]. In line with the findings reported for fullterm neonates, we found weaker long range functional connections between anterior and posterior cortical regions in preterm infants [START_REF] Fransson | Resting-state networks in the infant brain[END_REF][START_REF] Kwon | The role of neuroimaging in predicting neurodevelopmental outcomes of preterm neonates[END_REF][START_REF] Smyser | Functional connectivity MRI in infants: exploration of the functional organization of the developing brain[END_REF].

We also found that the increase in functional connectivity due to theta temporal activity was restricted to the temporal regions only. The TTA is not stimulus driven and appear as local endogenous generators most likely located in the subplate [START_REF] Kostović | The development of the subplate and thalamocortical connections in the human foetal brain[END_REF]). They occur from 24wGA on, before the connection of thalamic afferents with the cortical plate (28wGA). The very dense functional connectivity pattern associated with the occurrence of TTA at the temporal region might be related to the development of the language/communication regions [START_REF] Judaš | The significance of the subplate for evolution and developmental plasticity of the human brain[END_REF][START_REF] Kostović | The development of the subplate and thalamocortical connections in the human foetal brain[END_REF]. In contrast to the idea that the brain can establish long range connectivity during brief events of endogenous network activity" [START_REF] Omidvarnia | Functional bimodality in the brain networks of preterm and term human newborns[END_REF], we did not find strong long range connectivity between the hemispheres or between anterior and posterior regions during TTA. [START_REF] Omidvarnia | Functional bimodality in the brain networks of preterm and term human newborns[END_REF] have reported a random global functional network organization in preterm neonates [START_REF] Omidvarnia | Functional bimodality in the brain networks of preterm and term human newborns[END_REF]. We found the small-world properties in the preterm brain networks with locally dense and sparse and weak long distance functional connectivity within and between the two hemispheres. Our finding is in agreement with the results of other studies [START_REF] Heuvel | The Neonatal Connectome During Preterm Brain Development[END_REF]. The small-world functional organization of the brain networks seems to be topologically optimal for information segregation and integration in adults and neonates [START_REF] Fair | Functional brain networks develop from a "local to distributed" organization[END_REF]; [START_REF] Bassett | Small-world brain networks[END_REF][START_REF] Ratnarajah | Structural connectivity asymmetry in the neonatal brain[END_REF]. Our finding confirms the idea that most functional networks present in neonates are subject to functional reorganization and development [START_REF] Dosenbach | Prediction of individual brain maturity using fMRI[END_REF][START_REF] Fair | Functional brain networks develop from a "local to distributed" organization[END_REF] from functionally local segregated network to distributed networks.

One significant feature of the mature human brain lies in its asymmetry structurally and functionally [START_REF] Dehaene-Lambertz | The Infancy of the Human Brain[END_REF]. The rightward asymmetry in spectral power in the frontal and temporal regions has been reported in preterm neonates [START_REF] Field | Maternal Depression Effects on Infant Frontal Eeg Asymmetry[END_REF][START_REF] Mento | Functional hemispheric asymmetries in humans: electrophysiological evidence from preterm infants[END_REF] . The rightward asymmetry suggests more activity in the right hemisphere than the left hemisphere. We found higher values of clustering coefficient and efficiency in the right hemisphere compared to the left side. This finding, however, suggests the information processing is likely to be done more efficiently within the local regions of the right hemisphere. In preterm neonates, compared to the left side, the right hemisphere has shown higher cerebral blood flow at rest [START_REF] Roche-Labarbe | Near-infrared spectroscopy assessment of cerebral oxygen metabolism in the developing premature brain[END_REF] and higher hemodynamic responses in the superior temporal sulcus to auditory stimulation in preterm [START_REF] Mahmoudzadeh | Syllabic discrimination in premature human infants prior to complete formation of cortical layers[END_REF]. These findings may confirm that the right hemisphere in the preterm brain is relatively more developed in preterm infants [START_REF] Dehaene-Lambertz | The Infancy of the Human Brain[END_REF]. Conversely, the leftward asymmetry in parietooccipital areas, with or without TTA, might be partly explained by the stronger functional hemodynamic activity observed in the same regions during the phonemes stimulation in preterm [START_REF] Mahmoudzadeh | Syllabic discrimination in premature human infants prior to complete formation of cortical layers[END_REF].

Conclusion

The present findings provide more information on the functional organization of the brain networks in preterm neonates. We showed that the activity of the preterm brain networks is densely localized in bilateral frontal and posterior regions with the weaker direct long-range functional connectivity between hemispheres and between anterior/posterior regions. Endogenous activity such as TTA may play an important role in the neurodevelopment with dense functional connections and high degree of clustering coefficient and local efficiency within each temporal region. However, further studies are required to confirm the role of the TTA generators in the maturation process of the brain in preterm neonates.

Full-term EEG functional connectivity

Functional organization of full-term neonates during natural quiet and active sleep

Introduction

The early infancy is a crucial period concomitant with rapid neurodevelopment in human life. Though relatively small at birth, the brain structure develops quickly in the first few weeks after birth. Despite the tremendous advances in neonatal healthcare, neonates are highly at high risk of poor neurodevelopment [START_REF] Back | Brain injury in premature neonates: A primary cerebral dysmaturation disorder?[END_REF]. The period between 37 and 42-week gestational age is a critical transitional period and constitutes a break in the maturation process between utero and ex-utero. This period is also considered as the beginning of a more linear progression of cerebral activities with a gradual increase in the frequency of brain activities and specialization [START_REF] Wallois | Synopsis of maturation of specific features in EEG of premature neonates[END_REF]. So far, there has been little attempt to investigate the functional neonatal connectome using the functional Magnetic Resonance Imagining (fMRI) [START_REF] Ball | Rich-club organization of the newborn human brain[END_REF][START_REF] Doria | Emergence of resting state networks in the preterm human brain[END_REF][START_REF] Fransson | Spontaneous Brain Activity in the Newborn Brain During Natural Sleep-An fMRI Study in Infants Born at Full Term[END_REF][START_REF] Fransson | Resting-state networks in the infant brain[END_REF]. [START_REF] Fransson | The functional architecture of the infant brain as revealed by resting-state fMRI[END_REF]2007) have revealed the existence of cortical hubs at primary sensory and motor brain regions in infant brain. In adults, the majority of cortical hubs and hub-related networks are located in the heteromodal association cortex. These findings provide some evidence on how brain connectivity evolves quickly from the immature neonatal brain to the mature brain in adults due to mainly the process of myelination and tangential connectivity which speed up the transfer of information [START_REF] Kostović | The development of the subplate and thalamocortical connections in the human foetal brain[END_REF][START_REF] Stiles | The Basics of Brain Development[END_REF]. In neonates, brain electrical activity is characterized by some endogenous bursts of activity such as the frontal transients, and period of discontinuity in quiet sleep [START_REF] André | Electroencephalography in premature and full-term infants. Developmental features and glossary[END_REF]. Compared to fMRI, due to its high temporal resolution, EEG is well suited to investigate the functional connectivity associated with these transient activities in full-term neonates. There have been efforts to assess the functional connectivity of neonatal brain activity with low density EEG [START_REF] Grieve | EEG functional connectivity in term age extremely low birth weight infants[END_REF]. To characterize the spatial specificity of the EEG data as well as the functional connectivity patterns in neonates, the acquisition of high density EEG data is required [START_REF] Odabaee | Spatial patterning of the neonatal EEG suggests a need for a high number of electrodes[END_REF]. Recent EEG studies [START_REF] Grieve | EEG functional connectivity in term age extremely low birth weight infants[END_REF][START_REF] Omidvarnia | Structural damage in early preterm brain changes the electric resting state networks[END_REF][START_REF] Omidvarnia | Functional bimodality in the brain networks of preterm and term human newborns[END_REF][START_REF] Tokariev | Functional Brain Connectivity Develops Rapidly Around Term Age and Changes Between Vigilance States in the Human Newborn[END_REF] have shown the benefit of high-density EEG for studying the functional neuronal activity at the early stage of neurodevelopment in preterm and full-term babies.

The neonatal sleep architecture consists of active and quite sleep with intermixed transitional or intermediate sleep segments [START_REF] André | Electroencephalography in premature and full-term infants. Developmental features and glossary[END_REF]. The differentiation between quiet and active periods with amplitude correlation [START_REF] Tokariev | Functional Brain Connectivity Develops Rapidly Around Term Age and Changes Between Vigilance States in the Human Newborn[END_REF] has revealed intra and interhemispheric connectivity during the active sleep in higher frequencies compared to the quite sleep. This observation suggests that functional brain networks are rapidly evolving from in-utero to ex-utero situations.

In the present study we investigated the brain functional connectivity patterns in full term neonates during both the quiet and active sleep stages using the spectral power and functional connectivity analyses. We also used different graph metrics to characterize the brain functional connectivity. We further searched for biomarkers of the brain functional maturation in neonates by exploring their brain functional topology for short-or long-range connections during the quiet and active sleep stages.

Material and methods

Subjects and EEG recordings

High Density EEG (HD-EEG) data recorded from 14 healthy full-term neonates (35.81 ± 2.71 weeks, Gestational age, GA) were included in this study from the clinical database of the pediatric functional exploration of the nervous system service in Amiens University Hospital, France. The inclusion criteria were the absence of neurological disorders and illness. The HD-EEG data were recorded in the neonatal intensive care unit of the university hospital of Amiens, France. The data had been recorded for clinical routine use during both quite sleep (QS) and active sleep (AS) using the ANT's EEG acquisition system (ANT, Netherlands) with a sampling rate of 1024Hz and a high density EEG cap (Medelopt™, France) adapted for full term neonates with 64 channels positioned according to the international 10-10 standard system. Two electrophysiology experts selected 3 seconds of 25 segments during the QS and AS conditions separately for each subject.

EEG data preprocessing

EEG data were first band-pass filtered between 0.5 and 40 Hz to exclude very low frequency activities as well as high frequency noise. The EEG trials were then re-referenced using a Laplacian montage (current source density, CSD) [START_REF] Perrin | Spherical splines for scalp potential and current density mapping[END_REF] to effectively minimized volume conduction artifacts. CSD has been shown to have optimal source separation and performance required for the connectivityanalysis [START_REF] Srinivasan | EEG and MEG coherence: measures of functional connectivity at distinct spatial scales of neocortical dynamics[END_REF]. Considering missing or bad channels, 59 electrodes were used for all the neonates for further analysis.

Power spectral analysis and EEG source analysis

We performed the spectral power analysis in four frequency bands (δ, θ, α and β) in both sensor and source spaces. The scalp spectral power was divided into different brain regions based on their anatomical locations as shown in Table 6.3. We used the neonatal MRI template [START_REF] Fonov | Unbiased average age-appropriate atlases for pediatric studies[END_REF] for the construction of the head model. The template was segmented by SPM8 [START_REF] Ashburner | SPM8 manual[END_REF] into scalp, skull and brain compartments defining 3 homogeneous conductive mediums. The lead field was calculated using FieldTrip [START_REF] Oostenveld | FieldTrip: Open Source Software for Advanced Analysis of MEG, EEG, and Invasive Electrophysiological Data[END_REF] with 6 mm spatial resolution. In total, 4744 source locations were generated inside the brain. The leadfield wa calculated using the Boundary Element Method (BEM) [START_REF] Oostendorp | Source parameter estimation in inhomogeneous volume conductors of arbitrary shape[END_REF] The eLORETA [START_REF] Pascual-Marqui | Discrete, 3D distributed, linear imaging methods of electric neuronal activity. Part 1: exact, zero error localization[END_REF] inverse solution was used to calculate three dimensional current density distributions in the four frequency bands. We used eigen decomposition method [START_REF] Sekihara | Asymptotic SNR of scalar and vector minimum-variance beamformers for neuromagnetic source reconstruction[END_REF] to determine the dominant dipole orientation and to obtain high SNR for reconstructed current density.

Frequency-domain signal

The frequency-domain signal was computed using the Morlet wavelet, which is localized in both time and frequency and useful for processing nonstationary signals. However, Morlet wavelet, w (t,f ) is defined as:

𝑤(𝑡, 𝑓) = (𝜎 𝑡 √𝜋) - 1 2 𝑒 - 𝑡 2 2𝜎 𝑡 2 𝑒 -𝑖2𝜋𝑓𝑡 (6. 8)
Here, f is the center frequency and σt is the temporal standard deviation. The time-frequency complex signal Z (t,f) of a signal z(t) was computed by convolving it with w(t,f):

𝑍(𝑡, 𝑓) = 𝑧(𝑡) * 𝑤(𝑡, 𝑓) (6.9)

We choose the spectral bandwidth for each frequency band by controlling the center frequency, f and its ratio to the standard deviation (σf). The following center frequencies 2.5, 6, 10 and 15 were used for the these frequency bands ( 1 -4 Hz), ( 4.17 -7.83 Hz), ( 7.5 -12.5 Hz) and  (12 -18 Hz).

Functional connectivity analysis

To investigate the functional connectivity patterns for each condition, Phase Locking Value (PLV) was computed between all pairs of EEG channels ( [START_REF] Lachaux | Measuring phase synchrony in brain signals[END_REF][START_REF] Mormann | Mean phase coherence as a measure for phase synchronization and its application to the EEG of epilepsy patients[END_REF]. The PLV between electrodes X and Y is computed as:

𝑃𝐿𝑉(𝑥, 𝑦) = 1 𝑁 |∑ 𝑒 𝑖(𝜑 𝑥 (𝑡)-𝜑 𝑦 (𝑡)) 𝑁 𝑡=1 | (6.10)
Where φx and φy are the instantaneous phases computed using the complex signals of X and Y.

The PLV ranged from 0 to 1, with 0 and 1 indicating no connection and maximum connection between any given pair of signals, respectively. The end-result of computing the PLV for all pairs of channels was a square connectivity matrix of size 59 (number of EEG channels), in which each entry Nx,y(= Ny,x) contained the PLV for channels X and Y.

Single-and group-level statistical analysis

To evaluate the significance of PLV, we generated 200 time-shifted surrogate signals sharing statistical characteristics of the original data [START_REF] Theiler | Testing for nonlinearity in time series: the method of surrogate data[END_REF]. The PLV between the first signal and all the time-shifted versions of the second signal yielded a null distribution for statistical testing. The significance was defined by the difference between the original and the mean of the surrogate values of statistics, divided by the standard deviation of the surrogate values: 𝑍 = 𝑃𝐿𝑉 -𝜇 𝑠𝑢𝑟𝑟𝑜𝑔𝑎𝑡𝑒 𝜎 𝑠𝑢𝑟𝑟𝑜𝑔𝑎𝑡𝑒 (6.11) We used a criterion of 1%, which implies that the proportion of surrogate values higher than the original PLV (between x and y) must be less than 1% (99% significance level). This procedure was performed for each individual connectivity matrix (Figure 6.9). The error rate in multiple comparisons was also corrected by controlling the false discovery rate [START_REF] Nichols | Multiple testing corrections, nonparametric methods, and random field theory[END_REF] at 0.1% significance level for the grand average of individual connectivity matrices (Figure 6.9).

Graph theoretical measures

To compute graph metrics, the functional connectivity matrices were first thresholded and binarized using the Erdos-Renyi model [START_REF] Erdős | On the strength of connectedness of a random graph[END_REF], in which the threshold is determined in a way that most of the nodes remain fully connected at a connection density of 2ln(N)/N, where N is the number of nodes. In our study with 59 EEG channels, the connection density was approximately 14% using the Erdos-Renyi model. We then computed the following graph metrics [START_REF] Rubinov | Complex network measures of brain connectivity: uses and interpretations[END_REF]: Degree: the most common measure of centrality with a straight forward neurobiological interpretation. A node with high degree implies more interaction with many nodes in the network.

Betweeness centrality: a very sensitive measure of centrality that measures the fraction of all shortest paths that pass through a given node. Like the network degree, it is used to detect the important functional connection.

Clustering coefficient: computes the functional segregation by measuring the presence of clusters or modules in functional networks.

Characteristics path length: estimates the potential functional integration in the network and is computed by the average shortest path length between all pairs of the nodes in the network.

Small-worldness: a metric that measures the ability of the functional network to combine functionally segregated modules with robust integration links. This metric is measured by computing the ratio of the normalized clustering coefficient to the normalized path length. A network with a small-worldness greater than 1 is said to exhibit small-world property.

The details of the mathematical descriptions of these metrics are provided in the Appendix.

The degree measures the presence of cortical hubs and the bewteeness centrality was computed on order to investigate the region that are involved in the transfer of information from one region to the other. The functional segregation was estimated by clustering coefficient, and the global connectivity processing by characteristic path length. There is general idea that neonatal brain also estimated small-world features and this investigate by computing small-worldness which measures the ratio of normalized clustering coefficient to characteristic path length.

All computations and statistical analyses were performed in Matlab with custom scripts and open source toolboxes: EEGLAB (for 3D topological plots, http://sccn.ucsd.edu/eeglab/), and the brain connectivity toolbox (for graph parameter computations, https://sites.google.com/site/bctnet/).

Results

EEG power spectral and Source analysis

The results of the EEG power spectral and source analyses in all frequency bands are shown in Figures 6.10 and 6.11,respectively. As shown in Fig. 6.10, the power spectra decreased as the frequency increased (Figure 6.10). There was no difference between both sleep conditions in each region and in all the frequency bands. As shown in Fig. 6.11, the QS condition, significant increases in CSD were observed at the posterior region in the δ and θ bands and at the right temporal region in the α and β bands. In the AS condition, we found increased CSD at the frontal region in all the frequency bands. The AS condition also exhibited higher CSD at the posterior region compared to other regions in the δ and θ bands similar to that observed in QS. 6.3) for both conditions (QS and AS) Whole brain connectivity Figure 6.12 shows the average PLV matrices for both conditions and all the frequency bands. In both conditions, functional connectivity matrices look similar in each frequency band. However, the connectivity density (number of significance elements) increased with increasing frequency with weaker strengths in the α and β bands. No difference was observed between the two sleep conditions for all the frequency bands with p<0.10. However, the mean PLV as shown in Figure 6.13 shows higher mean PLVs in the δ and θ bands than in the α and β bands. Global networks properties Figure 6.14 shows the global network properties; mean betweenness centrality, clustering coefficient, characteristics path length and small-worldness, in both sleep conditions and all the frequency bands. All the network metrics were calculated with a connection density of 14% determined based on the Erdos-Renyi model [START_REF] Erdős | On the strength of connectedness of a random graph[END_REF] to make sure all the nodes are fully connected. There was no significant difference in all the graph metrics between both the sleep conditions within all the frequency bands. The graph metrics for both the conditions showed similar values for QS and AS with a betweenness centrality around 0.015, a relatively average path length around 2.7 and a clustering coefficient around 0.35.

Local network properties

The spatial topology of the degree (K), betweenness centrality (BC), and clustering coefficient (C) for QS and AS are shown in Figures 6.15 and 6.16,respectively. High degree (K) were found in the frontal and the posterior regions in all the frequency bands in both the sleep conditions. The degree was lower at the central region of the brain especially in the β band with no statistical differences between the two sleep conditions.

The betweenness centrality (BC) was lower in lower frequency bands. It increased significantly bilaterally in anterior temporal regions in the θ, α and β bands especially in the QS conditions. In both conditions, bilateral frontal-temporal regions showed increased betweenness centrality notably in the β band.

In both conditions, the spatial distribution of the clustering coefficient was similar in all the frequency bands. The average clustering coefficient (C) was about 0.35 over all the brain regions excluding the central areas indicates the strength of the metrics from zero (blue) to highest value (red) corresponding to 0.25, 0.03 and 0.6 for K, BC and C, respectively All the graph metrics were calculated from the thresholded connectivity matrix with a connection density of 14% determined using the Erdos-Renyi model.

Discussion

The results of our functional connectivity analysis strongly suggest that the functional organization of the brain networks in full term neonates is dominated by the short-range functional connections at the frontal, temporal and posterior regions. In contrast to previous results [START_REF] Omidvarnia | Functional bimodality in the brain networks of preterm and term human newborns[END_REF][START_REF] Tokariev | Functional Brain Connectivity Develops Rapidly Around Term Age and Changes Between Vigilance States in the Human Newborn[END_REF], our results indicate that long range functional connections in neonates are sparse and limited during both active and quiet sleeps. This discrepancy might be related to the higher EEG spatial resolution used in our study for functional connectivity analysis. Statistically, we did not find any differences in functional connectivity between the quite sleep (QS) and active sleep (AS). However, our results show some overlap with the structural and functional MRI studies in neonates [START_REF] Ball | Rich-club organization of the newborn human brain[END_REF][START_REF] Fransson | Spontaneous Brain Activity in the Newborn Brain During Natural Sleep-An fMRI Study in Infants Born at Full Term[END_REF] with the exception of lower activity at the central regions.

We found higher power in lower frequency bands and lower power in high frequency bands. This can be directly deduced from the finding that EEG activity in neonate has high amplitude and low frequency [START_REF] André | Electroencephalography in premature and full-term infants. Developmental features and glossary[END_REF]. In other word, EEG activity with higher frequency has lower power and vice versa in the mature brain. The higher current source density at the frontal region during active sleep is likely to be related to the occurrence of frontal transients and the slow anterior dysrhythmia that are well characterized during AS from 37wGA [START_REF] André | Electroencephalography in premature and full-term infants. Developmental features and glossary[END_REF]. Although, we cannot rule out with certainty the effect of rapid eye movement artifacts on the results of the spectral analysis during AS. In both AS and QS, higher source activity were observed at the posterior regions in lower frequency bands most likely due to the predominant slow delta waves at the occipital region [START_REF] André | Electroencephalography in premature and full-term infants. Developmental features and glossary[END_REF][START_REF] De Weerd | The development of sleep during the first months of life[END_REF]. The occurrence of slow delta waves at the temporal and occipital regions can be considered as one of the biomarkers used for studying the brain maturation in full-term neonates. In the lower frequency band, relatively higher source activity values were observed over rolandic areas in AS and to a lesser extent in QS. This increase in source activity might be partly explained by the presence of temporal specific activity such as theta temporal bursts which predominantly occur in the rolandic/temporal regions during AS [START_REF] André | Electroencephalography in premature and full-term infants. Developmental features and glossary[END_REF]. During QS, we observed an increase in high frequency source activity at the temporal lobe which is highly involved in communication, hearing and language skills. The temporal region as well as the amygdala and the hippocampus are highly involved in learning, memory, emotional responses, visual recognition memory and attention [START_REF] Bachevalier | Effects of selective neonatal temporal lobe lesions on visual recognition memory in rhesus monkeys[END_REF][START_REF] Málková | Long-term effects of selective neonatal temporal lobe lesions on learning and memory in monkeys[END_REF].

In our study, the graph-based network characterization demonstrated the small-world properties of the brain functional networks in full-term neonates, including high clustering coefficient and high centrality and betweenness [START_REF] Fransson | The functional architecture of the infant brain as revealed by resting-state fMRI[END_REF]. We further found nodes with high degrees and high betweenness centrality at the frontal, temporal and posterior regions that correspond to brain regions functionally classified as "polysensory", or "multimodal association areas". These regions might be related to the parietal and prefrontal cortical regions in which the presence of cortical hubs has been demonstrated [START_REF] Ball | Rich-club organization of the newborn human brain[END_REF][START_REF] Heuvel | The Neonatal Connectome During Preterm Brain Development[END_REF]. These regions are thought to provide a foundation for coherent neuronal activation across distal cortical regions [START_REF] Judaš | The significance of the subplate for evolution and developmental plasticity of the human brain[END_REF][START_REF] Kostović | The development of the subplate and thalamocortical connections in the human foetal brain[END_REF]. This supports the evidence that the frontal, and the posterior regions are functionally developing during the infancy period (Dehaene-Lambertz and Spelke, 2015; [START_REF] Dubois | Mapping the early cortical folding process in the preterm newborn brain[END_REF][START_REF] Pandit | Whole-brain mapping of structural connectivity in infants reveals altered connection strength associated with growth and preterm birth[END_REF]. These regions are established by the third trimester [START_REF] Judaš | The significance of the subplate for evolution and developmental plasticity of the human brain[END_REF] and have been reported to start to develop earlier than other brain regions with early functional and structural development of neuronal networks [START_REF] Stiles | The Basics of Brain Development[END_REF][START_REF] Teffer | Developmental changes in the spatial organization of neurons in the neocortex of humans and common chimpanzees[END_REF]. The spatial location of these regions (frontal and parietal regions) tend to show large overlaps with structural and functional hub regions in the adult brain (van den [START_REF] Van Den Heuvel | Network hubs in the human brain[END_REF]. Although the functional spatial topology of the brain is very complex in neonates but it is generally believed that the brain networks evolve from a local architecture dominated by frontal, temporal and parietal regions to a more diffuse topology in adults [START_REF] Dosenbach | Prediction of individual brain maturity using fMRI[END_REF][START_REF] Fair | Functional brain networks develop from a "local to distributed" organization[END_REF].

The neonatal functional networks exhibiting small-world properties may suggest that the neonatal brain support primary as well as higher cognitive functions [START_REF] Bullmore | Complex brain networks: graph theoretical analysis of structural and functional systems[END_REF][START_REF] Collin | The ontogeny of the human connectome: development and dynamic changes of brain connectivity across the life span[END_REF]. The presence of small-word features (high clustering coefficient and global efficiency/path length) in neonates and adults has been previously demonstrated [START_REF] Fair | Functional brain networks develop from a "local to distributed" organization[END_REF][START_REF] Fransson | The functional architecture of the infant brain as revealed by resting-state fMRI[END_REF] though small-world connectivity properties are likely to increase as functional connectivity spatial patterns evolve from local connectivity in neonates to long-distance connectivity in adult [START_REF] Cao | Topological organization of the human brain functional connectome across the lifespan[END_REF][START_REF] Gao | Development of human brain cortical network architecture during infancy[END_REF][START_REF] Supekar | Development of Large-Scale Functional Brain Networks in Children[END_REF]. The small-world features of EEG functional brain networks present in different frequency bands are highly heritable [START_REF] Smit | Heritability of "small-world" networks in the brain: a graph theoretical analysis of resting-state EEG functional connectivity[END_REF][START_REF] Stam | The organization of physiological brain networks[END_REF]. The clustering coefficient and characteristic path lengths were found to be increasing by age [START_REF] Betzel | Changes in structural and functional connectivity among resting-state networks across the human lifespan[END_REF]Smit et al., 2012) with a maximum value during the youth period. This means that as the brain matures, distant brain regions communicate through strong long distance connectivity. This finding is in contrast with those reported in the fMRI studies [START_REF] Fransson | The functional architecture of the infant brain as revealed by resting-state fMRI[END_REF][START_REF] Fransson | Resting-state networks in the infant brain[END_REF] which showed that neonates have distributed brain networks at some regions throughout the childhood and adolescence. This might be due to the differences between these modalities (for instance voxel/hemodynamic activity in fMRI and sensors/electrical activity in EEG). In general, the temporal dynamics of the brain neuronal signal [START_REF] André | Electroencephalography in premature and full-term infants. Developmental features and glossary[END_REF] cannot be captured by the fMRI. Previous comparisons between EEG and fMRI signals in adult [START_REF] Mantini | Electrophysiological signatures of resting state networks in the human brain[END_REF] have shown the consistency and discrepancy between them in different frequency bands. There is, however, very little information available on the relationships between underlying neuronal and hemodynamic mechanisms in neonates.

In conclusion, our findings indicate that only local connectivity is present in neonates with higher activity and connection density at the frontal, posterior and temporal regions. This study indicated that the long range functional connectivity is limited and healthy full-term neonatal brain network exhibit small word properties. Our study supports the hypothesis that the neonatal brain network developed from local networks in neonates toward more integrated networks in adults.

These studies show that early brain activity of preterm is densely localized at the frontal and the occipital regions and long-range functional connectivity is limited. The presence of endogenous activity such as theta temporal activity plays an important role in the neurodevelopmental period with increased connection density at the temporal regions. Full-term neonates exhibited high connection density at the frontal, posterior and temporal regions during both quiet and active sleeps. The small world network properties were present in neonates, suggesting the presence of both information segregation and integration at local networks.

Chapter 7

General conclusions

Introduction

This chapter summarizes all the studies carried out in this thesis. The directions for future are also discussed. The purpose of this thesis was to investigate changes in the resting-state EEG functional connectivity topology in BCECTS patients in comparison to healthy controls as well as to investigate functional organization of brain networks in preterm and full-term neonates during the resting state.

Benign childhood epilepsy with centrotemporal spikes

In the first part of this thesis, we investigated whether the resting-state brain functional connectivity patterns in BCECTS patients in comparison to healthy controls were disrupted. In the first study, the EEG spectral power analysis in both the sensor and source spaces revealed that BCECTS patients had significantly higher  power in all the brain regions and lower  power at the occipital region. The individual alpha frequency (IAF) was significantly lower in patients in all cortical regions compared to the healthy controls especially due to the presence of IEDs in EEG segments. The resting state EEG cortical source analysis also revealed stronger activity at the centrotemporal regions involved in the generation and propagation of the epileptic activity. Bilateral temporal regions displayed higher cortical activity in patients in all frequency bands and weaker activity at the frontal and occipital lobes in comparison to healthy controls.

We also found that the presence of IEDs impacted the global and local functional connectivity (FC) in comparison to healthy controls. For patients, the FC analysis using EEG segments with IEDs revealed significantly higher global  phase synchronization and lower global connection density in the  band in comparison to healthy controls. The topological distribution of the network degree revealed higher connection density at the epileptic zone (centrotemporal region) due to the presence of IEDs in all the frequency bands. A higher connection density was observed at the same zone in the absence of IEDs in higher frequency bands. Under both the epileptic conditions (with and without IEDs) patients exhibited lower connection density at the frontal and occipital regions especially in the  band in comparison to the healthy controls. Without IEDs, patients displayed higher lagged phase synchronization values (LPS) in the  and  bands and lower LPS in the  band. The changes in the FC pattern support the idea that the disruption in the functional connectivity topology in BCECTS patients may not be restricted to the epileptic zone.

The characterization of the brain functional connectivity networks by the graph metrics revealed that the BCECTS brain networks was functionally more ordered in low frequency bands compared to the healthy controls. However, patients under both conditions (with and without IEDs) were characterized with less global information processing and stronger integration in higher frequency bands. In the absence of IEDs, patients exhibited less ordered brain networks compared to the healthy controls, a pathological network presented for rapid transition to the onset of epileptic discharges.

The seed-based functional connectivity analysis confirmed the functional reorganization of the brain in BCECTS patients compared to healthy subjects. It was shown that the epileptogenic networks were always activated. The existence of functional connections between the epileptic zone and the ipsilateral frontal and temporal regions suggested the involvement of distant cerebral regions in the generation and propagation of IEDs. We further found higher local efficiency in the contralateral hemisphere of the epileptic zone and the frontal region and weaker functional connections between the prefrontal cortex and the regions that were correlated with the default mode network (DMN). This may imply that DMN in BCECTS patients might be impaired.

The last study on the BCECTS functional connectivity was the identification of major drivers (brain regions) that were involved in the generation and propagation of IEDs, and the connectivity pattern with the aid of time-varying effective connectivity. Major drivers identified with higher outflow were the epileptic zone (pre and post central regions), ipsilateral parietal, rolandic, supramarginal and supplementary motor areas (SMA) and superior frontal regions. There was stronger causal influence from these regions to the frontal regions, indicating the involvement of frontal regions in the propagation of IEDs. The BCECTS brain networks also exhibited laterality toward the epileptic focus.

Clinical relevance

Higher source activity and functional connection density at the epileptic zone with the presence of IEDs is expected due to high amplitude of IEDs. However, higher functional connection density in high frequency bands in the absence of IEDs at the epileptic zone revealed that functional connectivity can detect transient activity of IEDs in EEG segment without IEDs. Lower activity at the frontal (especially prefrontal), parietal and posterior regions indicate the primary effect of IEDs. These regions correlated with the default mode network (DMN) and consistent with fMRI studies [START_REF] Archer | fMRI "deactivation" of the posterior cingulate during generalized spike and wave[END_REF][START_REF] Ibrahim | Impaired development of intrinsic connectivity networks in children with medically intractable localization-related epilepsy[END_REF] that reported the deactivation of the epileptic zone. The lower activity at these regions might related to the cognitive impairment and learning problems [START_REF] Datta | Cognitive impairment and cortical reorganization in children with benign epilepsy with centrotemporal spikes[END_REF][START_REF] Jambaqué | Verbal and visual memory impairment in childrem with epilepsy[END_REF][START_REF] Verrotti | Memory impairment and Benign Epilepsy with centrotemporal spike (BECTS): a growing suspicion[END_REF] in these patients. In addition, lower activity and functional connection density at the frontal region at the ipsilateral of epileptic zone might be related to growth disturbance at the frontal region of the patients [START_REF] Kanemura | Serial changes of prefrontal lobe growth in the patients with benign childhood epilepsy with centrotemporal spikes presenting with cognitive impairments/behavioral problems[END_REF][START_REF] Kanemura | Growth disturbance of frontal lobe in BCECTS presenting with frontal dysfunction[END_REF].

Higher  spectral power and synchronization with and without IEDs is a common feature of epilepsy and other neurological disorders most especially in young children. However, lower  activity especially at the posterior of the patients might relate to their cognitive and mental skills deficits [START_REF] Holmes | Role of interictal epileptiform abnormalities in cognitive impairment[END_REF][START_REF] Klimesch | EEG alpha and theta oscillations reflect cognitive and memory performance: a review and analysis[END_REF][START_REF] Metz-Lutz | Cognitive development in benign focal epilepsies of childhood[END_REF]. The lower beta  synchronization in patients shows that brain network of patients is frequency dependent.

The presence of IEDs increase source activity and functional connectivity at the epileptogenic networks. Epileptogenic networks in this group of patients is similar to the sensorimotor network which include central regions and supplementary motor areas. Higher activity and functional connectivity at these regions might related to the movement disturbance and jerking of mouth and throat [START_REF] Boor | Combined spike-related functional MRI and multiple source analysis in the non-invasive spike localization of benign rolandic epilepsy[END_REF][START_REF] Tang | Altered Regional Homogeneity in Rolandic Epilepsy: A Resting-State fMRI Study[END_REF] in patients during IEDs. Also, in the presence of IEDs the ipsilateral temporal region always had higher source activity which might have impact on the imbalanced auditory processing in patients as well as language and phonologic deficits [START_REF] Amaral | Temporal auditory processing and phonological awareness in children with benign epilepsy with centrotemporal spikes[END_REF][START_REF] Overvliet | Correlation between language impairment and problems in motor development in children with rolandic epilepsy[END_REF]. The dynamic of directed interictal connectivity showed that the central regions drove frontal regions during IEDs which might be related clinical diagnosis of this type of epilepsy with the dipole pointing from from posterior to anterior position and vice versa. The occurrence of frontal-central connectivity during IEDs might also related to attention deficits and transient cognitive deficits in patients as some of these patients were diagnosed with attention deficit hyperactive disorder(ADHD) [START_REF] Dunn | Focusing on ADHD and attention in children with epilepsy[END_REF][START_REF] Dunn | ADHD and epilepsy in childhood[END_REF].

Brain functional connectivity in neonates

In the second part of the thesis, we assessed the brain functional connectivity in preterm and fullterm neonates using high density EEG. The brain neuronal activity in neonates is different from that in adults. The neonatal EEG is characterized with different features such as theta temporal activity (TTA) in preterm and slow delta waves at the occipital region in full-term neonates. In preterm neonates, the results of functional connectivity analysis showed high connection density at the bilateral frontal and posterior regions. We further found that the direct long-range functional connections between the two hemispheres and between the anterior and posterior regions were limited. However, the presence of TTA burst at the bilateral temporal regions increased the connection density at the temporal region especially in the  band and decreased the connection density at the left parietal regions in the  band. The presence of TTA at the temporal region increased also the global network degree, global clustering coefficient and global efficiency in comparison to the normal EEG activity. Meanwhile, the preterm brain network exhibited the small-worldness features with local dense short-range and sparse long-range functional connectivity within and between the brain regions. The preterm brain also showed functional rightward asymmetry in the frontal and temporal regions and leftward asymmetry in the posterior region in terms of the network degree, global efficiency and clustering coefficient.

In full-term neonates, we investigated changes in the brain functional connectivity pattern during the quiet (QS) and active (AS) sleep. The spectral power analysis showed decreases in power with increasing frequency during both the quiet and active sleep periods. We also found higher source activity at frontal regions during AS and higher source activity at posterior region during QS especially in lower frequency bands ( and  bands). The right temporal regions displayed higher source activity during QS in higher frequency band. The functional connectivity analysis revealed increased phase synchronization in lower frequency bands. The local functional connectivity topology was similar to that of preterm neonates. However, full term babies exhibited higher degree at the frontal and posterior regions and lower network degrees at the central region in all frequency bands under both conditions. We further found higher betweenness centrality at the bilateral temporal regions. Similarly, the full-term neonates showed distributed clustering coefficient throughout the brain excluding the central brain region. The global network metrics were also similar in all frequency bands. The full-term neonates exhibited small-worldness properties with an average small-worldness index of 2.7.

Methodological considerations and limitations

The thesis developed and implemented different techniques and analyses. Both EEG data of BCECTS patients and neonates were filtered within 0.5 to 40 Hz in order to remove high frequency noise. The laplacian Current Source Density (CSD) [START_REF] Perrin | Spherical splines for scalp potential and current density mapping[END_REF] was applied to neonate EEG data to obtained distinct topography, effectively reducing the negative impact of volume conduction, which widely blurs the EEG signal. The CSD wasn't applied to the study of BCECTS because the IEDs is at the cortical surface (not deeper structure) and application of CSD can reduced the strength and intensity of IEDs.

Phase synchronization is the common functional connectivity measure used in this thesis. Phase synchronization is a nonlinear functional connectivity that measure relative phase difference between two nodes or brain regions. The phase locking value (PLV) [START_REF] Lachaux | Measuring phase synchrony in brain signals[END_REF][START_REF] Schmidt | Whole brain functional connectivity using phase locking measures of resting state magnetoencephalography[END_REF] is zero-lag phase synchronization techniques that are developed based on scalp sensors and sensitive to volume conduction. The PLV was applied to all functional connectivity studies with scalp EEG data. For neonate EEG data, we created surrogate data to test for the significance of functional connectivity because neonatal EEG is different from mature adult EEG. In source space, the lagged phase synchronization (LPS) [START_REF] Pascual-Marqui | Instantaneous and lagged measurements of linear and nonlinear dependence between groups of multivariate time series: frequency decomposition[END_REF] was used to estimate the functional connectivity between brain regions. LPS is non-zero lag phase synchronization that is resistant to artifact of volume conduction by excluding instantaneous zerolag contribution. However, LPS is also sensitive to uncorrelated perturbation especially strong noise which can turn phase lags into leads which could be a problem in sensor space. In addition, LPS was motivated due to its implementation in the eLORETA toolbox that was used for functional connectivity study in source space. We further used a ROI-based approached to reduced volume conduction as it is shown that spatial correlation between sources decays with increasing distance between them [START_REF] Mehrkanoon | Intrinsic Coupling Modes in Source-Reconstructed Electroencephalography[END_REF]. The imaginary coherence was used to estimated voxel-wise whole brain functional connectivity in source space. The imaginary coherence is based on the imaginary part of spectral coherence between two signals and has been shown to be less sensitive to volume conduction [START_REF] Nolte | Identifying true brain interaction from EEG data using the imaginary part of coherency[END_REF] and measure true brain interaction. Imaginary coherence is one of the promising techniques have been proposed that are aimed at tackling the effects of field spread [START_REF] Nunez | EEG coherency: I: statistics, reference electrode, volume conduction, Laplacians, cortical imaging, and interpretation at multiple scales[END_REF][START_REF] Schoffelen | Source connectivity analysis with MEG and EEG[END_REF] which is common effect of source connectivity. In the dynamic interictal connectivity, the effective connectivity was estimated by the partial directed coherence (PDC), that measure the directed functional connectivity unlike PLV, LPS and imaginary coherence that measure non-directed functional connectivity.

Before the computation of graph metrics, the connectivity matrices were thresholded. However, the thresholding of the graph metrics were different for each study. This was motivated by the group of patients involved. Generally, threshold was applied in such a way all the groups and the conditions in the same study have the similar brain topology with similar connection density. However, in BCECTS studies compare to healthy control, both patients and control had similar topology and graph metrics were computed as a function of range of threshold values. In preterm neonates, the threshold was based on the first discovery rate (FDR) due to the nature of functional connectivity of the group.

The functional connectivity matrices in all the studies by the graph metrics most especially in term of functional integration and segregation. However, the degree was also computed which is the basic and the most important graph metric. For the second and third studies of BCECTS, the functional segregation was computed by clustering coefficient and functional integration by characteristics path length (or global efficiency). In the fourth study of BCECTS, the whole brain functional connectivity was characterized by the betweeness centrality and local efficiency. These graph metrics were employed in order to characterized the presence of regions involve in transfer of information between other regions and efficiency of local connectivity. Similarly, in preterm neonate, in addition to degree, the functional connectivity was characterized by the clustering coefficient and local efficiency both measured functional segregation. This was motivated by general idea that neonatal brain network consists of local connectivity in preterm neonate. However, in full-term neonate which is the starting period of linear brain progression, the functional connectivity was characterized by the betweeness centrality in order to detect the regions that involve in transfer of information between cortical regions; by functional segregation (by clustering coefficient) and functional segregation (by characteristic path length) and the smallworld index to investigate the presence of small-world features in full-term neonates.

Before the computation of graph metrics, the connectivity matrices were thresholded. However, the thresholding of the graph metrics were different for each study. This was motivated by the group of patients involved. Generally, threshold was applied in such a way all the groups and the conditions in the same study have the similar brain topology with similar connection density. However, in BCECTS studies compare to healthy control, both patients and control had similar topology and graph metrics were computed as a function of range of threshold values. In preterm neonates, the threshold was based on the first discovery rate (FDR) due to the nature of functional connectivity of the group.

Directions for future research

In this thesis, the majority of the studies conducted on BCECTS patients was conducted on a homogeneous group of patients with right centrotemporal spikes with the same age and epileptic zone. Only in one study, we included whose epileptic zone was located in the left centro-temporal regions. This helped us to study patients with similar epileptic characteristics. However, due to low sample size, statistical comparisons between the patient groups with right and left epileptic foci were not possible. It would be interesting to compare patients with right centro-temporal spikes with those with left hemispheric focus in terms of brain functional reorganization mainly because the left brain hemisphere is dominant in understanding and processing language, memory while the right brain hemisphere tends to be more dominant in creative activities such as decision making and non-verbal processing. Both of these studies will help us to investigate the impact of epileptic activity of the brain functional organization. In addition, we only used EEG signals to investigate the functional connectivity patterns in these patients. Combination of EEG and fMRI or Near-infrared spectroscopy (NIRS) would help to better investigate the topology of functional connections with high temporal and spatial resolutions.

Concerning neonates, our findings open new avenues to better understanding of brain functions during the early periods of neurodevelopment. However, there are still some features to be investigated in neonates such as frontal transients and slow delta waves superimposed with rapid activity (Delta Brushs) at the temporal/occipital region. Longitudinal studies would be very important to establish links between the brain functional organizations in preterm and full-term neonates. This could provide an opportunity for identifying functional biomarkers at early stages of the brain maturation process. However, it could be interesting to see how the brain networks are organized in the presence of neurological conditions such as neonatal seizures, hypoxic-ischemic, periventricular leukomalacia with Positive Rolandic Spikes (PRS), intracranial hemorrhage, cerebrovascular malformations, hydrocephalus and as well as newborn EEG abnormal patterns such as synchrony/asynchrony or symmetry/asymmetry. Further exploration of the EEG features and understanding of the brain functional organization in the outcome prediction of these abnormalities is needed to determine the urgent aids required in neonatal intensive care unit (NICU). Developing an integrated neonatal EEG assessment system with high density could assist not only for monitoring brain development but also for identification of neurological problems at earliest possible time after birth.

Résumé en Français de la problématique et des principaux résultats de la Thèse

Chapitre 1 : Introduction

Problématique

Des progrès importants ont été réalisés pour améliorer la compréhension de l'épilepsie notamment chez les jeunes enfants, portant par exemple sur la reconnaissance de nouveaux syndromes et l'utilisation de nouveaux traitements antiépileptiques. Il y a de nombreuses caractéristiques de l'épilepsie qui sont liées à l'âge, la clinique ou l'électroencéphalographiques (EEG). Les conséquences de l'épilepsie sur le développement cérébral en relation avec les fonctions cognitives n'est toujours pas totalement élucidés. Toutefois, le chemin à parcourir est encore long concernant la compréhension des différents mécanismes impliqués. La compréhension du développement cérébral fonctionnelle chez les jeunes enfants et en particulier chez les nouveau-nés est nécessaire pour guider la prise en charge clinique. Il est ainsi opportun de tirer profit des connaissances acquises dans le domaine de la science des réseaux pour étudier le réseau cérébral. Cette approche peut apporter des connaissances fondamentales sur les relations complexes des réseaux cérébraux et éclairer sur la dynamique de l'organisation fonctionnelle cérébrale. Cette thèse se concentre sur deux études portant (i) sur la connectivité fonctionnelle à l'état de repos chez les enfants atteints d'épilepsie bénigne avec pointes Centro-temporales (EPCT) et (ii) sur l'évaluation des réseaux cérébraux au cours du développement chez le nouveau-né à terme et prématuré. L'EPCT est le syndrome épileptique idiopathique le plus commun avec 8 à 20 % des épilepsies de l'enfant [START_REF] Holmes | Benign focal epilepsies of childhood[END_REF]Panayiotopoulos, 1999). Les décharges épileptiques intercritiques (IEDs) proviennent de régions centrales autour des zones sensorimotrices. L'EPCT et souvent appelé épilepsie rolandique en raison de l'implication des régions autour du sillon de Rolando. L'EPCT est une épilepsie focale sans changements structurels cérébraux majeurs (Camfield and Camfield, 2014) à l'inverse d'autres épilepsies temporales par exemple [START_REF] Taylor | Structural connectivity changes in temporal lobe epilepsy: Spatial features contribute more than topological measures[END_REF]. Toutefois, des déficiences cognitives ont été rapportées [START_REF] Datta | Cognitive impairment and cortical reorganization in children with benign epilepsy with centrotemporal spikes[END_REF] chez les enfants avec EPCT. Les altérations cognitives concernent entre autre l'attention, la mémoire auditive et visuelle. Toutefois, l'influence directe des pointes intercritiques sur les déficiences cognitives reste peu explorée. Plusieurs études [START_REF] Clemens | Pathological theta oscillations in idiopathic generalised epilepsy[END_REF][START_REF] Fonseca | Epileptiform EEG discharges in benign childhood epilepsy with centrotemporal spikes: reactivity and transitory cognitive impairment[END_REF] ont rapporté des altérations fonctionnelles de l'activité cérébrale dans les EPCT. Toutefois, certaines de ces études souffraient de l'hétérogénéité des patients, des approches méthodologiques et du nombre de patients évalués.

Chez les nouveau-nés, l'activité neuronale cérébrale précoce du cerveau néonatal immature est différente de l'activité observée dans le cerveau adulte mature. Particulièrement, l'électroencéphalographie (EEG) du prématuré est caractérisée par l'occurrence de courtes bouffées activités intriquées à des périodes de discontinuité [START_REF] André | Electroencephalography in premature and full-term infants. Developmental features and glossary[END_REF]. Il existe plusieurs neurobiomarqueurs (activités théta temporales, Delta brushs, Encoches Frontales) de l'activité cérébrale du prématuré qui sont utilisés en clinique pour caractériser l'activité fonctionnelle néonatale et la dynamique de la maturation cérébrale à cette période du développement [START_REF] André | Electroencephalography in premature and full-term infants. Developmental features and glossary[END_REF][START_REF] Wallois | Synopsis of maturation of specific features in EEG of premature neonates[END_REF]. L'organisation fonctionnelle du réseau cérébrale néonatale reste encore à préciser. Cependant, différentes études ont tentées de préciser la connectivité cérébrale chez le nouveau-né avec l'imagerie par résonance magnétique (IRM) [START_REF] Doria | Emergence of resting state networks in the preterm human brain[END_REF][START_REF] Fransson | The functional architecture of the infant brain as revealed by resting-state fMRI[END_REF][START_REF] Fransson | Resting-state networks in the infant brain[END_REF]. Cependant la faible résolution temporelle de l'IRM ne permet pas de rendre compte les caractéristiques dynamiques spécifiques de l'EEG du prématuré (asynchronie, discontinuité, neurobiomarqueurs spécifiques….). Plusieurs études [START_REF] González | Assessment of electroencephalographic functional connectivity in term and preterm neonates[END_REF]Meijer et coll., 2014) ont tentées d'évaluer la connectivité fonctionnelle chez les nouveau-nés à partir de l'EEG, mais l'interprétation des résultats est limitée par la faible résolution spatiale des EEG classiques utilisant 8 électrodes. [START_REF] Lamblin | EEG in the neonatal unit[END_REF]. Des études récentes en EEG [START_REF] Grieve | EEG functional connectivity in term age extremely low birth weight infants[END_REF]Omidvarnia et coll., 2014) avec une augmentation significative du nombre d'électrodes, ont permis de montrer qu'il était possible de préciser l'organisation fonctionnelle de l'activité électrique des nouveau-nés en prenant en considération l'impact de certains des biomarqueurs. En attendant, Il est généralement admis que les réseaux cérébraux évoluent à partir d'une connectivité essentiellement locale vers une connectivité plus distribuée chez l'adulte. (Foire et coll., 2009). Comprendre l'organisation fonctionnelle du réseau cérébrale chez les nouveau-nés élargira notre compréhension des étapes de la maturation cérébrale et pourrait permettre une meilleure prise en charge clinique.

Objectif de la thèse

La première partie de la thèse porte sur l'étude des modifications de la connectivité cérébrale à l'état de repos des patients présentant une EPCT en comparant des périodes avec et sans pointes intercritiques chez les patients avec EPCT et des périodes similaires chez des sujets sains sans EPCT. Les étapes de cette étude sont les suivantes :

• Étude à partir des données EEG à l'état de repos des modifications de la puissance spectrale et de la distribution spatiale des sources corticales dans différentes bandes de fréquence selon la présence ou non de pointes interictales en comparaison avec le sujet sains. • Étudier la connectivité fonctionnelle cérébrale dans les espaces capteur et source chez les patients EPCT vs témoins sains afin d'identifier plus particulièrement le pattern de connectivité cérébrale dans les EPCT. • Caractériser la connectivité fonctionnelle des patients EPCT en utilisant les outils de la théorie des graphs pour préciser la topologie locale et globale tels que la centralité, l'intégration et la ségrégation fonctionnelle des réseaux. • Evaluer les profils de connectivité en fonction de la présence ou non de pointes interictales dans les EPCT. • Identifier les profils de connectivité en étudiant la connectivité dynamique et les régions cérébrale impliquées dans la production et la propagation de l'activité épileptique.

La deuxième partie de la thèse porte sur l'évaluation fonctionnelle du réseau cérébral des prématurés et des nouveau-nés nés à terme à partir d'enregistrements EEG en haute densité pendant les périodes de sommeil calme et agité. Les étapes de cette étude sont les suivantes :

• Étudier l'organisation fonctionnelle cérébrale précoce chez les nouveau-nés prématurés et les nouveau-nés nés à terme. L'objectif est de mieux comprendre la fonctionnalité du réseau cérébrale et son organisation au cours du développement. • Etudier l'impact d'une activité endogène (Activité Theta Temporale, delta brush, Encoche frontal,)

sur la connectivité cérébrale chez les nouveau-nés. • Caractérisation de la connectivité fonctionnelle en utilisant les outils de théorie des graphs comme la centralité, l'intégration fonctionnelle et la ségrégation des réseaux pour une meilleure compréhension de la topologie cérébrale néonatal et la distribution spatiale de cette connectivité. • Étudier l'organisation fonctionnelle du cerveau chez les nouveau-nés nés à terme pendant les périodes de sommeil calme et agité qui pourrait donner un aperçu de la maturation cérébrale néonatale.

Les contours de la Thèse

Ce chapitre présente la vue d'ensemble et l'objectif principal de la thèse. Le reste de la thèse est organisé comme suit.

Le chapitre 2 présente le contexte lié à cette thèse. Le chapitre décrit brièvement l'évolution de l'anatomie du cerveau et de la maturation fonctionnelle du nouveau-né à l'adulte. Un rappel est réalisé du principe et de la méthodologie de l'enregistrement de l'EEG chez le nouveau-né et l'adulte. La dynamique de l'évolution de l'EEG néonatal est décrite. Une brève description de plusieurs fonctionnalités est réalisée. La dernière partie du chapitre 2 présente une vue d'ensemble de l'activité épileptique en EEG avec une attention particulière portée sur l'épilepsie bénigne à pointe centro-temporale (EPCT) Le chapitre 3 porte sur l'analyse de la connectivité cérébrale. Les trois types ou modes de connectivité cérébrale, notamment la connectivité structurelle, fonctionnelle et effective sont examinées. Une attention particulière est portée sur l'analyse de la connectivité fonctionnelle Différents concepts tels que la connectivité fonctionnelle axée sur la puissance, sur la phase et sur la théorie de l'information sont présentés dans des applications en neuro-imagerie. Quelques exemples sont donnés sur certaines mesures de connectivité fonctionnelle. De même, la connectivité effective est expliquée en détail avec certains aspects tels que la fonction de transfert direct et la cohérence partielle dirigée. Par la suite, la théorie des graphs est introduite avec une description des étapes requises pour la caractérisation des matrices de connectivité. Certains aspects de la théorie des graphs comme la centralité, la ségrégation et l'intégration fonctionnelle ainsi que la notion de « small world network » sont également abordés.

Dans le chapitre 4, l'impact des EPCT sur l'activité cérébrale est étudié en comparaison avec des sujets sains. Cette étude porte sur un groupe homogène de patients avec les mêmes sources épileptiques focales afin d'éliminer une éventuelle hétérogénéité et d'améliorer la comparaison méthodologique par rapport aux témoins sains. Les différences par rapport aux témoins sains de l'activité cérébrale à l'état de repos des patients EPCT sont étudiées par des mesures de puissance spectrale et de sources corticales dans différentes bandes de fréquence. La connectivité fonctionnelle dans l'espace capteur et l'espace source est évaluée pour étudier l'effet de la présence et de l'absence de pointes épileptiques interictales sur la dynamique de la connectivité des réseaux cérébraux. Les différentes mesures utilisant la théorie des graphs servent à caractériser la connectivité fonctionnelle en mesurant les caractéristiques d'intégration fonctionnelle globale et locale et de ségrégation des réseaux cérébraux des patients EPCT par rapport aux témoins sains.

De même, le chapitre 5 est centré sur l'analyse des patients EPCT. Certaines régions cérébrales sont initialement choisies en fonction des études antérieures et la connectivité est mesurée à partir des « seeds » points placés dans ces régions d'intérêts. Cela s'applique aux patients épileptiques avec ou sans pointes épileptiques interictales en comparaison aux sujets sains. La seconde étude porte sur la dynamique de la connectivité effective intercritique pour étudier la génération et la propagation et des pointes épileptiques interictales. Les principales sources et régions impliquées dans les EPCT sont identifiées à partir des patterns de connectivité.

Le chapitre 6 porte sur la connectivité des réseaux neuronaux chez le nouveau-né prématuré et le nouveau-né à terme. Les rythmes corticaux et la connectivité cérébrale fonctionnelle sont étudiés à partir des données EEG haute densité obtenus chez les nouveau-nés prématurés et les nouveau-nés à terme. Ils sont étudiés dans différentes gammes de fréquences. Les caractéristiques spécifiques de l'EEG des nouveau-nés prématurés comme les activités thêta temporales (TTA) sont prises en considérations dans les deux phases de sommeil calme et agité. Les mesures issues de la théorie des Graphs sont appliqués (centralité, ségrégation, intégration) à la connectivité fonctionnelle afin de mieux quantifier et caractériser l'organisation du réseau cérébral immature.

Le chapitré 7 constitue le résumé de la thèse. Il contient les principales conclusions de la thèse sur les patients EPCT et les caractéristiques des réseaux fonctionnelles chez les nouveau-nés. Il ouvre vers de nouvelles perspectives.

Chapitre 2 : EEG et Epilepsie

La dynamique temporelle des réseaux neuronaux est déterminée par des successions spatio-temporelles de modèles transitoires d'activités cérébrales qui sont intégrées au niveau de la structure cérébrale et qui sont sous tendues par des connections dont l'une des caractéristiques est leur importante adaptabilité. La cohérence temporelle est obtenue par la synchronisation des réseaux neuronaux fonctionnant en harmonie dans des bandes de fréquences distinctes. Le fonctionnement cérébral peut s'expliquer au niveau des réseaux neuronaux interconnectés par un modèle complexe. Dans cette perspective, le cerveau peut être considéré comme un ensemble de systèmes dynamiques connectés reliant les entrées et les sorties de ces différents constituants. Ce chapitre décrit brièvement l'anatomie cérébrale et ses principales fonctions, les caractéristiques de l'EEG, les rythmes de base de l'EEG à l'état de repos chez les adultes, les jeunes enfants et les nouveau-nés. Un bref aperçu des grands principes de l'épilepsie est également proposé avec une attention particulière portée aux EPCT.

Structure et fonction cérébrale

Le tissu cérébral est constitué de milliards de neurones qui sont protégés par le crâne, la dure mère, l'arachnoïde et la pie mère. L'espace entre la pie mère et l'arachnoïde est rempli de liquide céphalo-rachidien (LCR) [START_REF] Silverthorn | Human Physiology: An Integrated Approach[END_REF]. La structure du cerveau humain mature rapidement dès le début de la période foetale durant laquelle le cerveau est relativement lisse. Il développe progressivement un aspect mature plus caractéristique avec notamment une gyrification qui se met en place. La formation de circonvolutions et de sillons suit une séquence ordonnée, en fonction de l'âge [START_REF] Stiles | The Basics of Brain Development[END_REF]. Certaines structures cérébrales sont identifiées plus rapidement tels que le cortex cingulaire, le cortex pariétal et le cortex occipital (14-16 semaines). Les régions centrales temporales supérieures, puis le cortex frontal supérieur, precentral, frontal inférieur et les régions postcentrales apparaissent entre 20 et 26 semaines. Les sillons secondaires apparaissent plus tardivement entre 30 et 35 semaines.

La maturation cérébrale néonatale est fonctionnellement caractérisée par des graphoéléments EEG spécifiques qui servent de marqueurs biologiques pour le développement fonctionnel du cerveau [START_REF] André | Electroencephalography in premature and full-term infants. Developmental features and glossary[END_REF]. La plupart des systèmes sensoriels primaires sont déjà établis à la naissance mais la connectivité fonctionnelle est limitée chez les nourrissons âgés de moins de 2 ans [START_REF] Stiles | The Basics of Brain Development[END_REF]. Le développement fonctionnel cérébral chez les nouveau-nés est concomitant de la maturation fonctionnelle séquentielle des différentes régions corticales. Le cortex cérébral constitue un centre d'intégration des informations sensorielles et participe à la prise de décision. Le cortex cérébral est divisé en plusieurs régions [START_REF] Silverthorn | Human Physiology: An Integrated Approach[END_REF].

Origine et Enregistrement de l'EEG

L'EEG représente l'activité électrique du cerveau enregistré à distance au moyen délectrodes dispsoées sur le scalp. Plus précisément, cela représente la somme des flux extracellulaires de grand groupe de neurones [START_REF] Holmes | Basic Neurophysiology and the Cortical Basis of EEG[END_REF]. L'EEG découle de l'activité synaptique synchronisée dans de populations de neurones corticaux, appelées cellules pyramidales. Les neurones pyramidaux sont organisés de telle sorte que les arbres dendritiques voisins sont parallèles les uns aux autres et presque orthogonaux à la surface corticale. Ces neurones pyramidaux sont censés être le principal générateur de l'EEG. Pour plus d'informations sur la génération de l'EEG, les lecteurs peuvent consulter les commentaires suivants [START_REF] Holmes | Basic Neurophysiology and the Cortical Basis of EEG[END_REF]. La haute résolution temporelle de l'EEG représente un excellent outil de l'analyse de l'activité neuronale des différentes régions cérébrales.

Les enregistrements EEG sont effectués en plaçant des électrodes dans des positions standard prédéfinies sur la tête. La position des électrodes est basée sur des repères anatomiques. Dans la pratique clinique, généralement 20 à 32 électrodes sont utilisés chez l'adulte en routine. À des fins de recherche, il faut habituellement, pour augmenter la résolution spatiale, augmenter le nombre d'électrodes [START_REF] Sohrabpour | Effect of EEG electrode number on epileptic source localization in pediatric patients[END_REF].

Activité à l'état de repos

L'état de repos est le substrat dynamique de l'état actuel au repos du cerveau tout en considérant l'intégration des informations entrantes. Au repos, le cerveau englobe tous les modes de fonctionnement tels que la sensorialité, l'attention, le contrôle exécutif et le contrôle de certaines fonctions telles que le langage. Certaines régions du cerveau sont activées ou désactivées au repos, l'état de repos peut aussi être abordé avec l'imagerie par résonance magnétique fonctionnelle (IRMf). L'EEG à l'état de repos est utilisé pour caractériser l'activité cérébrale en l'absence de stimulation ou de tâche. Il peut être utilisé pour identifier certains dysfonctionnements en analysant les capacités d'intégration à partir des potentiels évoqués visuels ou autres dans différentes situations pathologiques à l'état de repos. La manière la plus courante utilisée pour caractériser l'EEG au repos est la séparation des patterns oscillatoires en différentes bandes de fréquence. L'analyse de la puissance spectrale est la méthode le plus couramment utilisée pour quantifier l'EEG à l'état de repos dans les différentes bandes de fréquence.

L'EEG chez le nouveau-né est très différent de celui de l'enfant plus âgé et de l'adulte. Il nécessite une expérience spécifique pour l'interprétation. Cela est dû aux changements de maturation rapides des réseaux neuronaux chez le nouveau-né et notamment le prématuré entre 26 et 40 semaines de gestation [START_REF] André | Electroencephalography in premature and full-term infants. Developmental features and glossary[END_REF]. L'EEG s'est avéré indispensable pour l'évaluation clinique des pathologies cérébrales telles que l'épilepsie, Il permet par ailleurs le monitoring en réanimation néonatale (Vecchierini et coll., 2003).

Activité épileptique et EEG

L'épilepsie est un trouble cérébral qui affecte environ 0,5 à 1 % de la population mondiale. Elle est caractérisée par une activité cérébrale récurrente, excessive et incontrôlée. L'épilepsie peut commencer à tous les âges, mais est plus fréquente chez les enfants par rapport aux adultes. La crise d'épilepsie est caractérisée par une décharge anormale hypersynchrone d'une large population neuronale. Les manifestations cliniques sont présentes sous de nombreuses formes selon les régions cérébrales impliquées dans l'activité épileptique. Les mécanismes sous-jacents à l'épilepsie sont encore mal connus. Il existe de nombreuses classifications de l'épilepsie. Selon l'étiologie de l'épilepsie ou selon le caractère focal ou distribué. Ainsi, elle peut être classée en épilepsie partielle ou généralisée. Les épilepsies partielles ont une origine focale. Elles peuvent être simple (sans perte de conscience) ou complexe (avec perte de conscience). L'épilepsie partielle peut évoluer vers une épilepsie généralisée. L'épilepsie généralisée implique de nombreuses régions cérébrales.

Une des applications importantes de l'EEG est l'étude de l'épilepsie. L'apparition des ondes d'amplitude supérieures (pointes) et de plusieurs autres paroxysmes sont des points de repère permettant de caractériser l'activité épileptique. Ces graphoéléments participent à l'identification, le classement et la localisation des phénomènes épileptiques (crises ou pointes interictales). Les graphoéléments épileptiques varient en termes de fréquence, de durée, et de topographie. Quand ils apparaissent entre les crises sous forme de pointes, pointes ondes ou polypointes ondes ils sont considérés comme des éléments épileptiques intercritiques et constituent des biomarqueurs de l'activité épileptique entre les crises.

Épilepsie bénigne de l'enfance

L'épilepsie bénigne de l'enfant représente 10 à 20 % des épilepsies de l'enfant (Camfield and Camfield, 2014). Le risque de déficit cognitif est plus élevé chez les enfants avec épilepsie bénigne que chez les enfants sains du même âge [START_REF] Datta | Cognitive impairment and cortical reorganization in children with benign epilepsy with centrotemporal spikes[END_REF]. L'épilepsie bénigne la plus courante est l'EPCT (Panayiotopoulos, 1999). Typiquement, la crise débute dans le sommeil ou à l'endormissement et correspond à une crise partielle. La généralisation secondaire n'est pas systématique. L'outil diagnostic le plus utile est certainement l'EEG dans les épilepsies bénignes, il permet de caractériser les pointes interictales qui ont un aspect bi ou triphasiques qui sont localisées dans les zones rolandiques ou périroloandiques et qui sont très évocatrices de l'EPCT. Elles apparaissent tantôt à droite, tantôt à gauche, le plus souvent asynchrones et de localisation variable d'un examen à l'autre entre les deux hémisphères.

Chapitre 3 : Analyse de la connectivité cérébrale

Le cerveau est un système complexe, distribué, à grande échelle, dans lequel un très grand nombre de processus sont traités simultanément, en parallèle. La complexité du cerveau peut être définie à partir de ses populations neuronales, qui, à l'échelle macroscopique ont un fonctionnement en modes aléatoires et/ou réguliers. L'architecture complexe du cerveau implique des réseaux neuronaux qui sont hautement spécialisés dans plusieurs opérations en parallèles fonctionnant en interaction pour permettre des perceptions et des actions cohérentes. La connectivité anatomique et fonctionnelle entre les réseaux de neurones peut se mettre en place entre des structures proches et/ou distantes. Les connections entre structures proches ayant une plus grande probabilité d'occurrence. Les connectivités fonctionnelles entre les réseaux cérébraux sont organisées de telle manière à permettre un traitement effectif de l'information incluant les capacités de ségrégation et d'intégration des informations. Plus particulièrement, la ségrégation et l'intégration des informations doivent pouvoir être traitées dans une architecture unique de réseaux cérébraux. À l'échelle microscopique, le cerveau est constitué de circuits électriques constitués par l'interconnexion de milliards d'unités élémentaires de traitement de l'information (neurones et cellules gliales) (Bear et coll., 2001).

Le cerveau adulte a été décrit comme correspondant à un maillage de type Web avec de nombreuses interconnections impliquant l'ensemble des réseaux neuronaux. Chez l'adulte certaines régions montrent un haut niveau, disproportionné, de connectivité anatomique appelée « cortical hubs » ou centres corticaux qui pourraient contrôler le flux d'information.

Les réseaux de hubs ou de centres corticaux recouvrent dans une large mesure le réseau en mode par défaut et le réseau attentionnel fronto-pariétal [START_REF] Buckner | Cortical Hubs Revealed by Intrinsic Functional Connectivity: Mapping, Assessment of Stability, and Relation to Alzheimer's Disease[END_REF]. Ainsi, l'organisation des réseaux adultes basée sur cette notion de hubs sous-tend complexité de la fonctionnalité cérébrale chez l'adulte [START_REF] Heuvel | Rich-Club Organization of the Human Connectome[END_REF].

Le cerveau de l'enfant contient des réseaux moins complexes avec des connexions relativement plus labiles et moins fonctionnelles. La connectivité fonctionnelle associée à des hubs corticaux recouvre chez l'enfant en grande partie les régions sensorimotrices, auditives et visuelles primaires [START_REF] Fransson | Spontaneous Brain Activity in the Newborn Brain During Natural Sleep-An fMRI Study in Infants Born at Full Term[END_REF][START_REF] Fransson | Resting-state networks in the infant brain[END_REF]. Au cours du processus de maturation, se produit une réorganisation progressive de la connectivité des réseaux qui passent d'une organisation '' local et ségrégée '' à une organisation '' distribuée et intégrée '' [START_REF] Fair | Functional brain networks develop from a "local to distributed" organization[END_REF].

Ce chapitre décrit les méthodes d'analyse de connectivité utilisées avec une attention particulière pour les mesures de connectivité fonctionnelle et effective. Les mesures utilisant la théorie de graphs sont également décrites. Le chapitre commence par un bref examen des signaux analytiques qui sont nécessaires au calcul de la connectivité fonctionnelle et imagerie de source EEG.

Connectivité cérébrale

La connectivité cérébrale révèle les voies par lesquelles, où la façon dont les informations sont échangées entre les régions du cerveau [START_REF] Breakspear | Neuronal Dynamics and Brain Connectivity[END_REF]. Les mesures de connectivité cérébrales sont bivariées, c'est-à-dire, qu'elles concernent les interactions entre deux régions cérébrales ou les électrodes du cuir chevelu.

Il existe trois modes de connectivité cérébrale structurelle, fonctionnelle et effective [START_REF] Friston | Models of Brain Function in Neuroimaging[END_REF][START_REF] Horwitz | The elusive concept of brain connectivity[END_REF]. La connectivité structurelle ou anatomique se réfère à un réseau de connexions (synaptiques) structurales, reliant des ensembles de neurones ou éléments neuronaux. Fondamentalement, la connectivité fonctionnelle est une notion statistique qui permet d'estimer la corrélation temporelle entre deux signaux au fil du temps. En général, la connectivité fonctionnelle capture les écarts par rapport à l'indépendance statistique entre les unités neuronales distribuées et souvent distantes. La connectivité effective examine la directionnalité du flux d'informations d'un élément neural par rapport à un autre.

Connectivité fonctionnelle

La connectivité fonctionnelle est définie en tant que dépendances statistiques entre deux régions cérébrales [START_REF] Friston | Functional and effective connectivity in neuroimaging: A synthesis[END_REF]. La connectivité fonctionnelle en neuro-imagerie peut être estimée à partir de l'IRMf et /ou de séries chronologiques EEG/MEG. Il y a beaucoup de mesures de la connectivité fonctionnelle. Dans cette thèse nous nous limiterons aux mesures de la connectivité fonctionnelle basées sur la puissance, sur la phase et sur l'information.

La connectivité fonctionnelle basée sur la puissance du signal

La connectivité fonctionnelle basée sur la puissance du signal est une mesure linéaire, dépendante, entre deux signaux dans le domaine temporel, évaluée par le coefficient de corrélation ou dans le domaine fréquentiel par la cohérence. Le coefficient de corrélation de Pearson est une méthode courante de corrélation utilisée et est définie comme la covariance de deux signaux x et y. La cohérence spectrale est semblable au coefficient de corrélation, mais dans le domaine fréquentiel. La cohérence spectrale inclut des informations sur la puissance (amplitude et phase).

La connectivité fonctionnelle basée sur la phase

Ce type de connectivité fonctionnelle est une mesure non linéaire. Elle repose sur l'hypothèse que les séries chronologiques neuronales ont des caractéristiques non linéaires. Une méthode commune pour obtenir la force de la synchronisation de phase entre les différentes régions du cerveau est la valeur de la phase de verrouillage (Phase Locking value, PLV) (Lachaux et coll., 1999). D'autres méthodes incluent le délai de phase (phase lag, PLI) (Stam et coll., 2007), ou l'indice de délai de phase pondéré (Weighted phase lag indice, wPLI) [START_REF] Vinck | An improved index of phase-synchronization for electrophysiological data in the presence of volume-conduction, noise and sample-size bias[END_REF].

La connectivité fonctionnelle basée sur l'information

la connectivité fonctionnelle basée sur l'information capture les dépendance statistiques linéaires et non linéaires entre deux séries temporelles [START_REF] Hurtado | Statistical Method for Detection of Phase-Locking Episodes in Neural Oscillations[END_REF][START_REF] Jeong | Mutual information analysis of the EEG in patients with Alzheimer's disease[END_REF]. Cette technique est basée sur le concept d'entropie qui mesure la probabilité de la variable.

Connectivité effective

La connectivité effective correspond aux dépendances asymétriques ou causales entre les régions cérébrales. Elle identifie quelle région du cerveau, dans un réseau fonctionnel, influence d'autres régions cérébrales [START_REF] Friston | Functional and effective connectivity in neuroimaging: A synthesis[END_REF]. Contrairement à la connectivité fonctionnelle, la connectivité effective indique la direction du flux d'informations entre les différentes régions [START_REF] Friston | Functional and effective connectivity in neuroimaging: A synthesis[END_REF]. L'interaction directionnelle peut être définie comme une technique basée sur des modèles tels que la modélisation dynamique causale (Friston et coll., 2003), la modélisation par équation structurelle [START_REF] Ullman | Structural Equation Modeling[END_REF], ou le modèle libre avec la causalité de Granger [START_REF] Hesse | The use of time-variant EEG Granger causality for inspecting directed interdependencies of neural assemblies[END_REF].

La connectivité effective nécessite un model autorégressif et une estimation des paramètres du modèle avant l'estimation de la connectivité. Les mesures les plus courantes de connectivité incluent la cohérence partielle dirigée (partial directed coherence, PDC) [START_REF] Baccalá | Partial directed coherence: a new concept in neural structure determination[END_REF] et la fonction de transfert direct (direct transfer function , DTF) (Kamiński et coll., 2001).

Analyse des réseaux par la théorie des Graph

La théorie des graphs est un cadre mathématique mis au point pour étudier les systèmes physiques, biologiques et d'informations. Il y a une augmentation des applications de la théorie des graphs en neuroimagerie pour étudier les réseaux cérébraux fonctionnels et structurels. La théorie des Graphs est aussi utilisé pour caractériser la connectivité des réseaux dans les études expérimentales cognitives (il et Evans, 2010 ;[START_REF] Sporns | Networks of the Brain[END_REF] Cela permet d'élargir nos connaissances sur les maladies cérébrales, le vieillissement et les fonctions cognitives supérieures [START_REF] Bullmore | Brain Graphs: Graphical Models of the Human Brain Connectome[END_REF][START_REF] Deuker | Reproducibility of graph metrics of human brain functional networks[END_REF][START_REF] Netoff | Epilepsy in small-world networks[END_REF][START_REF] Stam | Modern network science of neurological disorders[END_REF].

Tous les réseaux sont constitués de deux éléments de base : les noeuds et les bords appariées (liens) entre les noeuds [START_REF] Bullmore | Complex brain networks: graph theoretical analysis of structural and functional systems[END_REF]. Les noeuds dans les réseaux cérébraux sont généralement représentés par les régions cérébrales ou les positions des électrodes EEG. Les noeuds sont parfois déterminés par l'activité fonctionnelle et la parcellisation de la surface du cortex ou de l'ensemble du cortex (Figure 3.3). La parcellisation se fait parfois à l'aide d'atlas de cerveau [START_REF] Stanley | Defining nodes in complex brain networks[END_REF]. Les bords et les liens sont généralement des mesures de la connectivité fonctionnelle et effective. Le choix des mesures de connectivité dépend des questions de recherche et des expériences menées. Tous les réseaux sont représentés par leurs matrices de connectivité (contiguïté). Lignes et colonnes dans ces matrices correspondent aux noeuds, tandis que les entrées désignent les bords.

Les mesures dans la théorie des Graphs

Il y a de nombreux paramètres qui peuvent être utilisés pour étudier la connectivité des réseaux à l'aide de la théorie des graphs (Roubinov et [START_REF] Rubinov | Complex network measures of brain connectivity: uses and interpretations[END_REF]. Avant de réalise le calcul des paramètres de réseaux, le graph est parfois seuillé. Le seuil est très important parce que les liens faibles et non significatifs peuvent représenter des connexions fallacieuses, qui pourraient augmenter le rapport signal / bruit. La méthode courante consiste à choisir une valeur arbitraire commune pour tous les sujets où une condition dans une expérience. Une autre option consiste à spécifier le nombre de connexions (densité de connexion) et garder les connexions les plus fortes tout en définissant le reste à zéro. Les autres méthodes de seuillage consistent à générer des données de remplacement pour l'évaluation statistique des mesures fonctionnelles, en particulier pour des signaux brefs [START_REF] Drakesmith | Overcoming the effects of false positives and threshold bias in graph theoretical analyses of neuroimaging data[END_REF][START_REF] Langer | The problem of thresholding in small-world network analysis[END_REF]. Les mesures de connectivité des réseaux cérébraux sont toujours classifiées selon les interprétations neurobiologiques comme la centralité des réseaux, la ségrégation fonctionnelle, l'intégration fonctionnelle, les réseaux de type petit monde (small word network), les patterns des réseaux et bien d'autres.

La centralité des réseaux est la propriété la plus importante de n'importe quel réseau. Elle évalue l'importance des noeuds individuels ou des régions du cerveau en mesurant combien de fois un noeud particulier interagit avec plusieurs autres noeuds du réseau. La mesure la plus commune de centralité est le degré qui correspond au nombre de connexions d'un des noeuds rattaché au reste du réseau. D'autres mesures incluent la betweenness centrality (BC) [START_REF] Freeman | Centrality in social networks conceptual clarification[END_REF] qui mesure la fraction de tous les chemins les plus courts dans le réseau qui passent par un noeud donné. La centralité de la proximité est une autre mesure.

La ségrégation fonctionnelle du réseau cérébrale est caractérisée par l'existence de régions cérébrales spécialisées comme des modules organisés en populations distinctes [START_REF] Tononi | A measure for brain complexity: relating functional segregation and integration in the nervous system[END_REF]. Des mesures de ségrégation fonctionnelle calculent la présence de clusters ou de modules au sein du réseau qui suggèrent une organisation de dépendances statistiques. La commune mesure de ségrégations fonctionnelle est le « clustering coefficient » qui mesure la fraction des triangles autour des noeuds individuels [START_REF] Watts | Collective dynamics of "small-world[END_REF]. Une alternative est la mesure de l'efficacité locale d'un noeud ou d'une région particulière du cerveau.

L'intégration fonctionnelle mesure la facilité de transfert d'information ou de communication entre les régions du cerveau [START_REF] Tononi | A measure for brain complexity: relating functional segregation and integration in the nervous system[END_REF]. La communication entre les réseaux neuronaux est mesurée par les chemins qui les relient. La longueur du trajet caractéristique (Characteristic path length, L) est le plus couramment utilisée pour mesurer l'intégration fonctionnelle. L est le plus court chemin entre les régions cérébrales [START_REF] Watts | Collective dynamics of "small-world[END_REF].

L'inverse de la moyenne de la longueur du plus court chemin est connu comme l'efficacité globale (E).

Le cerveau est un réseau complexe supportant le traitement d'informations spatio-temporelles. Un réseau cérébral normal combine la présence de modules fonctionnels distincts et de liens fonctionnels robustes. Ce type de réseau est appelé un réseau en petit monde (SWN) soutenant l'intégration fonctionnelle optimale et la ségrégation [START_REF] Bassett | Small-world brain networks[END_REF][START_REF] Sporns | The small world of the cerebral cortex[END_REF]. Cette structure en réseau SWN est ordonné avec un coefficient de clusters élevé (clustering coefficient élevé) et une longueur du plus court chemin courte (ou haute effectivité) entre les régions du cerveau qui est un intermédiaire entre un réseau ordonnée (C élevé et L long) et un réseau aléatoire (faible C et L court) [START_REF] Watts | Collective dynamics of "small-world[END_REF].

Chapitres 4 et 5 : Analyse de la connectivité à l'état de repos chez les enfants atteints d'épilepsie bénigne à pointes centrotemporales

La relation entre l'épilepsie et les incapacités cognitives et neuropsychologiques chez les enfants a été largement étudiée [START_REF] Datta | Cognitive impairment and cortical reorganization in children with benign epilepsy with centrotemporal spikes[END_REF]. Malgré le grand nombre d'études sur ce sujet, les effets propres de l'activité épileptique sur le fonctionnement cognitif et le développement ne sont pas encore clairement définis. De nombreuses études sont réalisées sur des patients avec différentes sources focales d'épilepsie, différents âges, selon la fréquence des crises et selon les syndromes épileptiques. Les déficits cognitifs et comportementaux observés chez des enfants épileptiques sont parfois considérés comme le résultat d'interactions complexes entre des facteurs biologiques, psychologiques et sociaux [START_REF] Ay | Neuropsychologic impairment in children with rolandic epilepsy[END_REF]Boucliers et Snead, 2009). L'épilepsie bénigne de l'enfant représente 10 à 20 % des épilepsies de l'enfant (Camfield and Camfield, 2014). Le risque de déficit cognitif est plus élevé chez les enfants avec épilepsie bénigne que chez les enfants sains du même âge [START_REF] Datta | Cognitive impairment and cortical reorganization in children with benign epilepsy with centrotemporal spikes[END_REF]. L'épilepsie bénigne la plus courante est l'EPCT (Panayiotopoulos, 1999). La plupart des crises surviennent pendant le sommeil ou à l'endormissement (Camfield et Camfield, 2014). Contrairement aux autre types d'épilepsie tels que l'épilepsie du lobe temporal [START_REF] Taylor | Structural connectivity changes in temporal lobe epilepsy: Spatial features contribute more than topological measures[END_REF], l'EPCT est connu pour ne pas être liée à des anomalies structurales [START_REF] Hughes | Benign epilepsy of childhood with centrotemporal spikes (BECTS): to treat or not to treat, that is the question[END_REF]. Toutefois, l'activité épileptique peut provoquer différents dysfonctionnements entre les régions souscorticales et corticales qui peuvent entraîner des changements dans l'activité EEG à l'état de repos.

Dans ce chapitre, nous examinons des différences d'activité cérébrale à l'état de repos les yeux fermés entre les patients EPCT et les témoins sains dans 2 conditions en présence et en absence de pointes épileptiques intercritiques (EEI). À cette fin, nous avons étudié les variations de la puissance spectrale de l'EEG et la connectivité fonctionnelle dans l'espace capteur et l'espace source. Les outils de la théorie de graphs ont aussi servis à caractériser la connectivité fonctionnelle entre réseaux cérébraux des patients EPCT par rapport aux témoins sains.

Analyse spectrale et source de puissance EEG

L'analyse de la puissance spectrale est l'une des méthodes standards utilisées pour la quantification de l'EEG. La puissance de la densité spectrale (spectre de puissance) reflète la distribution de la puissance du signal en fonction de la fréquence. L'analyse de la puissance spectrale dans les différentes bandes de fréquence mélange les différentes propriétés physiologiques (Clément et al., 2013 ;Klimesch et coll., 2007).

Il existe plusieurs études de l'analyse de la puissance spectrale de l'EEG et de l'analyse des sources dans les épilepsie bénignes de l'enfant [START_REF] Clemens | Theta EEG source localization using LORETA in partial epilepsy patients with and without medication[END_REF][START_REF] Kikumoto | EEG and seizure exacerbation induced by carbamazepine in Panayiotopoulos syndrome[END_REF]. Toutes montrent une puissance spectrale élevée notamment autour de la région épileptique. La plupart de ces études ont été effectuée sur divers groupes de patients avec différentes sortes de foyers épileptiques, différents groupes d'âge et une hétérogénéité syndromique.

Dans la première étude, nous avons recruté vingt et un patients avec EPCT avec une moyenne d'âge de 9,84 ± 1,75 ans et onze témoins sains dans la même tranche d'âge pour analyser l'état de repos. Les données EEG en haute densité ont été enregistrées sous la condition yeux fermés pendant au moins 14 minutes pour chaque sujet. Un groupe homogène de douze patients a été sélectionné à partir de la localisation des sources des décharges épileptiques intercritiques (IEDs). Les données EEG Haute densité ont été prétraitées pour supprimer les artefacts. Les segments sans artéfact ont été ensuite segmentés par époques de 2s sans overlap pour chaque sujet. Deux conditions ont été utilisées pour les patients épileptiques, les segments avec ou sans pointe épileptiques intercritiques. Les puissances spectrales absolue et relative ont été calculées pour ces conditions dans cinq bandes de fréquences différentes (δ, θ, α, β1 et β2) dans l'espace capteur. Statistiquement, les trois conditions ont été comparées avec des tests statistiques non paramétriques.

Nos résultats ont montré que les réseaux à l'état de repos des patients EPCT étaient fonctionnellement perturbés en présence et en absence de pointes épileptiques. Les principales conclusions ont été de mettre en évidence un dysfonctionnement dans la région centrotemporale, le désengagement corticale dans les régions frontales et occipitales chez les patients, indiquant une dysfonction du réseau de repos chez les patients EPCT. On retrouve la puissance élevée dans la bande θ par rapport aux autres les régions cérébrales et une puissance spectrale significativement plus faible dans la bande α plus particulièrement dans les régions occipitales en présence de pointes épileptiques intercritiques.

L'interaction entre les régions du cerveau peut être analysée par des analyses bivariées et multivariées telles que de la connectivité cérébrale. La connectivité fonctionnelle se réfère à la relation fonctionnellement intégrée entre les régions cérébrales spatialement séparées. Ceci a été appliqué à plusieurs études, y compris l'épilepsie [START_REF] Centeno | Network connectivity in epilepsy: resting state fMRI and EEG-fMRI contributions[END_REF]. La caractérisation de la dynamique des réseaux corticaux en EEG et ECoG chez des patients épileptiques à l'état de repos a démontré des perturbations globales et régionales des réseaux neuronaux qui pouvaient être estimées par la connectivité fonctionnelle (Douw et al., 2010[START_REF] Douw | Epilepsy is related to theta band brain connectivity and network topology in brain tumor patients[END_REF]Coran et coll., 2013). La connectivité fonctionnelle des réseaux neuronaux est souvent caractérisée par la théorie des graphs (Roubinov et [START_REF] Rubinov | Complex network measures of brain connectivity: uses and interpretations[END_REF] qui est une application courante dans le domaine des neurosciences dont l'épilepsie [START_REF] Netoff | Epilepsy in small-world networks[END_REF]. Un grand nombre de paramètres de la théorie des graphs a été proposé et le plus commun est le degré qui mesure la centralité du réseau.

La théorie des graphs et la connectivité fonctionnelle

Dans cette étude, la théorie des graphs et la connectivité fonctionnelle ont été appliquées pour explorer l'altération fonctionnelle des réseaux cérébraux chez les patients EPCT en comparaison avec les sujets sains. Cela a été fait en présence et en l'absence de décharges intercritiques dans le groupe patient. Cela a été réalisé dans l'espace capteur et l'espace source pour étudier l'impact des décharges épileptiques intercritiques sur les interactions fonctionnelles entre réseaux cérébraux. Il existe différentes mesures de connectivité fonctionnelle et toutes ont leurs propres avantages et inconvénients. Dans la première étude, la valeur de verrouillage de phase (PLV) [START_REF] Lachaux | Measuring phase synchrony in brain signals[END_REF] a été appliquée pour estimer la connectivité fonctionnelle et caractériser la connectivité avec les différents paramètres issus de la théorie des graphs. La connectivité fonctionnelle dans la seconde étude a été estimée par le délai de synchronisation de phase (LPS) (Pascual-Marqui, 2007) dans l'espace source avec 84 régions cérébrales définies selon l'atlas de Brodmann [START_REF] Brodmann | Vergleichende Lokalisationslehre der Großhirnrinde[END_REF]. La mesure de LPS est moins sensible aux signaux non physiologiques, y compris les artefacts et l'effet de volume de conduction [START_REF] Pascual-Marqui | Assessing interactions in the brain with exact low-resolution electromagnetic tomography[END_REF]. Dans l'espace capteur, les patients présentent une densité de connexion plus élevée autour de la zone épileptique dans toutes les bandes de fréquences. Le réseau cérébral des patients EPCT a été dévié du mode small word par rapport aux témoins sains selon la fréquence analysée. Le réseau cérébral des patients EPCT était plus ordonné en présence de pointes interictales quand il était comparé au réseau des sujets sains. Toutefois, en l'absence de pointes interictales, le réseau cérébral des patients EPCT était moins ordonné par rapport aux contrôles sains dans toutes les bandes de fréquence.

La connectivité fonctionnelle peut perturber les résultats du fait du volume de conduction dans la mesure où l'EEG de surface détecte une moyenne spatiale de signaux se chevauchant provenant de plusieurs sources cérébrales. Ceci a motivée la troisième étude dans l'espace source et l'analyse du délai de la synchronisation de phase (LPS) qui est généralement considéré comme insensible au volume de conduction par rapport aux autres métriques de connectivité fonctionnelle tel que le zéro délai ou la mesure de cohérence classique. Dans cette étude, 84 région d'intérêts (ROIs) ont été définis par l'atlas de Brodmann afin de réduire la variabilité de la taille du cerveau pour l'ensemble des sujets et de minimiser l'effet de volume de conduction par rapport à l'approche voxel-par-voxel. Par rapport aux témoins, les patients (sans pointes interictales) ont montré plus de LPS dans la bande θ et α mais moins de LPS dans la bande β. Les patients affichent aussi des valeurs d'intégration supérieures et de ségrégations inférieures dans les bandes θ et α par rapport aux témoins sains. Ils montrent également une connectivité fonctionnelle locale plus élevée au niveau du réseau épileptogène comprenant les aires motrices, la région centrale et la région temporale ipsilatérale à la zone épileptique. La connectivité locale est aussi plus faible dans la région frontale controlatérale chez les patients. Toutes ces résultats sont en faveur d'une altération de la connectivité fonctionnelle à l'état de repos chez les patients EPCT et ce dans différentes bandes de fréquence.

Ces deux études montrent que la connectivité fonctionnelle à l'état de repos chez les patients EPCT avec et sans pointes interictales a été modifiée selon la fréquence des activités cérébrales. Toutefois, dans ce chapitre, nous avons utilisé la connectivité fonctionnelle non dirigé. Dans le chapitre suivant, nous nous concentrons sur le sens de circulation de l'information entre les différentes régions cérébrales chez les patients EPCT.

Connectivité fonctionnelle à l'état de repos dans l'espace Source

Dans cette étude, nous avons étudié l'impact des pointes interictales sur la connectivité fonctionnelle (FC) dans l'espace source à l'état de repos chez les patients EPCT par rapport aux témoins sains. Le FC dans l'espace source a été calculé par la cohérence imaginaire (IC), qui a été démontrée pour être insensible au volume de conduction [START_REF] Nolte | Identifying true brain interaction from EEG data using the imaginary part of coherency[END_REF] et donc qui permet de refléter plus exactement la mesure de la connectivité cérébrale à partir des données EEG à l'état de repos. Certaines régions d'intérêts (ROIs) ont été choisies comme « seed points » incluant la zone épileptique (centrale droite), le cortex central gauche, le cortex préfrontal et les régions occipitales. Ces régions se sont révélées être activées/désactivées dans nos études précédentes. Les patterns de FC issus de ces régions vers d'autres régions ont été étudiés sous trois conditions (contrôles, avec ou sans pointes intercritique chez les patients). La topologie de la connectivité fonctionnelle était caractérisée en utilisant deux types de mesures : la betweenness et l'effectivité locale.

Grâce à l'analyse de connectivité fonctionnelle dans l'espace source à l'état de repos, nous avons constaté que les régions centrales, y compris les aires motrices supplémentaires ont montré une activation en présence de pointes interictales. Des patterns de FC plus élevée ont été également observés dans la région frontale supérieure homolatérale à la zone épileptique chez ces patients Cette étude présente une méthode claire et robuste permettant d'évaluer les patterns de connectivité fonctionnelle à l'état de repos dans l'espace source et de démontrer leurs perturbations chez les patients EPCT. Bien que nos études antérieures aient montré la forte incidence des pointes épileptique intercritiques sur l'organisation fonctionnelle cérébrale des patients EPCT, les techniques dynamiques de connectivité intercritique apportent des informations importantes sur la directionnalité des interactions entre les régions cérébrales chez les patients EPCT.

Directionnalité et dynamique de la connectivité interictale

Dans cette étude, le modèle de directionnalité de la connectivité intercritique associé aux pointes intercritiques a été étudié tout d'abord en reconstruisant la source de l'EEG pour 90 ROIs à l'aide de l'EEG haute densité pour chaque patient épileptique. Nous avons ensuite utilisé la cohérence partielle dirigée (PDC) en guise de mesure de la connectivité effective entre les régions cérébrales. La sortie de la matrice de connectivité a été étudiée afin d'identifier les principaux triggers dans les différentes régions cérébrales impliqués dans la génération et la propagation de l'activité épileptique. Nous avons constaté que les régions centrales rolandiques, les aires motrices supplémentaires et les régions frontales supérieures toutes ipsilatérales aux zones épileptiques étaient les principaux triggers chez les patients EPCT. La PDC nous a permis d'étudier le sens de circulation de l'information entre les régions du cerveau de manière causale. En outre, la PDC est insensible à l'artefact de volume de conduction.

Chapitre 6 : Connectivité fonctionnelle chez les nouveau-nés

Le réseau cérébral adulte est le résultat d'interactions complexes entre les différentes régions du cerveau. Plusieurs études utilisant la science des réseaux ou la théorie des graphs ont élargi notre connaissance sur la connectome fonctionnelle du cerveau adulte [START_REF] Bassett | Small-world brain networks[END_REF][START_REF] Bassett | Understanding complexity in the human brain[END_REF]Sporns et coll., 2000). Néanmoins, on connaît mal la connectome fonctionnelle du cerveau chez les nouveau-nés. Il y a eu des hypothèses selon lesquelles la connectivité fonctionnelle du cerveau humain évolue à partir d'un réseau organisé de manière locale à la naissance, vers un réseau distribué chez l'adulte (Foire et coll., 2009). Plusieurs études en IRMf chez les nouveau-nés ont montré la présence de centres corticaux dans les régions postérieures, frontales et sensorimotrices [START_REF] Ball | Rich-club organization of the newborn human brain[END_REF]Fransson et coll., 2007). Cependant, l'activité cérébrale précoce en particulier chez les nouveau-nés prématurés est très différente de celle du cerveau mature. L'activité neuronale cérébrale néonatale est caractérisée par la présence de graphoéléments caractéristiques comme les activités thêta temporales chez les grands prématurés ou les encoches frontales chez le nouveau-né à terme. L'EEG chez le prématuré est aussi caractérisé par des périodes de discontinuité. Toutes ces caractéristiques spécifiques servent de biomarqueurs utilisés en clinique pour préciser les stades de maturation cérébrales [START_REF] André | Electroencephalography in premature and full-term infants. Developmental features and glossary[END_REF][START_REF] Wallois | Synopsis of maturation of specific features in EEG of premature neonates[END_REF]. Les études récentes [START_REF] González | Assessment of electroencephalographic functional connectivity in term and preterm neonates[END_REF]Meijer et coll., 2014 ;Omidvarnia et coll., 2014 ;Tokariev et coll., 2016) ont tenté d'introduire la notion de connectivité fonctionnelle chez le nouveau-né. Toutes ces études ont été réalisées à l'aide d'un nombre restreint d'électrodes. Cependant, les études de connectivité fonctionnelle chez les nouveau-nés nécessitent un grand nombre d'électrodes en raison de la spécificité spatiale de l'EEG chez le prématuré (Odabaee et coll., 2013). En outre, la plupart des spécificités néonatales y compris les stades du sommeil n'ont pas été prise en considération dans ces études de connectivité fonctionnelle.

Dans ce chapitre, les patterns de connectivité fonctionnelle cérébrale chez les nouveau-nés prématurés et nouveau-nés à terme ont été étudiés en utilisant des données EEG haute densité. Les spécificités de l'EEG du prématuré comme les activités thêta temporales et les phases de sommeil ont été prises en considération.

Ces études montrent que l'activité cérébrale précoce des nouveau-nés prématurés est densément localisée aux régions frontales et occipitales et surtout que la connectivité fonctionnelle à longue distance est limitée. La présence d'une activité endogène comme l'activité thêta temporale joue un rôle important dans cette période de développement avec une densité de connexion accrue dans les régions temporales. Les nouveau-nés à terme montrent une haute densité de connexion dans les régions frontales, postérieures et temporales durant le sommeil calme et agité. Les propriétés de « small world network » présents chez les nouveau-nés, suggèrent que les principes de ségrégation et d'intégration de l'information sont présents à cette période du développement.

Chapitre 7 : Conclusions générales

Ce chapitre résume toutes les études menées dans cette thèse. Les différentes perspectives sont explorées The characteristic path length Li of a node i is defined as

𝐿 𝑖 = ∑ 𝑑 𝑖𝑗 𝑁 𝑗=1,𝑗≠𝑖 𝑁 -1
Where is dij is the absolute distance between the nodes i and j and the mean characteristic path length L over a network is defined as: Resting-state EEG functional connectivity analysis in benign childhood epilepsy and neonates

Abstract

The thesis investigated the functional connectivity in children with benign childhood epilepsy with centrotemporal spike and functional brain network organization in preterm and full-term neonates. The patients with the epilepsy had functional brain disruption and the alterations of resting state functional connectivity is frequency dependent in comparison to the healthy controls. The epileptic brain network is disrupted in the presence and absence of interictal epileptic discharges. The regions involved in the generation and propagation of epilepsy were identified including epileptic zone (central region), rolandic region and the supplementary motor areas. In the neonates, preterm neonates were characterized with the high functional connectivity at the frontal and posterior regions. The presence of endogenous activity in preterm such as theta temporal activity revealed high functional connectivity at the temporal region. Similar functional brain network organization was observed in full-term neonates with the high functional activity at the frontal, temporal and posterior regions in both active and quite sleep periods.

Analyse de connectivité EEG régime reposant dans l'épilepsie bénigne de l'enfance et des nouveau-nés

Résumé

Le travail réalisé au cours de cette thèse a porté sur l'étude de la connectivité cérébrale fonctionnelle des réseaux épileptiques chez des enfants présentant des épilepsies avec pointes centro temporales (EPCT), et sur l'organisation fonctionnelle des réseaux de repos chez des nouveau-né sains et des prématurés. Les patients épileptiques présentent une désorganisation fonctionnelle cérébrale qui participe à une altération des réseaux de repos selon la gamme de fréquence des activités cérébrales. Cette désorganisation fonctionnelle bien que plus importante durant les périodes de pointes épileptiques intercritiques est aussi observée dans les périodes sans pointes intercritiques. Les régions impliquées dans la genèse et la propagation des pointes intercritiques englobent la région centrale (zone épileptiques), la région rolandique et l'aire prémotrice. Chez le nouveau-né et le prématuré la connectivité fonctionnelle est majeure dans les régions frontales et postérieures. Les activités endogènes thêta temporales du prématuré présentent une connectivité restreinte aux seules régions temporales. Chez le nouveau-né à terme l'organisation fonctionnelle est similaire avec une forte connectivité dans les régions frontales temporales et postérieures dans le sommeil calme et le sommeil agité.

© Azeez [START_REF] Adebimpe | EEG Resting State Functional Connectivity Analysis in Children with Benign Epilepsy with Centrotemporal Spikes[END_REF]

Figure 2 . 1 :Figure 2 . 2 : 6 Figure 2 . 3 :Figure 2 . 4 :Figure 2 . 5 :Figure 2 . 6 :Figure 2 . 7 :Figure 3 . 1 :

 21226232425262731 Figure 2.1: Brain structure…………...................................................................................5 Figure 2.2: Brain structural development ………..……………………………………….6 Figure 2.3: The cerebral cortex …………………………………………………………..7 Figure 2.4: The neural source of EEG……………………………………………….…...7 Figure 2.5: International standard EEG configuration……………………………….…...8 Figure 2.6: Commonly used EEG channels in neonates …………………………….…...9 Figure 2.7: Sample of EEG rhythms…………...……………………………...………...10 Figure 2.8: EEG sample of 28-week preterm baby……………………………………...11 Figure 2.9: Synopsis of brain maturation ……………………………………………….12 Figure 2.10: EEG sample of a BCECTS patients………...……………………………...14 Figure 3.1: Modes of brain connectivity………………………………………………...17

Figure 3 . 2 :Figure 3 . 3 :Figure 3 . 4 :Figure 3 . 5 :Figure 3 . 6 :Figure 5 . 1 :Figure 5 . 2 :Figure 5 . 3 :Figure 5 . 4 :Figure 5 . 5 :Figure 5 . 6 :Figure 5 . 11 :Figure 5 . 12 :Figure 6 . 1 :Figure 6 . 2 :Figure 6 . 3 :Figure 6 . 4 :Figure 6 . 5 :Figure 6 . 6 :Figure 6 . 7 :Figure 6 . 8 :Figure 6 Figure 6 .Figure 6 .Figure 6 .Figure 6 .Figure 6 . 14 :Figure 6 . 15 :Figure 6 . 16 :

 3233343536515253545556511512616263646566676866666614615616 Figure 3.2: EEG source imaging…………………………...…………………………....20 Figure 3.3: Brain network…………………………………………………………….....27 Figure 3.4: Construction of brain network…………………………………………...….28 Figure 3.5: Network centrality………………………………………………………......29 Figure 3.6: Functional integration and segregation...……………………………….......30 Figure 3.7: Small-world network……………………………………………………......32 Figure 5.1: Right central seed region………………………………………………..…..77 Figure 5.2: Left central seed region………………………………………………......…79 Figure 5.3: Left frontal central seed region……………………………………………..81 Figure 5.4: Right occipital seed region……………………………………………….....82 Figure 5.5: Betweenness centrality……………………………………………….……..84 Figure 5.6: Local efficiency…………………………………………………….….…....85 Figure 5.7: eLORETA source imaging………………………………………………….89 Figure 5.8: EEG source reconstruction…………..……………………………………...91 Figure 5.9: Time-frequency spectrum…………………………………………………..91

Figure 2 . 1 :

 21 Figure 2.1: Brain structure. Brain is protected by the skull, scalp and CSF with the pia matter and arachnoid membrane (adapted from[START_REF] Silverthorn | Human Physiology: An Integrated Approach[END_REF]

  Figure 2.2: Brain structural development. cortical surface in premature infants (shown at several gestational ages), full-term infants, and adults (adapted from (Van Essen and Dierker, 2007))

Figure 2 . 4 :

 24 Figure 2.4: The neural source of EEG: (a) parallel pyramidal cells with positive and negative charges at soma and apical dendrites, respectively. A negative deflection of EEG is measured when soma is positive and vice versa.Figure (b) shows that signals are attenuated by the scalp and skull, and the hair on the scalp surface ( this figure was modified from (Jackson and Bolger, 2014) ).

Figure 2 . 5 :

 25 Figure 2.5: International 10-20 Standard EEG electrode configuration, Nz and Iz refer to nasion and inion, respectively.

Figure 2 . 6 :

 26 Figure 2.6: Commonly used EEG channels with ECG, EMG and respiratory recording for neonates

Figure 2 . 8 :

 28 Figure 2.8: EEG Sample from a 28-week Preterm baby: Long discontinuity intertwined with short burst EEG activity (a) and theta temporal activity at both temporal regions (T3 and T4) (b).

Figure 2 . 9 :

 29 Figure 2.9: Synopsis of maturation of specific features in EEG of premature neonates(adapted from (Wallois, 2010))

Figure 2 .

 2 Figure 2.10: EEG sample from a BCECTS patient: EEG spikes are shown at the C2, C4, T8, FC4, and FT8 electrodes, all at the right hemisphere.

Figure 3 . 1 :

 31 Figure 3.1: Modes of brain connectivity: Structural connectivity shows the white matter connections between the gray matter brain regions. Functional and effective connectivity show the connections between the neuronal activity of the brain regions. Unlike functional connectivity, effective connectivity shows the directionality of the connections.

Figure 3 . 2 :

 32 Figure 3.2: EEG source Imaging: Forward and inverse problems.

Figure 3 . 3

 33 Figure 3.3 Brain Networks: Both structural and functional brain network analyses involve four steps before graph theoretical analysis. The first step is to define the network nodes. The second step involves the estimation of time series signal of each node. The third step is to estimate coupling between the nodes before calculating the network parameters (step 4) (adapted from Bullmore and Sporns (2009)).

  Figure 3.4. Construction of brain networks: Functional networks are commonly represented by their connectivity matrices, with rows and columns representing nodes and matrix entries representing links. Networks are often reduced to a sparse binary undirected form, through thresholding and binarization.

Figure 3 . 5 :

 35 Figure3.5: Network Centrality: Higher degree at the blue node with higher number of connections and high betweenness at the green node due to the high number of shortest paths.

Figure 3 . 6 :

 36 Figure 3.6: Functional Segregation and Integration: The measures of segregation are usually based on triangle counts (red) while the integration is based on shortest path lengths (green) between two nodes (for instance 1 to 2).

Figure 3 .

 3 Figure 3.7 Small-world network: Clustering coefficient (C) and path length (L) are plotted as a function of rewiring probability (adapted from Watts and Strogatz (1998)). A small-world network is the network with high C and short L in which nearest neighbours are connected to each other (segregation) and there are short paths to other neighbours (integration). The probability of rewiring indicates the increase in randomness of the network.

Figure 5 . 1 :

 51 Figure 5.1: Right central seed region: Functional connection from the right central to other regions for each of the group; control (CON), patients group with the spike segments (WSC) and non-spike segments(NSC) and, comparison between the three conditions (WSC vs CON, NSC vs CON and WSC vs NSC).

Figure 5 . 2 :

 52 Figure 5.2: Left central seed region: Functional connections from the left central to other regions for each of the group; control (CON), patients group with the spike segments (WSC) and non-spike segments(NSC) and, comparison between the three conditions (WSC vs CON, NSC vs CON and WSC vs NSC).

Figure 5

 5 Figure 5.3. Left Frontal seed region: Functional connectivity from the left frontal to other region for each of the group; control (CON), patients group with the spike segments (WSC) and non-spike segments(NSC) and, comparison between the three conditions (WSC vs CON, NSC vs CON and WSC vs NSC).

Figure 5 . 4 :

 54 Figure5.4: Right Occipital seed region: Functional connectivity from the right occipital to other region for each of the group; control (CON), patients group with the spike segments (WSC) and non-spike segments(NSC) and, comparison between the three conditions (WSC vs CON, NSC vs CON and WSC vs NSC).

Figure 5

 5 Figure 5.5: Betweeness centrality: comparison between controls (CON), patients group with the spike segments (WSC) and nonspike segments(NSC) (WSC vs CON, NSC vs CON and WSC vs NSC).

Figure 5 . 6 :

 56 Figure 5.6: Local efficiency: comparison between controls (CON), patients group with the spike segments (WSC) and non-spike segments(NSC) (WSC vs CON, NSC vs CON and WSC vs NSC).

Figure 5 . 7 :

 57 Figure 5.7: EEG source imaging: Average eLORETA source localization of interictal spikes for 12 and 4 BCECTS patients with (A) right and (B) left epileptic focus, respectively

Figure 5 . 8 .

 58 Figure 5.8. Electrical source imaging: EEG source reconstruction using the AAL atlas for 90 regions

Figure 5 . 9 :

 59 Figure 5.9: Power spectrum. Average power spectrum for patients with (A) right and (B) left epileptic foci in the θ band

Figure 5 .

 5 Figure 5.10: EEG source imaging: Average eLORETA source localization of interictal spikes from 12 and 4 BCECTS patients with (A) right and (B) left epileptic foci, respectively.

Figure 5 .

 5 Figure 5.11: Outflow density. Temporal evolution of outflow density compared to the baseline. Only the ROIs in which more than 8 out of 12 patients showed significance differences compared to the baseline were plotted for the group with right epileptic foci (A). The 3D images inside each graph represent the outflow during the rising phase of the spike compared to the baseline.

Figure 5 .

 5 Figure 5.12: Effective connectivity. The connectivity pattern for patients with (A) right and (B) left epileptic foci, respectively, from the ROI to the whole brain region.

Figure 6 . 1 :

 61 Figure 6.1: Schematic illustration of the processing pipeline.

Figure 6 . 2 :

 62 Figure 6.2: Examples of EEG in preterm babies. (A) discontinuous EEG pattern with short burst activity, and (B) EEG signals with TTA at the temporal channels.

Figure 6 . 3 :

 63 Figure 6.3: Synchronization index: (A) Filtered EEG segment with TTA on T7, (B), the dynamic synchronization index between EEG channels for the delta (blue) and theta (red) frequency bands.

Figure 6 . 4 :

 64 Figure 6.4: Spatial topology of functional connectivity. The group average is for normal activity (NAT) and theta temporal activity (TTA) shows the prominent functional connectivity in frontal and posterior regions and statistical difference between the two activities reveals increased functional connectivity at each of the temporal region due to TTA in θ band.

Figure 6 . 5 :

 65 Figure 6.5: Spatial topology of functional connectivity pattern. The degree for normal activity (NAT) and theta temporal activity (TTA) indicated prominent functional connections in the frontal and posterior regions. The statistical differences between the two activities revealed stronger functional connections at each of the temporal regions due to the occurrence of TTA.

  [START_REF] Gong | Effective Connectivity of Hippocampal Neural Network and Its Alteration in Mg2+-Free Epilepsy Model[END_REF]. The clustering coefficient (C) in δ band was higher at the bilateral frontal and posterior regions but lower (mainly in θ band) at central region for both NAT and TTA. Compared to NAT, the presence of TTA also resulted in increased C values over the temporal regions in θ band, and decreased C values over the frontal regions in δ band. The local efficiency (LE) presented topological patterns similar to the one that was found for the clustering coefficient with higher LE at the frontal and posterior regions and lower LE at the central region, especially in θ band, for both NAT and TTA.

Figure 6 . 6 :

 66 Figure 6.6: Spatial topology of the network metrics, clustering coefficient C, and local efficiency LE for TTA and NAT and their statistical differences. The first column is the group average with the bar indicating the range on changes. The second column shows the statistical differences between TTA and NAT with the bar indicating t-values.

Figure 6 . 7 :Figure 6 . 8 :

 6768 Figure 6.7: Global network metrics. Global network degree (K), clustering coefficient (C) and global efficiency (E) for both TTA and NAT. The asterisks indicate statistical significance with p<0.05.

Figure 6 . 9 :

 69 Figure 6.9: Statistical procedures:The single-level significance was tested using distributions derived from time shifted surrogates, while the group-level testing was done with the FDR control at 0.1% significance level. The individual significance matrix was thresholded at 14% connection density based on the Eros-Renyi model before computing the graph metrics.

Figure 6 .

 6 Figure 6.10: EEG spectral power results. Average power for the four frequency bands and each region (see Table6.3) for both conditions (QS and AS)

Figure 6 .

 6 Figure 6.11. Results of the Statistical analysis of eLORETA current source density for both conditions (QS and AS) in all the frequency bands. The color bar indicates t-values.

Figure 7 .

 7 Figure 7.12: Mean PLV connectivity matrices for both conditions (QS and AS) with 59 EEG channels. Each matrix is the result of the group average with a FDR value of 0.1 for all the frequency bands. The colorbar indicates the strength of the elements in the matrix.

Figure 6 .

 6 Figure 6.13: Mean PLV for both conditions (QS and AS) in all the frequency bands

Figure 6 .

 6 Figure 6.14:Global network metrics: Betweenness, Clustering coefficient, Characteristics Path length and Small-worldness for both conditions and all the frequency bands. All the graph metrics were calculated from the thresholded connectivity matrix with a connection density of 14% determined using the Erdos-Renyi model.

Figure 6 .

 6 Figure 6.15: Spatial topology of the network degree (K), betweenness (BC) and clustering coefficient (C) during QS. The colorbar indicates the strength of the metrics from zero (blue) to highest value (red) corresponding to 0.25, 0.03 and 0.6 for K, BC and C, respectively. All the graph metrics were calculated from the thresholded connectivity matrix with a connection density of 14% determined using the Erdos-Renyi model.

Figure 6 .

 6 Figure 6.16 Spatial topology of the network degree (K), betweenness (BC) and clustering coefficient (C) during AS The colorbar indicates the strength of the metrics from zero (blue) to highest value (red) corresponding to 0.25, 0.03 and 0.6 for K, BC and C, respectively All the graph metrics were calculated from the thresholded connectivity matrix with a connection density of 14% determined using the Erdos-Renyi model.

Figure S3 .

 S3 Figure S3. Statistical maps of differences between cortical sources computed under the eyes-closed condition for the control group (ECCT, left boxplots) and patient group (ECWS, with spike condition, right boxplots) in δ, β1 and β2. The results have been projected onto the cortical layer of the realistic head model (a) and the MNI152 MRI (b). Color bars indicate significant differences between ECCT and ECWS, red (ECCT > ECWS) and blue (ECCT < ECWS).

Figure S4 .

 S4 Figure S4. Statistical maps of differences between cortical sources computed under the no-spike (ECNS, left boxplots) and withspike (ECWS, right boxplots) eyes-closed conditions in θ, β1 and β2 bands for the epileptic group. The results have been projected onto the cortical layer of the realistic head model (a) and the MNI152 MRI (b). Color bars indicate significant differences between ECNS and ECWS, red (ECNS > ECWS) and blue (ECNS > ECWS).

  for computation of degree Before computing the graph parameters, we applied the threshold (τ) based on the three constraints described in Methods. The first method consists of obtaining one standard deviation above the median connectivity value as shown in S3 Fig. The connectivity matrix before thresholding has shown in Figure A of S3Fig. The distribution of the PLV values has been plotted in Figure B of S3 Fig. In this plot, the vertical pink line represents τ (one standard deviation above the median connectivity value) for a particular subject and frequency band. The optimal threshold was applied to the connectivity matrix (Figure A of S3 Fig) to obtain the binary matrix, as shown in Figure C of S3 Fig. S3 Fig. (a) Example of the functional connectivity matrix obtained for Subject 1, (b) the distribution of the PLV values of the functional connectivity matrix; the vertical line shows the optimal threshold, (c) the binarized functional connectivity matrix obtained after applying the optimal threshold.

Table 5 . 2 :

 52 Patients EEG recordings…………………………………………………….89

Table 6 . 1 :

 61 Preterm neonates…………………………………………………………...100

Table 6 . 2 :

 62 EEG channels in each region……………………………………………....107

Table 6 . 3 :

 63 EEG channels in each region……………………………………………....112

xv Chapter

1 Introduction 1.1 Thesis Overview and Problem definitions

Table 5 .1: Characteristics of the control and patient groups Control Group Patient Group

 5

	Subject	Age	EEG	Patient Age	EEG	Neuropsychological	Description of ictal	Medication
		(years)	duration		(years)	duration	assessment	EEG
			(min)			(min)
	1	6.73	16	1	12.63	50	Normal	Partial seizure	Sodium valproate
	2	11.28	19	2	12.64	17	Normal	Partial seizure	Sodium valproate
	3	10.48	19	3	9.25	44	Attention deficit	Generalized tonic-	Oxcarbezepine
								clonic seizure
	4	10.66	17	4	6.03	43	-	Brachiofacial	Oxcarbezepine
								nocturnal seizure
	5	7.39	13	5	10.47	50	Attention deficit	Partial seizure	Sodium valproate
	6	7.31	20	6	7.16	14	-	Brachiofacial	Sodium valproate
								nocturnal seizure
	7	11.92	30	7	8.51	30	Attention deficit	Nocturnal seizure	-
	8	8.44	75	8	13.16	20	Normal	Generalized tonic-	Sodium valproate
								clonic seizure
	9	9.36	28	9	9.67	15	Language deficit	Generalized tonic-	Lamotrigine
								clonic seizure
	10	9.48	45	10	7.79	23	Normal	Generalized tonic-	Micropakine
								clonic seizure
	11	10.32	18	11	8.91	16	Normal	Generalized tonic-	Trileptal
								clonic seizure
	12	7.98	20		-	-	-	-	-
	Mean±sd 9.3±1.7 27±17		9.6±2.4 29.7±14

Table 5 .2: Patients EEG recordings and clinical characteristics

 5

	Patient	Age	Epileptic focus	Neuropsychological	Medication
		(years)		assessment
		12.63	Right	Normal	Sodium valproate
		12.64	Right	Normal	Sodium valproate
		9.25	Right	Attention deficit	Oxcarbezepine
		6.03	Right	-	Oxcarbezepine
		10.47	Right	Attention deficit	Sodium valproate
		7.16	Right	-	Sodium valproate
		8.51	Right	Attention deficit	-
		13.16	Right	Normal	Sodium valproate
		9.67	Right	Language deficit	Lamotrigine
	10	7.79	Right	Normal	Micropakine
	11	8.91	Right	Normal	Trileptal
	12	9.81	Right	Normal	Sodium valproate
	13	8.30	Left	Language disabilities	Sodium valproate
	14	7.52	Left	Language disabilities	Oxcarbamazepine
	15	8.00	Left	Normal	-
	16	7.01	Left	Attentional deficit	Sodium valproate

Table 6 .1. Overview of the characteristics of the preterm babies included in the study.

 6

	Preterm babies	12 (6F)
	Gestational age at birth (weeks)	29.11 ± 1.39
	Gestational age at recording (weeks)	31.26 ± 0.63
	Weight at Birth (gram)	1145 ± 297
	Weight at recording (gram)	1295 ± 262

Table 6 .3: EEG Channels in each region

 6 . R and L denote right and left hemisphere, respectively.

	Regions	EEG channels
	Right frontal (RF)	FP2, AF4, AF8, F2, F4, F6, F8
	Frontal (F)
	Left frontal (LF)	FP1, AF3, AF7, F1, F3, F5, F7
	Right temporal (RT)	FC6, C6, CP6, T8, TP8
	Temporal (T)
	Left temporal (LT)	FC5, C5, CP5, T7, TP7
	Right central (RC)	FC2, FC4, C2, C4, CP2, CP4
	Central (C)
	Left central (LC)	FC1, FC3, C1, C3, CP1, CP3
	Right posterior (RP)	P2, P4, P6, P8, PO4, PO8, O2
	Posterior (P)
	Left posterior (LP)	P1, P3, P5, P7, PO3, PO7, O1

Supplementary information in Appendix A

http://www.fieldtriptoolbox.org/tutorial/visual_artifact_rejection

my gratitude to my co-supervisor, Dr Ardalan Aarabi for all your efforts for the success of my PhD thesis. I am grateful for accepting me as your PhD student and your patience, enthusiasm, throughout the thesis period. Your tireless efforts in proofreading and correcting the drafts of my manuscripts and thesis is greatly appreciated. I gratefully acknowledge financial support from INSERM (Institut national de la santé et de la recherche médicale) for my PhD program. I express my sincere appreciation to the staff of INSERM at Lille (L'Inserm of all my requests. I also appreciate efforts of administrative staff at Doctoral School of UPJV.

Brain symmetry index

The functional brain symmetry index was computed from the relative differences in network metrics between the right and left hemispheres in both frequency bands. We divided the brain regions as shown in Table 6.2. The Brain Symmetry Index (BSI) was computed for the frontal (F), temporal (T), central (C) and posterior (P) regions. The BSI was defined as:

Where R and L for the right and left hemisphere, respectively, and M indicates the number of channels in each region. A positive value refers to the rightward asymmetry. The BSI result is shown in Figure 6.8 for all the graph metrics. Generally, there was a rightward asymmetry in the frontal region and a leftward asymmetry in the posterior region for all the network metrics and frequency bands. In θ band, there was a rightward asymmetry in the temporal region under both conditions, with and without TTA. The asymmetry was more pronounced for the TTA segments.

Appendix: Supplementary information Supporting information for section 4.2

Supporting information for section 4.3 Epileptic subjects

Dipole source analysis of the centrotemporal spikes region of the patients was performed with Advanced Source Analysis (ASA) software (http://www.ant-neuro.com). The location of interictal epileptic spikes (IES) was identified for each patient using the spatiotemporal dipole modeling method

Functional connectivity

The phase locking value (PLV) was computed from the analytical signals obtained from Hilbert transformation of the band-pass filtered signals, filtered by a linear-phase FIR (finite impulse response) filter. The analytical signals (x (t, f)) were first computed by: 𝑥 ̌(𝑡, 𝑓) = 𝑥(𝑡, 𝑓) + 𝑖𝑥 𝐻 (𝑡, 𝑓)

Where xH (t, f) is the Hilbert transform of the input signals x (t,f).

The phases of the analytical signals were then extracted:

𝜑 𝑥 (𝑡, 𝑓) = arctan ( 𝑥 𝐻 (𝑡, 𝑓) 𝑥(𝑡, 𝑓) )

The relative phase between each channel pair x and y was obtained by: ∅(𝑡) = 𝜑 𝑥 (𝑡, 𝑓) -𝜑 𝑦 (𝑡, 𝑓)

The PLV was finally computed by calculating the exponential of the relative phase:

Where N is the time point.

Computation of graph theory parameters

Degree

The degree of a node is the number of links connected to that node. The degree (K) is mathematically defined as:

Where Ki is the degree for the ith node, and Aij is the connection status between nodes i and j. The degree is a characteristic measure of the functional interactions between brain regions.

Clustering coefficient

The clustering coefficient C and characteristic path length L were computed as described in [2,3]. The clustering coefficient Ci of the node i is defined as:

Where n is the number of nodes, ti is the number of existing connections among the neighbours of node i, and ki is the actual number of neighbours of node i (i.e. degree). The mean clustering coefficient (C) of a network is defined as the mean clustering coefficient over all nodes in the network:

Characteristic path length