This dissertation proposes new statistical methods for modeling and inference for two specific types of time series: integer-valued data and multivariate nonstationary extreme data. We rely on the class of integer-valued autoregressive (INAR) processes for the former, proposing a novel, flexible and elegant way of modeling count phenomena. As for the latter, we are interested in the human brain and its multi-channel electroencephalogram (EEG) recordings, a natural source of extreme events. Thus, we develop new extreme value theory methods for analyzing such data, whether in modeling the conditional extremal dependence for brain connectivity or clustering extreme brain communities of EEG channels. Regarding integer-valued time series, INAR processes are generally defined by specifying the thinning operator and either the innovations or the marginal distributions. The major limitations of such processes include difficulties deriving the marginal properties and justifying the choice of the thinning operator. To overcome these drawbacks, this dissertation proposes a novel approach for building an INAR model that offers the flexibility to prespecify both marginal and innovation distributions. Thus, the thinning operator is no longer subjectively selected but is rather a direct consequence of the marginal and innovation distributions specified by the modeler. Novel INAR processes are introduced following this perspective; these processes include a model with geometric marginal and innovation distributions (Geo-INAR) and models with bounded innovations. We explore the Geo-INAR model, which is a natural alternative to the classical Poisson INAR model. The Geo-INAR process has interesting stochastic properties, such as MA($\infty$) representation, time reversibility, and closed forms for the $h$-th-order transition probabilities, which enables a natural framework to perform coherent forecasting. In the front of multivariate nonstationary extreme data, the focus lies on multi-channel epilepsy data. Epilepsy is a chronic neurological disorder affecting more than 50 million people globally. An epileptic seizure acts like a temporary shock to the neuronal system, disrupting normal electrical activity in the brain. Epilepsy is frequently diagnosed with EEGs. Current statistical approaches for analyzing EEGs use spectral and coherence analysis, which do not focus on extreme behavior in EEGs (such as bursts in amplitude), neglecting that neuronal oscillations exhibit non-Gaussian heavy-tailed probability distributions. To overcome this limitation, this dissertation proposes new approaches to characterize brain connectivity based on extremal features of EEG signals. Two extreme-valued methods to study alterations in the brain network are proposed. One method is Conex-Connect, a pioneering approach linking the extreme amplitudes of a reference EEG channel with the other channels in the brain network. The other method is Club Exco, which clusters multi-channel EEG data based on a spherical $k$-means procedure applied to the "pseudo-angles," derived from extreme amplitudes of EEG signals. Both methods provide new insights into how the brain network organizes itself during an extreme event, such as an epileptic seizure, in contrast to a baseline state.

No description available.

In this thesis we were interested in combining functional connectivity (from functional Magnetic Resonance Imaging) and structural connectivity (from Diffusion Tensor Imaging) with a data fusion approach. While data fusion approaches provide an abundance of information they are underutilized due to their complexity. To solve this problem, we integrated the ease of a neuroimaging toolbox, known as the Functional And Tractographic Analysis Toolbox (FATCAT) with a data fusion approach known as the anatomically weighted functional connectivity (awFC) approach - to produce a practical and more efficient pipeline. We studied the connectivity within resting-state networks of different populations using this novel pipeline. We performed separate analyses with traditional structural and functional connectivity for comparison with the awFC findings - across all three projects. In the first study we evaluated the awFC of participants with major depressive disorder compared to controls. We observed significant connectivity differences in the default mode network (DMN) and the ventral attention network (VAN). In the second study we studied the awFC of MDD remitters compared to non-remitters at baseline and week-8 (post antidepressant), and evaluated awFC in remitters longitudinally from baseline to to week-8. We found significant group differences in the DMN, VAN, and frontoparietal network (FPN) for remitters and non-remitters at week-8. We also found significant awFC longitudinally from baseline to week-8 in the dorsal attention network (DAN) and FPN. We also tested the associations between connectivity strength and cognition. In the third study we studied the awFC in children exposed to pre- and postnatal adversity compared to controls. We observed significant differences in the DMN, FPN, VAN, DAN, and limbic network (LIM). We also assessed the association between connectivity strength in middle childhood and motor and behavioural scores at age 3. Therefore, the FATCAT-awFC pipeline, we designed was capable of identifying group differences in RSN in a practical and more efficient manner. / Thesis / Doctor of Philosophy (PhD)

No description available.

Humans have an innate ability to deal with numerosity and other aspects of magnitude. This ability is generally honed through education in and experience with mathematics, which necessarily changes the brain structurally and functionally. These changes can be further manipulated through non-invasive electrical brain stimulation. Studying these processes in the case of maths not only constitutes research of great practical impact – given the importance of numerical skills in today's society – but also makes use of maths as a suitable domain in which to study plasticity. In this thesis, I aimed to explore how expertise with numbers shapes brain and behaviour, and also the degree to which processing numbers is similar to other domains in terms of the necessity of healthy brain regions believed to underlie normal processing within and across these domains. In Study 1, behavioural and structural brain differences were found cross-sectionally between mathematicians and non-mathematicians. A double dissociation between those groups was found between grey matter density in the frontal lobe and behavioural performance: their correlation was positive for mathematicians but negative for controls. These effects may have been caused by years of experience, by congenital predispositions, or, plausibly, by both of these factors, whose disambiguation is non-trivial. Study 2 used transcranial random noise stimulation (tRNS) to assist arithmetic learning. A novel montage was used to enhance brain function during the stage when it is believed to be most involved. Real as compared to sham tRNS enhanced reaction times (RTs) and learning rate on a calculation-based task, but not on a retrieval-based task. The effects were only observed in conditions of high task difficulty. Study 3 examined structural MRI measures before and after arithmetic training to determine how either frontal or parietal tRNS applied with the task changes the structure of the brain longitudinally as compared to sham. Previous results (including those of Study 2) of behavioural facilitation in terms of enhanced RTs to calculation problems were replicated, and further interpreted. Both frontal and parietal tRNS modulated the changes that occurred, pre-to-post training, in terms of cortical volume and gyrification of frontal, parietal and temporal areas. Study 4 investigated the shared neural and cognitive resources used for processing numerical magnitude and musical pitch, by probing how stimulus-response compatibility (SRC) effects for each of the two dimensions compare in a group of mainly temporoparietal lesion patients with numerical impairments versus controls. A double dissociation was found in that numerically impaired patients did not show the number-based SRC effect but did show the pitch-based one, while control subjects demonstrated the opposite trend. Overall, the results of these studies leave us with three main messages. First, expertise in numbers and mathematics, whether acquired through years of experience (Study 1) or through a few days of tRNS-assisted training (Study 3), appears to be associated with complex changes in the morphology of several brain structures. Some – but not all – of these structures are maths-relevant, and, in the case of tRNS-assisted training, they are distal to the site of the stimulating electrodes. Second, tRNS can improve performance in arithmetic (Studies 2 and 3), although the mechanisms by which this occurs are not yet fully understood, neither neurally nor behaviourally. Third, I found (Study 4) that brain lesions leading to impairment in the number domain do not necessarily affect processing in other domains – such as pitch – that are otherwise linked to number via a putative common code in the parietal lobes.

Esta dissertação desenvolve e aplica métodos para caracterizar regiões cerebrais durante o estado de repouso. Utilizam-se grafos para representar a inter-dependência temporal de sinais de ressonância magnética funcional provenientes de regiões cerebrais distintas. Vértices representam regiões cerebrais e arestas representam a conectividade funcional. Buscando superar os problemas de visualização e interpretação desta forma de representação, elaboram-se métodos quantitativos para caracterizar padrões de conectividade entre regiões cerebrais. Para cada sujeito analisado: 1) Faz-se a redução da dimensionalidade espacial das imagens de ressonância magnética funcional respeitando os limites anatômicos das regiões cerebrais. 2) Estima-se a rede de conectividade funcional pela coerência direcionada entre pares de regiões distintas. 3) Constrói-se um grafo direcionado e pesado pela medida de conectividade. 4) Quantificam-se os vértices por índices e faz-se o registro destes valores no espaço comum MNI. 5) Avalia-se a consistência de cada índice pelo teste não paramétrico de Friedman seguido de análises de múltiplas comparações. A análise de 198 imagens de sujeitos sadios produziu resultados consistentes e biologicamente plausíveis. Em sua maioria, revelou regiões associadas a conceitos anatômicos de conectividade e integração cerebral. Embora de implementação simples, o método proporciona informações de natureza dinâmica sobre as relações entre diferentes regiões cerebrais e pode ser utilizado futuramente para estudar e entender desordens psiquiátricas/neurológicas. / This dissertation develops and applies methods to characterize brain regions during resting state. Graphs are used to represent functional MRI connectivity from different brain regions. Vertices represent brain regions and edges represent connectivity. To overcome the visualization and interpretation problems of this form of representation, we developed quantitative methods to characterize its patterns. Methods: For each subject: 1) The reduction of spatial dimensionality of functional magnetic resonance imaging is carried out taking into account the anatomic limits of the brain regions. 2) The network is estimated by directed coherence between pairs of separate regions. 3) A directed graph with weights on its edges is constructed using the later connectivity measure. 4) The vertices are quantified by indexes that are registered in the MNI common space. 5) The consistency of each index is evaluated by the nonparametric Friedman followed by Post-Hoc analysis. Results: The analysis of 198 images of healthy subjects produced consistent and biologically plausible results. They revealed anatomical regions involved in brain integration. Conclusion: The method provides information about the dynamic nature of the relationships between different brain regions and can be used in future clinical studies to understand psychiatric and neurological disorders.

Functional Magnetic Resonance Imaging (fMRI) is one of the best techniques for neuroimaging and has revolutionized the way to understand the brain functions. It measures the changes in the blood oxygen level-dependent (BOLD) signal which is related to the neuronal activity. Complexity of the data, presence of different types of noises and the massive amount of data makes the fMRI data analysis a challenging one. It demands efficient signal processing and statistical analysis methods.  The inference of the analysis is used by the physicians, neurologists and researchers for better understanding of the brain functions.      The purpose of this study is to design a toolbox for fMRI data analysis. It includes methods to detect the brain activity maps, estimation of the hemodynamic response (HDR) and the connectivity of the brain structures. This toolbox provides methods for detection of activated brain regions measured with Bayesian estimator. Results are compared with the conventional methods such as t-test, ordinary least squares (OLS) and weighted least squares (WLS). Brain activation and HDR are estimated with linear adaptive model and nonlinear method based on radial basis function (RBF) neural network. Nonlinear autoregressive with exogenous inputs (NARX) neural network is developed to model the dynamics of the fMRI data.  This toolbox also provides methods to brain connectivity such as functional connectivity and effective connectivity.  These methods are examined on simulated and real fMRI datasets.

Orientador: Gabriela Castellano / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Ciências Médicas / Made available in DSpace on 2018-08-24T17:19:19Z (GMT). No. of bitstreams: 1 Pereira_FabricioRamosSilvestre_D.pdf: 32802688 bytes, checksum: 367566b29c460e1b33f48f861845217a (MD5) Previous issue date: 2013 / Resumo: O conectoma cerebral refere-se ao mapeamento dos circuitos neurais com os objetivos de 1) identificar regiões que dão suporte às atividades mentais e comportamentais, e 2) detectar alterações nesses circuitos que levam a distúrbios de ordem psiquiátrica e neurológica. Na prática, os estudos de conectoma cerebral consistem na integração de técnicas multimodais de imageamento como ressonância magnética (RM), eletroencefalograma (EEG) e magnetoencefalograma (MEG) com o intuito de estimar os tipos e os níveis de conexão entre regiões cerebrais remotas. Essa "conectividade" entre regiões cerebrais é geralmente classificada em três tipos: anatômica, funcional e efetiva. No presente trabalho, as técnicas de conectividade, usando dados de MR, foram aplicadas na comparação de grupos saudáveis e patológicos. Pela técnica de conectividade anatômica observou-se anomalias na substância branca de pacientes com mutação no gene SPG11. Essa anomalias foram detectadas através da redução da anisotropia fracional (FA) e aumento da difusividade média (MD), difusividade radial (RD) e difusividade axial (AD) em regiões subcorticais dos lobos temporal e frontal, bem como no giro do cíngulo, cuneus striatum, corpo caloso e tronco cerebral. Tais achados indicam que o dano neuronal é mais difuso do que indicava a literatura. Um segundo estudo de conectividade anatômica demonstrou que esses índices de difusividade não foram robustos para diferenciar idosos com e sem diagnóstico de depressão indicando a necessidade de avanços na formulação de novos índices com maior sensibilidade. A técnica de conectividade funcional foi empregada em três estudos. No primeiro, observou-se que pacientes com epilepsia de lobo temporal medial unilateral apresentam redução da conectividade funcional durante a execução de tarefas de memória verbal e visual. Essa redução foi predominantemente ipslateral à lesão e associada ao material-específico utilizado no teste de memória. No segundo estudo, verificou-se uma redução dos padrões de conectividade funcional hipotalâmica em sujeitos obesos e a sua parcial elevação após a cirurgia bariátrica concomitantemente à redução de indicadores bioquímicos de inflamação. No terceiro estudo, observou-se que pacientes com doença de Alzheimer apresentaram elevação dos níveis de conectividade funcional na rede saliente (Salience Network) e redução na rede de modo padrão (Default-mode network). Adicionalmente, verificou-se nos pacientes a correlação positiva da síndrome hiperativa com os níveis de conectividade funcional no cíngulo anterior e em áreas da ínsula direita. O conjunto desses resultados ilustra um possível significado clínico para futuro diagnóstico e tratamento da doença de Alzheimer. Pela técnica de conectividade efetiva observou-se que em função do envelhecimento sadio há uma mudança dos parâmetros de conectividade durante a codificação de palavras com conteúdo emocional. A influência do hipocampo sobre a amígdala ipslateral é reduzida nos sujeitos mais velhos enquanto a influência da amígdala direita sobre o hipocampo direito é elevada. Tais achados reforçam a tese da ininterrupta plasticidade etária e da dinâmica cerebral normal. Essa mesma técnica foi também empregada para demonstrar os diferentes padrões de influência entre os lobos frontal e temporal de pacientes com ELTM esquerda e sujeitos controle. Encontrou-se alteração nos padrões de conectividade efetiva dos pacientes, indicando que estes podem ser potenciais biomarcadores para a epilepsia / Abstract: Connectome refers to the neural circuitry mapping aiming to identify brain regions that support mental and behavioral functions as well as to detect circuit changes that are linked to psychiatric or neurologic disorders. In practice, connectome studies link several neuroimaging approaches such as MRI, EEG and MEG by means of the estimation of connections among remote brain regions. This "connectivity" among brain regions is usually classified as anatomic, functional or effective. In this work, the technique of connectivity, using MR data, was applied to compare healthy and pathological groups. By means of the anatomical connectivity abnormalities in the white matter of patients with SPG11 mutation were observed. These abnormalities were expressed as the reduction of the levels of fractional anisotropy (FA) and the increase in mean (MD) and radial diffusivities (RD) in sub-cortical regions of temporal and frontal lobe as well as in cingulated gyrus, cuneus, striatum, corpus callosum and brainstem. These findings suggest that neuronal damage/dysfunction is more widespread than previously recognized in this condition. Another anatomical connectivity study showed that such indices of diffusivity were not robust to statistically differentiate between old subjects with and without depression. This lacking on finding differences between both groups indicates that new indices of diffusivity have to emerge in order to provide complementary information about brain subtle microstructures. Functional connectivity was applied to three studies. In the first study, it was observed that patients with unilateral medial temporal lobe epilepsy presented lower levels of functional connectivity during visual or verbal memory tasks. Such reduction was ipsilateral to the side of the lesion and associated to the specific-material used in the memory task. In the second work, the levels of functional connectivity were reduced in hypothalamic regions of obese patients but a partial reversibility of hypothalamic dysfunction was observed after bariatric surgery. In the third, patients with Alzheimer disease presented higher values of functional connectivity in the salience network and a reduction of connectivity values in the default-mode network. Also in these patients, significant correlations between the levels of hyperactivity syndrome and the salience network were observed in the anterior cingulate cortex and right insula areas. These results indicate the potential clinical significance of resting state alterations in future diagnosis and therapy of Alzheimer disease. The effective connectivity approaches demonstrated that old and young subjects have significant differences when encoding words with emotional contents. The influence of the hippocampus on the ipsilateral amygdale was lower for older subjects whereas the influence of the right amygdale on the right hippocampus was increased for these subjects. These findings suggest that brain plasticity also happens as function of age. The same approach was used to estimate the influence from frontal to temporal lobes in patients with left MTLE compared to healthy subjects. The patterns of effective connectivity were changed in patients and may be potentially considered as biomarkers for epilepsy / Doutorado / Neurociencias / Doutor em Ciências

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

Esta dissertação desenvolve e aplica métodos para caracterizar regiões cerebrais durante o estado de repouso. Utilizam-se grafos para representar a inter-dependência temporal de sinais de ressonância magnética funcional provenientes de regiões cerebrais distintas. Vértices representam regiões cerebrais e arestas representam a conectividade funcional. Buscando superar os problemas de visualização e interpretação desta forma de representação, elaboram-se métodos quantitativos para caracterizar padrões de conectividade entre regiões cerebrais. Para cada sujeito analisado: 1) Faz-se a redução da dimensionalidade espacial das imagens de ressonância magnética funcional respeitando os limites anatômicos das regiões cerebrais. 2) Estima-se a rede de conectividade funcional pela coerência direcionada entre pares de regiões distintas. 3) Constrói-se um grafo direcionado e pesado pela medida de conectividade. 4) Quantificam-se os vértices por índices e faz-se o registro destes valores no espaço comum MNI. 5) Avalia-se a consistência de cada índice pelo teste não paramétrico de Friedman seguido de análises de múltiplas comparações. A análise de 198 imagens de sujeitos sadios produziu resultados consistentes e biologicamente plausíveis. Em sua maioria, revelou regiões associadas a conceitos anatômicos de conectividade e integração cerebral. Embora de implementação simples, o método proporciona informações de natureza dinâmica sobre as relações entre diferentes regiões cerebrais e pode ser utilizado futuramente para estudar e entender desordens psiquiátricas/neurológicas. / This dissertation develops and applies methods to characterize brain regions during resting state. Graphs are used to represent functional MRI connectivity from different brain regions. Vertices represent brain regions and edges represent connectivity. To overcome the visualization and interpretation problems of this form of representation, we developed quantitative methods to characterize its patterns. Methods: For each subject: 1) The reduction of spatial dimensionality of functional magnetic resonance imaging is carried out taking into account the anatomic limits of the brain regions. 2) The network is estimated by directed coherence between pairs of separate regions. 3) A directed graph with weights on its edges is constructed using the later connectivity measure. 4) The vertices are quantified by indexes that are registered in the MNI common space. 5) The consistency of each index is evaluated by the nonparametric Friedman followed by Post-Hoc analysis. Results: The analysis of 198 images of healthy subjects produced consistent and biologically plausible results. They revealed anatomical regions involved in brain integration. Conclusion: The method provides information about the dynamic nature of the relationships between different brain regions and can be used in future clinical studies to understand psychiatric and neurological disorders.