On the connectivity of the escaping set for complex exponential Misiurewicz parameters

Let $ E_{\lambda}(z)=\lambda {\rm exp}(z), \lambda\in \mathbb{C}$, be the complex exponential family. For all functions in the family there is a unique asymptotic value at 0 (and no critical values). For a fixed $ \lambda$, the set of points in $ \mathbb{C}$ with orbit tending to infinity is called the escaping set. We prove that the escaping set of $ E_{\lambda}$ with $ \lambda$ Misiurewicz (that is, a parameter for which the orbit of the singular value is strictly preperiodic) is a connected set.

Functional connectivity of reward processing in the brain

Controversial results have been reported concerning the neural mechanisms involved in the processing of rewards and punishments. On the one hand, there is evidence suggesting that monetary gains and losses activate a similar fronto-subcortical network. On the other hand, results of recent studies imply that reward and punishment may engage distinct neural mechanisms. Using functional magnetic resonance imaging (fMRI) we investigated both regional and interregional functional connectivity patterns while participants performed a gambling task featuring unexpectedly high monetary gains and losses. Classical univariate statistical analysis showed that monetary gains and losses activated a similar fronto-striatallimbic network, in which main activation peaks were observed bilaterally in the ventral striatum. Functional connectivity analysis showed similar responses for gain and loss conditions in the insular cortex, the amygdala, and the hippocampus that correlated with the activity observed in the seed region ventral striatum, with the connectivity to the amygdala appearing more pronounced after losses. Larger functional connectivity was found to the medial orbitofrontal cortex for negative outcomes. The fact that different functional patterns were obtained with both analyses suggests that the brain activations observed in the classical univariate approach identifi es the involvement of different functional networks in the current task. These results stress the importance of studying functional connectivity in addition to standard fMRI analysis in reward-related studies.

Predicting human resting-state functional connectivity from structural connectivity

In the cerebral cortex, the activity levels of neuronal populations are continuously fluctuating. When neuronal activity, as measured using functional MRI (fMRI), is temporally coherent across 2 populations, those populations are said to be functionally connected. Functional connectivity has previously been shown to correlate with structural (anatomical) connectivity patterns at an aggregate level. In the present study we investigate, with the aid of computational modeling, whether systems-level properties of functional networks-including their spatial statistics and their persistence across time-can be accounted for by properties of the underlying anatomical network. We measured resting state functional connectivity (using fMRI) and structural connectivity (using diffusion spectrum imaging tractography) in the same individuals at high resolution. Structural connectivity then provided the couplings for a model of macroscopic cortical dynamics. In both model and data, we observed (i) that strong functional connections commonly exist between regions with no direct structural connection, rendering the inference of structural connectivity from functional connectivity impractical; (ii) that indirect connections and interregional distance accounted for some of the variance in functional connectivity that was unexplained by direct structural connectivity; and (iii) that resting-state functional connectivity exhibits variability within and across both scanning sessions and model runs. These empirical and modeling results demonstrate that although resting state functional connectivity is variable and is frequently present between regions without direct structural linkage, its strength, persistence, and spatial statistics are nevertheless constrained by the large-scale anatomical structure of the human cerebral cortex.

Classifying minimally disabled multiple sclerosis patients from resting state functional connectivity.

Multiple sclerosis (MS), a variable and diffuse disease affecting white and gray matter, is known to cause functional connectivity anomalies in patients. However, related studies published to-date are post hoc; our hypothesis was that such alterations could discriminate between patients and healthy controls in a predictive setting, laying the groundwork for imaging-based prognosis. Using functional magnetic resonance imaging resting state data of 22 minimally disabled MS patients and 14 controls, we developed a predictive model of connectivity alterations in MS: a whole-brain connectivity matrix was built for each subject from the slow oscillations (<0.11Hz) of region-averaged time series, and a pattern recognition technique was used to learn a discriminant function indicating which particular functional connections are most affected by disease. Classification performance using strict cross-validation yielded a sensitivity of 82% (above chance at p<0.005) and specificity of 86% (p<0.01) to distinguish between MS patients and controls. The most discriminative connectivity changes were found in subcortical and temporal regions, and contralateral connections were more discriminative than ipsilateral connections. The pattern of decreased discriminative connections can be summarized post hoc in an index that correlates positively (ρ=0.61) with white matter lesion load, possibly indicating functional reorganisation to cope with increasing lesion load. These results are consistent with a subtle but widespread impact of lesions in white matter and in gray matter structures serving as high-level integrative hubs. These findings suggest that predictive models of resting state fMRI can reveal specific anomalies due to MS with high sensitivity and specificity, potentially leading to new non-invasive markers.

APOE status modulates the changes in network connectivity induced by brain stimulation in non-demented elders.

Behavioral consequences of a brain insult represent an interaction between the injury and the capacity of the rest of the brain to adapt to it. We provide experimental support for the notion that genetic factors play a critical role in such adaptation. We induced a controlled brain disruption using repetitive transcranial magnetic stimulation (rTMS) and show that APOE status determines its impact on distributed brain networks as assessed by functional MRI (fMRI).Twenty non-demented elders exhibiting mild memory dysfunction underwent two fMRI studies during face-name encoding tasks (before and after rTMS). Baseline task performance was associated with activation of a network of brain regions in prefrontal, parietal, medial temporal and visual associative areas. APOE ε4 bearers exhibited this pattern in two separate independent components, whereas ε4-non carriers presented a single partially overlapping network. Following rTMS all subjects showed slight ameliorations in memory performance, regardless of APOE status. However, after rTMS APOE ε4-carriers showed significant changes in brain network activation, expressing strikingly similar spatial configuration as the one observed in the non-carrier group prior to stimulation. Similarly, activity in areas of the default-mode network (DMN) was found in a single component among the ε4-non bearers, whereas among carriers it appeared disaggregated in three distinct spatiotemporal components that changed to an integrated single component after rTMS. Our findings demonstrate that genetic background play a fundamental role in the brain responses to focal insults, conditioning expression of distinct brain networks to sustain similar cognitive performance.

Basal ganglia-cortical structural connectivity in Huntington's disease.

Huntington's disease is an incurable neurodegenerative disease caused by inheritance of an expanded cytosine-adenine-guanine (CAG) trinucleotide repeat within the Huntingtin gene. Extensive volume loss and altered diffusion metrics in the basal ganglia, cortex and white matter are seen when patients with Huntington's disease (HD) undergo structural imaging, suggesting that changes in basal ganglia-cortical structural connectivity occur. The aims of this study were to characterise altered patterns of basal ganglia-cortical structural connectivity with high anatomical precision in premanifest and early manifest HD, and to identify associations between structural connectivity and genetic or clinical markers of HD. 3-Tesla diffusion tensor magnetic resonance images were acquired from 14 early manifest HD subjects, 17 premanifest HD subjects and 18 controls. Voxel-based analyses of probabilistic tractography were used to quantify basal ganglia-cortical structural connections. Canonical variate analysis was used to demonstrate disease-associated patterns of altered connectivity and to test for associations between connectivity and genetic and clinical markers of HD; this is the first study in which such analyses have been used. Widespread changes were seen in basal ganglia-cortical structural connectivity in early manifest HD subjects; this has relevance for development of therapies targeting the striatum. Premanifest HD subjects had a pattern of connectivity more similar to that of controls, suggesting progressive change in connections over time. Associations between structural connectivity patterns and motor and cognitive markers of disease severity were present in early manifest subjects. Our data suggest the clinical phenotype in manifest HD may be at least partly a result of altered connectivity. Hum Brain Mapp 36:1728-1740, 2015. © 2015 Wiley Periodicals, Inc.

Structural Brain Connectivity in School-Age Preterm Infants Provides Evidence for Impaired Networks Relevant for Higher Order Cognitive Skills and Social Cognition.

Extreme prematurity and pregnancy conditions leading to intrauterine growth restriction (IUGR) affect thousands of newborns every year and increase their risk for poor higher order cognitive and social skills at school age. However, little is known about the brain structural basis of these disabilities. To compare the structural integrity of neural circuits between prematurely born controls and children born extreme preterm (EP) or with IUGR at school age, long-ranging and short-ranging connections were noninvasively mapped across cortical hemispheres by connection matrices derived from diffusion tensor tractography. Brain connectivity was modeled along fiber bundles connecting 83 brain regions by a weighted characterization of structural connectivity (SC). EP and IUGR subjects, when compared with controls, had decreased fractional anisotropy-weighted SC (FAw-SC) of cortico-basal ganglia-thalamo-cortical loop connections while cortico-cortical association connections showed both decreased and increased FAw-SC. FAw-SC strength of these connections was associated with poorer socio-cognitive performance in both EP and IUGR children.

Metabolic connectivity as index of verbal working memory.

Positron emission tomography (PET) data are commonly analyzed in terms of regional intensity, while covariant information is not taken into account. Here, we searched for network correlates of healthy cognitive function in resting state PET data. PET with [(18)F]-fluorodeoxyglucose and a test of verbal working memory (WM) were administered to 35 young healthy adults. Metabolic connectivity was modeled at a group level using sparse inverse covariance estimation. Among 13 WM-relevant Brodmann areas (BAs), 6 appeared to be robustly connected. Connectivity within this network was significantly stronger in subjects with above-median WM performance. In respect to regional intensity, i.e., metabolism, no difference between groups was found. The results encourage examination of covariant patterns in FDG-PET data from non-neurodegenerative populations.

Microtubule-associated protein 6 mediates neuronal connectivity through Semaphorin 3E-dependent signalling for axonal growth.

Structural microtubule associated proteins (MAPs) stabilize microtubules, a property that was thought to be essential for development, maintenance and function of neuronal circuits. However, deletion of the structural MAPs in mice does not lead to major neurodevelopment defects. Here we demonstrate a role for MAP6 in brain wiring that is independent of microtubule binding. We find that MAP6 deletion disrupts brain connectivity and is associated with a lack of post-commissural fornix fibres. MAP6 contributes to fornix development by regulating axonal elongation induced by Semaphorin 3E. We show that MAP6 acts downstream of receptor activation through a mechanism that requires a proline-rich domain distinct from its microtubule-stabilizing domains. We also show that MAP6 directly binds to SH3 domain proteins known to be involved in neurite extension and semaphorin function. We conclude that MAP6 is critical to interface guidance molecules with intracellular signalling effectors during the development of cerebral axon tracts.

Simulation-based evaluation of susceptibility distortion correction methods in diffusion MRI for connectivity analysis

Connectivity analysis on diffusion MRI data of the whole- brain suffers from distortions caused by the standard echo- planar imaging acquisition strategies. These images show characteristic geometrical deformations and signal destruction that are an important drawback limiting the success of tractography algorithms. Several retrospective correction techniques are readily available. In this work, we use a digital phantom designed for the evaluation of connectivity pipelines. We subject the phantom to a âeurooetheoretically correctâeuro and plausible deformation that resembles the artifact under investigation. We correct data back, with three standard methodologies (namely fieldmap-based, reversed encoding-based, and registration- based). Finally, we rank the methods based on their geometrical accuracy, the dropout compensation, and their impact on the resulting connectivity matrices.

High connectivity in a long-lived High-Arctic seabird, the ivory gull Pagophila eburnea

Species may cope with rapid habitat changes by distribution shifts or adaptation to new conditions. A common feature of these responses is that they depend on how the process of dispersal connects populations, both demographically and genetically. We analyzed the genetic structure of a near-threatened high-Arctic seabird, the ivory gull (Pagophila eburnea) in order to infer the connectivity among gull colonies. We analyzed 343 individuals sampled from 16 localities across the circumpolar breeding range of ivory gulls, from northern Russia to the Canadian Arctic. To explore the roles of natal and breeding dispersal, we developed a population genetic model to relate dispersal behavior to the observed genetic structure of worldwide ivory gull populations. Our key finding is the striking genetic homogeneity of ivory gulls across their entire distribution range. The lack of population genetic structure found among colonies, in tandem with independent evidence of movement among colonies, suggests that ongoing effective dispersal is occurring across the Arctic Region. Our results contradict the dispersal patterns generally observed in seabirds where species movement capabilities are often not indicative of dispersal patterns. Model predictions show how natal and breeding dispersal may combine to shape the genetic homogeneity among ivory gull colonies separated by up to 2800 km. Although field data will be key to determine the role of dispersal for the demography of local colonies and refine the respective impacts of natal versus breeding dispersal, conservation planning needs to consider ivory gulls as a genetically homogeneous, Arctic-wide metapopulation effectively connected through dispersal.

Connectivity and tissue microstructural alterations in right and left temporal lobe epilepsy revealed by diffusion spectrum imaging.

Focal epilepsy is increasingly recognized as the result of an altered brain network, both on the structural and functional levels and the characterization of these widespread brain alterations is crucial for our understanding of the clinical manifestation of seizure and cognitive deficits as well as for the management of candidates to epilepsy surgery. Tractography based on Diffusion Tensor Imaging allows non-invasive mapping of white matter tracts in vivo. Recently, diffusion spectrum imaging (DSI), based on an increased number of diffusion directions and intensities, has improved the sensitivity of tractography, notably with respect to the problem of fiber crossing and recent developments allow acquisition times compatible with clinical application. We used DSI and parcellation of the gray matter in regions of interest to build whole-brain connectivity matrices describing the mutual connections between cortical and subcortical regions in patients with focal epilepsy and healthy controls. In addition, the high angular and radial resolution of DSI allowed us to evaluate also some of the biophysical compartment models, to better understand the cause of the changes in diffusion anisotropy. Global connectivity, hub architecture and regional connectivity patterns were altered in TLE patients and showed different characteristics in RTLE vs LTLE with stronger abnormalities in RTLE. The microstructural analysis suggested that disturbed axonal density contributed more than fiber orientation to the connectivity changes affecting the temporal lobes whereas fiber orientation changes were more involved in extratemporal lobe changes. Our study provides further structural evidence that RTLE and LTLE are not symmetrical entities and DSI-based imaging could help investigate the microstructural correlate of these imaging abnormalities.

Redox dysregulation in schizophrenia : effect on myelination of cortical structures and connectivity

Cette thèse traite du rôle qu'un facteur de risque génétique développé chez les patients souffrant de schizophrénie, à savoir un déficit de la synthèse du glutathion, peut jouer dans les anomalies de la connectivité cérébrale trouvées chez ces patients. L'essentiel du travail a été consacré à évaluer la structure de la substance blanche dans l'ensemble du cerveau chez un modèle animal par une méthode similaire à celle utilisée en recherche clinique avec l'imagerie par résonance magnétique (IRM). Cette approche de translation inverse chez la souris knock-out de glutamate-cystéine ligase modulateur sous-unité (Gclm KO), avait l'objectif d'étudier l'effet des défenses redox déficientes sur le développement des connexions cérébrales, tout en excluant celui des facteurs non liés au génotype. Après avoir établi le protocole de recherche, l'influence d'une manipulation environnementale a également été étudiée. Pour effectuer une analyse statistique fiable des données d'IRM obtenues, nous .avons d'abord créé un atlas du cerveau de la souris afin de l'utiliser comme modèle pour une segmentation précise des différentes régions du cerveau sur les images IRM obtenues in vivo. Les données provenant de chaque région d'intérêt ont ensuite été étudiées séparément. La qualité de cette méthode a été évaluée dans une expérience de simulation pour déduire la puissance statistique réalisable dans chaque région en fonction du nombre d'animaux utilisés. Ces outils d'analyse nous ont permis d'évaluer l'intégrité de la substance blanche dans le cerveau des souris durant le développement grâce à une expérience longitudinale, en utilisant l'imagerie du tenseur de diffusion (DTI). Nous avons ainsi observé des anomalies dans les paramètres dérivés du tenseur (diffusivité et anisotropie) dans la Commissure Antérieure et le Fimbria/Fornix des souris Gclm KO, par rapport aux animaux contrôles. Ces résultats suggèrent une substance blanche endommagée dans ces régions. Dans une expérience électrophysiologique, Pascal Steullet a montré que ces anomalies ont des conséquences fonctionnelles caractérisées par une réduction de la vitesse de conduction dans les fibres nerveuses. Ces données renforcent les conclusions des analyses d'imagerie. Le mécanisme par lequel une dérégulation redox affecte la structure de la substance blanche reste encore à définir, car une analyse immunohistochimique des protéines constituantes de la couche de myéline des fibres concernées n'a pas donné de résultats concluants. Nous avons également constaté un élargissement des ventricules dans les jeunes souris Gclm KO, mais pas chez les adultes et des anomalies neurochimiques déjà connues chez ces animaux (Duarte et al. 2011), à savoir une réduction du Glutathion et une augmentation de l'acide N-acétylaspartique, de l'Alanine et du ratio Glutamine/Glutamate. Nous avons ensuite testé l'effet d'un stress environnemental supplémentaire, l'élevage en isolement social, sur le phénotype. Ce stress n'a eu aucun effet sur la structure de la substance blanche évaluée par DTI, mais a réduit la concentration de myo-Inositol et augmenté le ratio de Glutamine/Glutamate dans le cortex frontal. Nous avons aussi reproduit dans ce groupe indépendant d'animaux les effets du génotype sur le profil neurochimique, sur la taille des ventricules et aussi sur les paramètres dérivés du tenseur de diffusion dans le Fimbria/Fornix, mais pas dans la Commissure Antérieure. Nos résultats montrent qu'une dérégulation redox d'origine génétique perturbe la structure et la fonction de la substance blanche dans des régions spécifiques, causant ainsi l'élargissement des ventricules. Ces phénotypes rassemblent certaines caractéristiques neuro-anatomiques de la schizophrénie, mais les mécanismes qui en sont responsables demeurent encore inconnus. L'isolement social n'a pas d'effet sur la structure de la substance blanche évaluée par DTI, alors qu'il est prouvé qu'il affecte la maturation des oligodendrocytes. La neurochimie corticale et en particulier le rapport Glutamine/Glutamate a été affecté par le dérèglement redox ainsi que par l'isolement social. En conséquence, ce ratio représente un indice prometteur dans la recherche sur l'interaction du stress environnemental avec le déséquilibre redox dans le domaine de la schizophrénie. -- The present doctoral thesis is concerned with the role that a genetic risk factor for the development of schizophrenia, namely a deficit in Glutathione synthesis, may play in the anomalies of brain connectivity found in patients. Most of the effort was devoted to perform a whole-brain assessment of white matter structure in the Glutamate-Cysteine ligase modulatory knockout mouse model (Gclm KO) using Magnetic Resonance Imaging (MRI) techniques similar to those used in state-of-the-art clinical research. Such reverse translational approach taking brain imaging from the bedside to the bench aimed to investigate the role that deficient redox defenses may play in the development of brain connections while excluding all influencing factors beside the genotype. After establishing the protocol, the influence of further environmental manipulations was also studied. Analysis of MRI images acquired in vivo was one of the main challenges of the project. Our strategy consisted in creating an atlas of the mouse brain to use as segmentation guide and then analyze the data from each region of interest separately. The quality of the method was assessed in a simulation experiment by calculating the statistical power achievable in each brain region at different sample sizes. This analysis tool enabled us to assess white matter integrity in the mouse brain along development in a longitudinal experiment using Diffusion Tensor Imaging (DTI). We discovered anomalies in diffusivity parameters derived from the tensor in the Anterior Commissure and Fimbria/Fornix of Gclm KO mice when compared to wild-type animals, which suggest that the structure of these tracts is compromised in the KO mice. In an elegant electrophysiological experiment, Pascal Steullet has provided evidence that these anomalies have functional consequences in form of reduced conduction velocity in the concerned tracts, thus supporting the DTI findings. The mechanism by which redox dysregulation affects WM structure remains unknown, for the immunohistochemical analysis of myelin constituent proteins in the concerned tracts produced inconclusive results. Our experiments also detected an enlargement of the lateral ventricles in young but not adult Gclm KO mice and confirmed neurochemical anomalies already known to affect this animals (Duarte et al. 2011), namely a reduction in Glutathione and an increase in Glutamine/Glutamate ratio, N-acetylaspartate and Alanine. Using the same methods, we tested the effect of an additional environmental stress on the observed phenotype: rearing in social isolation had no effect on white matter structure as assessed by DTI, but it reduced the concentration of myo-Inositol and increased the Glutamine/Glutamate ratio in the frontal cortex. We could also replicate in this separate group of animals the effects of genotype on the frontal neurochemical profile, ventricular size and diffusivity parameters in the Fimbria/Fornix but not in the Anterior Commissure. Our data show that a redox dysregulation of genetic origin may disrupt white matter structure and function in specific tracts and cause a ventricular enlargement, phenotypes that resemble some neuroanatomical features of schizophrenia. The mechanism responsible remains however unknown. We have also demonstrated that environmental stress in form of social isolation does not affect white matter structure as assessed by DTI even though it is known to affect oligodendrocyte maturation. Cortical neurochemistry, and specifically the Glutamine to Glutamate balance was affected both by redox dysregulation and social isolation, and is thus a good target for further research on the interaction of redox imbalance and environmental stress in schizophrenia.