Analyse de l'architecture de la matière blanche et projection de mesures sur la surface corticale

L'étude de l'architecture et de la connectivité structurelle du cerveau est possible grâce à l'imagerie par résonance magnétique de diffusion (IRMd). Ce type d’image, similaire à un champ vectoriel tridimensionnel, combiné à un algorithme nommé tractographie, permet d’inférer la distribution des fibres de matière blanche et ainsi de reconstruire la structure locale du tissu. Or, cette méthode demeure limitée par une basse résolution et un faible rapport signal sur bruit. Afin de contourner ces limitations, des modèles géométriques construits à partir d’aprioris anatomiques sont utilisés. Cette thèse montre que des règles et des contraintes basées sur la modélisation corticale peuvent être intégrées à la tractographie par le biais d’équations de géométrie différentielle. En effet, la structure axonale sous-jacente à la matière grise peut être approximée avec l'utilisation de la surface et d'un flot de courbure moyenne. Pondéré par l’information de densité, ce flot permet d’obtenir une meilleure représentation des projections des fibres de matière blanche sous le cortex. D'ailleurs, le fait d’incorporer la surface corticale, obtenue d’une image anatomique haute résolution, à l’IRMd permet d'augmenter la précision de la tractographie. Puisque l'acquisition d'une image anatomique (pondération T1) est toujours faite lors d'une IRMd, la combinaison des deux est une façon simple et peu coûteuse d'améliorer cette technique de reconstruction. Par ailleurs, discrétiser les surfaces corticales à l'aide de maillages, plutôt qu’avec des masques voxeliques, permet non seulement d'augmenter la précision de l'interface, mais d'intégrer facilement de nouveaux aprioris et de mieux choisir la répartition des positions initiales. L'ajout d'aprioris et de modèles géométriques permet de mieux modéliser près du cortex et ainsi connecter jusqu'aux surfaces corticales. Cette connexion rend possible la projection de mesures de la matière blanche le long du cortex, un domaine également utilisé pour plusieurs analyses anatomiques (ex. épaisseur corticale), magnéto-/électro-encéphalographie (MEG/EEG) et IRM fonctionnelle (IRMf). L'intégration de ces surfaces corticales à la tractographie a un impact important pour les recherches multimodales sur la connectivité cérébrale

Statistical analysis for longitudinal MR imaging of dementia

Serial Magnetic Resonance (MR) Imaging can reveal structural atrophy in the brains of subjects with neurodegenerative diseases such as Alzheimer’s Disease (AD). Methods of computational neuroanatomy allow the detection of statistically significant patterns of brain change over time and/or over multiple subjects. The focus of this thesis is the development and application of statistical and supporting methodology for the analysis of three-dimensional brain imaging data. There is a particular emphasis on longitudinal data, though much of the statistical methodology is more general. New methods of voxel-based morphometry (VBM) are developed for serial MR data, employing combinations of tissue segmentation and longitudinal non-rigid registration. The methods are evaluated using novel quantitative metrics based on simulated data. Contributions to general aspects of VBM are also made, and include a publication concerning guidelines for reporting VBM studies, and another examining an issue in the selection of which voxels to include in the statistical analysis mask for VBM of atrophic conditions. Research is carried out into the statistical theory of permutation testing for application to multivariate general linear models, and is then used to build software for the analysis of multivariate deformation- and tensor-based morphometry data, efficiently correcting for the multiple comparison problem inherent in voxel-wise analysis of images. Monte Carlo simulation studies extend results available in the literature regarding the different strategies available for permutation testing in the presence of confounds. Theoretical aspects of longitudinal deformation- and tensor-based morphometry are explored, such as the options for combining within- and between-subject deformation fields. Practical investigation of several different methods and variants is performed for a longitudinal AD study

Proceedings of the Second International Workshop on Mathematical Foundations of Computational Anatomy (MFCA'08) - Geometrical and Statistical Methods for Modelling Biological Shape Variability

International audienceThe goal of computational anatomy is to analyze and to statistically model the anatomy of organs in different subjects. Computational anatomic methods are generally based on the extraction of anatomical features or manifolds which are then statistically analyzed, often through a non-linear registration. There are nowadays a growing number of methods that can faithfully deal with the underlying biomechanical behavior of intra-subject deformations. However, it is more difficult to relate the anatomies of different subjects. In the absence of any justified physical model, diffeomorphisms provide a general mathematical framework that enforce topological consistency. Working with such infinite dimensional space raises some deep computational and mathematical problems, in particular for doing statistics. Likewise, modeling the variability of surfaces leads to rely on shape spaces that are much more complex than for curves. To cope with these, different methodological and computational frameworks have been proposed (e.g. smooth left-invariant metrics, focus on well-behaved subspaces of diffeomorphisms, modeling surfaces using courants, etc.) The goal of the Mathematical Foundations of Computational Anatomy (MFCA) workshop is to foster the interactions between the mathematical community around shapes and the MICCAI community around computational anatomy applications. It targets more particularly researchers investigating the combination of statistical and geometrical aspects in the modeling of the variability of biological shapes. The workshop aims at being a forum for the exchange of the theoretical ideas and a source of inspiration for new methodological developments in computational anatomy. A special emphasis is put on theoretical developments, applications and results being welcomed as illustrations. Following the very successful first edition of this workshop in 2006 (see http://www.inria.fr/sophia/asclepios/events/MFCA06/), the second edition was held in New-York on September 6, in conjunction with MICCAI 2008. Contributions were solicited in Riemannian and group theoretical methods, Geometric measurements of the anatomy, Advanced statistics on deformations and shapes, Metrics for computational anatomy, Statistics of surfaces. 34 submissions were received, among which 9 were accepted to MICCAI and had to be withdrawn from the workshop. Each of the remaining 25 paper was reviewed by three members of the program committee. To guaranty a high level program, 16 papers only were selected

Proceedings of the Third International Workshop on Mathematical Foundations of Computational Anatomy - Geometrical and Statistical Methods for Modelling Biological Shape Variability

International audienceComputational anatomy is an emerging discipline at the interface of geometry, statistics and image analysis which aims at modeling and analyzing the biological shape of tissues and organs. The goal is to estimate representative organ anatomies across diseases, populations, species or ages, to model the organ development across time (growth or aging), to establish their variability, and to correlate this variability information with other functional, genetic or structural information. The Mathematical Foundations of Computational Anatomy (MFCA) workshop aims at fostering the interactions between the mathematical community around shapes and the MICCAI community in view of computational anatomy applications. It targets more particularly researchers investigating the combination of statistical and geometrical aspects in the modeling of the variability of biological shapes. The workshop is a forum for the exchange of the theoretical ideas and aims at being a source of inspiration for new methodological developments in computational anatomy. A special emphasis is put on theoretical developments, applications and results being welcomed as illustrations. Following the successful rst edition of this workshop in 20061 and second edition in New-York in 20082, the third edition was held in Toronto on September 22 20113. Contributions were solicited in Riemannian and group theoretical methods, geometric measurements of the anatomy, advanced statistics on deformations and shapes, metrics for computational anatomy, statistics of surfaces, modeling of growth and longitudinal shape changes. 22 submissions were reviewed by three members of the program committee. To guaranty a high level program, 11 papers only were selected for oral presentation in 4 sessions. Two of these sessions regroups classical themes of the workshop: statistics on manifolds and diff eomorphisms for surface or longitudinal registration. One session gathers papers exploring new mathematical structures beyond Riemannian geometry while the last oral session deals with the emerging theme of statistics on graphs and trees. Finally, a poster session of 5 papers addresses more application oriented works on computational anatomy