Statistical models to learn the structural organisation of neural circuits from multimodal brain images - Application to Gilles de la Tourette syndrome

Pietro Gori 1
1 ARAMIS - Algorithms, models and methods for images and signals of the human brain
Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6, ICM - Institut du Cerveau et de la Moëlle Epinière = Brain and Spine Institute
Abstract : In this Thesis, we propose a statistical framework to analyse morphological and organisational anomalies altering the anatomy of the neural circuits of the brain in neurodevelopmental disorders. We evaluate it on a disease model about Gilles de la Tourette syndrome (GTS). Every circuit is composed of white matter projections and grey matter structures which are all virtually represented as 3D meshes. All components of the neural circuits are then integrated into a single complex. This makes possible to study their organisation, namely their relative position, and in particular the structural connectivity (i.e. the areas of the grey matter structures integrated by white matter fibers). Moreover, the use of meshes facilitates the visualisation of the circuits and the interpretation of their pathological alterations. The proposed methodology is based on a generative model. Given a population, the neural circuits of each subject are modelled as a deformed template complex plus a residuals noise. The template complex captures the common morphological characteristics within the population and it can be thought as an average. The deformations, usually defined as diffeomorphisms of the entire ambient space, model instead the morphological variability of the population. The joint estimate of the template complex and deformations is called atlas construction. In the first part of this Thesis, we propose a Bayesian framework to embed the aforementioned generative model. It is general and it can be applied to any parametric deformation framework and to all shape models with which is possible to define probability density functions. Using this framework, we can automatically estimate important balancing parameters which were fixed by the user in previous methods not based on a statistical setting, namely the trade-off between data-terms and deformation regularity. Moreover, it is also possible to estimate from the data a well-conditioned covariance matrix of the deformation parameters which can be directly employed in statistical analysis such as Principal Component Analysis. Furthermore, we propose to model both curve and surface meshes as Gaussian random varifolds for which we define finite-dimensional approximation spaces where it is possible to define probability density functions. This computational model does not need point-correspondences and it has a closed-form metric easily derivable. In the second part, we define a computational model for white matter fiber bundles called weighted currents. Similarly to currents, it does not need point correspondences or fiber correspondences and it augments its definition taking into consideration not only the pathway of the fibers but also the locations of their extremities. This makes thus possible to correctly register also the extremities of the bundles in the template-to-subjects deformations and not only the most dense parts of the bundles as in currents. This is fundamental to retrieve the variations in structural connectivity. Moreover, we also propose an approximation scheme for fiber bundles based on the framework of weighted currents. It results in a parsimonious representation which preserves both the shape and the structural connectivity of the original bundles. It facilitates the visualisation and interpretation and it makes it computationally possible to consider at the same time multiple fiber bundles and grey matter structures in an atlas construction. In the last part, we describe a new deformation scheme based on a cascade of two diffeomorphisms. It allows us to locate variations in structural connectivity and at the same time to capture global anatomical changes. This was not possible with previous single-diffeomorphic deformations. The proposed deformation setting is integrated into the Bayesian atlas construction previously presented. We show its effectiveness by comparing the cortico-putamen circuits of a group of GTS patients with the ones of a group of controls. Preliminary results highlight differences about both the shape of the grey matter structures and the structural connectivity. Moreover, we also show that the proposed approach leads to better classification scores than a single diffeomorphic method. This suggests that it might better characterise the anatomical alterations associated to GTS and therefore also improve our understanding of the pathophysiological mechanisms underlying this syndrome.
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Pietro Gori. Statistical models to learn the structural organisation of neural circuits from multimodal brain images - Application to Gilles de la Tourette syndrome. Medical Imaging. UPMC - Université Paris 6 Pierre et Marie Curie, 2016. English. ⟨tel-01352477⟩

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