Magnetic resonance imaging (MRI) has transformed the world of non-invasive imaging for diagnostic purposes. Modern techniques such as diffusion weighted imaging (DWI), diffusion tensor imaging (DTI), and diffusion spectrum imaging (DSI) have been used to reconstruct fiber pathways of the brain - providing a graphical picture of the so-called "connectome." However, there exists controversy in the literature as to the accuracy of the diffusion tractography reconstruction. Although various attempts at histological validation been attempted, there is still no 3D histological pathway validation of the fiber bundle trajectories seen in diffusion MRI. Such a validation is necessary in order to show the viability of current DSI tractography techniques in the ultimate goal for clinical diagnostic application. This project developed methods to provide this 3D histological validation using the rhesus monkey motor pathway as a model system. By injecting biotinylated dextran amine (BDA) tract tracer into the hand area of primary motor cortex, brain section images were reconstructed to create 3D fiber pathways labeled at the axonal level. Using serial coronal brain sections, the BDA label was digitized with a high resolution digital camera to create image montages of the fiber pathway with individual sections spaced at 1200 micron intervals through the brain. An MRI analysis system, OSIRX, was then used to reconstruct these sections into a 3D volume. This is an important technical step toward merging the BDA fiber tract histology with diffusion MRI tractography of the same brain, enabling identification of the valid and inaccurate aspects of diffusion fiber reconstruction. This will ultimately facilitate the use of diffusion MRI to quantify tractography, non-invasively and in vivo, in the human brain.

Cette thèse est consacrée à l'élaboration de nouvelles méthodes d'acquisition et de traitement de données en IRM de diffusion (IRMd) afin de caractériser la diffusion des molécules d'eau dans les fibres de matière blanche à l'échelle d'un voxel. Plus particulièrement, nous travaillons sur un moyen de reconstruction précis de l'Ensemble Average Propagator (EAP), qui représente la fonction de probabilité de diffusion des molécules d'eau. Plusieurs modèles de diffusion tels que le tenseur de diffusion ou la fonction de distribution d'orientation sont très utilisés dans la communauté de l'IRMd afin de quantifier la diffusion des molécules d'eau dans le cerveau. Ces modèles sont des représentations partielles de l'EAP et ont été développés en raison du petit nombre de mesures nécessaires à leurs estimations. Cependant, il est important de pouvoir reconstruire précisément l'EAP afin d'acquérir une meilleure compréhension des mécanismes du cerveau et d'améliorer le diagnostique des troubles neurologiques. Une estimation correcte de l'EAP nécessite l'acquisition de nombreuses images de diffusion sensibilisées à des orientations différentes dans le q-space. Ceci rend son estimation trop longue pour être utilisée dans la plupart des scanners cliniques. Dans cette thèse, nous utilisons des techniques de reconstruction parcimonieuses et en particulier la technique connue sous le nom de Compressive Sensing (CS) afin d’accélérer le calcul de l'EAP. Les multiples aspects de la théorie du CS et de son application à l'IRMd sont présentés dans cette thèse. / This thesis is dedicated to the development of new acquisition and processing methods in diffusion MRI (dMRI) to characterize the diffusion of water molecules in white matter fiber bundles at the scale of a voxel. In particular, we focus our attention on the accurate recovery of the Ensemble Average Propagator (EAP), which represents the full 3D displacement of water molecule diffusion. Diffusion models such that the Diffusion Tensor or the Orientation Distribution Function (ODF) are largely used in the dMRI community in order to quantify water molecule diffusion. These models are partial EAP representations and have been developed due to the small number of measurement required for their estimations. It is thus of utmost importance to be able to accurately compute the EAP and order to acquire a better understanding of the brain mechanisms and to improve the diagnosis of neurological disorders. Estimating the full 3D EAP requires the acquisition of many diffusion images sensitized todifferent orientations in the q-space, which render the estimation of the EAP impossible in most of the clinical dMRI scanner. A surge of interest has been seen in order to decrease this time for acquisition. Some works focus on the development of new and efficient acquisition sequences. In this thesis, we use sparse coding techniques, and in particular Compressive Sensing (CS) to accelerate the computation of the EAP. Multiple aspects of the CS theory and its application to dMRI are presented in this thesis.