Spherical deconvolution of multichannel diffusion MRI data with non-Gaussian noise models and spatial regularization

Spherical deconvolution (SD) methods are widely used to estimate the intra-voxel white-matter fiber orientations from diffusion MRI data. However, while some of these methods assume a zero-mean Gaussian distribution for the underlying noise, its real distribution is known to be non-Gaussian and to depend on the methodology used to combine multichannel signals. Indeed, the two prevailing methods for multichannel signal combination lead to Rician and noncentral Chi noise distributions. Here we develop a Robust and Unbiased Model-BAsed Spherical Deconvolution (RUMBA-SD) technique, intended to deal with realistic MRI noise, based on a Richardson-Lucy (RL) algorithm adapted to Rician and noncentral Chi likelihood models. To quantify the benefits of using proper noise models, RUMBA-SD was compared with dRL-SD, a well-established method based on the RL algorithm for Gaussian noise. Another aim of the study was to quantify the impact of including a total variation (TV) spatial regularization term in the estimation framework. To do this, we developed TV spatially-regularized versions of both RUMBA-SD and dRL-SD algorithms. The evaluation was performed by comparing various quality metrics on 132 three-dimensional synthetic phantoms involving different inter-fiber angles and volume fractions, which were contaminated with noise mimicking patterns generated by data processing in multichannel scanners. The results demonstrate that the inclusion of proper likelihood models leads to an increased ability to resolve fiber crossings with smaller inter-fiber angles and to better detect non-dominant fibers. The inclusion of TV regularization dramatically improved the resolution power of both techniques. The above findings were also verified in brain data

Doctor of Philosophy

dissertationDiffusion magnetic resonance imaging (dMRI) has become a popular technique to detect brain white matter structure. However, imaging noise, imaging artifacts, and modeling techniques, etc., create many uncertainties, which may generate misleading information for further analysis or applications, such as surgical planning. Therefore, how to analyze, effectively visualize, and reduce these uncertainties become very important research questions. In this dissertation, we present both rank-k decomposition and direct decomposition approaches based on spherical deconvolution to decompose the fiber directions more accurately for high angular resolution diffusion imaging (HARDI) data, which will reduce the uncertainties of the fiber directions. By applying volume rendering techniques to an ensemble of 3D orientation distribution function (ODF) glyphs, which we call SIP functions of diffusion shapes, one can elucidate the complex heteroscedastic structural variation in these local diffusion shapes. Furthermore, we quantify the extent of this variation by measuring the fraction of the volume of these shapes, which is consistent across all noise levels, the certain volume ratio. To better understand the uncertainties in white matter fiber tracks, we propose three metrics to quantify the differences between the results of diffusion tensor magnetic resonance imaging (DT-MRI) fiber tracking algorithms: the area between corresponding fibers of each bundle, the Earth Mover's Distance (EMD) between two fiber bundle volumes, and the current distance between two fiber bundle volumes. Based on these metrics, we discuss an interactive fiber track comparison visualization toolkit we have developed to visualize these uncertainties more efficiently. Physical phantoms, with high repeatability and reproducibility, are also designed with the hope of validating the dMRI techniques. In summary, this dissertation provides a better understanding about uncertainties in diffusion magnetic resonance imaging: where and how much are the uncertainties? How do we reduce these uncertainties? How can we possibly validate our algorithms

Compendio de métodos para caracterizar la geometría de los tejidos cerebrales a partir de imágenes de resonancia magnética por difusión del agua.

221 p.FIDMAG Hermanas Hospitalarias Research Foundation; CIBERSAM:Centro de Investigación Biomédica en Re

Normal Modes of the Structural Connectome

Division of the human cortex into distinct regions is of high importance to neuroscientific inquiry. Fully-automated, multi-modal schemes of achieving such parcellation on an individual subject basis are particularly advantageous, however difficulties in inter-modal and inter-subject registration of brain images, as well as obstacles in preserving group-level correspondence of individual parcellation maps have slowed progress in this area. In parallel, there exists a relative dearth of data-driven parcellation schemes that incorporate high resolution structural connectivity metrics; the majority of widely-accepted parcellation maps in the literature have primarily used functional connectivity. Here, a fully data-driven, automated routine based on structural geometry and connectivity which achieves subject-specific cortical parcellation maps while maintaining group-level correspondence of maps is presented and optimized. Using high resolution white matter surface meshes and advanced fiber tracking techniques, a novel vertex-wise structural connectivity graph is constructed for each of 10 unrelated subjects, and the first k eigenvectors of the Laplacian Matrix of the graph's adjacency matrix are calculated. These eigenvectors represent the steady-state modes of vibration of the manifold described by this graph, and thus provide subject-specific maps of modes of connectivity in white matter. In order to obtain parcellations at varying levels of coarseness of the cortex from these eigenvectors, hierarchical agglomerative clustering is then performed on the surface mesh, where each vertex's feature vector is its profile in spectral space. Further, a multi-layer graph of all subjects is constructed, and individual parcellations with group level correspondence are obtained by agglomerative clustering of the eigenvectors of the laplacian matrix of the multi-layer graph.Bachelor of Scienc

Anisotropy Across Fields and Scales

This open access book focuses on processing, modeling, and visualization of anisotropy information, which are often addressed by employing sophisticated mathematical constructs such as tensors and other higher-order descriptors. It also discusses adaptations of such constructs to problems encountered in seemingly dissimilar areas of medical imaging, physical sciences, and engineering. Featuring original research contributions as well as insightful reviews for scientists interested in handling anisotropy information, it covers topics such as pertinent geometric and algebraic properties of tensors and tensor fields, challenges faced in processing and visualizing different types of data, statistical techniques for data processing, and specific applications like mapping white-matter fiber tracts in the brain. The book helps readers grasp the current challenges in the field and provides information on the techniques devised to address them. Further, it facilitates the transfer of knowledge between different disciplines in order to advance the research frontiers in these areas. This multidisciplinary book presents, in part, the outcomes of the seventh in a series of Dagstuhl seminars devoted to visualization and processing of tensor fields and higher-order descriptors, which was held in Dagstuhl, Germany, on October 28–November 2, 2018

Anisotropy Across Fields and Scales

This open access book focuses on processing, modeling, and visualization of anisotropy information, which are often addressed by employing sophisticated mathematical constructs such as tensors and other higher-order descriptors. It also discusses adaptations of such constructs to problems encountered in seemingly dissimilar areas of medical imaging, physical sciences, and engineering. Featuring original research contributions as well as insightful reviews for scientists interested in handling anisotropy information, it covers topics such as pertinent geometric and algebraic properties of tensors and tensor fields, challenges faced in processing and visualizing different types of data, statistical techniques for data processing, and specific applications like mapping white-matter fiber tracts in the brain. The book helps readers grasp the current challenges in the field and provides information on the techniques devised to address them. Further, it facilitates the transfer of knowledge between different disciplines in order to advance the research frontiers in these areas. This multidisciplinary book presents, in part, the outcomes of the seventh in a series of Dagstuhl seminars devoted to visualization and processing of tensor fields and higher-order descriptors, which was held in Dagstuhl, Germany, on October 28–November 2, 2018

Modélisation locale en imagerie par résonance magnétique de diffusion : de l'acquisition comprimée au connectome

L’imagerie par résonance magnétique pondérée en diffusion est une modalité d’imagerie médicale non invasive qui permet de mesurer les déplacements microscopiques des molécules d’eau dans les tissus biologiques. Il est possible d’utiliser cette information pour inférer la structure du cerveau. Les techniques de modélisation locale de la diffusion permettent de calculer l’orientation et la géométrie des tissus de la matière blanche. Cette thèse s’intéresse à l’optimisation des métaparamètres utilisés par les modèles locaux. Nous dérivons des paramètres optimaux qui améliorent la qualité des métriques de diffusion locale, de la tractographie de la matière blanche et de la connectivité globale. L’échantillonnage de l’espace-q est un des paramètres principaux qui limitent les types de modèle et d’inférence applicable sur des données acquises en clinique. Dans cette thèse, nous développons une technique d’échantillonnage de l’espace-q permettant d’utiliser l’acquisition comprimée pour réduire le temps d’acquisition nécessaire

Generation of realistic white matter substrates with controllable morphology for diffusion MRI simulations

Numerical phantoms have played a key role in the development of diffusion MRI (dMRI) techniques seeking to estimate features of the microscopic structure of tissue by providing a ground truth for simulation experiments against which we can validate and compare techniques. One common limitation of numerical phantoms which represent white matter (WM) is that they oversimplify the true complex morphology of the tissue which has been revealed through ex vivo studies. It is important to try to generate WM numerical phantoms that capture this realistic complexity in order to understand how it impacts the dMRI signal. This thesis presents work towards improving the realism of WM numerical phantoms by generating fibres mimicking natural fibre genesis. A novel phantom generator is presented which was developed over two works, resulting in Contextual Fibre Growth (ConFiG). ConFiG grows fibres one-by-one, following simple rules motivated by real axonal guidance mechanisms. These simple rules enable ConFiG to generate phantoms with tuneable microstructural features by growing fibres while attempting to meet morphological targets such as user-specified density and orientation distribution. We compare ConFiG to the state-of-the-art approach based on packing fibres together by generating phantoms in a range of fibre configurations including crossing fibre bundles and orientation dispersion. Results demonstrate that ConFiG produces phantoms with up to 20% higher densities than the state-of-the-art, particularly in complex configurations with crossing fibres. We additionally show that the microstructural morphology of ConFiG phantoms is comparable to real tissue, producing diameter and orientation distributions close to electron microscopy estimates from real tissue as well as capturing complex fibre cross sections. ConFiG is applied to investigate the intra-axonal diffusivity and probe assumptions in a family of dMRI modelling techniques based on spherical deconvolution (SD), demonstrating that the microscopic variations in fibres’ shapes affects the diffusion within axons. This leads to variations in the per-fibre signal contrary to the assumptions inherent in SD which may have a knock-on effect in popular techniques such as tractography

Reconstruction de l'activité corticale à partir de données MEG à l'aide de réseaux cérébraux et de délais de transmission estimés à partir d'IRMd

White matter fibers transfer information between brain regions with delays that are observable with magnetoencephalography and electroencephalography (M/EEG) due to their millisecond temporal resolution. We can represent the brain as a graph where nodes are the cortical sources or areas and edges are the physical connections between them: either local (between adjacent vertices on the cortical mesh) or non-local (long-range white matter fibers). Long-range anatomical connections can be obtained with diffusion MRI (dMRI) tractography which yields a set of streamlines representing white matter fiber bundles. Given the streamlines’ lengths and the information conduction speed, transmission delays can be estimated for each connection. dMRI can thus give an insight into interaction delays of the macroscopicbrain network.Localizing and recovering electrical activity of the brain from M/EEG measurements is known as the M/EEG inverse problem. Generally, there are more unknowns (brain sources) than the number of sensors, so the solution is non-unique and the problem ill-posed. To obtain a unique solution, prior constraints on the characteristics of source distributions are needed. Traditional linear inverse methods deploy different constraints which can favour solutions with minimum norm, impose smoothness constraints in space and/or time along the cortical surface, etc. Yet, structural connectivity is rarely considered and transmission delays almost always neglected.The first contribution of this thesis consists of a multimodal preprocessing pipeline used to integrate structural MRI, dMRI and MEG data into a same framework, and of a simulation procedure of source-level brain activity that was used as a synthetic dataset to validate the proposed reconstruction approaches.In the second contribution, we proposed a new framework to solve the M/EEG inverse problem called Connectivity-Informed M/EEG Inverse Problem (CIMIP), where prior transmission delays supported by dMRI were included to enforce temporal smoothness between time courses of connected sources. This was done by incorporating a Laplacian operator into the regularization, that operates on a time-dependent connectivity graph. Nonetheless, some limitations of the CIMIP approach arised, mainly due to the nature of the Laplacian, which acts on the whole graph, favours smooth solutions across all connections, for all delays, and it is agnostic to directionality.In this thesis, we aimed to investigate patterns of brain activity during visuomotor tasks, during which only a few regions typically get significantly activated, as shown by previous studies. This led us to our third contribution, an extension of the CIMIP approach that addresses the aforementioned limitations, named CIMIP_OML (“Optimal Masked Laplacian”). We restricted the full source space network (the whole cortical mesh) to a network of regions of interest and tried to find how the information is transferred between its nodes. To describe the interactions between nodes in a directed graph, we used the concept of network motifs. We proposed an algorithm that (1) searches for an optimal network motif – an optimal pattern of interaction between different regions and (2) reconstructs source activity given the found motif. Promising results are shown for both simulated and real MEG data for a visuomotor task and compared with 3 different state-of-the-art reconstruction methods.To conclude, we tackled a difficult problem of exploiting delays supported by dMRI for the reconstruction of brain activity, while also considering the directionality in the information transfer, and provided new insights into the complex patterns of brain activity.Les fibres de la matière blanche permettent le transfert d’information dans le cerveau avec des délais observables en Magnétoencéphalographie et Électroencéphalographie (M/EEG) grâce à leur haute résolution temporelle. Le cerveau peut être représenté comme un graphe où les nœuds sont les régions corticales et les liens sont les connexions physiques entre celles-ci: soit locales (entre sommets adjacents sur le maillage cortical), soit non locales (fibres de la matière blanche). Les connexions non-locales peuvent être reconstruites avec la tractographie de l’IRM de diffusion (IRMd) qui génère un ensemble de courbes («streamlines») représentant des fibres de la matière blanche. Sachant les longueurs des fibres et la vitesse de conduction de l’information, les délais de transmission peuvent être estimés. L’IRMd peut donc donner un aperçu des délais d’interaction du réseau cérébral macroscopique.La localisation et la reconstruction de l’activité électrique cérébrale à partir des mesures M/EEG est un problème inverse. En général, il y a plus d’inconnues (sources cérébrales) que de capteurs. La solution n’est donc pas unique et le problème est dit mal posé. Pour obtenir une solution unique, des hypothèses sur les caractéristiques des distributions de sources sont requises. Les méthodes inverses linéaires traditionnelles utilisent différentes hypothèses qui peuvent favoriser des solutions de norme minimale, imposer des contraintes de lissage dans l’espace et/ou dans le temps, etc. Pourtant, la connectivité structurelle est rarement prise en compte et les délais de transmission sont presque toujours négligés.La première contribution de cette thèse est un pipeline de prétraitement multimodal utilisé pour l’intégration des données d’IRM, IRMd et MEG dans un même cadre, et d’une méthode de simulation de l’activité corticale qui a été utilisée comme jeu de données synthétiques pour valider les approches de reconstruction proposées. Nous proposons également une nouvelle approche pour résoudre le problème inverse M/EEG appelée «Problème Inverse M/EEG Informé par la Connectivité» (CIMIP pour Connectivity-Informed M/EEG Inverse Problem), où des délais de transmission provenant de l’IRMd sont inclus pour renforcer le lissage temporel entre les décours des sources connectées. Pour cela, un opérateur Laplacien, basé sur un graphe de connectivité en fonction du temps, a été intégré dans la régularisation. Cependant, certaines limites de l’approche CIMIP sont apparues en raison de la nature du Laplacien qui agit sur le graphe entier et favorise les solutions lisses sur toutes les connexions, pour tous les délais, et indépendamment de la directionnalité.Lors de tâches visuo-motrices, seules quelques régions sont généralement activées significativement. Notre troisième contribution est une extension de CIMIP pour ce type de tâches qui répond aux limitations susmentionnées, nommée CIMIP_OML («Optimal Masked Laplacian») ou Laplacien Masqué Optimal. Nous essayons de trouver comment l’information est transférée entre les nœuds d’un sous-réseau de régions d’intérêt du réseau complet de l’espace des sources. Pour décrire les interactions entre nœuds dans un graphe orienté, nous utilisons le concept de motifs de réseau. Nous proposons un algorithme qui 1) cherche un motif de réseau optimal- un modèle optimal d’interaction entre régions et 2) reconstruit l’activité corticale avec le motif trouvé. Des résultats prometteurs sont présentés pour des données MEG simulées et réelles (tâche visuo-motrice) et comparés avec 3 méthodes de l’état de l’art. Pour conclure, nous avons abordé un problème difficile d’exploitation des délais de l’IRMd lors l’estimation de l’activité corticale en tenant compte de la directionalité du transfert d’information, fournissant ainsi de nouvelles perspectives sur les patterns complexes de l’activité cérébrale