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Despite the immense advances of science and medicine in recent years, several aspects regarding the physiology and the anatomy of the human brain are yet to be discovered and understood. A particularly challenging area in the study of human brain anatomy is that of brain connectivity, which describes the intricate means by which different regions of the brain interact with each other. The study of brain connectivity is deeply dependent on understanding the organization of white matter. The latter is predominantly comprised of bundles of myelinated axons, which serve as connecting pathways between approximately 10¹¹ neurons in the brain. Consequently, the delineation of fine anatomical details of white matter represents a highly challenging objective, and it is still an active area of research in the fields of neuroimaging and neuroscience, in general. Recent advances in medical imaging have resulted in a quantum leap in our understanding of brain anatomy and functionality. In particular, the advent of diffusion magnetic resonance imaging (dMRI) has provided researchers with a non-invasive means to infer information about the connectivity of the human brain. In a nutshell, dMRI is a set of imaging tools which aim at quantifying the process of water diffusion within the human brain to delineate the complex structural configurations of the white matter. Among the existing tools of dMRI high angular resolution diffusion imaging (HARDI) offers a desirable trade-off between its reconstruction accuracy and practical feasibility. In particular, HARDI excels in its ability to delineate complex directional patterns of the neural pathways throughout the brain, while remaining feasible for many clinical applications. Unfortunately, HARDI presents a fundamental trade-off between its ability to discriminate crossings of neural fiber tracts (i.e., its angular resolution) and the signal-to-noise ratio (SNR) of its associated images. Consequently, given that the angular resolution is of fundamental importance in the context of dMRI reconstruction, there is a need for effective algorithms for de-noising HARDI data. In this regard, the most effective de-noising approaches have been observed to be those which exploit both the angular and the spatial-domain regularity of HARDI signals. Accordingly, in this thesis, we propose a formulation of the problem of reconstruction of HARDI signals which incorporates regularization assumptions on both their angular and their spatial domains, while leading to a particularly simple numerical implementation. Experimental evidence suggests that the resulting cross-domain regularization procedure outperforms many other state of the art HARDI de-noising methods. Moreover, the proposed implementation of the algorithm supersedes the original reconstruction problem by a sequence of efficient filters which can be executed in parallel, suggesting its computational advantages over alternative implementations.

Magnetic resonance imaging (MRI) has long become one of the most powerful and accurate tools of medical diagnostic imaging. Central to the diagnostic capabilities of MRI is the notion of contrast, which is determined by the biochemical composition of examined tissue as well as by its morphology. Despite the importance of the prevalent T₁, T₂, and proton density contrast mechanisms to clinical diagnosis, none of them has demonstrated effectiveness in delineating the morphological structure of the white matter - the information which is known to be related to a wide spectrum of brain-related disorders. It is only with the recent advent of diffusion-weighted MRI that scientists have been able to perform quantitative measurements of the diffusivity of white matter, making possible the structural delineation of neural fibre tracts in the human brain. One diffusion imaging technique in particular, namely high angular resolution diffusion imaging (HARDI), has inspired a substantial number of processing methods capable of obtaining the orientational information of multiple fibres within a single voxel while boasting minimal acquisition requirements. HARDI characterization of fibre morphology can be enhanced by increasing spatial and angular resolutions. However, doing so drastically reduces the signal-to-noise ratio. Since pronounced measurement noise tends to obscure and distort diagnostically relevant details of diffusion-weighted MR signals, increasing spatial or angular resolution necessitates application of the efficient and reliable tools of image denoising. The aim of this work is to develop an effective framework for the filtering of HARDI measurement noise which takes into account both the manifold to which the HARDI signal belongs and the statistical nature of MRI noise. These goals are accomplished using an approach rooted in non-local means (NLM) weighted averaging. The average includes samples, and therefore dependencies, from the entire manifold and the result of the average is used to deduce an estimate of the original signal value in accordance with MRI statistics. NLM averaging weights are determined adaptively based on a neighbourhood similarity measure. The novel neighbourhood comparison proposed in this thesis is one of spherical neighbourhoods, which assigns large weights to samples with similar local orientational diffusion characteristics. Moreover, the weights are designed to be invariant to both spatial rotations as well as to the particular sampling scheme in use. This thesis provides a detailed description of the proposed filtering procedure as well as experimental results with synthetic and real-life data. It is demonstrated that the proposed filter has substantially better denoising capabilities as compared to a number of alternative methods.

Despite the immense advances of science and medicine in recent years, several aspects regarding the physiology and the anatomy of the human brain are yet to be discovered and understood. A particularly challenging area in the study of human brain anatomy is that of brain connectivity, which describes the intricate means by which different regions of the brain interact with each other. The study of brain connectivity is deeply dependent on understanding the organization of white matter. The latter is predominantly comprised of bundles of myelinated axons, which serve as connecting pathways between approximately 10¹¹ neurons in the brain. Consequently, the delineation of fine anatomical details of white matter represents a highly challenging objective, and it is still an active area of research in the fields of neuroimaging and neuroscience, in general. Recent advances in medical imaging have resulted in a quantum leap in our understanding of brain anatomy and functionality. In particular, the advent of diffusion magnetic resonance imaging (dMRI) has provided researchers with a non-invasive means to infer information about the connectivity of the human brain. In a nutshell, dMRI is a set of imaging tools which aim at quantifying the process of water diffusion within the human brain to delineate the complex structural configurations of the white matter. Among the existing tools of dMRI high angular resolution diffusion imaging (HARDI) offers a desirable trade-off between its reconstruction accuracy and practical feasibility. In particular, HARDI excels in its ability to delineate complex directional patterns of the neural pathways throughout the brain, while remaining feasible for many clinical applications. Unfortunately, HARDI presents a fundamental trade-off between its ability to discriminate crossings of neural fiber tracts (i.e., its angular resolution) and the signal-to-noise ratio (SNR) of its associated images. Consequently, given that the angular resolution is of fundamental importance in the context of dMRI reconstruction, there is a need for effective algorithms for de-noising HARDI data. In this regard, the most effective de-noising approaches have been observed to be those which exploit both the angular and the spatial-domain regularity of HARDI signals. Accordingly, in this thesis, we propose a formulation of the problem of reconstruction of HARDI signals which incorporates regularization assumptions on both their angular and their spatial domains, while leading to a particularly simple numerical implementation. Experimental evidence suggests that the resulting cross-domain regularization procedure outperforms many other state of the art HARDI de-noising methods. Moreover, the proposed implementation of the algorithm supersedes the original reconstruction problem by a sequence of efficient filters which can be executed in parallel, suggesting its computational advantages over alternative implementations.

Magnetic resonance imaging (MRI) has long become one of the most powerful and accurate tools of medical diagnostic imaging. Central to the diagnostic capabilities of MRI is the notion of contrast, which is determined by the biochemical composition of examined tissue as well as by its morphology. Despite the importance of the prevalent T₁, T₂, and proton density contrast mechanisms to clinical diagnosis, none of them has demonstrated effectiveness in delineating the morphological structure of the white matter - the information which is known to be related to a wide spectrum of brain-related disorders. It is only with the recent advent of diffusion-weighted MRI that scientists have been able to perform quantitative measurements of the diffusivity of white matter, making possible the structural delineation of neural fibre tracts in the human brain. One diffusion imaging technique in particular, namely high angular resolution diffusion imaging (HARDI), has inspired a substantial number of processing methods capable of obtaining the orientational information of multiple fibres within a single voxel while boasting minimal acquisition requirements. HARDI characterization of fibre morphology can be enhanced by increasing spatial and angular resolutions. However, doing so drastically reduces the signal-to-noise ratio. Since pronounced measurement noise tends to obscure and distort diagnostically relevant details of diffusion-weighted MR signals, increasing spatial or angular resolution necessitates application of the efficient and reliable tools of image denoising. The aim of this work is to develop an effective framework for the filtering of HARDI measurement noise which takes into account both the manifold to which the HARDI signal belongs and the statistical nature of MRI noise. These goals are accomplished using an approach rooted in non-local means (NLM) weighted averaging. The average includes samples, and therefore dependencies, from the entire manifold and the result of the average is used to deduce an estimate of the original signal value in accordance with MRI statistics. NLM averaging weights are determined adaptively based on a neighbourhood similarity measure. The novel neighbourhood comparison proposed in this thesis is one of spherical neighbourhoods, which assigns large weights to samples with similar local orientational diffusion characteristics. Moreover, the weights are designed to be invariant to both spatial rotations as well as to the particular sampling scheme in use. This thesis provides a detailed description of the proposed filtering procedure as well as experimental results with synthetic and real-life data. It is demonstrated that the proposed filter has substantially better denoising capabilities as compared to a number of alternative methods.

The connectivity and structural integrity of the white matter of the brain is known to be implicated in a wide range of brain-related diseases and injuries. However, it is only since the advent of diffusion magnetic resonance imaging (dMRI) that researchers have been able to probe the miscrostructure of white matter in vivo. Presently, among a range of methods of dMRI, high angular resolution diffusion imaging (HARDI) is known to excel in its ability to provide reliable information about the local orientations of neural fasciculi (aka fibre tracts). It preserves the high angular resolution property of diffusion spectrum imaging (DSI) but requires less measurements. Meanwhile, as opposed to the more traditional diffusion tensor imaging (DTI), HARDI is capable of distinguishing the orientations of multiple fibres passing through a given spatial voxel. Unfortunately, the ability of HARDI to discriminate neural fibres that cross each other at acute angles is always limited. The limitation becomes the motivation to develop numerous post-processing tools, aiming at the improvement of the angular resolution of HARDI. Among such methods, spherical deconvolution (SD) is the one which attracts the most attentions. Due to its ill-posed nature, however, standard SD relies on a number of a priori assumptions needed to render its results unique and stable. In the present thesis, we introduce a novel approach to the problem of non-blind SD of HARDI signals, which does not only consider the existence of anisotropic diffusion component of HARDI signal but also explicitly take the isotropic diffusion component into account. As a result of that, in addition to reconstruction of fODFs, our algorithm can also yield a useful estimation of its related IDM, which quantifies a relative contribution of the isotropic diffusion component as well as its spatial pattern. Moreover, one of the principal contributions is to demonstrate the effectiveness of exploiting different prior models for regularization of the spatial-domain behaviours of the reconstructed fODFs and IDMs. Specifically, the fibre continuity model has been used to force the local maxima of the fODFs to vary consistently throughout the brain, whereas the bounded variation model has helped us to achieve piecewise smooth reconstruction of the IDMs. The proposed algorithm is formulated as a convex minimization problem, which admits a unique and stable minimizer. Moreover, using ADMM, we have been able to find the optimal solution via a sequence of simpler optimization problems, which are both computationally efficient and amenable to parallel computations. In a series of both in silico and in vivo experiments, we demonstrate how the proposed solution can be used to successfully overcome the effect of partial voluming, while preserving the spatial coherency of cerebral diffusion at moderate to severe noise levels. The performance of the proposed method is compared with that of several available alternatives, with the comparative results clearly supporting the viability and usefulness of our approach. Moreover, the results illustrate the power of applied spatial regularization terms.

abstract: Magnetic Resonance Imaging (MRI) is limited in speed and resolution by the inherently low Signal to Noise Ratio (SNR) of the underlying signal. Advances in sampling efficiency are required to support future improvements in scan time and resolution. SNR efficiency is improved by sampling data for a larger proportion of total imaging time. This is challenging as these acquisitions are typically subject to artifacts such as blurring and distortions. The current work proposes a set of tools to help with the creation of different types of SNR efficient scans. An SNR efficient pulse sequence providing diffusion imaging data with full brain coverage and minimal distortion is first introduced. The proposed method acquires single-shot, low resolution image slabs which are then combined to reconstruct the full volume. An iterative deblurring algorithm allowing the lengthening of spiral SPoiled GRadient echo (SPGR) acquisition windows in the presence of rapidly varying off-resonance fields is then presented. Finally, an efficient and practical way of collecting 3D reformatted data is proposed. This method constitutes a good tradeoff between 2D and 3D neuroimaging in terms of scan time and data presentation. These schemes increased the SNR efficiency of currently existing methods and constitute key enablers for the development of SNR efficient MRI. / Dissertation/Thesis / Ph.D. Electrical Engineering 2011

Stroke is a major cause of disability and death worldwide. Although different clinical studies and trials used Magnetic Resonance Imaging (MRI) to examine patterns of change in different imaging modalities (eg: perfusion and diffusion), we still lack a clear and definite answer to the question: “How does an acute ischemic stroke lesion grow?” The inability to distinguish viable and dead tissue in abnormal MR regions in stroke patients weakens the evidence accumulated to answer this question, and relying on static snapshots of patient scans to fill in the spatio-temporal gaps by “thinking/guessing” make it even harder to tackle. Different opposing observations undermine our understanding of ischemic stroke evolution, especially at the acute stage: viable tissue transiting into dead tissue may be clear and intuitive, however, “visibly” dead tissue restoring to full recovery is still unclear. In this thesis, we search for potential answers to these raised questions from a novel dynamic modelling perspective that would fill in some of the missing gaps in the mechanisms of stroke evolution. We divided our thesis into five parts. In the first part, we give a clinical and imaging background on stroke and state the objectives of this thesis. In the second part, we summarize and review the literature in stroke and medical imaging. We specifically spot gaps in the literature mainly related to medical image analysis methods applied to acute-subacute ischemic stroke. We emphasize studies that progressed the field and point out what major problems remain. Noticeably, we have discovered that macroscopic (imaging-based) dynamic models that simulate how stroke lesion evolves in space and time were completely overlooked: an untapped potential that may alter and hone our understanding of stroke evolution. Progress in the dynamic simulation of stroke was absent –if not inexistent. In the third part, we answer this new call and apply a novel current-based dynamic model âpreviously applied to compare the evolution of facial characteristics between Chimpanzees and Bonobos [Durrleman 2010] – to ischemic stroke. This sets a robust numerical framework and provides us with mathematical tools to fill in the missing gaps between MR acquisition time points and estimate a four-dimensional evolution scenario of perfusion and diffusion lesion surfaces. We then detect two characteristics of patterns of abnormal tissue boundary change: spatial, describing the direction of change –outward as tissue boundary expands or inward as it contracts–; and kinetic, describing the intensity (norm) of the speed of contracting and expanding ischemic regions. Then, we compare intra- and inter-patients estimated patterns of change in diffusion and perfusion data. Nevertheless, topology change limits this approach: it cannot handle shapes with different parts that vary in number over time (eg: fragmented stroke lesions, especially in diffusion scans, which are common). In the fourth part, we suggest a new mathematical dynamic model to increase rigor in the imaging-based dynamic modeling field as a whole by overcoming the topology-change hurdle. Metamorphosis. It morphs one source image into a target one [Trouvé 2005]. In this manuscript, we extend it into dealing with more than two time-indexed images. We propose a novel extension of image-to-image metamorphosis into longitudinal metamorphosis for estimating an evolution scenario of both scattered and solitary ischemic lesions visible on serial MR. It is worth noting that the spatio-temporal metamorphosis we developed is a generic model that can be used to examine intensity and shape changes in time-series imaging and study different brain diseases or disorders. In the fifth part, we discuss our main findings and investigate future directions to explore to sharpen our understanding of ischemia evolution patterns.

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1er objectif : Mieux caractériser les surdités neuro-sensoriellesNous avons démontré dans ce travail de thèse que nous étions capablesd’individualiser le saccule et l’utricule pour faire le diagnostic d’hydropscompartiment par compartiment. L’intérêt repose sur les propriétés biomecaniquesdifferentes de ces deux structures notamment en terme decompliance. En isolant l’hydrops sacculaire, nous avons démontré qu’ilétait lié à la présence de surdité neurosensorielle pour les patients avecune Maladie de Ménière mais également qu’il pouvait être détecté pourdes patients présentant des surdités isolées sur les basses fréquences, quine sont habituellement pas classées comme porteurs cliniquement de laMaladie de Ménière. Nous avons mis au point une séquence 3D-FLAIRutilisable en pratique clinique pour la détection d’hydrops sacculaire,utilisable quelque soit le champ magnétique et le constructeur.Pour les patients porteurs de schwannomes cochléo-vestibulaires, nousavons démontré que le degré de perte auditive était cette fois liée à laprésence d’un hydrops utriculaire. Ce diagnostic peut être porté sansinjection de produit de contraste puisque la présence d’un schwannomeobstructif entraine mécaniquement une augmentation du taux protidiquedans la périlymphe et donc une discrimination périlymphe/endolymphesur les séquences T2 en echo de gradient.En revisitant l’anatomie histologique avec la remnographie, nous avonsproposé une théorie bi-compartimentale pour les échanges endolymphe/liquidecéphalorachidien ; supposant que l’utricule et le saccule joue un rôle detampon entre le cerveau et la cochlée. En cas d’obstruction mécanique,au niveau de l’aqueduc du vestibule pour la maladie de Ménière et dunerf cochléo-vestibulaire pour les tumeurs du conduit auditif interne ; letampon ne joue plus son rôle. Surviennent alors des lésions cellulaires desstéréocils de la cochlée et la surdité attenante.2ème objectif : Mieux caractériser les altérations structurelles neuronalesrétro-cochléaires des surdités neurosensoriellesDu point de vue biophysique de l’IRM, l’étude du nerf cochléaire possèdel’avantage de posséder une structure simple essentiellement composéed’une seule population de fibre à modéliser par voxel, au prix d’une régiond’étude compliquée intricant de l’os, du liquide et de l’air dans l’ostemporal. Nous avons donc commencer par développer un algorithmede pré-traitement des données de diffusion qui utilise toutes les toolboxrécentes pour corriger les artéfacts de susceptibilité magnétique, de mouvements, de champ B0 et B1, les courants de Foucaults, les arrtéfactsde Gibbs. Nous avons utilisée une séquence de Diffusion optimisée pourêtre utilisable en pratique clinique en cas de mouvements des patients,construite par bloc de 15 directions.Nous avons ensuite appris à utiliser des biomarqueurs quantitatifs, notammentle coefficient de diffusion apparent des fibres, directement issusdu signal de Diffusion dont nous avons préalablement testé la fiabilitésur des données de diffusion multi-compartimentale de haute qualité auniveau de l’encéphale. Nous avons ensuite proposée une méthode originaled’extraction de l’information des voxels du nerf cochléaire appelée spectralclustering pour obtenir ce coefficient de densité des fibres de façon robusteau niveau de notre population témoin. Enfin, nous avons implémenté unalgorithme de Manifold Learning pour l’analyse de ce signal de diffusion,qui surpasse les biomarqueurs scalaires en confrontation à des modèlespathologiques auditifs en tenant compte de l’hétérogénité du signal dediffusion dans un cluster. Nous avons ainsi démontré que les patientsporteurs de la maladie de Ménière présentaient une augmentation de ladensité de fibre, en faisant de particulier bosn candidats à l’implantationcochléaire, en accord avec les premières études cliniques fonctionnellessur le sujet. / Sensorineural hearing loss (SNHL) is a common functional disorder in humans. Besides clinical investigations, magnetic resonance imaging (MRI) is the modality of choice to explore the central auditory pathways. Indeed, new MRI sequences and postprocessing methods have revolutionized our understanding of inner ear and brain disorders.The inner ear is the organ of sound detection and balance. Within the inner ear, there are two distinct compartments filled with endolymph and perilymph.The accumulation of endolymph fluid is called “endolymphatic hydrops”. Endolymphatic hydrops may occur as a consequence of a variety of disorders, including Meniere’s Disease, immune-mediated diseases or internal auditory canal tumors.Previous classification for grading the amount of endolymph liquid using MRI has proposed a global semi-quantitative evaluation, without distinguishing the utricle from the saccule, whose biomechanical properties are different in terms of compliance.This work had two main objectives: 1°) to better characterize the role of endolymphatic hydrops in SNHL occurrence; 2°) to study secondary auditory pathways alterations.Part 1: Understanding the role and pathophysiology of endolymphatic hydrops in SNHL occurrence.Endolymphatic hydrops can be identified using MRI, acquired 4-6-hours after injection of contrast media. This work has demonstrated the feasibility and improved this technique in a clinical setting.Using optimized morphological sequences, we were able to illustrate inner ear microanatomy based on temporal bone dissection, and to distinguish the saccule and the utricle.In accordance with a multi-compartmental model, we observed that the saccular hydrops was a specific biomarker of low-tone SNHL in the context of typical or atypical forms of Meniere’s Disease. In addition, utricular hydrops was linked to the degree of hearing loss in patients with schwannomas. We raise the hypothesis that both saccule and utricle compartment play the role of a buffer in endolymph reabsorption. When their compliance is overstretched, inner ear endolymph regulation fails, subsequently leading to cochlear lesions such as loss of the shorter stereocilia of the hair cells, as suggested by experimental animal modelsThus, we were able to prove the high prevalence of endolymphatic hydrops in patients with SNHL.Part 2: Development of new imaging biomarkers to study the central auditory pathways.Diffusion-Weighted Imaging play a crucial role because it can help to assess the intracellular compartment by displaying the Brownian movements of water molecules. In the context of cochlear lesions, anterograde axonal degeneration has only been demonstrated in animal models. In the context of retrocochlear lesions, no MRI sequences have previously showed efficiency in distinguishing the cochlear from the facial nerve. This is crucial for safe surgery procedure.We have designed optimized postprocessing tools to explore SNHL patients with High-Angular Resolution DWI acquisition. We have included in the clinical setting software tools for B0 and B1 bias field artifacts’ correction, Denoising process, Gibbs artifacts’ correction, Susceptibility and Eddy Current artifacts management.The ultimate goal was to properly study the Fiber Orientation Distribution (FOD) along the auditory pathways in case-controlled studies, using top-of-the-art methods of fixels analysis and a newly developed toolbox with Machine Learning analysis of the Diffusion signal.We have studied reproducibility of these two methods on Multi-Shell Diffusion gradient scheme by test-retest procedure. We have then used the fixel method to seek for auditory pathways alterations in Meniere’s Disease and Machine Learning automatic analyses to extract Inner Auditory Canal cranial nerves.Thus, we have developed a new method for cranial nerves’ tractography using FOD spectral clustering, efficient in terms of computer requirement and in tumor condition.