Resolving Intravoxel White Matter Structures in the Human Brain Using Regularized Regression and Clustering

The human brain is a complex system of neural tissue that varies significantly between individuals. Although the technology that delineates these neural pathways does not currently exist, medical imaging modalities, such as diffusion magnetic resonance imaging (dMRI), can be leveraged for mathematical identification. The purpose of this work is to develop a novel method employing machine learning techniques to determine intravoxel nerve number and direction from dMRI data. The method was tested on multiple synthetic datasets and showed promising estimation accuracy and robustness for multi-nerve systems under a variety of conditions, including highly noisy data and imprecision in parameter assumptions

Anatomical Modeling of Cerebral Microvascular Structures: Application to Identify Biomarkers of Microstrokes

Les réseaux microvasculaires corticaux sont responsables du transport de l’oxygène et des substrats énergétiques vers les neurones. Ces réseaux réagissent dynamiquement aux demandes énergétiques lors d’une activation neuronale par le biais du couplage neurovasculaire. Afin d’élucider le rôle de la composante microvasculaire dans ce processus de couplage, l’utilisation de la modélisation in-formatique pourrait se révéler un élément clé. Cependant, la manque de méthodologies de calcul appropriées et entièrement automatisées pour modéliser et caractériser les réseaux microvasculaires reste l’un des principaux obstacles. Le développement d’une solution entièrement automatisée est donc important pour des explorations plus avancées, notamment pour quantifier l’impact des mal-formations vasculaires associées à de nombreuses maladies cérébrovasculaires. Une observation courante dans l’ensemble des troubles neurovasculaires est la formation de micro-blocages vascu-laires cérébraux (mAVC) dans les artérioles pénétrantes de la surface piale. De récents travaux ont démontré l’impact de ces événements microscopiques sur la fonction cérébrale. Par conséquent, il est d’une importance vitale de développer une approche non invasive et comparative pour identifier leur présence dans un cadre clinique. Dans cette thèse,un pipeline de traitement entièrement automatisé est proposé pour aborder le prob-lème de la modélisation anatomique microvasculaire. La méthode de modélisation consiste en un réseau de neurones entièrement convolutif pour segmenter les capillaires sanguins, un générateur de modèle de surface 3D et un algorithme de contraction de la géométrie pour produire des mod-èles graphiques vasculaires ne comportant pas de connections multiples. Une amélioration de ce pipeline est développée plus tard pour alléger l’exigence de maillage lors de la phase de représen-tation graphique. Un nouveau schéma permettant de générer un modèle de graphe est développé avec des exigences d’entrée assouplies et permettant de retenir les informations sur les rayons des vaisseaux. Il est inspiré de graphes géométriques déformants construits en respectant les morpholo-gies vasculaires au lieu de maillages de surface. Un mécanisme pour supprimer la structure initiale du graphe à chaque exécution est implémenté avec un critère de convergence pour arrêter le pro-cessus. Une phase de raffinement est introduite pour obtenir des modèles vasculaires finaux. La modélisation informatique développée est ensuite appliquée pour simuler les signatures IRM po-tentielles de mAVC, combinant le marquage de spin artériel (ASL) et l’imagerie multidirectionnelle pondérée en diffusion (DWI). L’hypothèse est basée sur des observations récentes démontrant une réorientation radiale de la microvascularisation dans la périphérie du mAVC lors de la récupéra-tion chez la souris. Des lits capillaires synthétiques, orientés aléatoirement et radialement, et des angiogrammes de tomographie par cohérence optique (OCT), acquis dans le cortex de souris (n = 5) avant et après l’induction d’une photothrombose ciblée, sont analysés. Les graphes vasculaires informatiques sont exploités dans un simulateur 3D Monte-Carlo pour caractériser la réponse par résonance magnétique (MR), tout en considérant les effets des perturbations du champ magnétique causées par la désoxyhémoglobine, et l’advection et la diffusion des spins nucléaires. Le pipeline graphique proposé est validé sur des angiographies synthétiques et réelles acquises avec différentes modalités d’imagerie. Comparé à d’autres méthodes effectuées dans le milieu de la recherche, les expériences indiquent que le schéma proposé produit des taux d’erreur géométriques et topologiques amoindris sur divers angiogrammes. L’évaluation confirme également l’efficacité de la méthode proposée en fournissant des modèles représentatifs qui capturent tous les aspects anatomiques des structures vasculaires. Ensuite, afin de trouver des signatures de mAVC basées sur le signal IRM, la modélisation vasculaire proposée est exploitée pour quantifier le rapport de perte de signal intravoxel minimal lors de l’application de plusieurs directions de gradient, à des paramètres de séquence variables avec et sans ASL. Avec l’ASL, les résultats démontrent une dif-férence significative (p <0,05) entre le signal calculé avant et 3 semaines après la photothrombose. La puissance statistique a encore augmenté (p <0,005) en utilisant des angiogrammes capturés à la semaine suivante. Sans ASL, aucun changement de signal significatif n’est trouvé. Des rapports plus élevés sont obtenus à des intensités de champ magnétique plus faibles (par exemple, B0 = 3) et une lecture TE plus courte (<16 ms). Cette étude suggère que les mAVC pourraient être carac-térisés par des séquences ASL-DWI, et fournirait les informations nécessaires pour les validations expérimentales postérieures et les futurs essais comparatifs.----------ABSTRACT Cortical microvascular networks are responsible for carrying the necessary oxygen and energy substrates to our neurons. These networks react to the dynamic energy demands during neuronal activation through the process of neurovascular coupling. A key element in elucidating the role of the microvascular component in the brain is through computational modeling. However, the lack of fully-automated computational frameworks to model and characterize these microvascular net-works remains one of the main obstacles. Developing a fully-automated solution is thus substantial for further explorations, especially to quantify the impact of cerebrovascular malformations associ-ated with many cerebrovascular diseases. A common pathogenic outcome in a set of neurovascular disorders is the formation of microstrokes, i.e., micro occlusions in penetrating arterioles descend-ing from the pial surface. Recent experiments have demonstrated the impact of these microscopic events on brain function. Hence, it is of vital importance to develop a non-invasive and translatable approach to identify their presence in a clinical setting. In this thesis, a fully automatic processing pipeline to address the problem of microvascular anatom-ical modeling is proposed. The modeling scheme consists of a fully-convolutional neural network to segment microvessels, a 3D surface model generator and a geometry contraction algorithm to produce vascular graphical models with a single connected component. An improvement on this pipeline is developed later to alleviate the requirement of water-tight surface meshes as inputs to the graphing phase. The novel graphing scheme works with relaxed input requirements and intrin-sically captures vessel radii information, based on deforming geometric graphs constructed within vascular boundaries instead of surface meshes. A mechanism to decimate the initial graph struc-ture at each run is formulated with a convergence criterion to stop the process. A refinement phase is introduced to obtain final vascular models. The developed computational modeling is then ap-plied to simulate potential MRI signatures of microstrokes, combining arterial spin labeling (ASL) and multi-directional diffusion-weighted imaging (DWI). The hypothesis is driven based on recent observations demonstrating a radial reorientation of microvasculature around the micro-infarction locus during recovery in mice. Synthetic capillary beds, randomly- and radially oriented, and op-tical coherence tomography (OCT) angiograms, acquired in the barrel cortex of mice (n=5) before and after inducing targeted photothrombosis, are analyzed. The computational vascular graphs are exploited within a 3D Monte-Carlo simulator to characterize the magnetic resonance (MR) re-sponse, encompassing the effects of magnetic field perturbations caused by deoxyhemoglobin, and the advection and diffusion of the nuclear spins. The proposed graphing pipeline is validated on both synthetic and real angiograms acquired with different imaging modalities. Compared to other efficient and state-of-the-art graphing schemes, the experiments indicate that the proposed scheme produces the lowest geometric and topological error rates on various angiograms. The evaluation also confirms the efficiency of the proposed scheme in providing representative models that capture all anatomical aspects of vascular struc-tures. Next, searching for MRI-based signatures of microstokes, the proposed vascular modeling is exploited to quantify the minimal intravoxel signal loss ratio when applying multiple gradient di-rections, at varying sequence parameters with and without ASL. With ASL, the results demonstrate a significant difference (p<0.05) between the signal-ratios computed at baseline and 3 weeks after photothrombosis. The statistical power further increased (p<0.005) using angiograms captured at week 4. Without ASL, no reliable signal change is found. Higher ratios with improved significance are achieved at low magnetic field strengths (e.g., at 3 Tesla) and shorter readout TE (<16 ms). This study suggests that microstrokes might be characterized through ASL-DWI sequences, and provides necessary insights for posterior experimental validations, and ultimately, future transla-tional trials

Processing of diffusion MR images of the brain: from crossing fibres to distributed tractography

Diffusion-weighted (DW) magnetic resonance imaging allows the quantification of water diffusion within tissue. Due to the hindrance of water molecules by the various tissue compartments, probing for the diffusive properties of a region can provide information on the underlying structure. This is particularly useful for the human brain, whose anatomy is complex. Diffusion imaging provides currently the only tool to study the brain connectivity and organization non-invasively and in-vivo, through a group of methods, commonly referred to as tractography methods. This thesis is concerned with brain anatomical connectivity and tractography. The goal is to elucidate problems with existing approaches used to process DW images and propose solutions and methods through new frameworks. These concern data from two popular DW imaging protocols, diffusion tensor imaging (DTI) and high angular resolution diffusion imaging (HARDI), or Q-ball imaging in particular. One of the problems tackled is resolving crossing fibre configurations, a major concern in DW imaging, using data that can be routinely acquired in a clinical setting. The physical constraint of spatial continuity of the diffusion environment is imposed throughout the brain volume, using a multi-tensor model and a regularization method. The new approach is shown to improve tractography results through crossing regions. Quantitative tractography algorithms are also proposed that, apart from reconstructing the white matter tracts, assign relative indices of anatomical connectivity to all regions. A fuzzy algorithm is presented for assessing orientational coherence of neuronal tracts, reflecting the fuzzy nature of medical images. As shown for different tracts, where a-priori anatomical knowledge exists, regions that are coherently connected and possibly belong to the same tract can be differentiated from the background. In a different framework, elements of graph theory are used to develop a new tractography algorithm that can utilize information from multiple image modalities to assess brain connectivity. Both algorithms inherently consider crossing fibre information and are shown to solve problems that affect existing methods

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

Contributions to MCMC Methods in Constrained Domains with Applications to Neuroimaging

Markov chain Monte Carlo (MCMC) methods form a rich class of computational techniques that help its user ascertain samples from target distributions when direct sampling is not possible or when their closed forms are intractable. Over the years, MCMC methods have been used in innumerable situations due to their flexibility and generalizability, even in situations involving nonlinear and/or highly parametrized models. In this dissertation, two major works relating to MCMC methods are presented. The first involves the development of a method to identify the number and directions of nerve fibers using diffusion-weighted MRI measurements. For this, the biological problem is first formulated as a model selection and estimation problem. Using the framework of reversible jump MCMC, a novel Bayesian scheme that performs both the above tasks simultaneously using customizable priors and proposal distributions is proposed. The proposed method allows users to set a prior level of spatial separation between the nerve fibers, allowing more crossing paths to be detected when desired or a lower number to potentially only detect robust nerve tracts. Hence, estimation that is specific to a given region of interest within the brain can be performed. In simulated examples, the method has been shown to resolve up to four fibers even in instances of highly noisy data. Comparative analysis with other state-of-the-art methods on in-vivo data showed the method\u27s ability to detect more crossing nerve fibers. The second work involves the construction of an MCMC algorithm that efficiently performs (Bayesian) sampling of parameters with support constraints. The method works by embedding a transformation called inversion in a sphere within the Metropolis-Hastings sampler. This creates an image of the constrained support that is amenable to sampling using standard proposals such as Gaussian. The proposed strategy is tested on three domains: the standard simplex, a sector of an n-sphere, and hypercubes. In each domain, a comparison is made with existing sampling techniques

Quantitative Magnetic Resonance Imaging of Tissue Microvasculature and Microstructure in Selected Clinical Applications

This thesis is based on four papers and aims to establish perfusion and diffusion measurements with magnetic resonance imaging (MRI) in selected clinical applications. While structural imaging provides invaluable geometric and anatomical information, new disease relevant information can be obtained from measures of physiological processes inferred from advanced modelling. This study is motivated by clinical questions pertaining to diagnosis and treatment effects in particular patient groups where inflammatory processes are involved in the disease. Paper 1 investigates acquisition parameters in dynamic contrast enhanced (DCE)-MRI of the temporomandibular joint (TMJ) with possible involvement of juvenile idiopathic arthritis. High level elastic motion correction should be applied to DCE data from the TMJ, and the DCE data should be acquired with a sample rate of at least 4 s. Paper 2 investigates choices of arterial input functions (AIFs) in dynamic susceptibility contrast (DSC)-MRI in brain metastases. AIF shapes differed across patients. Relative cerebral blood volume estimates differentiated better between perfusion in white matter and grey matter when scan-specific AIFs were used than when patient-specific AIFs and population-based AIFs were used. Paper 3 investigates DSC-MRI perfusion parameters in relation to outcome after stereotactic radiosurgery (SRS) in brain metastases. Low perfusion prior to SRS may be related to unfavourable outcome. Paper 4 applies free water (FW) corrected diffusion MRI to characterise glioma. Fractional anisotropy maps of the tumour region were significantly impacted by FW correction. The estimated FW maps may also contribute to a better description of the tumour. Although there are challenges related to post-processing of MRI data, it was shown that the advanced MRI methods applied can add to a more accurate description of the TMJ and of brain lesions.Doktorgradsavhandlin

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

Advances in Quantitative MRI: Acquisition, Estimation, and Application

Quantitative magnetic resonance imaging (QMRI) produces images of potential MR biomarkers: measurable tissue properties related to physiological processes that characterize the onset and progression of specific disorders. Though QMRI has potential to be more diagnostic than conventional qualitative MRI, QMRI poses challenges beyond those of conventional MRI that limit its feasibility for routine clinical use. This thesis first seeks to address two of those challenges. It then applies these solutions to develop a new method for myelin water imaging, a challenging application that may be specifically indicative of certain white matter (WM) disorders. One challenge that presently precludes widespread clinical adoption of QMRI involves long scan durations: to disentangle potential biomarkers from nuisance MR contrast mechanisms, QMRI typically requires more data than conventional MRI and thus longer scans. Even allowing for long scans, it has previously been unclear how to systematically tune the "knobs" of MR acquisitions to reliably enable precise biomarker estimation. Chapter 4 formalizes these challenges as a min-max optimal acquisition design problem and solves this problem to design three fast steady-state (SS) acquisitions for precise T1/T2 estimation, a popular QMRI application. The resulting optimized acquisition designs illustrate that acquisition design can enable new biomarker estimation techniques from established MR pulse sequences, a fact that subsequent chapters exploit. Another QMRI challenge involves the typically nonlinear dependence of MR signal models on the underlying biomarkers: these nonlinearities cause conventional likelihood-based estimators to either scale very poorly with the number of unknowns or risk producing suboptimal estimates due to spurious local minima. Chapter 5 instead introduces a fast, general method for dictionary-free QMRI parameter estimation via regression with kernels (PERK). PERK first uses prior distributions and the nonlinear MR signal model to simulate many parameter-measurement pairs. Inspired by machine learning, PERK then takes these pairs as labeled training points and learns from them a nonlinear regression function using kernel functions and convex optimization. Chapter 5 demonstrates PERK for T1/T2 estimation using one of the acquisitions optimized in Chapter 4. Simulations as well as single-slice phantom and in vivo experiments demonstrated that PERK and two well-suited maximum-likelihood (ML) estimators produce comparable T1/T2 estimates, but PERK is consistently at least 140x faster. Similar comparisons to an ML estimator in a more challenging problem (Chapter 6) suggest that this 140x acceleration factor will increase by several orders of magnitude for full-volume QMRI estimation problems involving more latent parameters per voxel. Chapter 6 applies ideas developed in previous chapters to design a new fast method for imaging myelin water content, a potential biomarker for healthy myelin. It first develops a two-compartment dual-echo steady-state (DESS) signal model and then uses a Bayesian variation of acquisition design (Chapter 4) to optimize a new DESS acquisition for precise myelin water imaging. The precision-optimized acquisition is as fast as conventional SS myelin water imaging acquisitions, but enables 2-3x better expected coefficients of variation in fast-relaxing fraction estimates. Simulations demonstrate that PERK (Chapter 5) and ML fast-relaxing fraction estimates from the proposed DESS acquisition exhibit comparable root mean-squared errors, but PERK is more than 500x faster. In vivo experiments are to our knowledge the first to demonstrate lateral WM myelin water content estimates from a fast (3m15s) SS acquisition that are similar to conventional estimates from a slower (32m4s) MESE acquisition.PHDElectrical and Computer EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/147486/1/gnataraj_1.pd

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