Single- and Multiple-Shell Uniform Sampling Schemes for Diffusion MRI Using Spherical Codes

In diffusion MRI (dMRI), a good sampling scheme is important for efficient acquisition and robust reconstruction. Diffusion weighted signal is normally acquired on single or multiple shells in q-space. Signal samples are typically distributed uniformly on different shells to make them invariant to the orientation of structures within tissue, or the laboratory coordinate frame. The Electrostatic Energy Minimization (EEM) method, originally proposed for single shell sampling scheme in dMRI, was recently generalized to multi-shell schemes, called Generalized EEM (GEEM). GEEM has been successfully used in the Human Connectome Project (HCP). However, EEM does not directly address the goal of optimal sampling, i.e., achieving large angular separation between sampling points. In this paper, we propose a more natural formulation, called Spherical Code (SC), to directly maximize the minimal angle between different samples in single or multiple shells. We consider not only continuous problems to design single or multiple shell sampling schemes, but also discrete problems to uniformly extract sub-sampled schemes from an existing single or multiple shell scheme, and to order samples in an existing scheme. We propose five algorithms to solve the above problems, including an incremental SC (ISC), a sophisticated greedy algorithm called Iterative Maximum Overlap Construction (IMOC), an 1-Opt greedy method, a Mixed Integer Linear Programming (MILP) method, and a Constrained Non-Linear Optimization (CNLO) method. To our knowledge, this is the first work to use the SC formulation for single or multiple shell sampling schemes in dMRI. Experimental results indicate that SC methods obtain larger angular separation and better rotational invariance than the state-of-the-art EEM and GEEM. The related codes and a tutorial have been released in DMRITool.Comment: Accepted by IEEE transactions on Medical Imaging. Codes have been released in dmritool https://diffusionmritool.github.io/tutorial_qspacesampling.htm

Diffusion sampling schemes: A generalized methodology with nongeometric criteria

Producción CientíficaPurpose:The aim of this paper is to show that geometrical criteria for designingmultishellq-space sampling procedures do not necessarily translate into recon-struction matrices with high figures of merit commonly used in the compressedsensing theory. In addition, we show that a well-known method for visitingk-space in radial three-dimensional acquisitions, namely, the Spiral Phyllotaxis,is a competitive initialization for the optimization of our nonconvex objectivefunction.Theory and Methods:We propose the gradient design method WISH (WeIght-ing SHells) which uses an objective function that accounts for weighted dis-tances between gradients withinM-tuples of consecutive shells, withMrangingbetween 1 and the maximum number of shellsS. All theM-tuples share thesame weight�M. The objective function is optimized for a sample of theseweights, using Spiral Phyllotaxis as initialization. State-of-the-art General Elec-trostatic Energy Minimization (GEEM) and Spherical Codes (SC) were used forcomparison. For the three methods, reconstruction matrices of the attenuationsignal using MAP-MRI were tested using figures of merit borrowed from theCompressed Sensing theory (namely, Restricted Isometry Property —RIP— andCoherence); we also tested the gradient design using a geometric criterion basedon Voronoi cells.Results:For RIP and Coherence, WISH got better results in at least one com-bination of weights, whilst the criterion based on Voronoi cells showed anunrelated pattern.Conclusion:The versatility provided by WISH is supported by better results.Optimization in the weight parameter space is likely to provide additionalimprovements. For a practical design with an intermediate number of gradients,our results recommend to carry out the methodology here used to determine theappropriate gradient table.Agencia Estatal de Investigación,(under Grants RTI2018-094569-B-I00,PID2020-115339RB-I00 and TED2021-130090B-I00)ESAOTE, Ltd (Grant/Award Number: 18IQBM

Denoising and fast diffusion imaging with physically constrained sparse dictionary learning

International audienceDiffusion-weighted imaging (DWI) allows imaging the geometry of water diffusion in biological tissues. However, DW images are noisy at high b-values and acquisitions are slow when using a large number of measurements, such as in Diffusion Spectrum Imaging (DSI). This work aims to denoise DWI and reduce the number of required measurements, while maintaining data quality. To capture the structure of DWI data, we use sparse dictionary learning constrained by the physical properties of the signal: symmetry and positivity. The method learns a dictionary of diffusion profiles on all the DW images at the same time and then scales to full brain data. Its performance is investigated with simulations and two real DSI datasets. We obtain better signal estimates from noisy measurements than by applying mirror symmetry through the q-space origin, Gaussian denoising or state-of- the-art non-local means denoising. Using a high-resolution dictionary learnt on another subject, we show that we can reduce the number of images acquired while still generating high resolution DSI data. Using dictionary learning, one can denoise DW images effectively and perform faster acquisitions. Higher b-value acquisitions and DSI techniques are possible with approximately 40 measurements. This opens important perspectives for the connectomics community using DSI

Improved Quantification of Connectivity in Human Brain Mapping

Diffusion magnetic resonance imaging (dMRI) is an advanced MRI methodology that can be used to probe the microstructure of biological tissue. dMRI can provide orientation information by modeling the process of water diffusion in white matter. This thesis presents contributions in three areas of diffusion imaging technology: diffusion reconstruction, quantification, and validation of derived metrics. It presents a novel reconstruction method by combining generalized q-sampling imaging, spherical harmonic basis functions and constrained spherical deconvolution methods to estimate the fiber orientation distribution function (ODF). This method provides improved spatial localization of brain nuclei and fiber tract separation. A novel diffusion anisotropy metric is presented that provides anatomically interpretable measurements of tracts that are robust in crossing areas of the brain. The metric, directional Axonal Volume (dAV) provides an estimate of directional water content of the tract based on the (ODF) and proton density map. dAV is a directionally sensitive metric and can separate anisotropic water content for each fiber population, providing a quantification in milliliters of water. A method is provided to map voxel-based dAV onto tracts that is not confounded by crossing areas and follows the tract morphology. This work introduces a novel textile based hollow fiber anisotropic phantom (TABIP) for validation of reconstruction and quantification methods. This provides a ground truth reference for axonal scale water tubular structures arranged in various anatomical configurations, crossing and mixing patterns. Analysis shows that: 1) the textile tracts are identifiable with scans used in human imaging and produced tracts and voxel metrics in the range of human tissue; 2) the current methods could resolve crossing at 90o and 45o but not 30o; 3) dAV/NODDI model closely matches (r=0.95) the number of fibers whereas conventional metrics poorly match (i.e., FA r=0.32). This work represents a new accurate quantification of axonal water content through diffusion imaging. dAV shows promise as a new anatomically interpretable metric of axonal connectivity that is not confounded by factors such as axon dispersion, crossing and local isotropic water content. This will provide better anatomical mapping of white matter and potentially improve the detection of axonal tract pathology

Joint Spatial-Angular Sparse Coding, Compressed Sensing, and Dictionary Learning for Diffusion MRI

Neuroimaging provides a window into the inner workings of the human brain to diagnose and prevent neurological diseases and understand biological brain function, anatomy, and psychology. Diffusion Magnetic Resonance Imaging (dMRI) is an emerging medical imaging modality used to study the anatomical network of neurons in the brain, which form cohesive bundles, or fiber tracts, that connect various parts of the brain. Since about 73% of the brain is water, measuring the flow, or diffusion of water molecules in the presence of fiber bundles, allows researchers to estimate the orientation of fiber tracts and reconstruct the internal wiring of the brain, in vivo. Diffusion MRI signals can be modeled within two domains: the spatial domain consisting of voxels in a brain volume and the diffusion or angular domain, where fiber orientation is estimated in each voxel. Researchers aim to estimate the probability distribution of fiber orientation in every voxel of a brain volume in order to trace paths of fiber tracts from voxel to voxel over the entire brain. Therefore, the traditional framework for dMRI processing and analysis has been from a voxel-wise vantage point with added spatial regularization considered post-hoc. In contrast, we propose a new joint spatial-angular representation of dMRI data which pairs signals in each voxel with the global spatial environment, jointly. This has the ability to improve many aspects of dMRI processing and analysis and re-envision the core representation of dMRI data from a local perspective to a global one. In this thesis, we propose three main contributions which take advantage of such joint spatial-angular representations to improve major machine learning tasks applied to dMRI: sparse coding, compressed sensing, and dictionary learning. First, we will show that we can achieve sparser representations of dMRI by utilizing a global spatial-angular dictionary instead of a purely voxel-wise angular dictionary. As dMRI data is very large in size, we provide a number of novel extensions to popular spare coding algorithms that perform efficient optimization on a global-scale by exploiting the separability of our dictionaries over the spatial and angular domains. Next, compressed sensing is used to accelerate signal acquisition based on an underlying sparse representation of the data. We will show that our proposed representation has the potential to push the limits of the current state of scanner acceleration within a new compressed sensing model for dMRI. Finally, sparsity can be further increased by learning dictionaries directly from datasets of interest. Prior dictionary learning for dMRI learn angular dictionaries alone. Our third contribution is to learn spatial-angular dictionaries jointly from dMRI data directly to better represent the global structure. Traditionally, the problem of dictionary learning is non-convex with no guarantees of finding a globally optimal solution. We derive the first theoretical results of global optimality for this class of dictionary learning problems. We hope the core foundation of a joint spatial-angular representation will open a new perspective on dMRI with respect to many other processing tasks and analyses. In addition, our contributions are applicable to any general signal types that can benefit from separable dictionaries. We hope the contributions in this thesis may be adopted in the larger signal processing, computer vision, and machine learning communities. dMRI signals can be modeled within two domains: the spatial domain consisting of voxels in a brain volume and the diffusion or angular domain, where fiber orientation is estimated in each voxel. Computationally speaking, researchers aim to estimate the probability distribution of fiber orientation in every voxel of a brain volume in order to trace paths of fiber tracts from voxel to voxel over the entire brain. Therefore, the traditional framework for dMRI processing and analysis is from a voxel-wise, or angular, vantage point with post-hoc consideration of their local spatial neighborhoods. In contrast, we propose a new global spatial-angular representation of dMRI data which pairs signals in each voxel with the global spatial environment, jointly, to improve many aspects of dMRI processing and analysis, including the important need for accelerating the otherwise time-consuming acquisition of advanced dMRI protocols. In this thesis, we propose three main contributions which utilize our joint spatial-angular representation to improve major machine learning tasks applied to dMRI: sparse coding, compressed sensing, and dictionary learning. We will show that sparser codes are possible by utilizing a global dictionary instead of a voxel-wise angular dictionary. This allows for a reduction of the number of measurements needed to reconstruct a dMRI signal to increase acceleration using compressed sensing. Finally, instead of learning angular dictionaries alone, we learn spatial-angular dictionaries jointly from dMRI data directly to better represent the global structure. In addition, this problem is non-convex and so we derive the first theories to guarantee convergence to a global minimum. As dMRI data is very large in size, we provide a number of novel extensions to popular algorithms that perform efficient optimization on a global-scale by exploiting the separability of our global dictionaries over the spatial and angular domains. We hope the core foundation of a joint spatial-angular representation will open a new perspective on dMRI with respect to many other processing tasks and analyses. In addition, our contributions are applicable to any separable dictionary setting which we hope may be adopted in the larger image processing, computer vision, and machine learning communities

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

DEVELOP NOVEL FRAP TECHNIQUES FOR DETERMINING ANISOTROPIC SOLUTE DIFFUSION IN CARTILAGINOUS TISSUES

Cartilaginous tissue is a connective tissue composed of specialized cells (e.g., chondrocytes and fibroblasts) that produce a large amount of extracellular matrix (ECM), which is comprised mostly of collagen fibers, abundant ground substance rich in proteoglycan, and elastic fibers. It is characterized by its avascular structures within the tissue, implying that nutrition for normal tissue cells, for maintaining a healthy ECM, is mainly supplied through diffusion from nearby vascularized tissues and synovial fluid. Poor nutritional supply to the cartilaginous tissue is believed to be an important factor leading to tissue degeneration. Moreover, due to the complex collagen fiber structures, the solute diffusion properties in cartilaginous tissues are mainly anisotropic (i.e., orientation dependent) in three-dimensional (3D) space. Thus, the determination of nutrient solute anisotropic diffusion properties is crucial for understanding the mechanism of nutrient transport in cartilaginous tissues. Furthermore, characterization of the solute diffusive transport properties in cartilaginous tissues will delineate the relationship between solute diffusion and tissue morphology for further understanding the pathophysiology and etiology of tissue dysfunction and degeneration. Fluorescence recovery after photobleaching (FRAP) is a versatile and widely used tool for the determination of local diffusion properties within solutions, cells, and tissues due to its high spatial resolution offering the possibility to microscopically examine a specific region of a sample. However, there is a lack of FRAP techniques which can determine the two-dimensional (2D) and 3D anisotropic solute diffusion properties in cartilaginous tissues. Therefore, the objective of this project is to develop novel FRAP techniques for determining 2D and 3D anisotropic solute diffusion properties in cartilaginous tissues. First, a new 2D FRAP technique solely based on the spatial Fourier analysis (SFA) was developed to determine the 2D anisotropic diffusion tensor in cartilaginous tissues. The major innovations of this study included the derivation of a close-form solution for the 2D diffusion equation by solely using Fourier transform and the complete determination of three independent components of the 2D diffusion tensor. The new theory was validated by computer simulated FRAP experiments indicating the high accuracy and robustness. The new method was applied to determine the 2D diffusion tensor of 4kDa FITC-Dextran in porcine TMJ discs. It was found that the diffusion of this solute in TMJ discs was inhomogeneous and anisotropic. This study has provided a new method to quantitatively investigate the relationship between transport properties and tissue composition and structure. The obtained transport properties are crucial for future development of numerical models studying nutritional supply within the TMJ disc. Next, the relationship between solute diffusion properties and tissue morphology was investigated by using the new FRAP technique and scanning electron microscopy (SEM). The SEM results demonstrated that the collagen fibers in the TMJ disc aligned anteroposteriorly in the medial, intermediate and lateral regions while aligning mediolaterally in the posterior region. Interestingly, fibers aligned in both the anteroposterior and mediolateral directions were found in the anterior region of the TMJ disc. The diffusion properties were highly correlated with tissue morphology. It was found again that the solute diffusion in the TMJ disc was anisotropic and inhomogeneous, which suggested that tissue structure (i.e., the collagen fiber alignment) and composition (e.g., water content) could be key factors that affect the solute diffusion properties within TMJ discs. Lastly, a new 3D MP-FRAP technique was fully developed for determining 3D anisotropic solute diffusion in cartilaginous tissues. A closed-form solution for the 3D anisotropic diffusion equation was derived by using SFA and all the components of the 3D diffusion tensor were obtained by averaging the diffusivities over a shell of a spherical surface in the frequency domain. The new method was well validated by analyzing computer simulated MP-FRAP data as well as measuring the diffusivities of FICT-Dextran (FD) molecules in the glycerol/PBS solutions. Quantitative analysis of 3D MP-FRAP experiments in the ligament tissues was demonstrated as an in vitro application of our new technique. The results demonstrated that the 3D diffusion properties of two types of FD solutes (FD70 and FD150) in the ligament tissue slices were anisotropic and the diffusion along the fiber orientation was always faster than the other two directions. The advantages of the new 2D and 3D FRAP techniques includes (1) the boundary and initial conditions for these analyses are flexible, so bleaching volume could be any 2D or 3D geometries, (2) the real first recovery image frame or stack right after photobleaching is not required for the diffusion tensor calculation, and (3) the diffusion tensor can be calculated without measuring the point spread function or optical transfer function of the microscope. Due to these features, our techniques can be conveniently carried out on a commercial confocal or multiphoton laser scanning microscope for the 2D or 3D anisotropic diffusion measurements. Future work for this project involves incorporating high-speed fluorescence imaging techniques into our FRAP methods in order to enhance the capabilities and broaden the applications of our method. In addition, investigating diffusion properties in cartilaginous tissues by using other imaging modalities [e.g., magnetic resonance imaging (MRI) and computed tomography (CT)] may lead to translational applications for the FRAP techniques developed in this dissertation

IRM de diffusion par encodage tenseur-b : déconvolution sphérique contrainte et décomposition de la variance diffusionnelle

Le cerveau humain est composé de plusieurs milliards de neurones qui forment une multitude de connexions, se regroupant en fibres de matière blanche (WM) sur plus de 160 000 kilomètres au total. L’imagerie par résonance magnétique (IRM) de diffusion (IRMd) tire profit de l’atténuation du signal de résonance magnétique causée par la diffusion des molécules d’eau dans le cerveau pour étudier ces structures sous-jacentes de manière non invasive. Le modèle d’imagerie par tenseur de diffusion (DTI) permet d’accéder à différentes mesures procurant de l’information sur la mésostructure du cerveau à partir de données d'IRMd, en manquant cependant de spécificité face à la nature microscopique du signal. Le modèle de déconvolution sphérique contrainte (CSD) permet de reconstruire une carte des fonctions de distribution d'orientations de fibres (fODF) de WM dans le cerveau de façon précise à partir de l'imagerie de diffusion à haute résolution angulaire (HARDI), ce qui peut être utilisé par un algorithme de tractographie pour cartographier le connectome structurel humain. Afin de surmonter le manque de spécificité présent en DTI, l’IRM de diffusion par encodage tenseur-b a vu le jour dans les années 2000. Cette technique utilise différents encodages de gradients de diffusion (p. ex., encodages linéaire, planaire et sphérique) pour donner accès à des mesures plus fines de la structure microscopique des tissus cérébraux, sous la forme de mesures de microstructure novatrices. Cependant, les données d'IRMd par encodage tenseur-b sont complexes et ne s'appliquent pas directement au modèle de CSD, sans compter que l'impact de ces données sur la reconstruction des fODFs est inconnu. Le présent mémoire vise donc à élaborer les fondations mathématiques et techniques d'une CSD adaptée aux données d'IRMd par encodage tenseur-b. Une évaluation des performances de reconstruction des fODFs par ce modèle est ensuite effectuée sur des données simulées, en parallèle avec des mesures d'efficacité du calcul des mesures de microstructure. L'étude révèle que l'ajout d'un encodage planaire ou sphérique à un encodage linéaire réduit de seulement quelques degrés la résolution angulaire des fODFs reconstruites. De plus, la combinaison d'encodages linéaire et sphérique mène à un calcul précis des mesures de microstructure. Les résultats de ces travaux, incluant la proposition d'un protocole d'IRMd par encodage tenseur-b d'une durée de 10 minutes et 30 secondes, ouvrent la porte à la reconstruction des fODFs jumelée au calcul des précieuses mesures de microstructure