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Supervised Learning for White Matter Bundle SegmentationBertò, Giulia 03 June 2020 (has links)
Accurate delineation of anatomical structures in the white matter of the human brain is of paramount importance for multiple applications, such as neurosurgical planning, characterization of neurological disorders, and connectomic studies. Diffusion Magnetic Resonance Imaging (dMRI) techniques can provide, in-vivo, a mathematical representation of thousands of fibers composing such anatomical structures, in the form of 3D
polylines called streamlines. Given this representation, a task of invaluable interest is known as white matter bundle segmentation, whose aim is to virtually group together streamlines sharing a similar pathway into anatomically meaningful structures, called white matter bundles.
Obtaining a good and reliable bundle segmentation is however not trivial, mainly because of the intrinsic complexity of the data. Most of the current methods for bundle segmentation require extensive neuroanatomical knowledge, are time consuming, or are not able to adapt to different data settings. To overcome these limitations, the main goal of this thesis is to develop a new automatic method for accurate white matter bundle segmentation, by exploiting, combining and extending multiple up-to-date supervised learning techniques.
The main contribution of the project is the development of a novel streamline-based bundle segmentation method based on binary linear classification, which simultaneously combines information from atlases, bundle geometries, and connectivity patterns. We prove that the proposed method reaches unprecedented quality of segmentation, and that is robust to a multitude of diverse settings, such as when there are differences in bundle size, tracking algorithm, and/or quality of dMRI data. In addition, we show that some of the state-of-the-art bundle segmentation methods are deeply affected by a geometrical property of the shape of the bundles to be segmented, their fractal dimension.
Important factors involved in the task of streamline classification are: (i) the need for an effective streamline distance function and (ii) the definition of a proper feature space. To this end, we compare some of the most common streamline distance functions available in the literature and we provide some guidelines on their practical use for the task of supervised bundle segmentation. Moreover, we investigate the possibility to include, in a streamline-based segmentation method, additional information to the typically employed streamline distance measure. Specifically, we provide evidence that considering additional anatomical information regarding the cortical terminations of the streamlines and their proximity to specific Regions of Interest (ROIs) helps to improve the results of bundle segmentation.
Lastly, significant attention is paid to reproducibility in neuroscience. Following the FAIR (Findable, Accessible, Interoperable and Reusable) Data Principles, we have integrated our pipelines of analysis into an online open platform devoted to promoting reproducibility of scientific results and to facilitating knowledge discovery.
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Implicações do polimorfismo Y402H de fator H para a concentração plasmática de proteinas do sistema complemento e do perfil lipídico em pacientes com degeneração da mácula relacionada a idade. / Implications of complement factor H polymorphism Y402H for plasmatic levels of complement proteins and lipidic profile in patients with age-related macular degeneration.Silva, Aldacilene Souza da 26 November 2009 (has links)
A Degeneração da Mácula Relacionada a Idade (DMRI) acomete pessoas com mais de 50 anos, comprometendo gravemente a visão. Desde 2005, têm-se sugerido uma correlação entre DMRI e o polimorfismo Y402H do Fator H (FH). Os mecanismos pelos quais a proteína FH participa da etiopatogenia dessa doença têm sido alvo de muitos estudos, desde então. Neste trabalho, investigamos a correlação entre esse polimorfismo e a expressão de proteínas da via alternativa e parâmetros do perfil lipídico de pacientes com DMRI. As concentrações de FH, Fator B, C3 e Proteína C-reativa foram semelhantes entre os grupos controle e paciente. As concentrações de Fator D e os autoanticorpos encontravam-se reduzidos nos pacientes; enquanto Fator I e os demais parâmetros do perfil lipídico estavam aumentados nesses pacientes. A variante Y402 aparentemente aderiu melhor à superfície das leptospiras (superfície ativadora da via alternativa) em relação à variante H402, mas não houve diferença entre as variantes em relação à ligação a células endoteliais (superfície não ativadora). / Age-related Macular Degeneration (AMD) affects people over 50 years, and severely prejudice the vision. Since 2005, it has been suggested a correlation between AMD and the Y402H polymorphism of Factor H (FH). After this, the mechanisms by which FH protein participates in the pathogenesis of this disease have been extensively studied. In this study, we investigated the correlation between this polymorphism and expression of proteins of the alternative pathway and lipid profile of patients with AMD. The concentrations of FH, Factor B, C3 and C-reactive protein were similar between the control and patient groups.Factor D concentrations and autoantibodies levels were reduced in patients, while Factor I concentrations and the levels of the other parameters of lipid profile were increased in these patients.Apparently, Y402 variant displays better adhesion to the surface of Leptospira (alternative pathway activating surface) than the H402 variant, but no difference between the variants of the linkage to endothelial cells (non-alternative pathway activating surface).
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Implicações do polimorfismo Y402H de fator H para a concentração plasmática de proteinas do sistema complemento e do perfil lipídico em pacientes com degeneração da mácula relacionada a idade. / Implications of complement factor H polymorphism Y402H for plasmatic levels of complement proteins and lipidic profile in patients with age-related macular degeneration.Aldacilene Souza da Silva 26 November 2009 (has links)
A Degeneração da Mácula Relacionada a Idade (DMRI) acomete pessoas com mais de 50 anos, comprometendo gravemente a visão. Desde 2005, têm-se sugerido uma correlação entre DMRI e o polimorfismo Y402H do Fator H (FH). Os mecanismos pelos quais a proteína FH participa da etiopatogenia dessa doença têm sido alvo de muitos estudos, desde então. Neste trabalho, investigamos a correlação entre esse polimorfismo e a expressão de proteínas da via alternativa e parâmetros do perfil lipídico de pacientes com DMRI. As concentrações de FH, Fator B, C3 e Proteína C-reativa foram semelhantes entre os grupos controle e paciente. As concentrações de Fator D e os autoanticorpos encontravam-se reduzidos nos pacientes; enquanto Fator I e os demais parâmetros do perfil lipídico estavam aumentados nesses pacientes. A variante Y402 aparentemente aderiu melhor à superfície das leptospiras (superfície ativadora da via alternativa) em relação à variante H402, mas não houve diferença entre as variantes em relação à ligação a células endoteliais (superfície não ativadora). / Age-related Macular Degeneration (AMD) affects people over 50 years, and severely prejudice the vision. Since 2005, it has been suggested a correlation between AMD and the Y402H polymorphism of Factor H (FH). After this, the mechanisms by which FH protein participates in the pathogenesis of this disease have been extensively studied. In this study, we investigated the correlation between this polymorphism and expression of proteins of the alternative pathway and lipid profile of patients with AMD. The concentrations of FH, Factor B, C3 and C-reactive protein were similar between the control and patient groups.Factor D concentrations and autoantibodies levels were reduced in patients, while Factor I concentrations and the levels of the other parameters of lipid profile were increased in these patients.Apparently, Y402 variant displays better adhesion to the surface of Leptospira (alternative pathway activating surface) than the H402 variant, but no difference between the variants of the linkage to endothelial cells (non-alternative pathway activating surface).
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Modélisation et simulation de l’IRM de diffusion des fibres myocardiques / Modeling and simulation of diffusion magnetic resonance imaging for cardiac fibersWang, Lihui 21 January 2013 (has links)
L’imagerie par résonance magnétique de diffusion (l’IRMd) est actuellement la seule technique non-invasive pour étudier l’architecture tridimensionnelle des fibres myocardiques du cœur humain à la fois ex vivo et in vivo. Cependant, il est difficile de savoir comment les caractéristiques de diffusion calculées à partir des images de diffusion reflètent les propriétés des microstructures du myocarde à cause de l’absence de la vérité-terrain sans parler de l’influence de divers facteurs tels que la résolution spatiale, le bruit et les artéfacts. L'objectif principal de cette thèse est donc de développer des simulateurs de l’IRM de diffusion basés sur des modèles réalistes afin de simuler, en intégrant différentes modalités d'imagerie, les images pondérées en diffusion des fibres myocardiques à la fois ex vivo et in vivo, et de proposer un outil générique permettant d’évaluer la qualité de l’imagerie et les algorithmes de traitement d’images. Pour atteindre cet objectif, le présent travail se focalise sur quatre parties principales. La première partie concerne la formulation de la théorie de simulation IRMd pour la génération d’images de diffusion et pour les applications sur les modèles simples de fibres cardiaques chez l’homme, et essaie de comprendre la relation sous-jacente entre les propriétés mesurées de la diffusion et les caractéristiques à la fois physiques et structurelles des fibres cardiaques. La seconde partie porte sur la simulation des images de résonance magnétique de diffusion à différentes échelles en s’appuyant sur des données du cœur humain issues de l'imagerie par lumière polarisée. En comparant les propriétés de diffusion à différentes échelles, la relation entre la variation de la microstructure et les propriétés de diffusion observée à l'échelle macroscopique est étudiée. La troisième partie consacre à l’analyse de l'influence des paramètres d'imagerie sur les propriétés de diffusion en utilisant une théorie de simulation améliorée. La dernière partie a pour objectif de modéliser la structure des fibres cardiaques in vivo et de simuler les images de diffusion correspondantes en combinant la structure des fibres cardiaques et le mouvement cardiaque connu a priori. Les simulateurs proposés nous fournissent un outil générique pour générer des images de diffusion simulées qui peuvent être utilisées pour évaluer les algorithmes de traitement d’images, pour optimiser le choix des paramètres d’IRM pour les fibres cardiaque aussi bien ex vivo que in vivo, et pour étudier la relation entre la structure de fibres microscopique et les propriétés de diffusion macroscopiques. / Diffusion magnetic resonance imaging (dMRI) appears currently as the unique imaging modality to investigate noninvasively both ex vivo and in vivo three-dimensional fiber architectures of the human heart. However, it is difficult to know how well the diffusion characteristics calculated from diffusion images reflect the microstructure properties of the myocardium since there is no ground-truth information available and add to that the influence of various factors such as spatial resolution, noise and artifacts, etc. The main objective of this thesis is then to develop realistic model-based dMRI simulators to simulate diffusion-weighted images for both ex vivo and in vivo cardiac fibers by integrating different imaging modalities, and propose a generic tool for the evaluation of imaging quality and image processing algorithms. To achieve this, the present work focuses on four parts. The first part concerns the formulation of basic dMRI simulation theory for diffusion image generation and subsequent applications on simple cardiac fiber models, and tries to elucidate the underlying relationship between the measured diffusion anisotropic properties and the cardiac fiber characteristics, including both physical and structural ones. The second part addresses the simulation of diffusion magnetic resonance images at multiple scales based on the polarized light imaging data of the human heart. Through both qualitative and quantitative comparison between diffusion properties at different simulation scales, the relationship between the microstructure variation and the diffusion properties observed at macroscopic scales is investigated. The third part deals with studying the influence of imaging parameters on diffusion image properties by means of the improved simulation theory. The last part puts the emphasis on the modeling of in vivo cardiac fiber structures and the simulation of the corresponding diffusion images by combining the cardiac fiber structure and the a priori known heart motion. The proposed simulators provide us a generic tool for generating the simulated diffusion images that can be used for evaluating image processing algorithms, optimizing the choice of MRI parameters in both ex vivo and in vivo cardiac fiber imaging, and investigating the relationship between microscopic fiber structure and macroscopic diffusion properties.
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Desenvolvimento de nanoemulsões biocompatíveis como sistema de liberação intraocular do celecoxibe. /Perissinato, Aline Gravinez January 2019 (has links)
Orientador: Anselmo Gomes de Oliveira / Resumo: O celecoxibe (CEL) é um inibidor específico de ciclooxigenase 2 e vem sendo estudado também como inibidor da atividade angiogênica em razão de sua propriedade de inibir o fator de crescimento endotelial vascular (VEGF). Devido às suas características físico-químicas, o CEL possui baixa solubilidade em água e alta permeabilidade, sendo classificado como fármaco pertencente à classe 2 do Sistema de Classificação Biofarmacêutica. Alguns anti-inflamatórios não esteróides têm sido utilizados por via tópica no tratamento de grande parte das doenças do segmento anterior dos olhos, mas também apresentam bom prognóstico para o tratamento de doenças do segmento posterior dos olhos, tais como a retinopatia diabética (RD), degeneração macular relacionada à idade (DMRI) e oclusão venosa retinal (OVR). Na maioria dos casos as concentrações locais dos fármacos no segmento posterior dos olhos não conseguem atender às necessidades quantitativas e temporais dos estímulos dessas doenças quando administrados pela via oral, ocular tópica ou parenteral sistêmica. Assim, o objetivo deste projeto foi desenvolver e caracterizar nanoemulsões (NEs) biocompatíveis visando à administração intraocular do CEL. Os sistemas nanoemulsionados contêm Fosfatidilcolina de Soja (FS) e Tween®20 (Tw) como tensoativos, Captex®200 como fase oleosa e tampão fosfato de potássio pH 7,2 como fase aquosa. As NEs foram desenvolvidas e sua nanoestrutura foi caracterizada através do diâmetro médio de gotículas onde as NEs vaz... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Celecoxib (CEL) is a specific inhibitor of cyclooxygenase 2 and has also been studied as an inhibitor of angiogenic activity because of its property of inhibiting vascular endothelial growth factor (VEGF). Due to its physico-chemical characteristics, CEL has low solubility in water and high permeability being classified as a drug belonging to class 2 of the Biopharmaceutical Classification System. Some anti-inflammatory drugs have been used topically to treat most of the anterior segment eye diseases, but also have a good prognosis for the treatment of diseases of the posterior segment of the eye such as diabetic retinopathy (DR), age-related macular degeneration (AMD) and retinal venous occlusion (RVO). In most cases the local concentrations of the drugs in the posterior segment of the eye fail to reach the quantitative and temporal needs of the stimuli of these diseases when administered by the oral, topical ocular and systemic parenteral rout. The aim of this project was to develop and characterize biocompatible nanoemulsions (NEs) capable of increasing the apparent solubility of CEL for intraocular administration. Nanoemulsified systems contain Soy Phosphatidylcholine (FS) and Tween®20 (Tw) as surfactants, Captex®200 as oily phase and potassium phosphate buffer pH 7.2 as the aqueous phase. The NEs were developed and their nanostructure was characterized by the mean diameter of droplets where the empty NEs had an average diameter of the order of 40 nm with a zeta potential... (Complete abstract click electronic access below) / Doutor
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MR microscopy of neuronal tissue : acquisition acceleration, modelling and experimental validation of water diffusion / Microscopie du tissu neuronal par IRM : accélération des acquisitions, modélisation et validation expérimentale de la diffusion de l'eauNguyen, Van Khieu 10 April 2017 (has links)
La technique d’acquisition comprimée ou compressed sensing (CS) exploite la compressibilité de différents types d’images pour reconstruire des données sous-échantillonnées sans perte d’informations. Cette technique peut être appliquée à l’IRM pour réduire les temps d’acquisition. CS est basée sur trois composantes majeures : (1) la représentation parcimonieuse du signal dans un domaine de transformation, (2) des mesures incohérentes et (3) une méthode de reconstruction non-linéaire avec une contrainte de parcimonie. Dans la première résultats partie de cette thèse, nous proposons un nouveau modèle de sous-échantillonnage basé sur la théorie de l’agrégation limitée par la diffusion (DLA) et montrons qu’il est plus performant que la méthode de sous-échantillonnage aléatoire. Le modèle de sous-échantillonnage DLA a été utilisé pour implémenter la technique de CS pour l’imagerie haute résolution pondérée T2 et T1 sur un champ magnétique très intense (17.2T). Pour chacune des pondérations, le temps d’acquisition a été réduit de 50% tout en conservant la qualité des images en termes de résolution spatiale, rapport contraste sur bruit et quantification de l’intensité du signal. Les deux nouvelles séquences d’impulsions CS (csRARE et csFLASH) ont été implémentées sur le logiciel commercial ParaVision 5.1. La seconde résultats partie de la thèse est centrée sur l’étude de la dépendance en temps de la diffusivité dans le ganglion abdominal de l’Aplysia Californica. Le ganglion abdominal de l’aplysie a été choisi pour cette étude d’imagerie car l’IRM à haute résolution permet la description anatomique fine du réseau cellulaire (taille des neurones individuels et orientation des axones). Utiliser les tissus neuronaux de l’aplysie pour étudier la relation entre la structure cellulaire et le signal d’IRM de diffusion peut permettre de comprendre cette relation pour des organismes plus complexes. Le signal d’IRM de diffusion (IRMd) a été mesuré à différents temps de diffusion dans le ganglion abdominal et des simulations de la diffusion de l’eau dans des géométries obtenues à partir de la segmentation d’images haute résolution pondérées T2 et l’incorporation d’informations sur la structure cellulaire trouvées dans la littérature ont été réalisées. Pour comparer le signal d’IRMd dans des neurones composés d’une seule cellule avec le signal des simulations numériques, des cellules de grande taille ont été segmentées à partir d’images anatomiques pondérées T2. A l’intérieur des cellules, un noyau à forme irrégulière a été généré manuellement (environ 25-30% en fraction volumique). Les petites cellules ont été modélisées comme des petites sphères avec un petit noyau sphérique concentrique (environ 25% en fraction volumique). Le nerf a été modélisé en combinant des axones (cylindres) de différents diamètres en cohérence avec la littérature. Le signal numérique d’IRMd a été simulé en résolvant l’équation de Bloch-Torrey pour les domaines géométriques décris ci-dessus. En fittant le signal expérimental avec le signal simulé pour différents types de cellules comme les grandes cellules neuronales (diamètre entre 150 et 420 µm), des agrégats de petites cellules neuronales ayant la forme d’un sac (jusqu’à 400 cellule chez l’aplysie adulte dans chaque sac avec une taille cellulaire entre 40 et 100 µm de diamètre), des nerfs (groupes d’axones de forme cylindrique avec un diamètre de moins de 1 à 25 µm) pour une grande gamme de temps de diffusions, nous avons obtenu des estimations du coefficient de diffusion intrinsèque dans le noyau et le cytoplasme (pour les neurones) et le coefficient de diffusion intrinsèque dans les axones (pour les nerfs). Nous avons aussi évalué la pertinence d’utiliser une formule préexistante décrivant la dépendance en temps du coefficient de diffusion pour estimer la taille des cellules. / Compressed sensing (CS) exploits the compressibility of different types of images to reconstruct undersampled data without loss of information. The technique can be applied to MRI to reduce the acquisition times. The CS is based on three major components: (1) sparsity representation of the signal in some transform domain, (2) incoherent measurements, and (3) sparsity-constrained nonlinear reconstruction method. If the total number of points in the image is larger than four times the number of sparse coefficients, then the reconstruction of under sampled data is feasible. In the first results part of this thesis, we propose a new under sampling model based on the diffusion limited aggregation (DLA) theory and show that it performs better than the random variable under sampling method. The DLA under sampling model was used to implement the CS for T2-weighted and T1-weighted high resolution imaging at the ultra-high magnetic field (17.2T). In both cases, the acquisition time was reduced by 50% while maintaining the quality of the images in terms of spatial resolution, contrast to noise ratio, and signal intensity quantification. Both new CS pulse sequences (csRARE and csFLASH) were implemented in ParaVision 5.1 commercial software. The second results part of the thesis is focused on the study of the time-dependent diffusivity in the abdominal ganglion of Aplysia California. The Aplysia abdominal ganglion was chosen in this imaging study because high resolution MR imaging allows the fine anatomical description of the cellular network (size of individual neurons and orientation of axons). Using the Aplysia ganglia to study the relationship between the cellular structure and the diffusion MRI signal can shed light on this relationship for more complex organisms. We measured the dMRI signal at several diffusion times in the abdominal ganglion and performed simulations of water diffusion in geometries obtained after segmenting high resolution T2-weighted images and incorporating known information about the cellular structure from the literature. To match the dMRI signal in the single cell neurons with numerical simulations signal, the large cell outline was segmented from the anatomical T2 weighted image. Inside this cell shape, an irregularly shaped nucleus was manually generated (around 25-30% volume fraction). The small cells were modeled as small spheres with a smaller concentric spherical nucleus (around 25% volume fraction). The nerve was modeled by combining axons (cylinders) of different diameters consistent with the literature. The numerical dMRI signal can be simulated by solving Bloch-Torrey equation under the geometries domain described above. By fitting the experimental signal to the simulated signal for several types of cells such as: large cell neurons (diameter between 150 µm and 420 µm); cluster of small neuron cells gathered in the shape of a bag (up to 400 cells in adult Aplysia in each bag with cell size between 40 µm to 100 µm in diameter); and nerves (group of axons cylindrical shape diameter from less than 1 µm to 25 µm) at a wide range of diffusion times, we obtained estimates of the intrinsic diffusion coefficient in the nucleus and the cytoplasm (for cell neurons) and the intrinsic diffusion coefficient in the axons (for the nerves). We also evaluated the reliability of using an existing formula for the time-dependent diffusion coefficient to estimate cell size.
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Simulace syntetických difúzních MRI dat na základě Brownova pohybu / Simulations of synthetic diffusion MRI data based on Brownian motionValla, Radek January 2015 (has links)
This master thesis focuses on dMRI (diffusion magnetic resonance imaging) and its dependance on diffusion in human brain tissue. It is described how to retrieve an image from gained data and its properties, advantages and disadvantages. It mentions problem in detecting kissing fibres due to its similarity with crossing fibres. Design of mathematical models of axons is decribed and suggested measurement to detect difference in signals for kissing and crossing fibres. It describes new simulator of diffusion-weighted MRI (dMRI) data which is able to generate it based on random walk algorithm with geometrical constraints not only for crossing fiber geometry, but also as o novelty for bending and kissing fiber geometries. This study contains results of simulations and disscusion about their usefulness with suggestions for simulator improvement. Simulated dMRI data shows significant difference in certain gradients. Data reconstruction shows, that these reults cannot be reconstructed into the same geometry as it was simulated for.
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Multi-tensorové zobrazování detailu míchy z dMRI dat s vysokým úhlovým rozlišením / Multi-tensor imaging of spinal cord detail from high anglular resolution dMRI dataZimolka, Jakub January 2017 (has links)
The aim of this work was to establish a comprehensive processing pipeline of cervical spinal cord HARDI dMRI data and T2-weighted anatomical MRI images in high-resolution. In the research part we provide description of anatomical data processing, theoretical background of dMRI, description of current approaches to 3D anisotropic diffusion estimation as well as current imaging methods of spinal cord axonal bundles. As one of the first in the world, we are investigating multiple-direction diffusion models for human in-vivo spinal cord white matter minority bundles imaging. We designed our own processing pipeline utilizing Spinal Cord Toolbox (SCT), FSL, in-house developer scripts and TORQUE-based batch system for grid computation, tested on real data from cervical spinal cord area between segments C4-C6 from 26 healthy volunteers. Designed processing pipeline with one non-automatic step, works from pre-processing to parcelation of selected spinal cord structures based on co-registration with anatomical spinal cord template for 25 subjects. One person data includes motion artifacts for which the proces failed. There are visible waves in sagittal images of some subjects caused probably by blood-vessel pulsing. Local quantification metrics of spinal cord anatomy (fractional anisotropy – FA, fractional volumes of first – f1 and second – f2 direction of anisotropic diffusion) from different parts (white matter, gray matter, cortico-spinal tract) and from different population groups (men vs. women), were extracted from dMRI data. As we expected, FA maps show visible decreases in areas of gray matter. We also detected second diffusion dirrection in slices, where the spinal roots come out. In some areas, fractional volume of second diffusion direction reaches up to 40% of the total component of the dMRI signal. All mentioned parameters probability density functions for all mentioned groups are non-normal distributions. Between male and female groups there were no significant distribution differences for f1 and f2 volumes. The distribution of FA values between men and women is statistically different. Unfortunatelly, there is a significant inter-subject variability in results, which has much higher dispersion than differences between different group distributions. Despite the inter-subject variability, this work significantly extends the knowledge about data acquisiton capabilities and MRI and dMRI data from cervical spinal cord image processing. This work also lays down foundations for utilization of the imaging method in future and planned clinical research, where it will be possible to test the alteration of the spinal cord anatomy on the minor secondary bundles separately.
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Optimal Q-Space Sampling Scheme : Using Gaussian Process Regression and Mutual InformationHassler, Ture, Berntsson, Jonathan January 2022 (has links)
Diffusion spectrum imaging is a type of diffusion magnetic resonance imaging, capable of capturing very complex tissue structures, but requiring a very large amount of samples in q-space and therefore time. The purpose of this project was to create and evaluate a new sampling scheme in q-space for diffusion MRI, trying to recreate the ensemble averaged propagator (EAP) with fewer samples without significant loss of quality. The sampling scheme was created by greedily selecting the measurements contributing with the most mutual information. The EAP was then recreated using the sampling scheme and interpolation. The mutual information was approximated using the kernel from a Gaussian process machine learning model. The project showed limited but promising results on synthetic data, but was highly restricted by the amount of available computational power. Having to resolve to using a lower resolution mesh when calculating the optimal sampling scheme significantly reduced the overall performance.
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