09302 Abstracts Collection -- New Developments in the Visualization and Processing of Tensor Fields

From 19.07. to 24.07.2009, the Dagstuhl Seminar 09302 ``New Developments in the Visualization and Processing of Tensor Fields \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Cerebral white matter analysis using diffusion imaging

Thesis (Ph. D.)--Harvard-MIT Division of Health Sciences and Technology, 2006.Includes bibliographical references (p. 183-198).In this thesis we address the whole-brain tractography segmentation problem. Diffusion magnetic resonance imaging can be used to create a representation of white matter tracts in the brain via a process called tractography. Whole brain tractography outputs thousands of trajectories that each approximate a white matter fiber pathway. Our method performs automatic organization, or segmention, of these trajectories into anatomical regions and gives automatic region correspondence across subjects. Our method enables both the automatic group comparison of white matter anatomy and of its regional diffusion properties, and the creation of consistent white matter visualizations across subjects. We learn a model of common white matter structures by analyzing many registered tractography datasets simultaneously. Each trajectory is represented as a point in a high-dimensional spectral embedding space, and common structures are found by clustering in this space. By annotating the clusters with anatomical labels, we create a model that we call a high-dimensional white matter atlas.(cont.) Our atlas creation method discovers structures corresponding to expected white matter anatomy, such as the corpus callosum, uncinate fasciculus, cingulum bundles, arcuate fasciculus, etc. We show how to extend the spectral clustering solution, stored in the atlas, using the Nystrom method to perform automatic segmentation of tractography from novel subjects. This automatic tractography segmentation gives an automatic region correspondence across subjects when all subjects are labeled using the atlas. We show the resulting automatic region correspondences, demonstrate that our clustering method is reproducible, and show that the automatically segmented regions can be used for robust measurement of fractional anisotropy.by Lauren Jean O'Donnell.Ph.D

Measures for validation of DTI tractography

pre-printThe evaluation of analysis methods for diffusion tensor imaging (DTI) remains challenging due to the lack of gold standards and validation frameworks. Significant work remains in developing metrics for comparing fiber bundles generated from streamline tractography. We propose a set of volumetric and tract oriented measures for evaluating tract differences. The different methods developed for this assessment work are: an overlap measurement, a point cloud distance and a quantification of the diffusion properties at similar locations between fiber bundles. The application of the measures in this paper is a comparison of atlas generated tractography to tractography generated in individual images. For the validation we used a database of 37 subject DTIs, and applied the measurements on five specific fiber bundles: uncinate, cingulum (left and right for both bundles) and genu. Each measurments is interesting for specific use: the overlap measure presents a simple and comprehensive metric but is sensitive to partial voluming and does not give consistent values depending on the bundle geometry. The point cloud distance associated with a quantile interpretation of the distribution gives a good intuition of how close and similar the bundles are. Finally, the functional difference is useful for a comparison of the diffusion properties since it is the focus of many DTI analysis to compare scalar invariants. The comparison demonstrated reasonable similarity of results. The tract difference measures are also applicable to comparison of tractography algorithms, quality control, reproducibility studies, and other validation problems

Optimization of the diffusion-weighted MRI processing pipeline for the longitudinal assessment of the brain microstructure in a rat model of Alzheimer’s disease

Tese de mestrado integrado, Engenharia Biomédica e Biofísica (Radiações em Diagnóstico e Terapia) Universidade de Lisboa, Faculdade de Ciências, 2019The mechanism that triggers Alzheimer’s disease (AD) is not well-established, with amyloid plaques, neurofibrillary tangles of tau protein, microgliosis and glucose hypometabolism all likely involved in the early cascade. One main advantage of animal models is the possibility to tease out the impact of each insult on the neurodegeneration. Following an intracerebroventricular (icv) injection of streptozotocin (STZ), rats and monkeys develop impaired brain glucose metabolism, i.e. “diabetes of the brain”. Nu-merous studies have reported AD-like features in icv-STZ animals, but this model has never been char-acterized in terms of Magnetic Resonance Imaging (MRI)-derived biomarkers beyond structural brain atrophy. White matter degeneration has been proposed as a promising biomarker for AD that well pre-cedes cortical atrophy and correlates strongly with disease severity. Therefore, this project proposes a longitudinal study of white matter degeneration in icv-STZ rats using diffusion MRI. An existing image processing pipeline was primarily used to obtain preliminary results and propose an optimization strat-egy to improve it in terms of data quality and reliability. These strategies were tested and implemented in the pipeline when confirmed to be valuable, in order to achieve results as reproducible as possible and find the spatio-temporal pattern of brain degeneration in this animal model. All experiments were approved by the local Service for Veterinary Affairs. Male Wistar rats (N=18) (236±11 g) underwent a bilateral icv-injection of either streptozotocin (3 mg/kg, STZ group, N=10) or buffer (control group, CTL, N=8). Rats were scanned at four timepoints following surgery on a 14 T Varian system. Diffusion data were acquired using a semi-adiabatic SE-EPI PGSE sequence as follows: 4 (b=0 ms/μm2), 12 (b=0.8 ms/μm2), 16 (b=1.3 ms/μm2) and 30 (b=2 ms/μm2) directions; TE/TR=48/2500 ms, 9 coronal 1 mm slices, δ/Δ=4/27 ms, FOV=23x17 mm2, matrix=128x64 and 4 shots. The existing image processing pipeline included image denoising and eddy-correction. Moreover, diffusion and kurtosis tensors were calculated for each voxel, producing parametric maps of fractional anisotropy (FA), mean, axial and radial diffusivity (MD, AxD and RD) and mean, axial and radial kur-tosis (MK, AK and RK). Additionally, the two-compartment WMTI-Watson model was further esti-mated to provide specificity to the microstructure assessment. The following metrics were derived from the model: volume water fraction , parallel intra-axonal diffusivity , parallel ,║ and perpendicular extra-axonal diffusivities ,ꓕ and dispersion of fiber orientations 2. Since the model allows for two mathematical solutions, the >,║ solution was retained based on recent evidence. Considering pre-vious findings, the corpus callosum, cingulum, fornix and fimbria were chosen as white matter regions of interest (ROIs) and automatically segmented using anatomical atlas-based registration. Mean diffu-sion metrics were calculated in each ROI for each dataset. CTL and STZ groups were compared using two-sided t-tests at each timepoint. Within-group longitudinal changes were assessed using one-way ANOVA. Because of the small cohort, statistical analysis excluded the last time point. In the course of this project, strategies to optimize the existing pipeline were developed and tested. The existing brain atlas template was supplemented with white matter labels, rat brain extraction was semi-automated, and bias field correction of anatomical data was added before registration. Ventricle enlargement is typically reported in icv-STZ animals and normally constitutes an issue of misalignment in registration. In order to better match the label ROIs with the respective underlying tissue, several registration procedures were tested with different FA and color-coded FA template images. Color-coded FA-based registration dramatically improved the segmentation of the corpus callosum and the fimbria and reliability of diffusion metrics extracted from these regions. Moreover, additional fiber metrics were extracted from a newly developed tractography pipeline to compare with tensors metrics and finally, tensors metrics were evaluated in the gray matter for a more comprehensive spatio-temporal character-ization of brain degeneration. Results from statistical analysis were obtained after implementing the successful optimization strat-egies into the pipeline. There were few significant differences within groups over time. However, be-tween-group differences at each time point were more pronounced. White matter microstructure altera-tions were consistent with previous studies of histology and cognitive performance of the icv-STZ model. Changes in tensors metrics indicate early axonal injury in the fimbria and fornix at 2 weeks after injection, a period of potential recovery at 6 weeks after injection and late axonal injury at 13 weeks in all ROIs. The WMTI-Watson biophysical model provided specificity to the underlying microstructure, by showing intra-axonal damage in the fimbria and corpus callosum as early as 2 weeks, followed by a recover period and definite axonal loss at 13 weeks after injection. Results from tensors metrics and the WMTI-Watson model are not only complementary, they are consistent with each other and with previously-established trends for structural thickness, memory per-formance, amyloid deposition and inflammation. The icv-STZ model displays white matter changes in tracts reportedly affected by AD, while the degeneration is induced primarily by impaired brain glucose metabolism. The icv-STZ constitutes an excellent model to reproduce sporadic AD and should allow to further explore the hypothesis of AD being “type III diabetes”. The combination of diffusion information extracted from tensor imaging and biophysical modelling is a promising set of tools to assess white matter in the AD brain and might be the upcoming strategy to assess the human brain. Regarding future work, it will focus on estimating the correlation between microstructural alterations and functional con-nectivity (from resting-state functional MRI), glucose hypometabolism (from FDG-PET), and patholog-ical features (from histological stainings) – all currently under processing at CIBM. Tractography is a cutting-edge methodology to assess brain connectivity and the pipeline created could be further devel-oped to improve understanding and support diffusion metrics. The relationship between white and gray matter will also improve the understanding of spatio-temporal degeneration and the progression nature of the disease.O mecanismo que desencadeia a doença de Alzheimer (DA) não é bem conhecido, contudo sabe-se que a presença de placas amilóides e de emaranhados neurofibrilares da proteína tau, microgliose e ainda hipometabolismo de glucose estão envolvidos na fase inicial da cascata de desenvolvimento da doença. A principal vantagem dos modelos animais é justamente a possibilidade de estudar individualmente o impacto de cada um destes mecanismos no processo de neurodegeneração. Após uma injeção intracere-broventricular (icv) de estreptozotocina (STZ), várias espécies de animais mostraram um metabolismo anormal de glucose no cérebro, processo que foi referido como “diabetes do cérebro”. Vários estudos demonstraram que animais icv-STZ são portadores de características típicas de DA, mas este modelo animal nunca foi estudado em termos de biomarcadores derivados de técnicas de imagem por ressonân-cia magnética (IRM), exceto atrofia estrutural do cérebro. Um biomarcador promissor de DA que se acredita preceder a atrofia do córtex cerebral é a degeneração da matéria branca do cérebro, uma vez que foi fortemente correlacionado com a progressão e gravidade da doença. Logo, este projeto propõe um estudo longitudinal da degeneração da matéria branca em ratazanas icv-STZ utilizando IRM de di-fusão. O plano de processamento de imagem existente foi utilizado primeiramente para obter resultados preliminares e viabilizar a proposta de estratégias de otimização da mesma, em termos de melhoramento da qualidade de imagem e credibilidade das variáveis extraídas das imagens resultantes. Estas estratégias foram testadas e implementadas no plano de processamento quando a sua performance confirmou ser de valor, para que os resultados fossem o mais reproduzíveis possível em caracterizar a distribuição espácio-temporal da degeneração do cérebro neste modelo animal. Todos os procedimentos aqui descritos foram aprovados pelo serviço local dos assuntos veterinários. Ratazanas macho Wistar (N=18, 236±11 g) foram submetidas a uma injeção icv de STZ (3 mg/kg) no caso do grupo infetado (N=10) ou de um buffer no caso do grupo de controlo (N=8). As ratazanas foram examinadas no scanner de IRM do tipo Varian de 14 T em quatro momentos no tempo: 2, 6, 13 e 21 semanas após a injeção. As imagens por difusão foram adquiridas com uma sequência semi-adiabática spin-echo EPI PGSE com os seguintes parâmetros: 4 (b=0), 12 (b=0.8 ms/μm2), 16 (b=1.3 ms/μm2) and 30 (b=2 ms/μm2) direções; TE/TR=48/2500 ms, 9 secções coronais de 1 mm, δ/Δ=4/27 ms, FOV=23x17 mm2, matriz=128x64 e 4 shots. O plano existente de processamento de imagem incluía a correção das imagens ao nível de ruído e correntes-eddy. Posteriormente, os tensores de difusão e curtose foram estimados para cada voxel e os mapas paramétricos de anisotropia fracional (FA), difusão média, axial e radial (MD, AD e RD) e cur-tose média, axial e radial (MK, AK e RK) foram calculados. Adicionalmente, um modelo de difusão de água nas fibras da matéria branca foi utilizado para providenciar maior especificidade ao estudo da microestrutura do cérebro. Como tal, o modelo de dois compartimentos denominado WMTI-Watson foi também estimado e as seguintes variáveis foram derivadas do mesmo: a fração do volume de água , a difusividade paralela intra-axonal , as difusividades paralela ,║ e perpendicular ,ꓕ extra-axonais e, finalmente, a orientação da dispersão axonal 2. Este modelo matemático tem duas soluções possíveis dada a sua natureza quadrática, pelo que a solução >,║ foi imposta com base em evidências re-centes. Considerando estudos anteriores, as regiões de interesse (RDIs) da matéria branca escolhidas para analisar a microestrutura cerebral foram o corpo caloso, o cíngulo, a fimbria e a fórnix. Estes foram automaticamente segmentados através de registo de imagem de um atlas das regiões do cérebro da rata-zana e as médias das medidas extraídas dos tensores de difusão e curtose e ainda do modelo biofísico neuronal foram calculadas em cada RDI para cada conjunto de imagens obtidas. Os dois grupos de teste e controlo foram comparados usando testes t de Student bilaterais em cada momento do tempo, e a comparação das alterações longitudinais em cada grupo foi feita usando uma ANOVA. Devido ao baixo número de amostras, o último momento no tempo às 21 semanas foi excluído da análise. No decorrer deste projeto, várias estratégias para otimizar o processamento de imagem ou comple-mentar a análise da informação disponível foram testadas. Nomeadamente, o atlas cerebral da ratazana foi aperfeiçoado relativamente às regiões de matéria branca, a segmentação do cérebro foi testada com algoritmos automáticos e a correção do bias field em imagens estruturais de IRM foi adicionada ao plano antes do registo de imagem. O aumento dos ventrículos cerebrais é uma característica frequente em animais icv-STZ, constituindo um problema de alinhamento nos métodos de registo de imagem. No sentido de otimizar a correspondência entre as regiões do atlas e as respetivas regiões na imagem estru-tural e por difusão, vários procedimentos de registo de imagem foram testados. O co-registo de imagem convencional utiliza imagens estruturais para normalizar o espaço das imagens por difusão, no entanto os mapas paramétricos de FA têm vindo a substituir este conceito dado o excelente contraste que provi-denciam entre a matéria branca e cinzenta do cérebro. Mapas de FA com diferentes direções predomi-nantes mostraram uma melhoria significante da segmentação do corpo caloso e da fimbria e também do poder estatístico das variáveis extraídas destas RDIs. Adicionalmente, um novo plano de processamento de tratografia foi construído de raiz no âmbito deste projeto para extrair variáveis adicionais das fibras de interesse e compará-las com as variáveis de difusão obtidas por análise voxel-a-voxel. Por último, as variáveis calculadas através dos tensores de difusão e curtose foram avaliadas na matéria cinzenta do cérebro para uma caracterização espácio-temporal da degeneração cerebral na DA. Os resultados da análise estatística foram obtidos após integrar no plano de processamento as estra-tégias que mostraram valorizar o projeto em termos de qualidade de imagem ou credibilidade das vari-áveis. Houve poucas diferenças significativas ao longo do tempo em cada grupo, no entanto as diferen-ças entre grupos foram bastante acentuadas. As alterações ao nível da microestrutura da matéria branca foram consistentes com estudos prévios em animais icv-STZ usando métodos histológicos e avaliações das suas capacidades cognitivas. Alterações nas variáveis extraídas dos tensores indicaram deficiência axonal inicial na fimbria e no fórnix 2 semanas após injeção no grupo de teste, um potencial período de recuperação às 6 semanas e novamente deficiência axonal às 13 semanas, sendo que neste período tardio todas as RDIs foram afetadas. O modelo biofísico WMTI-Watson confirmou aumentar especificidade ao estudo da microestrutura, visto que demostrou danos intra-axonais na fimbria e no corpo caloso 2 semanas após injeção, seguidos de um período de recuperação e de perda de estrutura axonal definitiva às 13 semanas em todas as RDIs. Não só estes dois métodos de análise de IRM de difusão se complementam, como são também con-sistentes entre eles e com as tendências de alterações ao longo do tempo descritas noutros estudos. Além disso, o animal icv-STZ mostrou alterações características da DA, mesmo tendo a degeneração cerebral sido induzida pela disrupção do metabolismo de glucose no cérebro. Como tal, este modelo animal é excelente para reproduzir a doença e deverá continuar a ser avaliado nas diferentes áreas multidiscipli-nares para explorar a hipótese de a DA ser desencadeada pela falha do sistema insulina/glucose. A com-binação da informação de difusão obtida dos tensores e da modelação da difusão neuronal provou ser uma ferramenta promissora no estudo das fibras da matéria branca do cérebro e poderá vir a ser o desafio futuro no que toca a investigação clínica da DA. Este estudo focar-se-á em correlacionar as alterações microestruturais aqui descritas com dados de conectividade funcional (obtida por IRM funcional em repouso), hipometabolismo de glucose (por FDG-PET) e outras características patológicas (por colora-ção histológica) – todos já em curso no CIBM. Tratografia é a metodologia topo de gama para aceder à conetividade cerebral e o plano de processamento gerado neste projeto poderá continuar a ser desenvol-vido no futuro para informação adicional, assim como a relação entre a matéria branca e cinzenta poderá suplementar a compreensão da progressão da doença no espaço e no tempo

Group analysis of DTI fiber tract statistics with application to neurodevelopment

Diffusion tensor imaging (DTI) provides a unique source of information about the underlying tissue structure of brain white matter in vivo including both the geometry of major fiber bundles as well as quantitative information about tissue properties represented by derived tensor measures. This paper presents a method for statistical comparison of fiber bundle diffusion properties between populations of diffusion tensor images. Unbiased diffeomorphic atlas building is used to compute a normalized coordinate system for populations of diffusion images. The diffeomorphic transformations between each subject and the atlas provide spatial normalization for the comparison of tract statistics. Diffusion properties, such as fractional anisotropy (FA) and tensor norm, along fiber tracts are modeled as multivariate functions of arc length. Hypothesis testing is performed non-parametrically using permutation testing based on the Hotelling T2 statistic. The linear discriminant embedded in the T2 metric provides an intuitive, localized interpretation of detected differences. The proposed methodology was tested on two clinical studies of neurodevelopment. In a study of one and two year old subjects, a significant increase in FA and a correlated decrease in Frobenius norm was found in several tracts. Significant differences in neonates were found in the splenium tract between controls and subjects with isolated mild ventriculomegaly (MVM) demonstrating the potential of this method for clinical studies

Anisotropy Across Fields and Scales

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

Anisotropy Across Fields and Scales

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

Homogeneity based segmentation and enhancement of Diffusion Tensor Images : a white matter processing framework

In diffusion magnetic resonance imaging (DMRI) the Brownian motion of the water molecules, within biological tissue, is measured through a series of images. In diffusion tensor imaging (DTI) this diffusion is represented using tensors. DTI describes, in a non-invasive way, the local anisotropy pattern enabling the reconstruction of the nervous fibers - dubbed tractography. DMRI constitutes a powerful tool to analyse the structure of the white matter within a voxel, but also to investigate the anatomy of the brain and its connectivity. DMRI has been proved useful to characterize brain disorders, to analyse the differences on white matter and consequences in brain function. These procedures usually involve the virtual dissection of white matters tracts of interest. The manual isolation of these bundles requires a great deal of neuroanatomical knowledge and can take up to several hours of work. This thesis focuses on the development of techniques able to automatically perform the identification of white matter structures. To segment such structures in a tensor field, the similarity of diffusion tensors must be assessed for partitioning data into regions, which are homogeneous in terms of tensor characteristics. This concept of tensor homogeneity is explored in order to achieve new methods for segmenting, filtering and enhancing diffusion images. First, this thesis presents a novel approach to semi-automatically define the similarity measures that better suit the data. Following, a multi-resolution watershed framework is presented, where the tensor field’s homogeneity is used to automatically achieve a hierarchical representation of white matter structures in the brain, allowing the simultaneous segmentation of different structures with different sizes. The stochastic process of water diffusion within tissues can be modeled, inferring the homogeneity characteristics of the diffusion field. This thesis presents an accelerated convolution method of diffusion images, where these models enable the contextual processing of diffusion images for noise reduction, regularization and enhancement of structures. These new methods are analysed and compared on the basis of their accuracy, robustness, speed and usability - key points for their application in a clinical setting. The described methods enrich the visualization and exploration of white matter structures, fostering the understanding of the human brain

Population-wise consistent segmentation of diffusion weighted magnetic resonance images

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.Includes bibliographical references (p. 161-167).In this thesis, we investigate unsupervised and semi-supervised methods to construct anatomical atlases and segment medical images. We propose an integrated registration and clustering algorithm to compute an anatomical atlas of fiber-bundles as well as deep gray matter structures from a population of diffusion tensor MR images (DT-MRI). We refer to this algorithm as "Consistency Clustering" since the outputs of the algorithm include population-wise consistent segmentations and correspondence between the subjects. The consistency is ensured through using a single anatomical model for the whole population, which is similar to the atlases used by experts for manual labeling. We experiment with both parametric and non-parametric models for the gray matter and white matter segmentation problems, each model resulting in a different kind of atlas. Consistent population-wise segmentations require development of several integrated algorithms for clustering, registration, atlas-building and outlier rejection. In this thesis we develop, implement and evaluate these tools individually and together as a population-wise segmentation tool. Together, Consistency Clustering enables automatic atlas construction in DT-MRI for a population, either normal or affected by a neural disorder. Consistency Clustering also provides the user the choice to include prior knowledge through a few labeled subjects (semi-supervised) or compute an anatomical atlas in a completely data driven manner (unsupervised). Furthermore, resulting anatomical models are compact representations of populations and can be used for population-wise morphometry. We implement and evaluate these methods using in vivo DT-MRI datasets. We investigate the benefits of population-wise segmentation as opposed to individually segmenting subjects, as well as effects of noise and initialization on the segmentations.by Ulas Ziyan.Ph.D