Visualization of Tensor Fields in Mechanics

Tensors are used to describe complex physical processes in many applications. Examples include the distribution of stresses in technical materials, acting forces during seismic events, or remodeling of biological tissues. While tensors encode such complex information mathematically precisely, the semantic interpretation of a tensor is challenging. Visualization can be beneficial here and is frequently used by domain experts. Typical strategies include the use of glyphs, color plots, lines, and isosurfaces. However, data complexity is nowadays accompanied by the sheer amount of data produced by large-scale simulations and adds another level of obstruction between user and data. Given the limitations of traditional methods, and the extra cognitive effort of simple methods, more advanced tensor field visualization approaches have been the focus of this work. This survey aims to provide an overview of recent research results with a strong application-oriented focus, targeting applications based on continuum mechanics, namely the fields of structural, bio-, and geomechanics. As such, the survey is complementing and extending previously published surveys. Its utility is twofold: (i) It serves as basis for the visualization community to get an overview of recent visualization techniques. (ii) It emphasizes and explains the necessity for further research for visualizations in this context

Visual analytics methods for shape analysis of biomedical images exemplified on rodent skull morphology

In morphometrics and its application fields like medicine and biology experts are interested in causal relations of variation in organismic shape to phylogenetic, ecological, geographical, epidemiological or disease factors - or put more succinctly by Fred L. Bookstein, morphometrics is "the study of covariances of biological form". In order to reveal causes for shape variability, targeted statistical analysis correlating shape features against external and internal factors is necessary but due to the complexity of the problem often not feasible in an automated way. Therefore, a visual analytics approach is proposed in this thesis that couples interactive visualizations with automated statistical analyses in order to stimulate generation and qualitative assessment of hypotheses on relevant shape features and their potentially affecting factors. To this end long established morphometric techniques are combined with recent shape modeling approaches from geometry processing and medical imaging, leading to novel visual analytics methods for shape analysis. When used in concert these methods facilitate targeted analysis of characteristic shape differences between groups, co-variation between different structures on the same anatomy and correlation of shape to extrinsic attributes. Here a special focus is put on accurate modeling and interactive rendering of image deformations at high spatial resolution, because that allows for faithful representation and communication of diminutive shape features, large shape differences and volumetric structures. The utility of the presented methods is demonstrated in case studies conducted together with a collaborating morphometrics expert. As exemplary model structure serves the rodent skull and its mandible that are assessed via computed tomography scans

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

Doctor of Philosophy

dissertationDiffusion magnetic resonance imaging (dMRI) has become a popular technique to detect brain white matter structure. However, imaging noise, imaging artifacts, and modeling techniques, etc., create many uncertainties, which may generate misleading information for further analysis or applications, such as surgical planning. Therefore, how to analyze, effectively visualize, and reduce these uncertainties become very important research questions. In this dissertation, we present both rank-k decomposition and direct decomposition approaches based on spherical deconvolution to decompose the fiber directions more accurately for high angular resolution diffusion imaging (HARDI) data, which will reduce the uncertainties of the fiber directions. By applying volume rendering techniques to an ensemble of 3D orientation distribution function (ODF) glyphs, which we call SIP functions of diffusion shapes, one can elucidate the complex heteroscedastic structural variation in these local diffusion shapes. Furthermore, we quantify the extent of this variation by measuring the fraction of the volume of these shapes, which is consistent across all noise levels, the certain volume ratio. To better understand the uncertainties in white matter fiber tracks, we propose three metrics to quantify the differences between the results of diffusion tensor magnetic resonance imaging (DT-MRI) fiber tracking algorithms: the area between corresponding fibers of each bundle, the Earth Mover's Distance (EMD) between two fiber bundle volumes, and the current distance between two fiber bundle volumes. Based on these metrics, we discuss an interactive fiber track comparison visualization toolkit we have developed to visualize these uncertainties more efficiently. Physical phantoms, with high repeatability and reproducibility, are also designed with the hope of validating the dMRI techniques. In summary, this dissertation provides a better understanding about uncertainties in diffusion magnetic resonance imaging: where and how much are the uncertainties? How do we reduce these uncertainties? How can we possibly validate our algorithms

Transferring principles of solid-state and Laplace NMR to the field of in vivo brain MRI

Magnetic resonance imaging (MRI) is the primary method for non-invasive investigations of the human brain in health, disease, and development, but yields data that are difficult to interpret whenever the millimeter scale voxels contain multiple microscopic tissue environments with different chemical and structural properties. We propose a novel MRI framework to quantify the microscopic heterogeneity of the living human brain as spatially resolved five-dimensional relaxation-diffusion distributions by augmenting a conventional diffusion-weighted imaging sequence with signal encoding principles from multidimensional solid-state nuclear magnetic resonance (NMR) spectroscopy, relaxation-diffusion correlation methods from Laplace NMR of porous media, and Monte Carlo data inversion. The high dimensionality of the distribution space allows resolution of multiple microscopic environments within each heterogeneous voxel as well as their individual characterization with novel statistical measures that combine the chemical sensitivity of the relaxation rates with the link between microstructure and the anisotropic diffusivity of tissue water. The proposed framework is demonstrated on a healthy volunteer using both exhaustive and clinically viable acquisition protocols

Developing novel diffusion MRI methods for comprehensive analysis of restricted and anisotropic self-diffusion system

Diffusion MRI is a non-invasive imaging technique used to study the microstructural properties of biological tissues by observing the self-diffusion of water molecules. Traditional diffusion MRI methods, based on the pulsed gradient spin-echo sequence, employ magnetic field gradients to encode information about translational motion. However, this approach combines various aspects of diffusion, such as restriction, anisotropy, and flow, into a single observable, leading to interpretation ambiguities, especially in complex heterogeneous materials like living biological tissues.In this thesis, we address these challenges and push the boundaries of diffusion MRI by introducing innovative techniques for studying biological tissue microstructure. Our approach centers around the "double-rotation" technique borrowed from solid-state NMR, which generates modulated gradient waveforms, enabling us to explore the 2D frequency-anisotropy domain in-depth. By integrating this technique with oscillating gradients and tensor-valued encoding, we create a comprehensive methodology for data acquisition. Drawing inspiration from the "model-free" analytical strategies originally designed for studying rotational dynamics in macromolecules, we extend its applicability to MRI techniques for understanding diffusion in biological tissues.Through a series of proof-of-principle experiments, we validate our novel acquisition and analysis strategy across various samples. These experiments encompass the study of isotropic and anisotropic Gaussian diffusion in simple liquids, characterizing anisotropic Gaussian diffusion in a lyotropic liquid crystal with lamellar microstructure, and exploring restricted diffusion in a yeast cell sediment. Additionally, we showcase the effectiveness of our methods on ex vivo mouse brain and tumor tissue, highlighting the practical potential of our approach.Our proposed double-rotation gradient waveforms enable comprehensive sampling of both the frequency and "shape" dimensions of diffusion encoding, providing detailed insights into restriction and anisotropy in heterogeneous materials. The implications of our work extend to model-free investigations, allowing us to understand microstructural changes linked with pathology or normal brain development

Image Based Biomarkers from Magnetic Resonance Modalities: Blending Multiple Modalities, Dimensions and Scales.

The successful analysis and processing of medical imaging data is a multidisciplinary work that requires the application and combination of knowledge from diverse fields, such as medical engineering, medicine, computer science and pattern classification. Imaging biomarkers are biologic features detectable by imaging modalities and their use offer the prospect of more efficient clinical studies and improvement in both diagnosis and therapy assessment. The use of Dynamic Contrast Enhanced Magnetic Resonance Imaging (DCE-MRI) and its application to the diagnosis and therapy has been extensively validated, nevertheless the issue of an appropriate or optimal processing of data that helps to extract relevant biomarkers to highlight the difference between heterogeneous tissue still remains. Together with DCE-MRI, the data extracted from Diffusion MRI (DWI-MR and DTI-MR) represents a promising and complementary tool. This project initially proposes the exploration of diverse techniques and methodologies for the characterization of tissue, following an analysis and classification of voxel-level time-intensity curves from DCE-MRI data mainly through the exploration of dissimilarity based representations and models. We will explore metrics and representations to correlate the multidimensional data acquired through diverse imaging modalities, a work which starts with the appropriate elastic registration methodology between DCE-MRI and DWI- MR on the breast and its corresponding validation. It has been shown that the combination of multi-modal MRI images improve the discrimination of diseased tissue. However the fusion of dissimilar imaging data for classification and segmentation purposes is not a trivial task, there is an inherent difference in information domains, dimensionality and scales. This work also proposes a multi-view consensus clustering methodology for the integration of multi-modal MR images into a unified segmentation of tumoral lesions for heterogeneity assessment. Using a variety of metrics and distance functions this multi-view imaging approach calculates multiple vectorial dissimilarity-spaces for each one of the MRI modalities and makes use of the concepts behind cluster ensembles to combine a set of base unsupervised segmentations into an unified partition of the voxel-based data. The methodology is specially designed for combining DCE-MRI and DTI-MR, for which a manifold learning step is implemented in order to account for the geometric constrains of the high dimensional diffusion information.The successful analysis and processing of medical imaging data is a multidisciplinary work that requires the application and combination of knowledge from diverse fields, such as medical engineering, medicine, computer science and pattern classification. Imaging biomarkers are biologic features detectable by imaging modalities and their use offer the prospect of more efficient clinical studies and improvement in both diagnosis and therapy assessment. The use of Dynamic Contrast Enhanced Magnetic Resonance Imaging (DCE-MRI) and its application to the diagnosis and therapy has been extensively validated, nevertheless the issue of an appropriate or optimal processing of data that helps to extract relevant biomarkers to highlight the difference between heterogeneous tissue still remains. Together with DCE-MRI, the data extracted from Diffusion MRI (DWI-MR and DTI-MR) represents a promising and complementary tool. This project initially proposes the exploration of diverse techniques and methodologies for the characterization of tissue, following an analysis and classification of voxel-level time-intensity curves from DCE-MRI data mainly through the exploration of dissimilarity based representations and models. We will explore metrics and representations to correlate the multidimensional data acquired through diverse imaging modalities, a work which starts with the appropriate elastic registration methodology between DCE-MRI and DWI- MR on the breast and its corresponding validation. It has been shown that the combination of multi-modal MRI images improve the discrimination of diseased tissue. However the fusion of dissimilar imaging data for classification and segmentation purposes is not a trivial task, there is an inherent difference in information domains, dimensionality and scales. This work also proposes a multi-view consensus clustering methodology for the integration of multi-modal MR images into a unified segmentation of tumoral lesions for heterogeneity assessment. Using a variety of metrics and distance functions this multi-view imaging approach calculates multiple vectorial dissimilarity-spaces for each one of the MRI modalities and makes use of the concepts behind cluster ensembles to combine a set of base unsupervised segmentations into an unified partition of the voxel-based data. The methodology is specially designed for combining DCE-MRI and DTI-MR, for which a manifold learning step is implemented in order to account for the geometric constrains of the high dimensional diffusion information