Higher-Order Tensors and Differential Topology in Diffusion MRI Modeling and Visualization

Diffusion Weighted Magnetic Resonance Imaging (DW-MRI) is a noninvasive method for creating three-dimensional scans of the human brain. It originated mostly in the 1970s and started its use in clinical applications in the 1980s. Due to its low risk and relatively high image quality it proved to be an indispensable tool for studying medical conditions as well as for general scientific research. For example, it allows to map fiber bundles, the major neuronal pathways through the brain. But all evaluation of scanned data depends on mathematical signal models that describe the raw signal output and map it to biologically more meaningful values. And here we find the most potential for improvement. In this thesis we first present a new multi-tensor kurtosis signal model for DW-MRI. That means it can detect multiple overlapping fiber bundles and map them to a set of tensors. Compared to other already widely used multi-tensor models, we also add higher order kurtosis terms to each fiber. This gives a more detailed quantification of fibers. These additional values can also be estimated by the Diffusion Kurtosis Imaging (DKI) method, but we show that these values are drastically affected by fiber crossings in DKI, whereas our model handles them as intrinsic properties of fiber bundles. This reduces the effects of fiber crossings and allows a more direct examination of fibers. Next, we take a closer look at spherical deconvolution. It can be seen as a generalization of multi-fiber signal models to a continuous distribution of fiber directions. To this approach we introduce a novel mathematical constraint. We show, that state-of-the-art methods for estimating the fiber distribution become more robust and gain accuracy when enforcing our constraint. Additionally, in the context of our own deconvolution scheme, it is algebraically equivalent to enforcing that the signal can be decomposed into fibers. This means, tractography and other methods that depend on identifying a discrete set of fiber directions greatly benefit from our constraint. Our third major contribution to DW-MRI deals with macroscopic structures of fiber bundle geometry. In recent years the question emerged, whether or not, crossing bundles form two-dimensional surfaces inside the brain. Although not completely obvious, there is a mathematical obstacle coming from differential topology, that prevents general tangential planes spanned by fiber directions at each point to be connected into consistent surfaces. Research into how well this constraint is fulfilled in our brain is hindered by the high precision and complexity needed by previous evaluation methods. This is why we present a drastically simpler method that negates the need for precisely finding fiber directions and instead only depends on the simple diffusion tensor method (DTI). We then use our new method to explore and improve streamsurface visualization.<br /

Uncertainty-aware Visualization in Medical Imaging - A Survey

Medical imaging (image acquisition, image transformation, and image visualization) is a standard tool for clinicians in order to make diagnoses, plan surgeries, or educate students. Each of these steps is affected by uncertainty, which can highly influence the decision-making process of clinicians. Visualization can help in understanding and communicating these uncertainties. In this manuscript, we aim to summarize the current state-of-the-art in uncertainty-aware visualization in medical imaging. Our report is based on the steps involved in medical imaging as well as its applications. Requirements are formulated to examine the considered approaches. In addition, this manuscript shows which approaches can be combined to form uncertainty-aware medical imaging pipelines. Based on our analysis, we are able to point to open problems in uncertainty-aware medical imaging

Validation of deep learning techniques for quality augmentation in diffusion MRI for clinical studies

The objective of this study is to evaluate the efficacy of deep learning (DL) techniques in improving the quality of diffusion MRI (dMRI) data in clinical applications. The study aims to determine whether the use of artificial intelligence (AI) methods in medical images may result in the loss of critical clinical information and/or the appearance of false information. To assess this, the focus was on the angular resolution of dMRI and a clinical trial was conducted on migraine, specifically between episodic and chronic migraine patients. The number of gradient directions had an impact on white matter analysis results, with statistically significant differences between groups being drastically reduced when using 21 gradient directions instead of the original 61. Fourteen teams from different institutions were tasked to use DL to enhance three diffusion metrics (FA, AD and MD) calculated from data acquired with 21 gradient directions and a b-value of 1000 s/mm2. The goal was to produce results that were comparable to those calculated from 61 gradient directions. The results were evaluated using both standard image quality metrics and Tract-Based Spatial Statistics (TBSS) to compare episodic and chronic migraine patients. The study results suggest that while most DL techniques improved the ability to detect statistical differences between groups, they also led to an increase in false positive. The results showed that there was a constant growth rate of false positives linearly proportional to the new true positives, which highlights the risk of generalization of AI-based tasks when assessing diverse clinical cohorts and training using data from a single group. The methods also showed divergent performance when replicating the original distribution of the data and some exhibited significant bias. In conclusion, extreme caution should be exercised when using AI methods for harmonization or synthesis in clinical studies when processing heterogeneous data in clinical studies, as important information may be altered, even when global metrics such as structural similarity or peak signal-to-noise ratio appear to suggest otherwise

Neuro4Neuro: A neural network approach for neural tract segmentation using large-scale population-based diffusion imaging

Subtle changes in white matter (WM) microstructure have been associated with normal aging and neurodegeneration. To study these associations in more detail, it is highly important that the WM tracts can be accurately and reproducibly characterized from brain diffusion MRI. In addition, to enable analysis of WM tracts in large datasets and in clinical practice it is essential to have methodology that is fast and easy to apply. This work therefore presents a new approach for WM tract segmentation: Neuro4Neuro, that is capable of direct extraction of WM tracts from diffusion tensor images using convolutional neural network (CNN). This 3D end-to-end method is trained to segment 25 WM tracts in aging individuals from a large population-based study (N=9752, 1.5T MRI). The proposed method showed good segmentation performance and high reproducibility, i.e., a high spatial agreement (Cohen's kappa, k = 0.72 ~ 0.83) and a low scan-rescan error in tract-specific diffusion measures (e.g., fractional anisotropy: error = 1% ~ 5%). The reproducibility of the proposed method was higher than that of a tractography-based segmentation algorithm, while being orders of magnitude faster (0.5s to segment one tract). In addition, we showed that the method successfully generalizes to diffusion scans from an external dementia dataset (N=58, 3T MRI). In two proof-of-principle experiments, we associated WM microstructure obtained using the proposed method with age in a normal elderly population, and with disease subtypes in a dementia cohort. In concordance with the literature, results showed a widespread reduction of microstructural organization with aging and substantial group-wise microstructure differences between dementia subtypes. In conclusion, we presented a highly reproducible and fast method for WM tract segmentation that has the potential of being used in large-scale studies and clinical practice.Comment: Preprint to be published in NeuroImag

Doctor of Philosophy

dissertationImage-based biomechanics, particularly numerical modeling using subject-specific data obtained via imaging, has proven useful for elucidating several biomechanical processes, such as prediction of deformation due to external loads, applicable to both normal function and pathophysiology of various organs. As the field evolves towards applications that stretch the limits of imaging hardware and acquisition time, the information traditionally expected as input for numerical routines often becomes incomplete or ambiguous, and requires specific acquisition and processing strategies to ensure physical accuracy and compatibility with predictive mathematical modeling. These strategies, often derivatives or specializations of traditional mechanics, effectively extend the nominal capability of medical imaging hardware providing subject-specific information coupled with the option of using the results for predictive numerical simulations. This research deals with the development of tools for extracting mechanical measurements from a finite set of imaging data and finite element analysis in the context of constructing structural atlases of the heart, understanding the biomechanics of the venous vasculature, and right ventricular failure. The tools include: (1) application of Hyperelastic Warping image registration to displacement-encoded MRI for reconstructing absolute displacement fields, (2) combination of imaging and a material parameter identification approach to measure morphology, deformation, and mechanical properties of vascular tissue, and (3) extrapolation of diffusion tensor MRI acquired at a single time point for the prediction the structural changes across the cardiac cycle with mechanical simulations. Selected tools were then applied to evaluate structural changes in a reversible animal model for right ventricular failure due to pressure overload