Estimation of a Multi-fascicle Model from Single B-Value Data with a Population-Informed Prior

Diffusion tensor imaging cannot represent heterogeneous fascicle orientations in one voxel. Various models propose to overcome this limitation. Among them, multi-fascicle models are of great interest to characterize and compare white matter properties. However, existing methods fail to estimate their parameters from conventional diffusion sequences with the desired accuracy. In this paper, we provide a geometric explanation to this problem. We demonstrate that there is a manifold of indistinguishable multi-fascicle models for single-shell data, and that the manifolds for different b-values intersect tangentially at the true underlying model making the estimation very sensitive to noise. To regularize it, we propose to learn a prior over the model parameters from data acquired at several b-values in an external population of subjects. We show that this population-informed prior enables for the first time accurate estimation of multi-fascicle models from single-shell data as commonly acquired in clinical context. The approach is validated on synthetic and in vivo data of healthy subjects and patients with autism. We apply it in population studies of the white matter microstructure in autism spectrum disorder. This approach enables novel investigations from large existing DWI datasets in normal development and in disease

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 /

Advanced MRI methods for probing disease severity and functional decline in multiple sclerosis

Multiple sclerosis (MS) is a chronic and severe disease of the central nervous system characterized by complex pathology including inflammatory demyelination and neurodegeneration. MS impacts >2.8 million people worldwide, with most starting with a relapsing-remitting form (RRMS) in young adulthood, and many of them worsening to a secondary-progressive course (SPMS) despite treatment. So, there is a clear need for improved disease characterization. MRI is an ideal tool for non-invasive assessment of MS pathology, but there is still no established measure of disease activity and functional consequences. This project aims to overcome the challenge by developing novel imaging measures based on brain diffusion MRI and phase congruency texture analysis of conventional MRI. Through advanced modeling and analysis of clinically feasible brain MRI, this thesis investigates whether and how the derived measures differentiate MS pathology types and disease severity and predict functional outcomes in MS. The overall process has led to important technical innovations in several aspects. These include: innovative modeling of simple diffusion acquisitions to generate high angular resolution diffusion imaging (HARDI) measures; new optimization and harmonization techniques for diffusion MRI; innovative neural network models to create new diffusion data for comprehensive HARDI modeling; and novel methods and a graphic user interface for optimizing phase congruency analyses. Assisted by different machine learning methods, collective findings show that advanced measures from both diffusion MRI and phase congruency are highly sensitive to subtle differences in MS pathology, which differentiate disease severity between RRMS and SPMS through multi-dimensional analyses including chronic active lesions, and predict functional outcomes especially in physical and neurocognitive domains. These results are clinically translational and the new measures and techniques can help improve the evaluation and management of both MS and similar diseases