Orientation of Sticks and Spheres - Estimating Tensor Shape and Orientation Distribution using Diffusion NMR

Abstract: The diffusion characteristics of water can be measured by using NMR methods. Specifically, the diffusion profiles in samples containing domains of water barriers are of major importance to be able to describe in applications such as diffusion tensor imaging or diffusion MRI-sequences. These sequences can be used to study the internal structure of samples of complex diffusion profiles. The diffusion characteristics can be described by a diffusion tensor matrix which can be parameterised by the isotropic diffusion coefficient and the level of anisotropy. This thesis work aims to measure diffusion weighted NMR signals from a triple-stimulated spin-echo pulse sequence to simultaneously determine both the diffusion tensor characteristics and the orientation density function, ODF. Traditionally, obtaining the ODF is based on assuming a fixed diffusion tensor in a diffusion-weighted NMR experiment to describe the different signal attenuations along different directions as differences in the shape of the microscopic water domains. By the work presented in this report, it is proven by measurements on lyotropic liquid crystal systems that the shape of the diffusion tensor and the ODF indeed can be extracted from the same measurement. This is shown for samples having either prolate or oblate diffusion tensors.