Accurate and precise parameter estimation for diffusion magnetic resonance imaging

Abstract:

Diffusion magnetic resonance imaging (dMRI) offers a unique way of imaging the human brain noninvasively. By carefully controlling various acquisition parameters, the dMRI signal can be used to probe the movement of water molecules inside biological tissues, revealing important information about tissue structure. However, this signal is subject to noise and other undesired electromagnetic effects that reduce the signal-to-noise ratio. Efficient acquisition schemes and robust estimators are required to obtain accurate and precise tissue maps of the human brain. In this thesis, we have aimed our efforts towards improving the accuracy, precision, generalizability and applicability of several dMRI analysis methods. Constrained spherical deconvolution (CSD) is a popular dMRI technique that can be used to infer the local tissue densities and their orientations in the human brain, which consists of cerebrospinal fluid, anisotropic white matter and isotropic gray matter. This is achieved by densely sampling q-space, the space of q-vectors representing the direction and strength of diffusion weighting. After sampling q-space in multiple shells, tissue densities and orientations can be estimated by deconvolving this multi-shell dMRI signal with the respective response functions for white matter, gray matter and cerebrospinal fluid. These response functions are typically represented using spherical harmonics (SH) basis functions. However, when sampling is nonspherical, either due to inhomogeneous gradients or by design such as Cartesian sampling, the estimated tissue maps suffer from biases. To counter this issue, we adopted a compact response function model that accounts for nonspherical sampling. On multi-shell data, our approach provides fiber orientation density functions and tissue densities indistinguishable from those estimated using SH. On Cartesian data, estimates are on par with those obtained from shell-wise data, significantly broadening the range of data sets analyzable using CSD. In addition, inhomogeneous gradients can be accounted for, resulting in more accurate apparent tissue densities and connectivity metrics. Q-space trajectory imaging is a dMRI technique that uses time-varying q-vectors to sensitize the dMRI signal to microscopic variations in heterogeneous tissues. By modelling the dMRI signal with a diffusion tensor distribution (DTD), this approach allows teasing apart variations in diffusivity from microscopic anisotropy, orientation dispersion, and mixtures of multiple isotropic diffusivities. To improve the estimation of the DTD parameters, we propose an efficient acquisition scheme optimized for the most used QTI-derived microstructural parameters. A constrained iteratively reweighted least squares estimator is used to further improve the bias and precision of the DTD parameters.

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