| The spinal cord, brainstem, and cerebellum are crucial yet vulnerable aspects of the central nervous system (CNS) but have been relatively understudied in vivo given that their unique anatomies present challenging imaging targets. This dissertation develops techniques to study the microarchitecture of these critical CNS structures through diffusion weighted (DW) magnetic resonance imaging (MRI) techniques. While this work may be applied to other DW techniques, we focus on diffusion tensor imaging (DTI) and q-space imaging. DTI enables investigation of microarchitecture and connectivity of oriented tissues (e.g., cerebral white matter) through three-dimensional tensor models of local diffusivity, while q-space imaging is an emerging diffusion weighted MRI technique to estimate one-dimensional projections of the local diffusivity without the need to assume a particular diffusivity model. To enable DW imaging of the spinal cord, brainstem, and cerebellum, we specifically focus on statistically motivated image analysis techniques to make best use of the information present in acquired DW images.;In this research, we make five major contributions. First, we conduct empirical and theoretical studies to assess the accuracy and precision of DTI techniques. In the brain, typical differences due to imaging sequences are nominal when compared to inter-scan and inter-session variability, but at lower signal-to-noise ratio, reproducibility depends strongly on interactions between the acquisition method, model estimation approach, and noise structure. Second, we present a new, general class of estimators for estimating the local variance of spatially variable noise fields (SVNF) with data already acquired in the course of typical DW MRI studies. These are the first SVNF estimation techniques to exploit stationary noise properties in MR images with varied signal contrast (e.g., different DWs). Third, we propose a new parameterization and a numerical framework for maximum likelihood tensor estimation, which is the first tensor estimation method to consider the joint likelihood of all observations. We generalize this approach to q-space MM to enable more detailed exploration of tissue properties. Fourth, we address two major unsolved problems that plague interpretation of tensor based analysis: (1) identifying multiple, independent intra-voxel orientations and (2) interpolation of diffusion tensors. We present the first application of compressed sensing to reconstruct intra-voxel diffusivity and enable reliable estimation of multiple intra-voxel orientations using traditional DTI data. Additionally, we propose a new interpolation method that preserves clinically relevant sets of non-orthogonal contrasts. Finally, we present new, robust protocols for quantitative study of the spinal cord, brainstem, and cerebellum in clinical research. These protocols enable multimodal MRI tissue characterization in a time efficient manner for exploratory, simultaneous study of diffusion, volumetric, MR properties for anatomies that were previously elusive. |
