| Magnetic resonance imaging (MRI) has revolutionized modern medical practice. MRI is an essentially noninvasive tool for eliciting information about both the function and structure of the human body. Investigators who use MRI are faced with many unique challenges in the design, analysis, and interpretation of their studies. I present novel statistical methodology for three types of MRI data: functional, phase contrast, and diffusion tensor.;Functional MRI (fMRI) measures the blood oxygen level dependent signal in tissue. When applied to the brain, the goal is to measure brain function where changes in blood oxygenation are surrogates for changes in neuronal function. One method for analyzing fMRI time series involves smoothing the data to induce a known autocorrelation structure. The goal of smoothing is to reduce the bias in estimates of linear model parameters. I present a method for spline smoothing of fMRI time series where the amount of smoothing is selected by generalized cross-validation. I show that this procedure substantially reduces bias.;Phase contrast MRI (PC-MRI) is sensitive to flow of fluids. PC-MRI is often applied to measure flow of blood. Information about blood flow and shear is particularly important since these properties are related to formation and progression of atherosclerotic plaque. I developed a nonparametric method for estimating blood flow and shear (proportional to the gradient of the velocity function) in a Matern reproducing kernel Hilbert space.;Diffusion tensor imaging (DTI) is a quantitative magnetic resonance imaging method that is widely used to study the microstructural properties of white matter in the brain. Tensor-derived quantities such as trace and fractional anisotropy (FA) are important for characterizing the normal, diseased, and developing brain. I derive asymptotic properties of the nonlinear least squares estimator of the diffusion tensor, trace, and FA. I show, with simulations, experimental designs where the asymptotic distributions are very close to the empirical distributions. The asymptotic methods are applied to estimate variances in a healthy volunteer. Variances of trace and FA are found to vary significantly throughout the brain. This renders many popular tests used in group analysis invalid. Unequal variances for tests with tensor-derived quantities is discussed. |
