Seminar

A number of magnetic resonance (MR) imaging modalities can be used to measure the diffusion of water in the brain. An important question is which of these modalities are most useful for differentiating between MR images of patients with multiple sclerosis (MS) and those of healthy controls. We propose a hypothesis test that facilitates this differentiation while taking advantage of the functional nature of the data. The methods represent the data using a common orthogonal basis expansion and reduce the dimension of the testing problem in a way that enables the application of traditional nonparametric univariate testing procedures. This results in a procedure that is not only computationally inexpensive but also allows for testing of higher order moments in functional principal component factor loadings. Simulation studies are presented to demonstrate the strength and validity of our approach. We also provide a comparison to a competing method. The proposed methodology is then illustrated by applying it to a state-of-the art diffusion tensor imaging (DTI) study where the objective is to compare white matter tract profiles in healthy individuals and multiple sclerosis (MS) patients.