A chi-square type test for time-invariant fiber pathways of the brain

A longitudinal diffusion tensor imaging (DTI) study on a single brain can be remarkably useful to probe white matter fiber connectivity that may or may not be stable over time. We consider a novel testing problem where the null hypothesis states that the trajectories of a coherently oriented fiber population remain the same over a fixed period of time. Compared to other applications that use changes in DTI scalar metrics over time, our test is focused on the partial derivative of the continuous ensemble of fiber trajectories with respect to time. The test statistic is shown to have the limiting chi-square distribution under the null hypothesis. The power of the test is demonstrated using Monte Carlo simulations based on both the theoretical and empirical critical values. The proposed method is applied to a longitudinal DTI study of a normal brain.