Longitudinal Image Analysis of Tumor/Healthy Brain Change in Contrast Uptake Induced by Radiation

This work is motivated by a quantitative Magnetic Resonance Imaging study of the differential tumor/healthy tissue change in contrast uptake induced by radiation. The goal is to determine the time in which there is maximal contrast uptake (a surrogate for permeability) in the tumor relative to healthy tissue. A notable feature of the data is its spatial heterogeneity. Zhang, Johnson, Little, and Cao (2008a and 2008b) discuss two parallel approaches to "denoise" a single image of change in contrast uptake from baseline to one follow-up visit of interest. In this work we extend the image model to explore the longitudinal profile of the tumor/healthy tissue contrast uptake in multiple images over time. We fit a two-stage model. First, we propose a longitudinal image model for each subject. This model simultaneously accounts for the spatial and temporal correlation and denoises the observed images by borrowing strength both across neighboring pixels and over time. We propose to use the Mann-Whitney U statistic to summarize the tumor contrast uptake relative to healthy tissue. In the second stage, we fit a population model to the U statistic and estimate when it achieves its maximum. Our initial findings suggest that the maximal contrast uptake of the tumor core relative to healthy tissue peaks around three weeks after initiation of radiotherapy, though this warrants further investigation.