Summary. The work is motivated by a quantitative magnetic resonance imaging study of the differential tumour–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 tumour relative to healthy tissue. A notable feature of the data is its spatial heterogeneity. Zhang and co-workers have discussed 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 tumour–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 neighbouring pixels and over time. We propose to use the Mann–Whitney U-statistic to summarize the tumour 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 tumour core relative to healthy tissue peaks around 3 weeks after initiation of radiotherapy, though this warrants further investigation.