A Spatio-Temporal Model for Longitudinal Image-on-Image Regression

Neurologists and radiologists often use magnetic resonance imaging (MRI) in the management of subjects with multiple sclerosis (MS) because it is sensitive to inflammatory and demyelinative changes in the white matter of the brain and spinal cord. Two conventional modalities used for identifying lesions are T1-weighted (T1) and T2-weighted fluid-attenuated inversion recovery (FLAIR) imaging, which are used clinically and in research studies. Magnetization transfer ratio (MTR), which is available only in research settings, is an advanced MRI modality that has been used extensively for measuring disease-related demyelination both in white-matter lesions as well across normal-appearing white matter. Acquiring MTR is not standard in clinical practice, due to the increased scan time and cost. Hence, prediction of MTR based on the modalities T1 and FLAIR could have great impact on the availability of these promising measures for improved patient management. We propose a spatio-temporal regression model for image response and image predictors that are acquired longitudinally, with images being co-registered within the subject but not across subjects. The model is additive, with the response at a voxel being dependent on the available covariates not only through the current voxel but also on the imaging information from the voxels within a neighboring spatial region as well as their temporal gradients. We propose a dynamic Bayesian estimation procedure that updates the parameters of the subject-specific regression model as data accumulate. To bypass the computational challenges associated with a Bayesian approach for high-dimensional imaging data, we propose an approximate Bayesian inference technique. We assess the model fitting and the prediction performance using longitudinally acquired MRI images from 46 MS patients.