Bayesian longitudinal tensor response regression for modeling neuroplasticity

A major interest in longitudinal neuroimaging studies involves investigating voxel‐level neuroplasticity due to treatment and other factors across visits. However, traditional voxel‐wise methods are beset with several pitfalls, which can compromise the accuracy of these approaches. We propose a novel Bayesian tensor response regression approach for longitudinal imaging data, which pools information across spatially distributed voxels to infer significant changes while adjusting for covariates. The proposed method, which is implemented using Markov chain Monte Carlo (MCMC) sampling, utilizes low‐rank decomposition to reduce dimensionality and preserve spatial configurations of voxels when estimating coefficients. It also enables feature selection via joint credible regions which respect the shape of the posterior distributions for more accurate inference. In addition to group level inferences, the method is able to infer individual‐level neuroplasticity, allowing for examination of personalized disease or recovery trajectories. The advantages of the proposed approach in terms of prediction and feature selection over voxel‐wise regression are highlighted via extensive simulation studies. Subsequently, we apply the approach to a longitudinal Aphasia dataset consisting of task functional MRI images from a group of subjects who were administered either a control intervention or intention treatment at baseline and were followed up over subsequent visits. Our analysis revealed that while the control therapy showed long‐term increases in brain activity, the intention treatment produced predominantly short‐term changes, both of which were concentrated in distinct localized regions. In contrast, the voxel‐wise regression failed to detect any significant neuroplasticity after multiplicity adjustments, which is biologically implausible and implies lack of power. In this article, we propose a novel Bayesian tensor response regression method for investigating voxel‐level longitudinal changes in neuroimaging data. The proposed method makes use of low‐rank tensor decomposition to reduce dimensionality and respect spatial contiguity across voxels, and pools information across voxels and longitudinal visits to allow for subject‐level inference. Using simulated and real datasets, we demonstrate that the proposed method allows for greater predictive performance and feature selection than routinely used voxel‐wise regression approaches.