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We develop a flexible framework for modeling high-dimensional imaging dataobserved longitudinally. The approach decomposes the observed variability ofrepeatedly measured high-dimensional observations into three additivecomponents: a subject-specific imaging random intercept that quantifies thecross-sectional variability, a subject-specific imaging slope that quantifiesthe dynamic irreversible deformation over multiple realizations, and asubject-visit-specific imaging deviation that quantifies exchangeable effectsbetween visits. The proposed method is very fast, scalable to studies includingultrahigh-dimensional data, and can easily be adapted to and executed on modestcomputing infrastructures. The method is applied to the longitudinal analysisof diffusion tensor imaging (DTI) data of the corpus callosum of multiplesclerosis (MS) subjects. The study includes $176$ subjects observed at $466$visits. For each subject and visit the study contains a registered DTI scan ofthe corpus callosum at roughly 30,000 voxels.

Longitudinal high-dimensional principal components analysis with application to diffusion tensor imaging of multiple sclerosis