  It is important to characterize the temporal trajectories of disease-related
biomarkers in order to monitor progression and identify potential points of
intervention. This is especially important for neurodegenerative diseases, as
therapeutic intervention is most likely to be effective in the preclinical
disease stages prior to significant neuronal damage. Longitudinal neuroimaging
allows for the measurement of structural, functional, and metabolic integrity
of the brain over time at the level of voxels. However, commonly used
longitudinal analysis approaches, such as linear mixed effects models, do not
account for the fact that individuals enter a study at various disease stages
and progress at different rates, and generally consider each voxelwise measure
independently. We propose a multivariate nonlinear mixed effects model for
estimating the trajectories of voxelwise neuroimaging biomarkers from
longitudinal data that accounts for such differences across individuals. The
method involves the prediction of a progression score for each visit based on a
collective analysis of voxelwise biomarker data within an
expectation-maximization framework that efficiently handles large amounts of
measurements and variable number of visits per individual, and accounts for
spatial correlations among voxels. This score allows individuals with similar
progressions to be aligned and analyzed together, which enables the
construction of a trajectory of brain changes as a function of an underlying
progression or disease stage. Application of our method to studying images of
beta-amyloid deposition, a hallmark of preclinical Alzheimer's disease,
suggests that precuneus is the earliest cortical region to accumulate amyloid.
The proposed method can be applied to other types of longitudinal imaging data,
including metabolism, blood flow, tau, and structural imaging-derived measures.
