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Patients with Alzheimer's disease and other brain disorders often show a similar spatial distribution of volume change throughout the brain over time, 1,2 but this information is not yet used in registration algorithms to refine the quantification of change. Here, we develop a mathematical basis to incorporate that prior information into a longitudinal structural neuroimaging study. We modify the canonical minimization problem for non-linear registration to include a term that couples a collection of registrations together to enforce group similarity. More specifically, throughout the computation we maintain a group-level representation of the transformations and constrain updates to individual transformations to be similar to this representation. The derivations necessary to produce the Euler-Lagrange equations for the coupling term are presented and a gradient descent algorithm based on the formulation was implemented. We demonstrate using 57 longitudinal image pairs from the Alzheimer's Disease Neuroimaging Initiative (ADNI) that longitudinal registration with such a groupwise coupling prior is more robust to noise in estimating change, suggesting such change maps may have several important applications.

A transformation similarity constraint for groupwise nonlinear registration in longitudinal neuroimaging studies