FIGURE 1.

Longitudinal registration with aMSM. Physical deformation of the cortical surface between two timepoints is calculated for each triplet of vertices on the input surface (red dots) and reference surface (blue dots). Similar to other popular surface registration techniques (Yeo et al., 2010) vertices from both the input surface and reference surface are projected to a spherical representation to simplify mathematical calculations. However, unlike other registration techniques, aMSM (gray box) regularizes vertex displacement to minimize physical deformation (strain energy based on mechanical properties of brain tissue) between the anatomical surfaces (2a, 2b). Based on these constraints, triplets on sphere 1 are shifted to bring them into alignment with triplets on sphere 2 (3). Once realigned, sphere 1 is projected to a new anatomical output surface (4), resulting in more realistic physical deformations of the cortical surface