Hyperbolic Ricci Flow and Geodesic Curve Lifting for Consistent Ventricular Surface Registration

Ventricular enlargement is an important biomarker of Alzheimer’s disease (AD). However, ventricular surface morphometry analysis remains challenging due to its complicated and branching topological structure. Here we propose a novel ventricular surface registration algorithm based on the hyperbolic Ricci flow and geodesic curve lifting methods for ventricular shape morphometry study. Unlike prior ventricular surface parameterization methods, the hyperbolic conformal parameterization computed with hyperbolic Ricci flow is angle-preserving and has no singularities. In the parameter domain, we compute consistent geodesic curves across subjects and map the curves back to the 3D ventricular surface, a method called geodesic curve lifting. The geodesic curves then serve as consistent boundary conditions to guide the one-toone diffeomorphic mappings between ventricular surfaces. Local shape deformations are measured by tensor-based morphometry (TBM). We applied the method on baseline MRI scans of a set of mild cognitive impairment (MCI) subjects from the Alzheimer’s Disease Neuroimaging Initiative (ADNI), including 71 individuals who converted to AD in the subsequent 36 months after screening and 62 subjects who did not covert to AD during the same period. Our method revealed significant differences in ventricular shapes between the two groups. We also studied the correlation between ventricular shape morphometry and a previously introduced brain functional index derived from the fluorodeoxyglucose positron emission tomography (FDG-PET) scans, as both a validation of the correctness of our method and an exploration of the relationship between brain structural and functional changes.