Deformation-based morphometry of the brain for the development of surrogate markers in Alzheimer's disease

The aim of the present thesis is to provide an e ective computationalframework for the analysis and quanti cation of the longitudinal structural changesin Alzheimer's disease (AD). The framework is based on the di eomorphic non-rigidregistration parameterized by stationary velocity elds (SVFs), and is hierachicallydeveloped to account for the di erent levels of variability which characterize thelongitudinal observations of T1 brain magnetic resonance images (MRIs). We devel-oped an e cient and robust method for the quanti cation of the structural changesobserved between pairs of MRIs. For this purpose, we propose the LCC-Demonsregistration framework which implements the local correlation coe cient as simi-larity metric, and we derived consistent and numerically stable measures of volumechange and boundary shift for the regional assessment of the brain atrophy. In or-der to consistently analyze group-wise longitudinal evolutions, we then investigatedthe parallel transport of subject-speci c deformation trajectories across di erentanatomical references. Based on the SVF parametrization of di eomorphisms, werelied on the Lie group theory to propose new and e ective strategies for the paralleltransport of SVFs, with particular interest into the practical application to the reg-istration setting. These contributions are the basis for the de nition of qualitativeand quantitative analysis for the pathological evolution of AD. We proposed severalanalysis frameworks which addressed the di erentiation of pathological evolutionsbetween clinical populations, the statistically powered evaluation of regional volumechanges, and the clinical diagnosis at the early/prodromal disease stages. Key-words: Alzheimer's disease, non rigid registration, longitudinal analysis, structuralMRI