The accurate monitoring of the structural changes in the brain plays a central role in the treatment of Alzheimer's disease (AD), for instance for diagnostic purposes and for the assessment of the drugs effi cacy in clinical trials. We propose here a framework based on the flux analysis of vector fi elds for the automatic quanti cation of the longitudinal regional atrophy in the brain. In particular, we present here the LCC-Demons algorithm for the symmetric and robust di ffeomorphic registration, which is used to quantify the longitudinal changes of a given subject by registration of follow-up images. The fl ux of the associated deformation across the boundaries of consistently defi ned group-wise regions provides the rate of longitudinal volume change. The proposed method was tested for the quantifi cation of the longitudinal hippocampal and ventricular volume changes at one and two years from baseline from a group of AD and healthy ADNI subjects. The resulting measures led to statistically powered results, and to consistent longitudinal measures in terms of symmetry, transitivity and linearity.