We propose in this paper an approach to quantifying the rate of atrophy of the brain of patients with Alzheimers disease. This approachis based on Computational Anatomy which al- lows the computation ofintermediate MR brain volumes be- tween the ones of regular scans.This increases dramatically the granularity of brain structure information, without requir- ing extra scans. We define two spaces: (i) the joint brain tissue deformation displacement vector magnitude andJacobian, (ii) the joint polar angles of the displacement vector. The shape of the distribution patterns in both spaces allow us to: (i)quan- tify atrophy rates of specific brain structures, such as, theven- tricles and the hippocampus, (ii) to build up models for the in- terpolation and extrapolation of atrophy rate parameters. The novelty of this approach is that it allows us to interpolate and extrapolate atrophy rate parameters computed from the two spaces, and thusderive precise models for patient diagnosis and/or prognosis. We tested this approach on a set of ADNI patients with diagnosed Alzheimers disease, mild cognitive impairment, and normal controls. This approach could also be used in the diagnosis of patients with other neurodegener- ative diseases, such as, frontal lobe dementia and Schizophre- nia.