Evaluating local contractions from large deformations using affine invariant spectral geometry

Abstract

We propose a geometric tool for quantifying dense local contractions of the left ventricle given its three dimensional segmented computed tomography (CT). Our approach is based on metric invariants in spectral geometry coupled to a non-rigid alignment algorithm, and can be implemented on data obtained by any modality as only a segmented surface is used. We assume local affine movement of the tissue, and generate a global piecewise constant affine invariant model to regularize the alignment. In contrast to traditional methods which seek diffeomorphic deformation, we show that an isomorphic paradigm can enhance alignment results. We show the superiority of utilizing the proposed metric as part of known non-rigid alignment algorithms on synthesized examples. We further analyzed local contractions and provide statistics for 9 healthy patients and demonstrate abnormal local contractions in atrial fibrillation.