Aneurysm Morphology Based on Conformal Geometry

Several morphological parameters such as aortic neck length, angulation, or centerline curvature have previously been evaluated to define "hostile" anatomies that predispose to poor outcomes after endovascular aneurysm repair. In this study, we present a new method for classifying aneurysm morphologies using their conformal structures. The conformal structure of a surface is determined by its Riemannian metric, and conformal mappings between surfaces with complex topologies preserve their conformal structures. To classify aneurysm shapes, the aortic aneurysm is first segmented from CT scans and represented as a discrete surface. Next, holomorphic differential forms are computed based on the discrete Hodge Theory. The aneurysm surface can be conformally mapped onto a pair of planar rectangles with an aortic bifurcation point by integrating a special holomorphic differential. This canonical configuration gives the conformal invariants, or "conformal fingerprints," which can then be used to classify aneurysm morphologies. This novel methodology shows promise in providing an improved understanding of aneurysm morphologies, which can aid in better predicting and managing potential complications after endovascular aneurysm repair.