The Geometric Evolution of Aortic Dissections: Predicting Surgical Success using Fluctuations in Integrated Gaussian Curvature

Abstract

Cross-sectional imaging, such as computed tomography (CTA) scans, provide unparalleled visualization of aortic anatomy. However, despite the immense geometric and anatomic detail provided by CTA imaging, surgeons continue to interact with this data in a linear and dimensionally reduced feature space. Aortic pathologies such as aneurysms and dissections are clinically quantified using a single scalar: maximum aortic diameter. To date, not feature of aortic shape has reproducibly captured what surgeons often describe qualitatively when looking at CT scans or when in the operating room observing the physical anatomy. Shape along with size plays a central role in differentiating normal from diseased aortas. We defined a geometric feature space using tools of modern differential geometry that incorporate shape and size. We show that size can be parameterized by l, the radial aortic extent commonly taken as aortic diameter. Size invariant shape is quantified by performing a Gauss map of local regions on the aortic surface and calculating the variance of the total integrated curvature (δK) across each aorta. While we do not inherently study aortic stability as it relates to clinical rupture in this paper, aortas appearing at high δK are clinically classified by size and qualitative appearance as high risk. It is therefor interesting to conjecture that divergence in the (δK,l)-space is a sign of aortic topologic instability. Projection into (δK, l)-space provides two independent variables that show a natural division of the data as it transitions from size to shape dominated behavior, an indictor of aortic fragility.