The geometric evolution of aortic dissections: Predicting surgical success using fluctuations in integrated Gaussian curvature

Clinical imaging modalities are a mainstay of modern disease management, but the full utilization of imaging-based data remains elusive. Aortic disease is defined by anatomic scalars quantifying aortic size, even though aortic disease progression initiates complex shape changes. We present an imaging-based geometric descriptor, inspired by fundamental ideas from topology and soft-matter physics that captures dynamic shape evolution. The aorta is reduced to a two-dimensional mathematical surface in space whose geometry is fully characterized by the local principal curvatures. Disease causes deviation from the smooth bent cylindrical shape of normal aortas, leading to a family of highly heterogeneous surfaces of varying shapes and sizes. To deconvolute changes in shape from size, the shape is characterized using integrated Gaussian curvature or total curvature. The fluctuation in total curvature (delta K) across aortic surfaces captures heterogeneous morphologic evolution by characterizing local shape changes. We discover that aortic morphology evolves with a power-law defined behavior with rapidly increasing delta K forming the hallmark of aortic disease. Divergent delta K is seen for highly diseased aortas indicative of impending topologic catastrophe or aortic rupture. We also show that aortic size (surface area or enclosed aortic volume) scales as a generalized cylinder for all shapes. Classification accuracy for predicting aortic disease state (normal, diseased with successful surgery, and diseased with failed surgical outcomes) is 92.8 +/- 1.7%. The analysis of delta K can be applied on any three-dimensional geometric structure and thus may be extended to other clinical problems of characterizing disease through captured anatomic changes. For decades, aortic dissections have proven among the most difficult aortic pathologies to classify. The aorta is the largest blood vessel in the human body. An aortic dissection is the appearance of an internal blister within the aortic wall. The predominant method of diagnosing an aortic dissection is with cross-sectional x-ray imaging like computed tomography or CT scans. The morphologic evolution of aortic dissections has been difficult to quantify. The pressing clinical need to better define the morphology both in terms of size and shape of aortic dissections using CT derived imaging data is based on the high rate of failure in current surgical methods of dissection repair. Current methods are largely based on a dimensional reduction of the aortic geometry from its native two-dimensional surface in three-dimensional space to a one-dimensional space-curve. We develop a robust method using differential geometry to define each aorta using its full surface geometry. Each aorta is now uniquely represented as a point in a two-dimensional shape-size feature space. This space can be used to in general follow aortic morphology from normal development (growth) to severe pathology. Moreover, we successfully use it to identify patients who had failed aortic surgeries.