Gaussian Surface Curvature Mapping Indicating High Risk Type B Thoracic Aortic Dissections

A Patient-Specific Morphoelastic Growth Model of Aortic Dissection Evolution

The human aorta undergoes complex morphologic changes that indicate the evolution of disease. Finite element analysis enables the prediction of aortic pathologic states, but the absence of a biomechanical understanding hinders the applicability of this computational tool. We incorporate geometric information from computed tomography angiography (CTA) imaging scans into finite element analysis (FEA) to predict a trajectory of future geometries for four aortic disease patients. Through defining a geometric correspondence between two patient scans separated in time, a patient-specific FEA model can recreate the deformation of the aorta between the two time points, showing pathologic growth drives morphologic heterogeneity. A shape-size geometric feature space plotting the variance of the shape index versus the inverse square root of aortic surface area (δ𝒮 vs. ) quantitatively demonstrates the simulated breakdown in aortic shape. An increase in δ𝒮 closely parallels the true geometric progression of aortic disease patients.

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 (δK) 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 δK forming the hallmark of aortic disease. Divergent δK 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 δK 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.