A Mesh-Free Curvature-Based Approach to Analyzing the Mechanics of Aortic Diseases

Aortic dissections present a mechanical problem of fracture in the aortic wall. The mechanism by which this occurs is unclear but is strongly influenced by the aorta's geometric complexity. As such, analyzing aortic geometry can enhance our understanding of its mechanical state. Our group has established a curvature-based geometric approach to analyzing the stability of aortic dissections. However, the calculation of curvature on the aortic surface requires the creation of a three-dimensional mesh, a process that is time-consuming and labor-intensive. We have developed a novel approach to measure curvatures on the aortic surface directly from raw imaging data, eliminating the need for meshing. By creating a model of the aorta from an isosurface of equal intensity values on computed tomography (CT) images and reconstructing derivatives on the neighboring data points, we extract the principal curvatures of a local region on the aortic surface. This new method allows us to connect aortic geometry with aortic stability in a more efficient process, providing possible avenues for future clinical applications.