Thoracic Aortic Shape: A Data-Driven Scale Space Approach

The scale and resolution of anatomical features extracted from medical CT images are crucial for advancing clinical decision-making tools. While traditional metrics, such as maximum aortic diameter, have long been the standard for classifying aortic diseases, these one-dimensional measures often fall short in capturing the rich geometrical nuances available in progressively advancing imaging modalities. Recent advancements in computational methods and imaging have introduced more sophisticated geometric signatures, in particular scale-invariant measures of aortic shape. Among these, the normalized fluctuation in total integrated Gaussian curvature ( $$ ) over a surface mesh model of the aorta has emerged as a particularly promising metric. However, there exists a critical tradeoff between noise reduction and shape signal preservation within the scale space parameters - namely, smoothing intensity, meshing density, and partitioning size. Through a comprehensive analysis of over 1200 unique scale space constructions derived from a cohort of 185 aortic dissection patients, this work pinpoints optimal resolution scales at which shape variations are most strongly correlated with surgical outcomes. Importantly, these findings emphasize the pivotal role of a secondary discretization step, which consistently yield the most robust signal when scaled to approximately 1 cm. This approach enables the development of models that are not only clinically effective but also inherently resilient to biases introduced by patient population heterogeneity. By focusing on the appropriate intermediate scales for analysis, this study paves the way for more precise and reliable tools in medical imaging, ultimately contributing to improved patient outcomes in cardiovascular surgery.