A Lagrangian cylindrical coordinate system for characterizing dynamic surface geometry of tubular anatomic structures

Vascular morphology characterization is useful for disease diagnosis, risk stratification, treatment planning, and prediction of treatment durability. To quantify the dynamic surface geometry of tubular-shaped anatomic structures, we propose a simple, rigorous Lagrangian cylindrical coordinate system to monitor well-defined surface points. Specifically, the proposed system enables quantification of surface curvature and cross-sectional eccentricity. Using idealized software phantom examples, we validate the method's ability to accurately quantify longitudinal and circumferential surface curvature, as well as eccentricity and orientation of eccentricity. We then apply the method to several medical imaging data sets of human vascular structures to exemplify the utility of this coordinate system for analyzing morphology and dynamic geometric changes in blood vessels throughout the body. Graphical abstract Pointwise longitudinal curvature of a thoracic aortic endograft surface for systole and diastole, with their absolute difference.