A Lagrangian cylindrical coordinate system for characterizing dynamic surface geometry of tubular anatomic structures
Journal article, 2018

Vascular morphology characterization is useful for disease diagnosis, risk stratification, treatment planning, and prediction oftreatment 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 systemenables quantification of surface curvature and cross-sectional eccentricity. Using idealized software phantom examples, wevalidate the method’s ability to accurately quantify longitudinal and circumferential surface curvature, as well as eccentricity andorientation of eccentricity. We then apply the method to several medical imaging data sets of human vascular structures toexemplify the utility of this coordinate system for analyzing morphology and dynamic geometric changes in blood vesselsthroughout the body.

Cylindrical coordinates

Vascular system



Surface curvature


Torbjörn Lundh

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Ga-Young Suh

Stanford University

Phillip DiGiacomo

Stanford University

Christopher P. Cheng

Stanford University

Medical and Biological Engineering and Computing

0140-0118 (ISSN)

Vol. 56 9 1659-1668

Subject Categories

Endocrinology and Diabetes

Fluid Mechanics and Acoustics

Radiology, Nuclear Medicine and Medical Imaging

Areas of Advance

Life Science Engineering (2010-2018)



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