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

Journal article
Authors Torbjörn Lundh
Ga Young Suh
Phillip DiGiacomo
Christopher Cheng
Published in Medical and Biological Engineering and Computing
Volume 56
Issue 9
Pages 1659–1668
ISSN 0140-0118
Publication year 2018
Published at Department of Mathematical Sciences
Pages 1659–1668
Language en
Keywords Cylindrical coordinates, Eccentricity, Lagrangian, Surface curvature, Vascular system
Subject categories Endocrinology and Diabetes, Fluid Mechanics and Acoustics, Radiology, Nuclear Medicine and Medical Imaging


© 2018 The Author(s) 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. [Figure not available: see fulltext.]

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