Technical Brief

A Geodesics-Based Surface Parameterization to Assess Aneurysm Progression

[+] Author and Article Information
Ly Phan

Design and Technology Solutions,
Intel Corporation (MS RA4-403),
2501 NW 229th,
Hillsboro, OR 97124
e-mail: ly.phan@intel.com

Katherine Courchaine

Biomedical Engineering,
Oregon Health & Science University,
3303 SW Bond Avenue,
M/C CH13B,
Portland, OR 97239
e-mail: courchai@ohsu.edu

Amir Azarbal

Department of Surgery,
Division of Vascular Surgery,
Oregon Health & Science University,
3181 SW Sam Jackson Park Road,
Portland, OR 97239
e-mail: azarbala@ohsu.edu

David Vorp

Department of Bioengineering,
University of Pittsburgh,
Suite 300 Center for Bioengineering (CNBIO),
300 Technology Drive,
Pittsburgh, PA 15219
e-mail: vorp@pitt.edu

Cindy Grimm

Mechanical Engineering,
Oregon State University,
204 Rogers Hall
Corvallis, OR 97331
e-mail: grimmc@onid.orst.edu

Sandra Rugonyi

Biomedical Engineering,
Oregon Health & Science University,
3303 SW Bond Avenue,
M/C CH13B,
Portland, OR 97239
e-mail: rugonyis@ohsu.edu

1Corresponding author.

Manuscript received March 31, 2015; final manuscript received March 9, 2016; published online April 1, 2016. Assoc. Editor: Thao (Vicky) Nguyen.

J Biomech Eng 138(5), 054503 (Apr 01, 2016) (7 pages) Paper No: BIO-15-1136; doi: 10.1115/1.4033082 History: Received March 31, 2015; Revised March 09, 2016

Abdominal aortic aneurysm (AAA) intervention and surveillance is currently based on maximum transverse diameter, even though it is recognized that this might not be the best strategy. About 10% of patients with small AAA transverse diameters, for whom intervention is not considered, still rupture; while patients with large AAA transverse diameters, for whom intervention would have been recommended, have stable aneurysms that do not rupture. While maximum transverse diameter is easy to measure and track in clinical practice, one of its main drawbacks is that it does not represent the whole AAA and rupture seldom occurs in the region of maximum transverse diameter. By following maximum transverse diameter alone clinicians are missing information on the shape change dynamics of the AAA, and clues that could lead to better patient care. We propose here a method to register AAA surfaces that were obtained from the same patient at different time points. Our registration method could be used to track the local changes of the patient-specific AAA. To achieve registration, our procedure uses a consistent parameterization of the AAA surfaces followed by strain relaxation. The main assumption of our procedure is that growth of the AAA occurs in such a way that surface strains are smoothly distributed, while regions of small and large surface growth can be differentiated. The proposed methodology has the potential to unravel different patterns of AAA growth that could be used to stratify patient risks.

Copyright © 2016 by ASME
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Fig. 1

AAA surface parameterization strategy. The AAA surface parameterization consists of quasi cross-sectional contour curves and longitudinal lines that are discretized using a grid. The surface medial axis is shown in red and reference curve in orange. (a) Quasi cross-sectional contours were generated by intersection of slicing planes with the surface. Each contour is then discretized to generate n equally spaced sampling points. (b) Sampling points were generated on m contours over the entire surface. The grid consists of pki points with i = 1… n, k = 1… m, (c) Connecting the ith sampling points on each contour, the ith longitudinal grid curve is generated. (d) Completed parameterized grid.

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Fig. 2

Correspondence on the AAA surfaces between times T1 and T2. (a) Sagittal view of patient AAAs. (b) Frontal view of patient AAAs. The correspondence is obtained after parameterization and optimization of the parameterization. The plot shows correspondence of lines, with the reference line for each patient marked with an arrow. Note that longitudinal grid lines follow the global shape of the surfaces, and the reference line is the shortest longitudinal line for each patient.

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Fig. 3

Principal stretch components λ1 and λ2 on the AAA surfaces at T2 (with respect to T1) for the six patients. The gray scale reflects the minimum and maximum of λ1 and λ2 for each patient.

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Fig. 4

Relative surface area expansion (λ1 λ2) and surface expansion rates shown on AAA surfaces at time T2. Gray scale reflects the minimum and maximum relative areas, first on an individual basis (individual scale) and then for all patients (common scale).




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