Annals of Biomedical Engineering

, Volume 41, Issue 3, pp 562–576 | Cite as

Surface Curvature as a Classifier of Abdominal Aortic Aneurysms: A Comparative Analysis

  • Kibaek Lee
  • Junjun Zhu
  • Judy Shum
  • Yongjie Zhang
  • Satish C. Muluk
  • Ankur Chandra
  • Mark K. Eskandari
  • Ender A. Finol


An abdominal aortic aneurysm (AAA) carries one of the highest mortality rates among vascular diseases when it ruptures. To predict the role of surface curvature in rupture risk assessment, a discriminatory analysis of aneurysm geometry characterization was conducted. Data was obtained from 205 patient-specific computed tomography image sets corresponding to three AAA population subgroups: patients under surveillance, those that underwent elective repair of the aneurysm, and those with an emergent repair. Each AAA was reconstructed and their surface curvatures estimated using the biquintic Hermite finite element method. Local surface curvatures were processed into ten global curvature indices. Statistical analysis of the data revealed that the L2-norm of the Gaussian and Mean surface curvatures can be utilized as classifiers of the three AAA population subgroups. The application of statistical machine learning on the curvature features yielded 85.5% accuracy in classifying electively and emergent repaired AAAs, compared to a 68.9% accuracy obtained by using maximum aneurysm diameter alone. Such combination of non-invasive geometric quantification and statistical machine learning methods can be used in a clinical setting to assess the risk of rupture of aneurysms during regular patient follow-ups.


Surface curvature Reconstruction Finite element method Rupture risk Geometry quantification Abdominal aortic aneurysm Machine learning 



The authors would like to acknowledge research funding from the Korean Government Scholarship Program for Study Overseas, and the Vlahakis Graduate Fellowship program. This work was also funded in part by NIH grants R21EB007651, R21EB008804 and R15HL087268. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. The authors would like to thank Drs. Michael Sacks and David Smith for their insightful discussions on the basics of the BQFE method and its implementation for surface curvature analysis.


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Copyright information

© Biomedical Engineering Society 2012

Authors and Affiliations

  • Kibaek Lee
    • 1
  • Junjun Zhu
    • 1
  • Judy Shum
    • 2
  • Yongjie Zhang
    • 1
  • Satish C. Muluk
    • 3
  • Ankur Chandra
    • 4
  • Mark K. Eskandari
    • 5
  • Ender A. Finol
    • 6
  1. 1.Mechanical Engineering DepartmentCarnegie Mellon UniversityPittsburghUSA
  2. 2.Biomedical Engineering DepartmentCarnegie Mellon UniversityPittsburghUSA
  3. 3.Division of Vascular Surgery, Allegheny-Singer Research InstituteWest Penn Allegheny Health SystemPittsburghUSA
  4. 4.Division of Vascular Surgery, Rochester Institute of TechnologyUniversity of Rochester School of Medicine, and DentistryRochesterUSA
  5. 5.Division of Vascular SurgeryNorthwestern University Feinberg School of MedicineChicagoUSA
  6. 6.Department of Biomedical EngineeringThe University of Texas at San AntonioSan AntonioUSA

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