Annals of Biomedical Engineering

, Volume 27, Issue 4, pp 469–479

In Vivo Three-Dimensional Surface Geometry of Abdominal Aortic Aneurysms


  • Michael S. Sacks
    • Department of BioengineeringUniversity of Pittsburgh
  • David A. Vorp
    • Department of BioengineeringUniversity of Pittsburgh
    • Department of SurgeryUniversity of Pittsburgh
    • Department of Mechanical EngineeringUniversity of Pittsburgh
  • M. L. Raghavan
    • Department of BioengineeringUniversity of Pittsburgh
  • Michael P. Federle
    • Department of RadiologyUniversity of Pittsburgh
  • Marshall W. Webster
    • Department of SurgeryUniversity of Pittsburgh

DOI: 10.1114/1.202

Cite this article as:
Sacks, M.S., Vorp, D.A., Raghavan, M.L. et al. Annals of Biomedical Engineering (1999) 27: 469. doi:10.1114/1.202


Abdominal aortic aneurysm (AAA) is a local, progressive dilation of the distal aorta that risks rupture until treated. Using the law of Laplace, in vivo assessment of AAA surface geometry could identify regions of high wall tensions as well as provide critical dimensional and shape data for customized endoluminal stent grafts. In this study, six patients with AAA underwent spiral computed tomography imaging and the inner wall of each AAA was identified, digitized, and reconstructed. A biquadric surface patch technique was used to compute the local principal curvatures, which required no assumptions regarding axisymmetry or other shape characteristics of the AAA surface. The spatial distribution of AAA principal curvatures demonstrated substantial axial asymmetry, and included adjacent elliptical and hyperbolic regions. To determine how much the curvature spatial distributions were dependent on tortuosity versus bulging, the effects of AAA tortuosity were removed from the three-dimensional (3D) reconstructions by aligning the centroids of each digitized contour to the z axis. The spatial distribution of principal curvatures of the modified 3D reconstructions were found to be largely axisymmetric, suggesting that much of the surface geometric asymmetry is due to AAA bending. On average, AAA surface area increased by 56% and abdominal aortic length increased by 27% over those for the normal aorta. Our results indicate that AAA surface geometry is highly complex and cannot be simulated by simple axisymmetric models, and suggests an equally complex wall stress distribution. © 1999 Biomedical Engineering Society.

PAC99: 8719Rr, 8759Fm, 8757Gg

Abdominal aortic aneurysmCurvatureTortuosityThree-dimensional reconstruction
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© Biomedical Engineering Society 1999