# A Framework for the Automatic Generation of Surface Topologies for Abdominal Aortic Aneurysm Models

- 183 Downloads
- 21 Citations

## Abstract

Patient-specific abdominal aortic aneurysms (AAAs) are characterized by local curvature changes, which we assess using a feature-based approach on topologies representative of the AAA outer wall surface. The application of image segmentation methods yields 3D reconstructed surface polygons that contain low-quality elements, unrealistic sharp corners, and surface irregularities. To optimize the quality of the surface topology, an iterative algorithm was developed to perform interpolation of the AAA geometry, topology refinement, and smoothing. Triangular surface topologies are generated based on a Delaunay triangulation algorithm, which is adapted for AAA segmented masks. The boundary of the AAA wall is represented using a signed distance function prior to triangulation. The irregularities on the surface are minimized by an interpolation scheme and the initial coarse triangulation is refined by forcing nodes into equilibrium positions. A surface smoothing algorithm based on a low-pass filter is applied to remove sharp corners. The optimal number of iterations needed for polygon refinement and smoothing is determined by imposing a minimum average element quality index with no significant AAA sac volume change. This framework automatically generates high-quality triangular surface topologies that can be used to characterize local curvature changes of the AAA wall.

## Keywords

Aneurysm Surface topology Smoothing Optimal polygon quality Rupture Curvature## Notes

### Acknowledgments

The authors would like to acknowledge research funding from the Bill and Melinda Gates Foundation, the John and Claire Bertucci Graduate Fellowship, Carnegie Mellon University’s Biomedical Engineering Department, and NIH Grants R21EB007651 and R21EB008804, from the National Institute of Biomedical Imaging and Bioengineering, and R15HL087268, from the National Heart, Lung, and Blood Institute. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. The contribution of Mr. Kyle Andrews in generating models for the code validation is greatly appreciated.

## References

- 1.Ateshian, G. A., M. P. Rosenwasser, and V. C. Mow. Curvature characteristics and congruence of the thumb carpometacarpal joint: differences between female and male joints.
*J. Biomech.*6:591–607, 1992.CrossRefGoogle Scholar - 2.Di Martino, E. S., A. Bohra, J. P. Vande Geest, N. Gupta, M. Makaroun, and D. A. Vorp. Biomechanical properties of ruptured versus electively repaired abdominal aortic aneurysm wall tissue.
*J. Vasc. Surg.*43:570–576, 2006.CrossRefPubMedGoogle Scholar - 3.Dobrin, P., W. Baker, and W. Gley. Elastolytic and collagenolytic studies of arteries.
*Arch. Surg.*119:405–409, 1984.PubMedGoogle Scholar - 4.Fillinger, M. F., J. Racusin, R. K. Baker, J. L. Cronenwett, A. Teutelink, M. L. Schermerhorn,
*et al*. Anatomic characteristics of ruptured abdominal aortic aneurysm on conventional CT scans: implications for rupture risk.*J. Vasc. Surg.*39:1243–1252, 2004.CrossRefPubMedGoogle Scholar - 5.Fillinger, M. F., M. L. Raghavan, S. P. Marra, J. L. Cronenwett, and F. E. Kennedy. In vivo analysis of mechanical wall stress and abdominal aortic aneurysm rupture risk.
*J. Vasc. Surg.*36:589–597, 2002.CrossRefPubMedGoogle Scholar - 6.Giannakoulas, G., G. Giannoglou, J. V. Soulis, G. Louridas, and G. Parharidis. Rupture of abdominal aortic aneurysms. What matters most: geometry or blood pressure?
*Eur. J. Vasc. Endovasc. Surg.*34:122–123, 2007.CrossRefPubMedGoogle Scholar - 7.Giannoglou, G., G. Giannakoulas, J. Soulis, Y. Chatzizisis, T. Perdikides, N. Melas,
*et al*. Predicting the risk of rupture of abdominal aortic aneurysms by utilizing various geometrical parameters: revisiting the diameter criterion.*Angiology*57:487–494, 2006.CrossRefPubMedGoogle Scholar - 8.Ma, B., R. E. Harbaugh, and M. L. Raghavan. Three-dimensional geometrical characterization of cerebral aneurysms.
*Ann. Biomed. Eng.*32:264–273, 2004.CrossRefPubMedGoogle Scholar - 9.Martufi, G., E. S. Di Martino, C. H. Amon, S. C. Muluk, and E. A. Finol. Three-dimensional geometrical characterization of abdominal aortic aneurysms: image-based wall thickness distribution.
*J. Biomech. Eng.*131:061015, 2009.CrossRefPubMedGoogle Scholar - 10.Mower, W., L. Baraff, and J. Sneyd. Stress distribution in vascular aneurysms: factors affecting risk of aneurysm rupture.
*J. Surg. Res.*55:155–161, 1993.CrossRefPubMedGoogle Scholar - 11.Nyilas, R. D., S. M. L Ng, J. Leung, and X. Y. Xu. Towards a new geometric approach to assess the risk of rupture of abdominal aortic aneurysms using patient specific modeling. In: 2005 Summer Bioengineering Conference, June 22–26, Vail Cascade Resort & Spa, Vail, CL.Google Scholar
- 12.Pappu, S., A. Dardik, H. Tagare, and R. J. Gusberg. Beyond fusiform and saccular: a novel quantitative tortuosity index may help classify aneurysm shape and predict aneurysm rupture potential.
*Ann. Vasc. Surg.*22:88–97, 2008.CrossRefPubMedGoogle Scholar - 13.Persson, P. O., and G. Strang. A simple mesh generator in MATLAB.
*SIAM Rev. Soc. Ind. Appl. Math.*46:329–345, 2004.Google Scholar - 14.Raghavan, M. L., J. Kratzberg, E. M. Castro de Tolosa, M. M. Hanaoka, P. Walker, and E. S. da Silva. Regional distribution of wall thickness and failure properties of human abdominal aortic aneurysm.
*J. Biomech.*39:3010–3016, 2006.CrossRefPubMedGoogle Scholar - 15.Raghavan, M. L., B. Ma, and R. E. Harbaugh. Quantified aneurysm shape and rupture risk.
*J. Neurosurg.*102:355–362, 2005.CrossRefPubMedGoogle Scholar - 16.Sacks, M. S., C. J. Chuong, G. H. Templeton, and R. Peshock. In vivo 3-D reconstruction and geometric characterization of the right ventricular free wall.
*Ann. Biomed. Eng.*21:263–275, 1993.CrossRefPubMedGoogle Scholar - 17.Sacks, M. S., D. A. Vorp, M. L. Raghavan, M. P. Federle, and M. W. Webster. In vivo three-dimensional surface geometry of abdominal aortic aneurysms.
*Ann. Biomed. Eng.*27:469–479, 1999.CrossRefPubMedGoogle Scholar - 18.Shum, J., E. S. DiMartino, A. Goldhammer, D. Goldman, L. Acker, G. Patel,
*et al*. Semi-automatic vessel wall detection and quantification of wall thickness in CT images of human abdominal aortic aneurysms.*Med. Phys.*37:638–648, 2010.CrossRefPubMedGoogle Scholar - 19.Smith, D. B., M. S. Sacks, P. M. Pattany, and R. Schroeder. Fatigue-induced changes in bioprosthetic heart valve three-dimensional geometry and the relation to tissue damage.
*J. Heart Valve Dis*8(1):25–33, 1999.PubMedGoogle Scholar - 20.Smith, D. B., M. S. Sacks, D. A. Vorp, and M. Thornton. Surface geometric analysis of anatomic structures using biquintic finite element interpolation.
*Ann. Biomed. Eng.*28:598–611, 2000.CrossRefPubMedGoogle Scholar - 21.Taubin, G. Signal processing approach to fair surface design. In: Proceedings of the 22nd Annual ACM Conference on Computer Graphics and Interactive Techniques, Los Angeles, CA, August 9–11. New York: ACM, 1995.Google Scholar
- 22.Upchurch, Jr., G. R., and T. A. Schaub. Abdominal aortic aneurysm.
*Am. Fam. Physician*73:1198–11204, 2006.PubMedGoogle Scholar - 23.Van Damme, H., N. Sakalihasan, and R. Limet. Factors promoting rupture of abdominal aortic aneurysms.
*Acta Chir. Belg.*105:1–11, 2005.PubMedGoogle Scholar - 24.Van de Geest, J. P., D. H. Wang, S. R. Wisniewski, M. S. Makaroun, and D. A. Vorp. Towards a noninvasive method for determination of patient-specific wall strength distribution in abdominal aortic aneurysms.
*Ann. Biomed. Eng.*34:1908–1916, 2006.CrossRefGoogle Scholar - 25.Venkatasubramaniam, A. K., M. J. Fagan, T. Mehta, K. J. Mylankal, B. Ray, G. Kuhan,
*et al*. A comparative study of aortic wall stress using finite element analysis for ruptured and non-ruptured abdominal aortic aneurysms.*Eur. J. Vasc. Endovasc. Surg.*28:168–176, 2004.PubMedGoogle Scholar - 26.Vorp, D. A. Biomechanics of abdominal aortic aneurysm.
*J. Biomech.*40:1887–1902, 2007.CrossRefPubMedGoogle Scholar - 27.Vorp, D. A., M. L. Raghavan, and M. W. Webster. Mechanical wall stress in abdominal aortic aneurysm: influence of diameter and asymmetry.
*J. Vasc. Surg.*27:632–639, 1998.CrossRefPubMedGoogle Scholar