Vascular Geometry Reconstruction and Grid Generation

  • Thomas Wischgoll
  • Daniel R. Einstein
  • Andrew P. Kuprat
  • Xiangmin Jiao
  • Ghassan S. Kassab


The geometry of vascular system is an important determinant of blood flow in health and disease. There is a strong geometric component to atherosclerosis in coronary heart disease since lesions are preferentially located at bifurcation points and regions of high curvature. The influence of these local structures on recirculation and deleterious shear stresses and their role in plaque development is widely accepted. Over time, researchers have turned to MR, CT, or biplane images of vascular trees to faithfully capture these features in the flow simulations. Historically, this has taken the form of labor-intensive manual reconstructions from morphometric measurements based on the centerline, whereby small idealized subsets of vascular trees are developed into computational grids. With improved imaging, image processing, and geometric reconstruction algorithms, researchers have begun to develop geometrically accurate computational models directly from the medical images. This chapter provides an overview of contemporary methods for image processing, centerline detection, boundary condition definition, and grid generation of both clinical and research images of cardiovascular structures.


Object Boundary Discretization Error Volumetric Image Distance Field Bifurcation Angle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This research was supported in part by Wright State University; the Ohio Board of Regents; the National Heart and Blood Institute HL055554-11, HL-084529, and HL073598; the National Institute of Environmental Health Sciences P01ES011617; and by the National Science Foundation DMS-0809285.


  1. 1.
    Canny JF. A computational approach to edge detection. IEEE Trans Pattern Anal Mach Intell. 1986;PAMI-8(6):679–98.CrossRefGoogle Scholar
  2. 2.
    Jain R, Kasturi R, Schunck BG. Machine vision. New York: McGraw-Hill, Inc., 1995.Google Scholar
  3. 3.
    Lorensen WE, Cline HE. Marching cubes: a high resolution 3D surface construction algorithm. Comput Graph. 1987;21(4).CrossRefGoogle Scholar
  4. 4.
    Carson JP, Einstein DR, Minard KR, Fanucchi MV, Wallis CD, Corley RA. Lung airway cast segmentation with proper topology, suitable for computational fluid-dynamic simulations. Comput Med Imaging Graph. (submitted).Google Scholar
  5. 5.
    Cornea ND, Silver D, Min P. Curve-skeleton applications. Proceedings of IEEE visualization, 2005, pp. 95–102.Google Scholar
  6. 6.
    Bertrand G, Aktouf Z. A three-dimensional thinning algorithm using subfields. Vis Geom III. 1994;2356:113–24.CrossRefGoogle Scholar
  7. 7.
    Brunner D, Brunnett G. Mesh segmentation using the object skeleton graph. Proceedings of IASTED international conference on computer graphics and imaging, 2004, pp. 48–55.Google Scholar
  8. 8.
    Dyedov V, Einstein DR, Jiao X, Kuprat AP, Carson JP, del Pin F. Variational generation of prismatic boundary-layer meshes for biomedical computing. Int J Numer Methods Eng. 2009;79(8):907–945.Google Scholar
  9. 9.
    Lee T, Kashyap RL, Chu CN. Building skeleton models via 3-D medial surface/axis thinning algorithms. CVGIP: Graph Model Image Process. 1994;56(6):462–78.CrossRefGoogle Scholar
  10. 10.
    Lohou C, Bertrand G. A 3D 12-subiteration thinning algorithm based on P-simple points. Discrete Appl Math. 2004;139:171–95.MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Palágyi K, Kuba A. Directional 3D thinning using 8 subiterations. Proceedings of discrete geometry for computer imagery, Lect Notes Comput Sci. 1999;1568:325–36.Google Scholar
  12. 12.
    Palágyi K, Kuba A. A parallel 3D 12-subiteration thinning algorithm. Graph Model Image Proc. 1999;61(4):199–221.CrossRefGoogle Scholar
  13. 13.
    Saha PK, Chaudhuri BB, Dutta Majumder D. A new shape preserving parallel thinning algorithm for 3D digital images. Pattern Recognit. 1997;30(12):1939–55.CrossRefGoogle Scholar
  14. 14.
    Tsao YF, Fu KS. A parallel thinning algorithm for 3-D pictures. Comput Graph Image Process. 1981;17:315–31.CrossRefGoogle Scholar
  15. 15.
    Lobregt S, Verbeek PW, Groen FCA. Three-dimensional skeletonization: principle and algorithm. IEEE Trans Pattern Anal Mach Intell. 1980;2(1):75–7.CrossRefGoogle Scholar
  16. 16.
    Sethian JA. Fast marching methods. SIAM Rev. 1999;41(2):199–235.MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Telea A, Vilanova A. A robust level-set algorithm for centerline extraction. Eurographics/IEEE symposium on data visualization, 2003, pp. 185–94.Google Scholar
  18. 18.
    Si H.TetGen. A quality tetrahedral mesh generator and three-dimensional Delaunay triangulator. WIAS Technical Report No. 9, 2004.Google Scholar
  19. 19.
    Wan M, Dachille F, Kaufman A. Distance-field based skeletons for virtual navigation. Proceedings of IEEE visualization, 2001, pp. 239–45.Google Scholar
  20. 20.
    Wischgoll T, Choy JS, Ritman ES, Kassab GS. Validation of image-based extraction method for morphometry of coronary arteries. Ann Biomed Eng. 2008;36(3):356–68.CrossRefGoogle Scholar
  21. 21.
    Zhou Y, Toga AW. Efficient skeletonization of volumetric objects. IEEE Trans Vis Comput Graph. 1999;5(3):196–209.CrossRefGoogle Scholar
  22. 22.
    Amenta N, Choi S, Kolluri R.The power crust. Proceedings of 6th ACM symposium on solid modeling, 2001, pp. 249–60.Google Scholar
  23. 23.
    Dey TK, Goswami S. Tight Cocone: a water-tight surface reconstructor. Proceedings of 8th ACM symposium. Solid modeling applications, 127–34. Journal version in J Comput Inform Sci Eng. 2003;30:302–7.CrossRefGoogle Scholar
  24. 24.
    Nordsletten DA, Blackett S, Bentley MD, Ritman EL, Smith NP. Structural morphology of renal vasculature. Am J Physiol Heart Circ Physiol. 2006;291(1):H296–309.CrossRefGoogle Scholar
  25. 25.
    Kuprat-AP, Einstein-DR. An anisotropic scale-invariant unstructured mesh generator suitable for volumetric imaging data. J Comput Phys. 2009;228:619–40.MathSciNetCrossRefGoogle Scholar
  26. 26.
    Jiao X, Zha H. Consistent computation of first- and second-order differential quantities for surface meshes. In ACM solid and physical modeling symposium, 2008.Google Scholar
  27. 27.
    Khamayseh A, Hansen G. Use of the spatial kD-tree in computational physics applications. Commun Comput Phys. 2007;2:545–76.MATHGoogle Scholar
  28. 28.
    Sethian JA. Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science. Cambridge: Cambridge University Press, 1999.MATHGoogle Scholar
  29. 29.
    Jiao X. Face offsetting: a unified approach for explicit moving interfaces. J Comput Phys. 2007;220:612–625.MathSciNetMATHCrossRefGoogle Scholar
  30. 30.
    Si H. Adaptive tetrahedral mesh generation by constrained Delaunay refinement. Int J Numer Methods Eng. 2008;856–80.Google Scholar
  31. 31.
    Cornea ND, Silver D, Yuan X, Balasubramanian R. Computing hierarchical curve-skeletons of 3D objects. Vis Comput. 2005;21(11):945–55.CrossRefGoogle Scholar
  32. 32.
    Luboz V, Wu X, Krissian K, Westin CF, Kikinis R, Cotin S, Dawson S. A segmentation and reconstruction technique for 3D vascular structures. MICCAI 2005, Lect Notes Comput Sci. 2005;3749:43–50.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Thomas Wischgoll
    • 1
  • Daniel R. Einstein
    • 2
  • Andrew P. Kuprat
    • 2
  • Xiangmin Jiao
    • 3
  • Ghassan S. Kassab
    • 4
    • 5
    • 6
    • 7
    • 8
  1. 1.Department of Computer Science and EngineeringWright State UniversityDaytonUSA
  2. 2.Pacific Northwest National LaboratoryRichlandUSA
  3. 3.Department of Applied Mathematics and StatisticsStony Brook UniversityStony BrookUSA
  4. 4.Weldon School of Biomedical EngineeringPurdue UniversityIndianapolisUSA
  5. 5.Department of Biomedical EngineeringIndianapolisUSA
  6. 6.Department of SurgeryIndianapolisUSA
  7. 7.Department of Cellular and Integrative PhysiologyIndianapolisUSA
  8. 8.Indiana Center for Vascular Biology and MedicineIUPUIIndianapolisUSA

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