Skip to main content

Advertisement

SpringerLink
Log in

Automatic reconstruction of a patient-specific high-order surface representation and its application to mesh generation for CFD calculations

  • Special Issue - Review
  • Published:
Medical & Biological Engineering & Computing Aims and scope Submit manuscript

Abstract

We describe a set of procedures for the shape reconstruction and mesh generation of unstructured high-order spatial discretization of patient-specific geometries from a series of medical images and for the simulation of flows in these meshes using a high-order hp-spectral solver. The reconstruction of the shape of the boundary is based on the interpolation of an implicit function through a set of points obtained from the segmentation of the images. This approach is favoured for its ability of smoothly interpolating between sections of different topology. The boundary of the object is initially represented as an iso-surface of an implicit function defined in terms of radial basis functions. This surface is approximated by a triangulation extracted by the method of marching cubes. The triangulation is then suitably smoothed and refined to improve its quality and permit its approximation by a quilt of bi-variate spline surface patches. Such representation is often the standard input format required for state-of-the-art mesh generators. The generation of the surface patches is based on a partition of the triangulation into Voronoi regions and dual Delaunay triangulations with an even number of triangles. The quality of the triangulation is optimized by imposing that the distortion associated with the energy of deformation by harmonic maps is minimized. Patches are obtained by merging adjacent triangles and this representation is then used to generate a mesh of linear elements using standard generation techniques. Finally, a mesh of high-order elements is generated in a bottom-up fashion by creating the additional points required for the high-order interpolation and projecting them on the edges and surfaces of the quilt of patches. The methodology is illustrated by generating meshes for a by-pass graft geometry and calculating high-order CFD solutions in these meshes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Aho A (1983) Data structures and algorithms. Addison-Wesley, Reading

  2. Antiga L, Steinman DA (2004) Robust and objective decomposition and mapping of bifurcating vessels. IEEE Trans Med Imaging 23(6):704–713

    Article  Google Scholar 

  3. Antiga L, Iordache BE, Caverni L, Cornalba GP, Remuzzi A (2002) Geometric reconstruction for computational mesh generation of arterial bifurcations from CT angiography. Comput Med Imaging Graph 26(4):227–235

    Article  Google Scholar 

  4. Ayache N (1998) L’analyse automatique des images médicales. Êtat de l’art et perspectives. Technical report 3364, INRIA

  5. Beatson RK, Light WA, Billings S (2000) Fast solution of the radial basis function interpolation equations: domain decomposition methods. SIAM J Sci Comput 22(5):1717–1740

    Article  MATH  MathSciNet  Google Scholar 

  6. Beatson RK, Cherrie JB, Ragozin DL (2001) Fast evaluation of radial basis functions: methods for four-dimensional polyharmonic splines. SIAM J Math Anal 32(6):1272–1310

    Article  MATH  MathSciNet  Google Scholar 

  7. Bloomenthal J (1994) An implicit surface polygonizer. In: Heckbert PS (ed) Graphics gems IV, Academic Press, London, pp 324–349

  8. Buhmann MD (2003) Radial basis functions. Cambridge University Press, Cambridge

  9. Burkard RE, Derigs U (1980) Assignment and matching problems: solution methods with FORTRAN programs. In: Lecture notes in economics and mathematical systems. Springer, Heidelberg

  10. Carr JC, Beatson RK, Cherrie JB, Mitchell TJ, Fright WR, McCallum BC, Evans TR (2001) Reconstruction and representation of 3D objects with radial basis functions. In: Computer graphics proceedings, SIGGRAPH2001, pp 67–76

  11. Cebral JR, Löhner R (2001) From medical images to anatomically accurate finite element grids. Int J Numer Methods Eng 51:985–1008

    Article  MATH  Google Scholar 

  12. Chernyaev E (1995) Marching cubes 33: Construction of topologically correct isosurfaces. Technical report CERN-CN/95-17, CERN

  13. Coppola G, Sherwin SJ, Peiró J (2001) Non-linear particle tracking for high-order elements. J Compuy Phys 172:356–380

    Article  MATH  Google Scholar 

  14. Dey S, O’Bara RM, Shephard MS (1999) Curvilinear mesh generation in 3D. Comput Aided Des 33:199–209

    Article  Google Scholar 

  15. Duncan M (1999) Applied geometry for computer graphics and CAD. Springer, Heidelberg

  16. Eck M, Hoppe H (1996) Automatic reconstruction of B-spline surfaces of arbitrary topological type. In: Computer graphics proceedings, SIGGRAPH96, pp 325–334

  17. Eck M, DeRose T, Duchamp T, Hoppe H, Lounsbery M, Stuetzle W (1995) Multiresolution analysis of arbitrary meshes. In: Computer graphics proceedings, SIGGRAPH95, pp 173–180

  18. Eells J, Sampson J (1964) Harmonic mappings of Riemannian manifolds. Am J Math 86:109–160

    Article  MATH  MathSciNet  Google Scholar 

  19. Floater MS (1997) Parameterization and smooth approximation of surface triangulations. Comput Aided Geom Des 14:231–250

    Article  MATH  MathSciNet  Google Scholar 

  20. Frey PJ (2004) Generation and adaptation of computational surface meshes from discrete anatomical data. Int J Numer Methods Eng 60:1049–1074

    Article  MATH  Google Scholar 

  21. Frey PJ, George PL (2000) Mesh generation. Hermes Science Publishing

  22. Gambaruto A, Radaelli A, Peiró J, Doorly DJ (2008) Reconstruction of shape and flow in anatomical conduits. Int J Numer Methods Fluids 57(5):495–517

    Article  MATH  Google Scholar 

  23. Giordana S (2004) Geometrical reconstruction from medical images, classification and modelling of arterial by-pass grafts. PhD thesis, Department of Aeronautics, Imperial College London

  24. Giordana S, Sherwin SJ, Peiró J, Doorly DJ, Papaharilaou Y, Caro CG, Watkins N, Cheshire N, Jackson M, Bicknall C, Zervas V (2005) Automated classification of peripheral distal by-pass geometries reconstructed from medical data. J Biomech 38:47–62

    Google Scholar 

  25. Hartmann E (1999) On the curvature of curves and surfaces defined by normalforms. Comput Aided Geom Des 16:355–376

    Article  MATH  MathSciNet  Google Scholar 

  26. Jackson MJ, Bicknelland CD, Zervas V, Cheshire NJW, Sherwin SJ, Giordana S, Peiró J, Papaharilaou Y, Doorly DJ, Caro CG (2003) Three-dimensional reconstruction of autologous vein bypass graft distal anastomoses imaged with magnetic resonance: clinical and research applications. J Vasc Surg 38:621–625

    Article  Google Scholar 

  27. Karniadakis GE, Israeli M, Orszag SA (1991) High-order splitting methods for the incompressible Navier-Stokes equations. J Comp Phys 97:414–443

    Article  MATH  MathSciNet  Google Scholar 

  28. Ladak HM, Milner JS, Steinman DA (2000) Rapid three-dimensional segmentation of the carotid bifurcation from serial MR images. J Biomech Eng 122:96–99

    Article  Google Scholar 

  29. Lorensen WE, Cline HE (1987) Marching cubes: a high resolution 3D surface reconstruction algorithm. Comput Graph 21(4):163–169

    Article  Google Scholar 

  30. McInerney T, Terzopoulos D (1996) Deformable models in medical image analysis: a survey. Med Image Anal 1(2):91–108

    Article  Google Scholar 

  31. NEMA (2007) Digital imaging and communications in medicine (DICOM). http://medical.nema.org/dicom/2007/, maintained by the National Electrical Manufacturers Association

  32. Okabe A, Boots B, Sugihara K (1992) Spatial tessellations. Concepts and applications of Voronoi diagrams. Wiley, London

  33. Peiró J (1999) Surface grid generation. In: Thompson JF, Soni BK, Weatherill NP (eds) Handbook of grid generation. CRC Press LLC, Chap 19, pp 19.1–19.20

  34. Peiró J, Sayma AI (1995) A 3-D unstructured multigrid Navier-Stokes solver. In: Morton KW, Baines MJ (eds) Numerical methods for fluid dynamics V, Oxford University Press, New York

  35. Peiró J, Formaggia L, Gazzola M, Radaelli A, Rigamonti V (2007) Shape reconstruction from medical images and quality mesh generation via implicit surfaces. Int J Numer Methods Fluids 53:1339–1360

    Article  MATH  Google Scholar 

  36. Peraire J, Morgan K, Peiró J (1993) Multigrid solution of the 3-D compressible Euler equations on unstructured tetrahedral grids. Int J Numer Methods Eng 36:1029–1044

    Article  MATH  Google Scholar 

  37. Peraire J, Peiró J, Morgan K (1999) Advancing front grid generation. In: Thompson JF, Soni BK, Weatherill NP (eds) Handbook of grid generation, CRC Press LLC, Chap 17, pp 17.1–17.22

  38. Russ JC (ed) (1999) The image processing handbook, 3rd edn. CRC Press with IEEE Press

  39. Sethian JA (1999) Level set methods and fast marching methods, 2nd edn. Cambridge University Press, London

  40. Sherwin SJ, Karniadakis GE (1996) Tetrahedral hp finite elements: algorithms and flow solutions. J Comput Phys 124:14–45

    Article  MATH  MathSciNet  Google Scholar 

  41. Sherwin SJ, Peiró J (2000) Mesh generation in curvilinear domains using high-order elements. Int J Numer Methods Eng 53:207–223

    Article  Google Scholar 

  42. Sonka M, Fitzpatrick JM (eds) (2000) Handbook of medical imaging, medical image processing and analysis, vol 2. SPIE press, Whashington

    Google Scholar 

  43. Tarjan RE (1983) Data structures and network algorithms. In: CMBS-NSF regional conference series in applied mathematics, SIAM

  44. Thompson JF, Soni BK, Weatherill NP (eds) (1999) Handbook of grid generation. CRC Press LLC

  45. Turk G, O’Brien JF, Yngve G (2001) Implicit surfaces that interpolate. In: Shape modelling international, Genova, Italy

  46. Wendland H (2002) Fast evaluation of radial basis functions: methods based on partition of unity. In: Chui CK, Schumaker LL, Stockler J (eds) Approximation theory X: wavelets, splines, and applications. Vanderbilt University Press, Nashville, pp 473–483

    Google Scholar 

  47. Wolters BJBM, Rutten MCM, Schurink GWH, Kose U, de Hart J, van de Vosse FN (2005) A patient-specific computational model of fluid-structure interaction in abdominal aortic aneurysms. Med Eng Phys 27:871–883

    Article  Google Scholar 

  48. Zhang Y, Bazilevs Y, Goswami S, Bajaj CL, Hughes TJR (2007) Patient-specific vascular NURBS modelling for isogeometric analysis of blood flow. Comput Methods Appl Mech Eng 196:2943–2959

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

We would like to thank some of the past and present members of the Biofluids group: Denis Doorly, Donal Taylor, Alberto Gambaruto, Kuan-Lok “Adrian” Lee and Alessandro Radaelli, for contributing with ideas and material to this paper.

Author information

Authors and Affiliations

  1. Department of Aeronautics, Imperial College London, South Kensington Campus, London, SW7 2AZ, UK

    Joaquim Peiró, Spencer J. Sherwin & Sergio Giordana

Authors
  1. Joaquim Peiró
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Spencer J. Sherwin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sergio Giordana
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Joaquim Peiró.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Peiró, J., Sherwin, S.J. & Giordana, S. Automatic reconstruction of a patient-specific high-order surface representation and its application to mesh generation for CFD calculations. Med Biol Eng Comput 46, 1069–1083 (2008). https://doi.org/10.1007/s11517-008-0390-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11517-008-0390-3

Keywords

Search

Navigation