Abstract
Biomedical simulations are often dependent on numerical approximation methods, including finite element, finite difference, and finite volume methods, to model the varied phenomena of interest. An important requirement of the numerical approximation methods above is the need to create a discrete decomposition of the model geometry into a ‘mesh’. Historically, the generation of these meshes has been a critical bottleneck in efforts to efficiently generate biomedical simulations which can be utilized in understanding, planning, and diagnosing biomedical conditions. In this paper we discuss a methodology for generating hexahedral meshes for biomedical models using an algorithm implemented in the SCIRun Problem Solving Environment. The method is flexible and can be utilized to build up conformal hexahedral meshes ranging from models defined by single isosurfaces to more complex geometries with multi-surface boundaries.








































Similar content being viewed by others
References
ANSYS (2007) ANSYS, http://www.ansys.com
Benzley SE, Perry E, Merkley K, Clark B (1995) A comparison of all hexagonal and all tetrahedral finite element meshes for elastic and elasto-plastic analysis. In: Proceedings, 4th international meshing roundtable. Sandia National Laboratories, pp 179–191
Borden MJ, Shepherd JF, Benzley SE (2002) Mesh cutting: fitting simple all-hexahedral meshes to complex geometries. In: Proceedings, 8th international society of grid generation conference
Brewer M, Freitag-Diachin L, Knupp P, Leurent T, Melander DJ (2003) The MESQUITE mesh quality improvement toolkit. In: Proceedings, 12th international meshing roundtable. Sandia National Laboratories, pp 239–250
Bussler ML, Ramesh A (1993) The eight-node hexahedral elements in FEA of part designs. In: Foundry management and technology, pp 26–28
Cifuentes AO, Kalbag A (1992) A performance study of tetrahedral and hexahedral elements in 3-D finite element structural analysis. Finite Elem Anal Des 12(3–4):313–318
The CUBIT geometry and mesh generation toolkit (2007) Sandia National Laboratories, http://cubit.sandia.gov/
Freitag L (1997) On combining Laplacian and optimization-based mesh smoothing techniques. AMD trends in unstructured mesh generation. ASME 220:37–43
Freitag LA, Plassmann P (2000) Local optimization-based simplicial mesh untangling and improvement. Int J Numer Methods Eng 49(1):109–125
Johnson C, MacLeod R, Parker S, Weinstein D (2004) Biomedical computing and visualization software environments. Commun ACM 47(11):64–71
Jones TR, Durand F, Desbrun M (2003) Non-iterative, feature-preserving mesh smoothing. ACM Trans Graph 22(3):943–949
Knupp P, Mitchell SA (1999) Integration of mesh optimization with 3D all-hex mesh generation, LDRD subcase 3504340000, final report. SAND 99-2852, October 1999
Knupp PM (2003) Hexahedral and tetrahedral mesh shape optimization. Int J Numer Methods Eng 58(1):319–332
Knupp PM (2000) Hexahedral mesh untangling and algebraic mesh quality metrics. In: Proceedings, 9th international meshing roundtable. Sandia National Laboratories, pp 173–183
Lorenson WE, Cline HE (1987) Marching cubes: a high resolution 3D surface construction algorithm. Comput Graph 21(4):163–169. Proceedings of SIGGRAPH ’87
Loriot M (2006) TetMesh-GHS3D v3.1 the fast, reliable, high quality tetrahedral mesh generator and optimiser, http://www.simulog.fr/mesh/tetmesh3p1d-wp.pdf
MESQUITE (2005) The mesh quality improvement toolkit, terascale simulation tools and technology center (TSTT), http://www.tstt-scidac.org/research/mesquite.html
Parker S, Weinstein D, Johnson C (1997) The SCIRun computational steering software system. In: Arge E, Bruaset A, Langtangen H (eds) Modern software tools in scientific computing. Birkhauser Press, Boston, pp 1–40
Scheidegger C, Schreiner J (2007) Afront, http://sourceforge.net/projects/afront/
Schneiders R (1996) A grid-based algorithm for the generation of hexahedral element meshes. Eng Comput 12:168–177
Schneiders R (1997) An algorithm for the generation of hexahedral element meshes based on an octree technique. In: Proceedings, 6th international meshing roundtable. Sandia National Laboratories, pp 183–194
SCIRun (2007) A scientific computing problem solving environment, scientific computing and imaging institute (SCI), download from http://software.sci.utah.edu/scirun.html
Scott MA, Earp MN, Benzley SE, Stephenson MB (2005) Adaptive sweeping techniques. In: Proceedings, 14th international meshing roundtable. Sandia National Laboratories, pp 417–432
Shephard MS, Georges MK (1991) Three-dimensional mesh generation by finite octree technique. Int J Numer Methods Eng 32:709–749
Shepherd JF (2007) Topologic and geometric constraint-based hexahedral mesh generation. Published Doctoral Dissertation, University of Utah
Shepherd JF, Mitchell SA, Knupp P, White DR (2000) Methods for multisweep automation. In: Proceedings, 9th international meshing roundtable. Sandia National Laboratories, pp 77–87
The verdict mesh verification library (2007) Sandia National Laboratories, http://cubit.sandia.gov/verdict.html
Vachal P, Garimella RV, Shashkov MJ (2002) Mesh untangling. LAU-UR-02-7271, T-7 Summer Report 2002
Weingarten VI (1994) The controversy over hex or tet meshing. Machine Design, pp 74–78, April 18
White DR, Leland RW, Saigal S, Owen SJ (2001) The meshing complexity of a solid: an introduction. In: Proceedings, 10th international meshing roundtable. Sandia National Laboratories, pp 373–384
White DR, Saigal S, Owen SJ (2003) Meshing complexity of single part CAD models. In: Proceedings, 12th international meshing roundtable. Sandia National Laboratories, pp 121–134
Yerry MA, Shephard MS (1984) Three-dimensional mesh generation by modified octree technique. Int J Numer Methods Eng 20:1965–1990
Zhang Y, Bajaj C (2005) Adaptive and quality quadrilateral/hexahedral meshing from volumetric imaging data. In: Proceedings, 13th international meshing roundtable. Sandia National Laboratories, pp 365–376
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Shepherd, J.F., Johnson, C.R. Hexahedral mesh generation for biomedical models in SCIRun. Engineering with Computers 25, 97–114 (2009). https://doi.org/10.1007/s00366-008-0108-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00366-008-0108-z