Computational strategies for iterative solutions of large FEM applications employing voxel data

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Van Rietbergen, B.¹; Weinans, H.¹; Huiskes, R.¹; Polman, B. J. W.²

Computational strategies for iterative solutions of large FEM applications employing voxel data

Int J Num Meth Eng. August 30, 1996;39(16):2743-2767

©1996 John Wiley & Sons, Ltd.

Affiliations

¹Biomechanics Section, Institute of Orthopaedics, University of Nijmegen, The Netherlands

²Department of Mathematics, University of Nijmegen, The Netherlands
Abstract and keywords

FE-models for structural solid mechanics analyses can be readily generated from computer images via a “voxel conversion” method, whereby voxels in a two- or three-dimensional computer image are directly translated to elements in a FE-model. The fact that all elements thus generated are the same creates the possibilities for fast solution algorithms that can compensate for a large number of elements. The solving methods described in this paper are based on an iterative solving algorithm in combination with a unique-element Element-by-Element (EBE) or with a newly developed Row-by-Row (RBR) matrix-vector multiplication strategy. With these methods it is possible to solve FE-models on the order of 10⁵ 3-D brick elements on a workstation and on the order of 10⁶ elements on a Cray computer.

The methods are demonstrated for the Boussinesq problem and for FE-models that represent a porous trabecular bone structure. The results show that the RBR method can be 3.2 times faster than the EBE method. It was concluded that the voxel conversion method in combination with these solving methods not only provides a powerful tool to analyse structures that can not be analysed in another way, but also that this approach can be competitive with traditional meshing and solving techniques.

Keywords: structural mechanics; voxel conversion; large FEM applications; iterative solving; element‐by‐element; row‐by‐row
Links

DOI: 10.1002/(SICI)1097-0207(19960830)39:16<2743::AID-NME974>3.0.CO;2-A

WoS: A1996VB59000003
History

Received: 1994-04-01

Revised: 1995-10-04

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Cited By (48)

Year	Entry
1996	van Rietbergen B. Mechanical Behavior and Adaptation of Trabecular Bone in Relation to Bone Morphology [PhD thesis]. Nijmegen, Netherlands: Catholic University of Nijmegen; 1996.
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2006	van Lenthe GH, Stauber M, Müller R. Specimen-specific beam models for fast and accurate prediction of human trabecular bone mechanical properties. Bone. December 2006;39(6):1182-1189.
2007	Nagaraja S, Lin ASP, Guldberg RE. Age-related changes in trabecular bone microdamage initiation. Bone. April 2007;40(4):973-980.
2002	van Rietbergen B, Majumdar S, Newitt D, MacDonald B. High-resolution MRI and micro-FE for the evaluation of changes in bone mechanical properties during longitudinal clinical trials: application to calcaneal bone in postmenopausal women after one year of idoxifene treatment. Clin Biomech (Bristol, Avon). February 2002;17(2):81-88.
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1996	van Rietbergen B, Odgaard A, Kabel J, Huiskes R. Direct mechanics assessment of elastic symmetries and properties of trabecular bone architecture. J Biomech. December 1996;29(12):1653-1657.
1997	Odgaard A, Kabel J, van Rietbergen B, Dalstra M, Huiskes R. Fabric and elastic principal directions of cancellous bone are closely related. J Biomech. 1997;30(5):487-495.
1998	Ulrich D, van Rietbergen B, Weinans H, Rüegsegger P. Finite element analysis of trabecular bone structure: a comparison of image-based meshing techniques. J Biomech. December 1998;31(12):1187-1192.
1999	Van Rietbergen B, Müller R, Ulrich D, Rüegsegger P, Huiskes R. Tissue stresses and strain in trabeculae of a canine proximal femur can be quantified from computer reconstructions. J Biomech. February 1999;32(2):165-173.
1999	Kabel J, van Rietbergen B, Dalstra M, Odgaard A, Huiskes R. The role of an effective isotropic tissue modulus in the elastic properties of cancellous bone. J Biomech. 1999;32(7):673-680.
1999	Ulrich D, van Rietbergen B, Laib A, Rüegsegger P. Load transfer analysis of the distal radius from in-vivo high-resolution CT-imaging. J Biomech. August 1999;32(8):821-828.
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2005	Nagaraja S, Couse TL, Guldberg RE. Trabecular bone microdamage and microstructural stresses under uniaxial compression. J Biomech. 2005;38(4):707-716.
2005	Ruimerman R, Hilbers P, van Rietbergen B, Huiskes R. A theoretical framework for strain-related trabecular bone maintenance and adaptation. J Biomech. April 2005;38(4):931-941.
2006	Verhulp E, van Rietbergen B, Huiskes R. Comparison of micro-level and continuum-level voxel models of the proximal femur. J Biomech. 2006;39(16):2951-2957.
2007	van Ruijven LJ, Mulder L, van Eijden TMGJ. Variations in mineralization affect the stress and strain distributions in cortical and trabecular bone. J Biomech. 2007;40(6):1211-1218.
2011	Green JO, Nagaraja S, Diab T, Vidakovic B, Guldberg RE. Age-related changes in human trabecular bone: relationship between microstructural stress and strain and damage morphology. J Biomech. 2011;44(12):2279-2285.
2012	Wirth AJ, Müller R, van Lenthe GH. The discrete nature of trabecular bone microarchitecture affects implant stability. J Biomech. April 5, 2012;45(6):1060-1067.
1999	Niebur GL, Yuen JC, Hsia AC, Keaveny TM. Convergence behavior of high-resolution finite element models of trabecular bone. J Biomech Eng. December 1999;121(6):629-635.
2011	Nagaraja S, Skrinjar O, Guldberg RE. Spatial correlations of trabecular bone microdamage with local stresses and strains using rigid image registration. J Biomech Eng. June 2011;133(6):064502.
2002	Boyd SK, Müller R, Zernicke RF. Mechanical and architectural bone adaptation in early stage experimental osteoarthritis. J Bone Miner Res. April 2002;17(4):687-694.
2003	Van Rietbergen B, Huiskes R, Eckstein F, Rüegsegger P. Trabecular bone tissue strains in the healthy and osteoporotic human femur. J Bone Miner Res. October 2003;18(10):1781-1788.
2003	van Ruijven LJ, Giesen EBW, Farella M, van Eijden TMGJ. Prediction of mechanical properties of the cancellous bone of the mandibular condyle. J Dent Res. October 2003;82(10):819-823.
1998	Van Rietbergen B, Odgaard A, Kabel J, Huiskes R. Relationships between bone morphology and bone elastic properties can be accurately quantified using high‐resolution computer reconstructions. J Orthop Res. January 1998;16(1):23-28.
1998	Viceconti M, Bellingeri L, Cristofolini L, Toni A. A comparative study on different methods of automatic mesh generation of human femurs. Med Eng Phys. January 1998;20(1):1-10.
2013	Madi K, Tozzi G, Zhang Q, Tong J, Cossey A, Au A, Hollis D, Hild F. Computation of full-field displacements in a scaffold implant using digital volume correlation and finite element analysis. Med Eng Phys. September 2013;35(9):1298.
2001	Homminga J, Weinans H, Gowin W, Felsenberg D, Huiskes R. Ostehoporosis changes the amount of vertebral trabecular bone at risk of fracture but not the vertebral load distribution. Spine. July 2001;26(14):1555-1560.
1997	Ulrich D, Hildebrand T, Van Rietbergen B, Müller R, Rüegsegger P. The quality of trabecular bone evaluated with micro-computed tomography, FEA and mechanical testing. Stud Health Technol Inform. 1997;40:97-112.
1998	van Rietbergen B, Majumdar S, Pistoia W, Newitt DC, Kothari M, Laib A, Rüegsegger P. Assessment of cancellous bone mechanical properties from micro-FE models based on micro-CT, pQCT and MR images. Technol Health Care. December 1998;6(5-6):413-420.
2005	Stauber M. Volumetric Spatial Decomposition of Porous Microstructures: A Framework for Element Based Analysis of Trabecular Bone [PhD thesis]. Swiss Federal Institute of Technology Zürich; 2005.
2006	Nagaraja S. Microstructural Stresses and Strains Associated With Trabecular Bone Microdamage [PhD thesis]. Atlanta, GA: Georgia Institute of Technology; December 2006.
2011	O'Neal JM. The Effects of Aging and Remodeling on Bone Quality and Microdamage [PhD thesis]. Atlanta, GA: Georgia Institute of Technology; August 2011.
2009	Lievers WB. Effects of Geometric and Material Property Changes on the Apparent Elastic Properties of Cancellous Bone [PhD thesis]. Queen's University; April 2009.
2005	Ruimerman R. Modeling and Remodeling in Bone Tissue [PhD thesis]. Eindhoven University of Technology; 2005.
2006	Verhulp E. Analyses of Trabecular Bone Failure [PhD thesis]. Eindhoven, The Netherlands: Eindhoven University of Technology; 2006.
2013	Christen P. Deciphering the Secret Message Within Bone Microstructure [PhD thesis]. Eindhoven University of Technology; 2013.
2014	Gross T. Development and Application of 3d CT Image-Based Micro and Macro Finite Element Models for Human Bones and Orthopedic Implant Systems [PhD thesis]. Vienna University of Technology; 2014.
2001	Boyd SK. Microstructural Bone Adaptation in an Experimental Model of Osteoarthritis [PhD thesis]. Calgary, AB: University of Calgary; January 2001.
2000	Niebur GL. A Computational Investigation of Multiaxial Failure in Trabecular Bone [PhD thesis]. Berkeley, CA: Berkeley, University of California; 2000.
2012	Mengoni M. On the Development of an Integrated Bone Remodeling Law for Orthodontic Tooth Movements Models Using the Finite Element Method [PhD thesis]. Liège, Belgique: Université de Liège; June 2012.
2010	Schwen LO. Composite Finite Elements for Trabecular Bone Microstructures [PhD thesis]. Bonn, Germany: Rheinische Friedrich-Wilhelms-Universität Bonn; July 2010.
2020	Zaluski D. Validation of Subject Specific Computed Tomography-Based Finite Element Models of the Human Proximal Tibia Using Full-Field Experimental Displacement Measurements from Digital Volume Correlation [Master's thesis]. University of Saskatchewan; December 2020.
2023	Egeonu IET. Bone Microstructure and Bone Strength At the Distal Radius in Relation to the Pubertal Growth Spurt in Adolescence [Master's thesis]. University of Saskatchewan; July 2023.