Skip to main content

Advertisement

SpringerLink
Log in

Numerical and experimental structural analysis of trabecular architectures

  • Original Paper
  • Published:
Meccanica Aims and scope Submit manuscript

Abstract

This paper presents the application of the Cell Method (CM) to the static analysis of 3D structures obtained from micro-computed tomography reconstructions of trabecular bone. The CM is a recently introduced numerical method, based on a direct discrete formulation of equilibrium equations, which is particularly promising for the analysis of complex structures. In fact, due to the direct discrete approach employed, no restriction is imposed by differentiability conditions and the characteristic length of the elementary cell of the discretization can be of the same order of magnitude as the heterogeneities of the structure. The same 3D microstructures used for the numerical simulations were reproduced by means of a rapid prototyping process, by selective laser sintering of polyamide powder. The compression elastic modulus of the replicas was experimentally determined and used as parameter for comparison with the simulations results. The experimental values are in good agreement with the numerical ones, thus validating the methodology employed.

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

Similar content being viewed by others

References

  1. Consensus Development Conference (1993) Diagnosis, prophylaxis and treatment of osteoporosis. AM J Med 94:646–650

    Google Scholar 

  2. Kleerekoper M, Villaneva AR, Stanciu J, Sudhaker Rao D, Parfitt AM (1985) The role of three dimensional trabecular microstructure in the pathogenesis of vertebral compression fractures. Calcif Tissue Int 37(Suppl):S594–S597

    Google Scholar 

  3. Uchiyama T, Tanizawa T, Muramatsu H, Endo N, Takahashi HE, Hara T (1999) Three-dimensional microstructural analysis of human trabecular bone in relation to its mechanical properties. Bone 25(4): 487–491

    Article  Google Scholar 

  4. Cowin SC (1985) The relationship between the elasticity tensor and the fabric tensor. Mech Mater 4:137-147

    Article  ADS  Google Scholar 

  5. Brear K, Currey JD, Raines S, Smith KJ (1988) Density and temperature effects on some mechanical properties of cancellous bone. Eng Med 17: 163–167

    Google Scholar 

  6. Hodgskinson R, Currey JD (1990) The effect of variation in structure on the Young’s modulus of cancellous bone: a comparison of human and non-human material. J Eng Med PIME part H 204:115–121

    Google Scholar 

  7. Müller R, Hildebrand T, Rüegsegger P (1994) Non-invasive bone biopsy: a new method to analyse and display the three-dimensional structure of trabecular bone. Phys Med Biol 39:145–164

    Article  Google Scholar 

  8. Zohdi TD, Wriggers P (2001) Computational micro-macro material testing. Arch Comput Methods Eng 8:131–228

    MATH  Google Scholar 

  9. Yeh OC, Keaveny TM (1999) Biomechanical effects of intraspecimen variations in trabecular architecture: a three-dimensional finite element study. Bone 25:223–228

    Article  Google Scholar 

  10. Van Rietbergen B, Weinans H, Huiskes R, Odgaar A (1995) A new method to determine trabecular bone elastic properties and loading using micromechanical finite-element models. J Biomech 28:69–81

    Article  Google Scholar 

  11. Van Rietbergen B, Odgaar A, Kabel J, Huiskes R (1996) Direct mechanics assessment of elastic symmetries and properties of trabecular bone architecture. J Biomech 29:1653–1657

    Article  Google Scholar 

  12. Ulrich D, van Rietbergen B, Weinans H, Rüegsegger P (1998) Finite element analysis of trabecular bone structures: a comparison of image-based meshing techniques. J Biomech 31:1187–1192

    Article  Google Scholar 

  13. Niebur GL, Feldstein MJ, Yuen JC, Chen TJ, Keaveny TM (2000) High resolution finite element models with tyssue strength asymmetry accurately predict failure of trabecular bone. J Biomech 33:1575–1583

    Article  Google Scholar 

  14. Hommiga J, Huiskes R, Van Rietbergen B, Rüegsegger P, Weinans H (2001) Introduction and evaluation of a gray-value voxel conversion technique. J Biomech 34:513–517

    Article  Google Scholar 

  15. Roux S (1990) Continuum and discrete description of elasticity. In: Herrmann HJ, Roux S (eds) Statistical models for the fracture of disordered media. Elsevier, North Holland, pp. 109–113

    Google Scholar 

  16. Van Rietbergen B, Weinans H, Huiskes R (1996) Computational strategies for iterative solutions of large FEM applications employing voxel data. Int J Num Methods Eng 39:2743–2767

    Article  MATH  Google Scholar 

  17. Tonti E (2001) A direct discrete formulation of field laws: the cell method. CMES, Comput Model Eng Sci 2:237–258

    Google Scholar 

  18. Prendergast PJ, Huiskes R (1995) The biomechanics of Wolff’s law: recent advances. J Med Sci 164(2):152–154

    Article  Google Scholar 

  19. Kak AC, Slaney M (1988) Principles of computerized tomographic imaging. IEEE Press, New york

    MATH  Google Scholar 

  20. Odgaard A (1997) Three-dimensional methods for quantification of cancellous bone architecture. Bone 4:315–328

    Article  Google Scholar 

  21. Smith T (1999) Layer manufacture. A new form of 3-D visualization for artists. http://www.agocg.ac.uk/train/hitch/hitch2.pdf

  22. Borah B, Gross GJ, Dufresne TE, Smith TS, Cockman MD, Chmielewski PA, Lundy MW, Hartke JR, Sod EW (2001) Three-dimensional microimaging (MRμI and μCT), finite element modeling, and rapid prototyping provide unique insights into bone architecture in osteoporosis. Anat Rec (New Anat) 206: 101–110

    Google Scholar 

  23. Cosmi F, Dreossi D, Scalici M (2004) Bone sintering for strength assessment: first results in BOSSA project. Trans FAMENA 28:35–42

    Google Scholar 

  24. Cosmi F (2001) Numerical solution of Plane elasticity problems with the cell method. CMES, Comput Model Eng Sc 2:365–372

    MATH  Google Scholar 

  25. Cosmi F (2005) Elastodynamics wih the cell method. CMES, Comput Model Eng Sci 8:191–200

    Google Scholar 

  26. Algebraic Formulation of Physical Fields (2006) http://www.dic.units.it/perspage/discretephysics/

  27. Cosmi F, Di Marino F (2001) Modelling of the mechanical behaviour of porous materials: a new approach. Acta Bioeng Biomech 3:55–65

    Google Scholar 

  28. Cosmi F (2004) Two-dimension estimate of effective properties of solid with random voids. Theor Appl Fract Mech, Elsevier Sci 42:183–186

    Article  Google Scholar 

  29. Cosmi F (2003) Numerical modeling of porous materials mechnical behaviour with the cell method. In: Proceedings of Second MIT conference on computational fluid Massachusetts Institute of Technology, and solid mechanics, 17–20, June 2003, Cambridge, MA, USA

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Ingegneria Meccanica, Università di Trieste, via A. Valerio 10, 34127, Trieste, Italy

    F. Cosmi & D. Dreossi

Authors
  1. F. Cosmi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Dreossi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to F. Cosmi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cosmi, F., Dreossi, D. Numerical and experimental structural analysis of trabecular architectures. Meccanica 42, 85–93 (2007). https://doi.org/10.1007/s11012-006-9024-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11012-006-9024-8

Keywords

Search

Navigation