Direct mechanics assessment of elastic symmetries and properties of trabecular bone architecture

Journal of Biomechanics

Volumn 29, Issue 12, 1996, Pages 1653-1657

  Van Rietbergen, B ^a   Odgaard, A ^b   Kabel, J ^b   Huiskes, R ^a  

^a RADBOUD UNIVERSITY NIJMEGEN   (Netherlands)

^b NONE

Author keywords

Bone architecture; Bone mechanics; Bone reconstruction; Finite element analysis; Trabecular bone

Indexed keywords

BONE; COMPUTER SIMULATION; ELASTICITY; FINITE ELEMENT METHOD; MATHEMATICAL TRANSFORMATIONS; OPTIMIZATION; STIFFNESS MATRIX;

BONE RECONSTRUCTION; COORDINATE TRANSFORMATION; ORTHOTROPIC ELASTIC SYMMETRIES; TRABECULAR BONE;

BIOMECHANICS;

ARTICLE; BIOMECHANICS; BONE STRUCTURE; ELASTICITY; PRIORITY JOURNAL; RIGIDITY; TRABECULAR BONE;

EID: 0030561004     PISSN: 00219290     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-9290(96)80021-2     Document Type: Article

References (23)

1. Ashman, R. B., Cowin, S. C., Van Buskirk, W. C. and Rice, J. C. (1984) A continuous wave technique for the measurement of the elastic properties of cortical bone. J. Biomechanics 17, 349-361.
2. Bunge, H. J. (1982) Texture Analysis in Material Science, Butterworths, London.
3. Cowin, S. C. (1989) Properties of the anisotropic elastic tensor. Q. Jl. Mech. Appl. Math. 42, 249-266.
4. Cowin, S. C. and Mehrabadi, M. (1987) On the identification of material symmetry for anisotropic elastic materials. Q. Jl. Mech. appl. Math. 40, 451-476.
5. Cowin, S. C. and Mehrabadi, M. (1989) Identification of the elastic symmetry of bone and other materials. J. Biomechanics 22, 503-515.
6. Cowin, S. C., Sadegh, A. M., and Luo, G. M. (1991) Correction formulae for the misalignment of axes in the measurement of the orthotropic elastic constants. J. Biomechanics 24, 637-641.
7. Harrigan, T. and Mann, R. W. (1984) Characterization of microstructural anisotropy in orthotropic materials using a second rank tensor. J. Mat. Sci. 19, 761-767.
8. Hill, R. (1963) Elastic properties of reinforced solids: some theoretical principles. J. Mech. Phys. Solids 11, 357-372.
9. Hollister, S. J., Fyhrie, D. P., Jepsen, K. J. and Goldstein, S. A. (1991) Application of homogenization theory to the study of trabecular bone mechanics. J. Biomechanics 24, 825-839.
10. Hollister, S. J. and Kikuchi, N. (1992) A comparison of homogenization and standard mechanics analyses for periodic porous composites. Comp. Mech. 10, 73-95.
11. Kinney, J. H., Nichols, M. C. and Lane, N. E. (1994) In vivo, three-dimensional histomorphometry: new perspectives of sequential changes in bone structures. Trans. Orthop. Res. Soc. 19, 56.
12. Kreyszig, E. (1993) Advanced Engineering Mathematics (7th Edn). Wiley, New York.
13. Nye, J. F. (1957) Physical properties of crystals: their representation by tensors and matrices. Clarendon Press, Oxford.
14. Müller, R., Hildebrand, T. and 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.
15. Odgaard, A., Andersen, K., Ullerup, R., Frich, L. H. and Melsen, F. (1994) Three-dimensional reconstruction of entire vertebral bodies. Bone 15, 335-342.
16. Press, W. H., Teukolsky, S. A., Vetterling, W. T. and Flannery, B. P. (1992) Numerical Recipes in Fortran (2nd Edn). Cambridge Univ. Press, Cambridge.
17. Snyder, B. D., Cheal, E. J., Hipp, J. A. and Hayes, W. C. (1989) Anisotropic structure-property relations for trabecular bone. Trans. Orthop. Res. Soc. 14, 265.
18. Suquet, P. M. (1985) Elements of homogenization theory for inelastic solid mechanics. In Homogenization Techniques for Composite Media (Edited by Sanchez-Palencia, E. and Zaoui, A.). Springer, Berlin.
19. Van Rietbergen, B., Weinans, H., Huiskes, R. and Odgaard, A. (1995a) A new method to determine trabecular bone elastic properties and loading using micromechanical finite-element models. J. Biomechanics 28, 69-81.
20. Van Rietbergen, B., Weinans, H., Huiskes., R. and Polman, J. W. (1994) A fast solving method for large-scale FE-models generated from computer images, based on a row-by-row matrix-vector multiplication scheme. ASME/CED 6, 47-52.
21. Van Rietbergen, B., Huiskes, R., Weinans, H., Odgaard, A. and Kabel, J. (1995b) The role of trabecular architecture in the anisotropic mechanical properties of bone. In Bone Structure and Remodeling (Edited by Odgaard, A. and Weinans, H.). World Scientific, Singapore.
22. Van Rietbergen, B., Weinans, H., Huiskes, R. and Polman, B. J. W. (1996) Computational strategies for iterative solution of large FEM applications employing voxel data. Int. J. Numer. Methods Eng. (in press).
23. Whitehouse, W. J. (1974) The quantitative morphology of anisotropic trabecular bone. J. Microsc. 101, 153-168.