Conclusions
Using 3-D reconstruction, micro-FEM and 3-D architectural analyses, we have studied the relation between various measures of architectural anisotropy, the influence of connectivity and trabecular material anisotropy on the elastic anisotropy of cancellous bone. We have reached the following conclusions: 1) the elastic anisotropy of the trabecular hone material seems only to have marginal influence on the anisotropic elastic properties of cancellous bone, 2) different architectural anisotropy measures are highly correlated, and methods studied are all highly related to the elastic anisotropy, and 3) connectivity has only marginal influence on elastic properties.
The ability to determine cancellous bone mechanical properties either indirectly from established architecture-mechanics relations or directly from architecture by the use of micro-FEM give promises for future in vivo evaluation of cancellous bone mechanical properties [20].
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Ashby, M. F. The mechanical properties of cellular solids. Metall Trans A, 14-A:1755–1769, 1983.
Cowin, S. C. The relationship between the elasticity tensor and the fabric tensor. Mech Mater, 4:137–147, 1985.
Cruz-Orive, L. M., Karlsson, L. M., Larsen, S. E., and Wainschtein, F. Characterizing anisotropy: a new concept. Micron Microscopica Acta, 23:75–76, 1992.
DeHoff, R. T. Quantitative serial sectioning analysis: preview. J Microsc, 131:259–263, 1983.
Feldkamp, L. A. and Davis, L. C. Topology and elastic properties of depleted media. Phys Rev B, 37:3448–3453, 1988.
Feldkamp, L. A., Goldstein, S. A., Parfitt, A. M., Jesion, G., and Kleerekoper M. The direct examination of three-dimensional bone architecture in vitro by computed tomography. J Bone Miner Res, 4:3–11, 1989.
Gibson, L. J. The mechanical behaviour of cancellous bone. J Biomech, 18:317–328, 1985.
Giger, H. Grundgleichungen der stereologie i. Metrika, 16:43–57, 1970.
Goldstein, S. A. The mechanical properties of trabecular bone: dependence on anatomic location and function. J Biomech, 20:1055–1061, 1987.
Goldstein, S. A., Goulet, R., and McCubbrey, D. Measurement and significance of three-dimensional architecture to the mechanical integrity of trabecular bone. Calcif Tissue Int, 53 Suppl 1:S127–32; discussion S132–3, 1993.
Goldstein, S. A., Hollister, S. J., Kuhn, J. L., and Kikuchi, N. The mechanical and remodeling properties of trabecular hone. In Mow, V. C., Ratcliffe, A., and Woo, S. L. Y., editors, Biomechanics of diarthrodial joints., volume II, pages 61–81, New York, 1990. Springer.
Goulet, R. W., Goldstein, S. A., Ciarelli, M. J., Kuhn, 3. L., Brown, M. B., and Feldkamp, L. A. The relationship between the structural and orthogonal compressive properties of trabecular bone. J Biomech, 27:375–389, 1994.
Gundersen, H. J., Boyce, R. W., Nyengaard, J. R., and Odgaard, A. The conneulor: unbiased estimation of connectivity using physical disectors under projection. Bone, 14:217–222, 1993.
Harrigan, T. P. and Mann, R. W. Characterization of microstructural anisotropy in orthotropic materials using a second rank tensor. J Mater Sci, 19:761–767, 1984.
Hildebrand, T. and Rüegsegger, P. A new method for the model-independent assessment of thickness in three-dimensional images. J Microsc, 185:67–75, 1997.
Hilliard, J. E. Determination of structural anisotropy. In Elias, H., editor, Proceedings of the second international congress for stereology., Berlin, 1967. Springer.
Hodgskinson, R. and Currey, J. D. The effect of variation in structure on the young’s modulus of cancellous bone: a comparison of human and non-human material. Proc Inst mech Eng [H], 204:115–121, 1990.
Kabel, J., Odgaard, A., van Rietbergen, B., and Huiskes, R. Connectivity and the elastic properties of cancellous bone Bone, 1998. submitted
Kabel, J., van Rietbergen, B., Dalstra, M., Odgaard, A., and Huiskes, R. The role of an effective isotropic tissue modulus in the elastic properties of cancellous bone J Biomech, 1998. submitted.
Kinney, J. H., Lane, N. E., and Haupt, D. L. In vivo, three-dimensional microscopy of trabecular bone. J Bone Miner Res, 10:264–270, 1995.
Kleerekoper, M., Villanueva, A. R., Stanciu, J., Rao, D. S., and Parfitt, A. M. ‘The role of three-dimensional trabecular microstructure in the pathogenesis of vertebral compression fractures. Calcif Tissue Int, 37:594–597, 1985.
Nafei, A. Properties of growing trabecular bone. Ph. D. thesis, University of Aarhus, 1993.
Odgaard, A. Three-dimensional methods for quantification of cancellous bone architecture. Bone, 20:315–328, 1997.
Odgaard A. and Gundersen, H. J. Quantification of connectivity in cancellous bone, with special emphasis on 3-D reconstructions. Bone, 14:173 182, 1993
Odgaard., k., Jensen E. B., and Gundersen, H. J. Estimation of structural anisatropy based on volume orientation. a new concept. J Microsc, 157 (Pt 2):149–162, 1990.
Odgaard, A., Kabel, J., van Rietbergen, B., Dalstra, M., and Huiskes, R. Fabric and elastic principal directions of cancellous bone are closely related. J Biomech, 30:487–495, 1997.
Parfitt, A. M., Mathews, C. H. E., Villaneuva, A. R., Kleerekoper, M., Frame, B., and Rao, D. S. Relationships between surface, volume, and thickness of iliac trabecular bone in aging and in osteoporosis. J Clin Invest, 72:1396–1409, 1983.
Rice, J. C., Cowin, S. C., and Bowman, J. A. On the dependence of the elasticity and strength of cancellous bone on apparent density. J Biomech, 21:155–168, 1988.
Smit, T. K., Schneider, E., and Odgaard, A. Star length distribution: a volume orientation based concept for the characterization of structural anisotrophy. J Microsc, 1998. submitted.
Snyder, B. D. and Hayes, W. C. Multiaxial structure-property relations in trabecular bone. In Mow, V. C., Ratcliffe, A., and Woo, S. E. Y., editors, Biomechanics of diarthrodial joints. Vol. II., pages 31–59, New York, 1990. Springer.
Thomsen, J. S., Ebbesen, E. N., and Mosekilde, L. Relationships between static histomorphometry and bone strength measurements in human iliac crest bone biopsies. Bone, 22:153–163, 1998.
Turner, C. H., Cowin, S. C., Rho, J. Y., Ashman, R. B., and Rice, J. C. The fabric dependence of the orthotropic elastic constants of cancellous bone. J Biomech, 23:549–561, 1990.
van Rietbergen, B., Odgaard, A., Kabel, J., and Huiskes, R. Direct mechanics assessment of elastic symmetries and properties of trabecular bone architecture. J Biomech, 29:1653–1657, 1996.
van Rietbergen, B., Weinans, H., Huiskes, R., and Odgaard, A. A new method to determine trabecular bone elastic properties and loading using micromechanical finite-element models. J Biomech, 28:69–81, 1995.
Weibel, E. R. Stereological methods. Volume 2: Theoretical foundations.. Academic Press, 1980.
Whitehouse, W. J. The quantitative morphology of anisotropic trabecular bone. J Microsc, 101:153–168, 1974.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Kluwer Academic Publishers
About this paper
Cite this paper
Odgaard, A., Kabel, J., Van Rietbergen, B., Huiskes, R. (1999). Architectural 3-D Parameters and Anisotropic Elastic Properties of Cancellous Bone. In: Pedersen, P., Bendsøe, M.P. (eds) IUTAM Symposium on Synthesis in Bio Solid Mechanics. Solid Mechanics and its Applications, vol 69. Springer, Dordrecht. https://doi.org/10.1007/0-306-46939-1_4
Download citation
DOI: https://doi.org/10.1007/0-306-46939-1_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-5615-8
Online ISBN: 978-0-306-46939-8
eBook Packages: Springer Book Archive