Fabric and elastic principal directions of cancellous bone are closely related

Journal of Biomechanics

Volumn 30, Issue 5, 1997, Pages 487-495

  Odgaard, Anders ^a   Kabel, Jesper ^a   Van Rietbergen, Bert ^b   Dalstra, Michel ^a   Huiskes, Rik ^b  

^a AARHUS UNIVERSITY HOSPITAL   (Denmark)

^b NONE

Author keywords

Anisotropy; Cancellous bone; Fabric; FEM; Trabecular architecture

Indexed keywords

ANISOTROPY; COMPUTATIONAL METHODS; FINITE ELEMENT METHOD; TENSORS;

CANCELLOUS BONES; MEAN INTERCEPT LENGTH (MIL); STAR LENGTH DISTRIBUTION (SLD); STAR VOLUME DISTRIBUTION (SVD);

BONE;

ANISOTROPY; ARTICLE; BIOMECHANICS; CANCELLOUS BONE; ELASTICITY; HUMAN; HUMAN TISSUE; PRIORITY JOURNAL; TRABECULAR BONE;

ANIMALS; ANISOTROPY; BIOMECHANICS; BONE AND BONES; ELASTICITY; IMAGE PROCESSING, COMPUTER-ASSISTED; MODELS, BIOLOGICAL; WHALES;

EID: 0031149547     PISSN: 00219290     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-9290(96)00177-7     Document Type: Article

References (40)

1. Cowin, S. C. (1985) The relationship between the elasticity tensor and the fabric tensor. Mech. Mater. 4, 137-147.
2. Cowin, S. C. (1986) Wolff's law of trabecular architecture at remodeling equilibrium. J. Biomech. Engng 108, 83-88.
3. Cruz-Orive, L. M., Karlsson, L. M., Larsen, S. E. and Wainschtein, F. (1992) Characterizing anisotropy: a new concept. Micron Microscopica Acta 23, 75-76.
4. Fisher, N. I., Lewis, T. L. and Embleton, B. J. (1987) Statistical Analysis of Spherical Data. Cambridge University Press, Cambridge.
5. Fyhrie, D. P., Hollister, S. J., Schaffler, M. B. and Kimura, J. (1992) Structural transformations indistinguishable by point-count stereology. J. Biomechanics 25, 685.
6. Goulet, R. W., Ciarelli, M. J., Goldstein, S. A., Kuhn, J. L., Feldkamp, L. A., Kruger, D., Viviano, D., Champlain, F. and Matthews, L. S. (1988) The effects of architecture and morphology on the mechanical properties of trabecular bone. Trans. Orthop. Res. Soc. 13, 73.
7. Goulet, R. W., Feldkamp, L. A. and Goldstein, S. A. (1992) Quantification of the architecture of cancellous bone by surface and volume orientation methods. Trans. Orthop. Res. Soc. 17, 159.
8. Goulet, R. W., Goldstein, S. A., Ciarelli, M. J., Kuhn, J. L., Brown, M. B. and Feldkamp, L. A. (1994) The relationship between the structural and orthogonal compressive properties of trabecular bone. J. Biomechanics 27, 375-389.
9. Goulet, R. W. and Hollister, S. J. (1996) Determination of minimum microstructural analysis volumes for trabecular bone using 3-D stereology and FFT analysis. Trans. Orthop. Res. Soc. 21, 715.
10. Gundersen, H. J. G. and Jensen, E. B. (1985) Stereological estimation of the volume-weighted mean volume of arbitrary particles observed on random sections. J. Microsc. 138, 127-142.
11. Harrigan, T. P., Jasty, M., Mann, R. W. and Harris, W. H. (1988) Limitations of the continuum assumption in cancellous bone. J. Biomechanics 21, 269-275.
12. Harrigan, T. P. and Mann, R. W. (1984) Characterization of microstructural anisotropy in orthotropic materials using a second rank tensor. J. Mater. Sci. 19, 761-767.
13. Hollister, S. J. (1995) The ability of representative volume element (RVE) methods to bound trabecular tissue strains: dependence on assumed boundary conditions. In Bone Structure and Remodeling (Edited by Odgaard, A. and Weinans, H.), pp. 147-155. World Scientific, Singapore.
14. Hollister, S. J. and Kikuchi, N. (1992) A comparison of homogenization and standard mechanics analyses for periodic porous composites. Comput. Mech. 10, 73-95.
15. Jacobs, C. R., Mandell, J. A. and Beaupre, G. S. (1993) A comparative study of automatic finite element mesh generation techniques in orthopaedic biomechanics. ASME/BED 24, 512.
16. Kanatani, K. I. (1984) Distribution of directional data and fabric tensors. Int. J. Engng Sci. 22, 149-164.
17. Karlsson, L. M. and Cruz-Orive, L. M. (1993) Application of the star volume distribution to characterize structural anisotropy of a duplex stainless steel. In Stereology in Materials Science: Demonstration of Some Methods. Royal Institute of Technology, Stockholm.
18. Mardia, K. V. (1972) Statistics of Directional Data. pp. 212-248. Academic Press, London.
19. Meriam, J. L. (1971) Dynamics, Chap. 8. Wiley, New York.
20. Mullender, M. G., Huiskes, R., Versleyen, H. and Buma, P. (1997) Osteocyte density and histomorphometric parameters in cancellous bone of the proximal femur in five mammalian species. J. orthop. Res. (in press).
21. Odgaard, A. (1994) Three-dimensional quantification of cancellous bone structure. In Imaging Techniques in Biomaterials (Edited by Barbosa, M. A. and Campilho, A.), pp. 181-188. Elsevier, Amsterdam.
22. Odgaard, A., Andersen, K., Melsen, F. and Gundersen, H. J. G. (1990a) A direct method for fast three-dimensional serial reconstruction. J. Microsc. 159, 335-342.
23. Odgaard, A., Andersen, K., Ullerup, R., Frich, L. H. and Melsen, F. (1994) Three-dimensional reconstruction of entire vertebral bodies. Bone 15, 335-342.
24. Odgaard, A. and Gundersen, H. J. G. (1993) Quantification of connectivity in cancellous bone, with special emphasis on 3-D reconstructions. Bone 14, 173-182.
25. Odgaard, A., Jensen, E. B. and Gundersen, H. J. G. (1990b) Estimation of structural anisotropy based on volume orientation. A new concept. J. Microsc. 157, 149-162.
26. Scheidegger, A. E. (1964) The tectonic stress and tectonic motion direction in Europe and Western Asia as calculated from earthquake fault plane solutions. Bull. Seismol. Soc. Am. 54, 1519-1528.
27. Schmidt-Nielsen, K. (1984) Scaling: Why is Animal Size so Important? Cambridge University Press, Cambridge.
28. Snyder, B. D. and Haves, W. C. (1990) Multiaxial structure-property relations in trabecular bone. In Biomechanics of Diarthrodial Joints, Vol. II (Edited by Mow, V. C., Ratcliffe, A. and Woo, S. L. Y.), pp. 31-59. Springer, New York.
29. Turner, C. H., Cowin, S. C., Rho, J. Y., Ashman, R. B. and Rice, J. C. (1990) The fabric dependence of the orthotropic elastic constants of cancellous bone. J. Biomechanics 23, 549-561.
30. van Rietbergen, B., Huiskes, R., Weinans, H., Odgaard, A. and Kabel, J. (1995a) The role of trabecular architecture in the anisotropic mechanical properties of bone. In Bone Structure and Remodeling (Edited by Odgaard, A. and Weinans, H.), pp. 137-145. World Scientific, Singapore.
31. van Rietbergen, B., Odgaard, A., Kabel, J. and Huiskes, R. (1996a) Direct calculation of the mechanical symmetry and properties of trabecular structures. J. Biomechanics.
32. van Rietbergen, B., Odgaard, A., Kabel, J. and Huiskes, R. (1996b) Fabric and density accurately predict the elastic properties of trabecular bone architecture. J. orthop. Res.
33. van Rietbergen, B., Weinans, H., Huiskes, R. and Odgaard, A. (1995b) A new method to determine trabecular bone elastic properties and loading using micromechanical finite-element models. J. Biomechanics 28, 69-81.
34. van Rietbergen, B., Weinans, H., Polman, B. J. W. and Huiskes, R. (1996c) Computational strategies for iterative solutions of large FEM applications employing voxel data. Int. J. Numer. Methods Engng 39, 2743-2767.
35. Vesterby, A. (1993) Star volume in bone research. A histomorphometric analysis of trabecular bone structure using vertical sections. Anat. Rec. 235, 325-334.
36. Watson, G. S. (1966) The statistics of orientation data. J. Geology 74, 786-797.
37. Whitehouse, W. J. (1974) The quantitative morphology of anisotropic trabecular bone. J. Microsc. 101, 153-168.
38. Whitehouse, W. J. (1981) Irregularities and asymmetries in trabecular bone in the innominate and elsewhere. Metab. Bone Dis. Res. Res. S2, 271-278.
39. Woodcock, N. H. (1977) Specification of fabric shapes using an eigen-value method. Geol. Soc. Am. Bull. 88, 1231-1236.
40. Zhu, M., Keller, T. S., Moeljanto, E. and Spengler, D. M. (1994) Multiplanar variations in the structural characteristics of cancellous bone. Bone 15, 251-259.