A review of morphology-elasticity relationships in human trabecular bone: Theories and experiments

Journal of Biomechanics

Volumn 36, Issue 10, 2003, Pages 1469-1485

  Zysset, Philippe K ^a  

^a EPFL   (Switzerland)

Author keywords

Elasticity; Fabric; Human; Mechanical properties; Trabecular bone

Indexed keywords

ANISOTROPY; BIOMEDICAL ENGINEERING; BONE; COMPUTERIZED TOMOGRAPHY; ELASTICITY; MATHEMATICAL MODELS; MORPHOLOGY; STIFFNESS; TENSORS; TISSUE;

ISOTROPIC MODELS;

BIOMECHANICS;

BONE STRUCTURE; COMPUTER ASSISTED TOMOGRAPHY; ELASTICITY; HUMAN; LINEAR REGRESSION ANALYSIS; MATHEMATICAL ANALYSIS; MULTIPLE REGRESSION; NUCLEAR MAGNETIC RESONANCE IMAGING; PRIORITY JOURNAL; QUANTITATIVE ANALYSIS; REVIEW; RIGIDITY; THEORETICAL MODEL; TRABECULAR BONE;

EID: 0141565392     PISSN: 00219290     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-9290(03)00128-3     Document Type: Article

References (47)

1. Ashman R.B., Rho J.Y., Turner C.H. Anatomical variation of orthotropic elastic moduli of the proximal human tibia. Journal of Biomechanics. 22:1989;895-900.
2. Boehler J.P. Applications of Tensor Functions in Solid Mechanics. 1987;Springer, Wien.
3. Chung H., Wehrli F.W., Williams J.L.et al. Relationship between NMR tranverse relaxation, trabecular bone architecture, and strength. Proceedings of the National Academy of Science. 90:1993;10250-10254.
4. Cowin S.C. The relationship between the elasticity tensor and the fabric tensor. Mechanics of Materials. 4:1985;137-147.
5. Cowin S.C. Imposing thermodynamic restrictions on the elastic constant-fabric tensor relationship. Journal of Biomechanics. 31:1998;759-762.
6. Cowin S.C., Buskirk W.C.V. Thermodynamic restriction of the elastic constants of bone. Journal of Biomechanics. 19:1986;85-87.
7. Cowin S.C., Yang G. Averaging anisotropic elastic constant data. Journal of Elasticity. 46:1997;151-180.
8. Cross S.S., Rogers S., Silcocks P.B.et al. Trabecular bone does not have a fractal structure on light microscopic examination. Journal of Pathology. 170:1993;311-313.
9. Cruz-Orive L.M., Karlsson L.M., Larsen S.E.et al. Characterizing anisotropy. a new concept Micron and Microscopica Acta. 23:1992;75-76.
10. Curnier A., He Q.-C., Zysset Ph. Conewise linear elastic materials. Journal of Elasticity. 37:1995;1-38.
11. Currey J.D. Power law models for the mechanical properties of cancellous bone. Engineering in Medicine. 15:1986;153-159.
12. Feldkamp L.A., Goldstein S.A., Parfitt A.M.et al. The direct examination of three-dimensional bone architecture in vitro by computed tomography. Journal of Bone and Mineral Research. 4:1989;3-11.
13. Gibson L.J. The mechanical behaviour of cancellous bone. Journal of Biomechanics. 18:1985;317-328.
14. Goulet R.W., Goldstein S.A., Ciarelli M.J.et al. The relationship between the structural and orthogonal compressive properties of trabecular bone. Journal of Biomechanics. 27:1994;375-389.
15. Hahn M., Vogel M., Pompesius-Kempa M.et al. Trabecular bone pattern factor - a new parameter for simple quantification of bone microarchitecture. Bone. 13:1992;327-330.
16. Harrigan T.P., Mann R.W. Characterization of microstructural anisotropy in orthotropic materials using a second rank tensor. Journal of Materials Science. 19:1984;761-767.
17. Harrigan T.P., Jasty M., Mann R.W.et al. Limitations of the continuum assumption in cancellous bone. Journal of Biomechanics. 21:1988;269-275.
18. Hashin Z., Shtrikman S. A variational approach to the theory of the elastic behaviour of mulitphase materials. Journal of the Mechanics and Physics of Solids. 6:1963;539-552.
19. He Q.-C., Curnier A. A more fundamental approach to damaged elastic stress-strain relations. International Journal of Solids and Structures. 32:1995;1433-1457.
20. Hildebrand T., Laib A., Müller R.et al. Direct three dimensional morphometric analysis of human cancellous bone. microstructural data from spine, femur, iliac crest and calcaneus Journal of Bone and Mineral Research. 14:1999;1167-1174.
21. Hodgskinson R., 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 Proceedings of Investigation of Mechanical Engineers. 204:1990;115-121.
22. Hollister S.J., Kikuchi N. A comparison of homogenization and standard mechanics analyses for periodic porous composites. Computational Mechanics. 10:1992;73-95.
23. Huber A.T., Gibson L.J. Anisotropy of foams. Journal of Material Science. 23:1988;3031-3040.
24. Kabel J., VanRietbergen B., Odgaard A.et al. Connectivity and the elastic properties of cancellous bone. Bone. 24:1999;115-120.
25. Kabel J., VanRietbergen B., Odgaard A.et al. Constitutive relationships of fabric, density and elastic properties in cancellous bone architecture. Bone. 25:1999;481-486.
26. Kanatani K. Distribution of directional data and fabric tensor. International Journal of Engineering and Science. 22:1984;149.
27. Keaveny T.M., Pinilla T.P., Crawford R.P.et al. Systematic and random errors in compression testing of trabecular bone. Journal of Orthopaedic Research. 15:1997;101-149110.
28. Majumdar S., Kothari M., Augat P.et al. High resolution magnetic resonance imaging. three dimensional trabecular bone architecture and biomechanical properties Bone. 22:1998;445-454.
29. Mueller R., Hildebrand T., Rüegsegger P. Non-invasive bone biopsy. A new method to analyse and display the three-dimensional structure of trabecular bone Physics in Medicine and Biology. 39:1994;145-164.
30. Odgaard A., Gundersen H.J.G. Quantification of connectivity in cancellous bone, with special emphasis on 3-D reconstructions. Bone. 14:1993;173-182.
31. Odgaard A., Andersen K., Melsen F.et al. A direct method for fast three-dimensional serial reconstruction. Journal of Microscopy. 159:1990;335-342.
32. Odgaard A., Jensen E.B., Gundersen H.J.G. Estimation of structural anisotropy based on volume orientation. A new concept. Journal of Microscopy. 159:1990;335-342.
33. Odgaard A., Kabel J., VanRietbergen B.et al. Fabric and elastic principal directions of cancellous bone are closely related. Journal of Biomechanics. 30:1997;487-495.
34. Rho J., Tsui T., Pharr O. Elastic properties of human cortical and trabecular lamellar bone measured by nanoindentation. Biomaterials. 18:1997;1325-1330.
35. Rice J.C., Cowin S.C., Bowman J.A. On the dependence of the elasticity and strength of cancellous bone on apparent density. Journal of Biomechanics. 21:1988;155-168.
36. Snyder B.D., Hayes W.C. Multiaxial structure-property relations in trabecular bone. Mow V.C., Ratcliffe A., Woo S.L.-Y. Biomechanics of Diarthrodial Joints. 1990;31-59 Springer, New York.
37. Turner C.H., Cowin S.C. Dependence of elastic constants of an anisotropic porous material upon porosity and fabric. Journal of Materials Science. 22:1987;3178-3184.
38. Turner C.H., Cowin S.C., Rho J.Y.et al. The fabric dependence of the orthotropic elastic constants of cancellous bone. Journal of Biomechanics. 23:1990;549-561.
39. vanRietbergen, B., 1996. Mechanical behaviour and adaptation of trabecular bone in relation to bone morphology. Ph.D. Thesis, University of Nijmegen.
40. Walpole L.J. Fourth-rank tensors of the thirty-two crystal classes. multiplication tables Proceedings of the Royal Society of London A. 391:1984;149-179.
41. Whitehouse W.J. The quantitative morphology of anisotropic trabecular bone. Journal of Microscopy. 101:1974;153-168.
42. Yahia L.H., Drouin G., Duval P. A methodology for mechanical measurements of technical constant of trabecular bone. Engineering in Medicine. 17:1988;169-173.
43. Yang G., Kabel J., VanRietbergen B.et al. The anisotropic Hooke's law for cancellous bone and wood. Journal of elasticity. 53:1999;125-146.
44. Zysset P.K., Curnier A. An alternative model for anisotropic elasticity based on fabric tensors. Mechanics of Materials. 21:1995;243-250.
45. Zysset P.K., Goulet R.W., Hollister S.J. A global relationship between trabecular morphology and homogenized elastic properties. Journal of Biomechanical Engineering. 120:1998;640-646.
46. Zysset P.K., Ominsky M.S., Goldstein S.A. A novel 3D microstructural model for trabecular bone I. the relationship between fabric and elasticity Computer Methods in Biomechanics and Biomedical Engineering. 1:1998;321-331.
47. Zysset P.K., Guo X.E., Hoffler C.E.et al. Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur. Journal of Biomechanics. 32:1999;1005-1012.