Micromechanical modelling of cortical bone

Computer Methods in Biomechanics and Biomedical Engineering

Volumn 10, Issue 3, 2007, Pages 159-169

  Mullins, L P ^a   Mcgarry, J P ^a   Bruzzi, M S ^a   Mchugh, P E ^a  

^a NATIONAL UNIVERSITY OF IRELAND   (Ireland)

Author keywords

Cortical bone; Finite element method; Mechanical properties; Micromechanical modelling; Periodic boundary conditions

Indexed keywords

CORTICAL BONE; FINITE ELEMENT MODELS; HAVERSIAN SYSTEM; HETEROGENEOUS MATERIALS; LOCAL DISTRIBUTIONS; MACROSCOPIC PROPERTIES; MATERIAL PROPERTY; MICROMECHANICAL MODELLING; MICROSTRUCTURAL FEATURES; MICROSTRUCTURAL MORPHOLOGY; PERIODIC BOUNDARY CONDITIONS; POISSON'S RATIO; SCALE MODELS; UNIT CELLS; VASCULAR POROSITY;

BIOMECHANICS; COMPOSITE MICROMECHANICS; FINITE ELEMENT METHOD; MECHANICAL PROPERTIES; MICROSTRUCTURAL EVOLUTION;

BONE;

ANIMAL; ARTICLE; BIOLOGICAL MODEL; BIOMECHANICS; BONE; COMPUTER SIMULATION; ELASTICITY; FINITE ELEMENT ANALYSIS; HUMAN; MECHANICAL STRESS; METHODOLOGY; PHYSIOLOGY; POROSITY; WEIGHT BEARING;

ANIMALS; BIOMECHANICS; BONE AND BONES; COMPUTER SIMULATION; ELASTICITY; FINITE ELEMENT ANALYSIS; HUMANS; MODELS, BIOLOGICAL; POROSITY; STRESS, MECHANICAL; WEIGHT-BEARING;

EID: 34547493600     PISSN: 10255842     EISSN: 14768259     Source Type: Journal    
DOI: 10.1080/10255840601110802     Document Type: Article

References (58)

1. B. Aoubiza, J.M. Crolet and A. Meunier, "On the mechanical characterization of compact bone structure using the homogenization theory", J. Biomech., 29(12), pp. 1539-1547, 1996.
2. S. Bensamoun, M.-C. Ho Ba Tho, S. Luu, J.-M. Gherbezza and J.-F. de Belleval, "Spatial distribution of acoustic and elastic properties of human femoral cortical bone", J. Biomech., 37(4), pp. 503-510, 2004.
3. H.J. Böhm, "A short introduction to basic aspects of continuum mechanics", CDL-FMD-Report 3, 1998.
4. Preliminary Version (Institute of Lightweight Structures and Aerospace Engineering, Vienna University of Technology, Austria) 1998.
5. H.J. Böhm and W. Han, "Multi-inclusion unit cell studies of reinforcement stresses and particle failure in discontinuously reinforced ductile matrix composites", Computational Modelling in Engineering and Sciences, 5, pp. 2-20, 2004.
6. H.J. Böhm, W. Han and A. Eckschlager, "Multi-inclusion unit cell models for metal matrix composites with randomly oriented discontinuous reinforcements", Comput. Mater. Sci., 25(85-91), pp. 42-53, 2002.
7. R.G.M. Breuls, B.G. Sengers, C.W.J. Oomens, C.V.C. Bouten and F.P.T. Baaijens, "Predicting local cell deformations in engineered tissue constructs: a multilevel finite element approach", J. Biomech. Eng., 124(2), pp. 198-207, 2002.
8. M.S. Bruzzi and P.E. McHugh, "Micromechanical modelling of the static loading of an Al 359-SiC MMC", J. Eng. Mater. Technol., 127(1), pp. 106-118, 2005.
9. D.B. Burr, M.B. Schaffler and R.G. Frederickson, "Composition of the cement line and its possible mechanical role as a local interface in human compact bone", J. Biomech., 21(11), pp. 939-941, 1988.
10. R.R. Cooper, J.W. Milgram and R.A. Robinson, "Morphology of osteons. An electron microscopic study", J. Bone Joint Surg. Am., 48, pp. 1239-1271, 1966.
11. C. Cooper, G. Campion and L.J. Melton, 3rd, "Hip fractures in the elderly: a world-wide projection", Osteoporos. Int., 2(6), pp. 285-289, 1992.
12. D.M.L. Cooper, A.L. Turninskey, C.W. Sensen and B. Hallgrimisson, "Quantitative 3D analysis of the canal network in cortical bone by micro-computed tomography", Anat. Rec. B New Anat., (274B), pp. 169-179, 2003.
13. S.C. Cowin, Bone Mechanics Handbook, CRC Press, 2001.
14. J.M. Crolet, B. Aoubiza and A. Meunier, "Compact bone: numerical simulation of mechanical characteristics", J. Biomech., 26(6), pp. 677-687, 1993.
15. J.D. Currey, "The effect of porosity and mineral content on the Young's modulus of elasticity of compact bone", J. Biomech., 21(2), pp. 131-139, 1988.
16. X.E. Dong and X.E. Guy, "Geometric determinants to cement line debonding and osteonal lamellae failure in osteon pushout tests", J. Biomech. Eng., 126(3), pp. 387-390, 2004.
17. A. Eckschlager, H.J. Böhm and W. Han, "A unit cell model for brittle fracture of particles embedded in a ductile matrix", Comput. Mater. Sci., (25), pp. 85-91, 2002.
18. Z. Fan, J.G. Swadener, J.Y. Rho, M.E. Roy and G.M. Pharr, "Anisotropic properties of human tibial cortical bone as measured by nanoindentation", J. Orthopaedic Research, 20(4), pp. 806-810, 2002.
19. K.J. Goodwin and N.A. Sharkey, "Material properties of interstitial lamellae reflect local strain environments", J. Orthopaedic Research, 20(3), pp. 600-606, 2002.
20. K. Hasegawa, C.H. Turner, R.R. Recker, E. Wu and D.B. Burr, "Elastic properties of osteoporotic bone measured by scanning acoustic microscopy", Bone, 16(1), pp. 85-90, 1995.
21. S. Hengsberger, A. Kulik and P.K. Zysset, "A combined atomic force microscopy and nanoindentation technique to investigate the elastic properties of bone structural units", Eur. Cell Mater., 1, pp. 12-17, 2001.
22. J. Hert, P. Fiala and M. Petrtyl, "Osteon orientation of the diaphysis of the long bones in man", Bone, 15(3), pp. 269-277, 1994.
23. C.E. Hoffler, K.E. Moore, K. Kozloff, P.K. Zysset, M.B. Brown and S.A. Goldstein, "Heterogeneity of bone lamellar-level elastic moduli", Bone, 26(6), pp. 603-609, 2000.
24. H.A. Hogan, "Micromechanics modeling of Haversian cortical bone properties", J. Biomech., 25(5), pp. 549-556, 1992.
25. M.S. Ingber and T.D. Papthanasiou, "A parallel-supercomputing investigation of teh stiffness of aligned short-fiber-reinforced composites using the boundary element method", International Journal of Numerical Methods in Engineering, 40, pp. 3477-3491, 1997.
26. A.C. Jones, A.P. Sheppard, R.M. Sok, C.H. Arns, A. Limaye, H. Averdunk, A. Brandwood, A. Sakellariou, T.J. Senden, B.K. Milthorpe and M.A. Knackstedt, "Three-dimensional analysis of cortical bone structure using X-ray micro-computed tomography", Physica A: Statistical Mechanics and its Applications, 339(1-2), pp. 125-130, 2004.
27. D.G. Kim, I.B. Brunski and D.P. Nicolella, "Microstrain fields for cortical bone in uniaxial tension: optical analysis method", Proceedings of the Institution of Mechanical Engineers. Part H, 219(2), pp. 119-128, 2005.
28. J. LLorca and J. Segurado, "Three-dimensional multiparticle cell simulations of deformation and damage in sphere-reinforced composites", Mater. Sci. Eng. A, 365(1-2), pp. 267-274, 2004.
29. M.A.K. Liebschner, "Biomechanical considerations of animal models used in tissue engineering of bone", Biomaterials, 25(9), pp. 1697-1714, 2004.
30. E. Luchinetti, Composite Models of Bone, S.C. Cowin, Ed., Bone Mechanics Handbook, 2001.
31. S. Mahanian and R. Piziali, "Incompressibility in bone", J. Biomech., 18(1), pp. 77-78, 1985.
32. R.B. Martin and J. Ishida, "The relative effects of collagen fiber orientation, porosity, density, and mineralization on bone strength", J. Biomech., 22(5), pp. 419-426, 1989.
33. R. McCalden, J. McGeough, M. Barker and C. Court-Brown, "Age-related changes in the tensile properties of cortical bone. The relative importance of changes in porosity, mineralization, and microstructure", J. Bone Joint Surg. Am., 75(8), pp. 1193-1205, 1993.
34. M.A. Moyad, "Osteoporosis: a rapid review of risk factors and screening methods", Urologic Oncology: Seminars and Original Investigations, 21(5), pp. 375-379, 2003.
35. M.G. Mullender, D.D. van der Meer, R. Huiskes and P. Lips, "Osteocyte density changes in aging and osteoporosis", Bone, 18(2), pp. 109-113, 1996.
36. R.K. Nalla, J.S. Stolken, J.H. Kinney and R.O. Ritchie, "Fracture in human cortical bone: local fracture criteria and toughening mechanisms", J. Biomech., 38(7), pp. 1517-1525, 2005.
37. X. Neil Dong and X. Edward Guo, "The dependence of transversely isotropic elasticity of human femoral cortical bone on porosity", J. Biomech., 37(8), pp. 1281-1287, 2004.
38. D.P. Nicolella, A.E. Nicholls, J. Lankford and D.T. Davy, "Machine vision photogrammetry: a technique for measurement of microstructural strain in cortical bone", J. Biomech., 34(1), pp. 135-139, 2001.
39. J.F. Nye, Physical Properties of Crystals, Their Representation by Tensors and Matrices, Oxford at the Clarendon Press, 1964.
40. M. Petrtyl, J. Hert and P. Fiala, "Spatial organization of the haversian bone in man", J. Biomech., 29(2), pp. 161-169, 1996.
41. H. Prendergast, "Microdamage and osteocyte-lacuna strain in bone: a microstructural finite element analysis", J. Biomech. Eng., 118, pp. 240-246, 1996.
42. R. Rao, S. Saha and J. Wood, "Investigation of non-homogenous deformities in bone via moire interferometry", Proceedings of Bioengineering Conference, ASME 2001, BED-Vol. 50, 2001.
43. J.Y. Rho and G.M. Pharr, "Effects of drying on the mechanical properties of bovine femur measured by nanoindentation", J. Mater. Sci. Mater. Med., 10, pp. 485-488, 1999.
44. J.-Y. Rho, L. Kuhn-Spearing and P. Zioupos, "Mechanical properties and the hierarchical structure of bone", Med. Eng. Phys., 20(2), pp. 92-102, 1998a.
45. J.Y. Rho, T.Y. Tsui and G.M. Pharr, "Elastic properties of osteon and trabecular bone measured by nanoindentation", Proceedings of Bone Research, p. 2, 1998b.
46. J.Y. Rho, M.E. Roy, 2nd, T.Y. Tsui and G.M. Pharr, "Elastic properties of microstructural components of human bone tissue as measured by nanoindentation", J. Biomed. Mater. Res., 45(1), pp. 48-54, 1999a.
47. J.Y. Rho, P. Zioupos, J.D. Currey and G.M. Pharr, "Variations in the individual thick lamellar properties within osteons by nanoindentation", Bone, 25(3), pp. 295-300, 1999b.
48. J.Y. Rho, P. Zioupos, J.D. Currey and G.M. Pharr, "Microstructural elasticity and regional heterogeneity in human femoral bone of various ages examined by nano-indentation", J. Biomech., 35(2), pp. 189-198, 2002.
49. B.L. Riggs and L.J. Melton, "The worldwide problem of osteoporosis: insights afforded by epidemiology", Bone, 17(5, Supplement 1), pp. S505-S511, 1995.
50. M.B. Schaffler, E.L. Radin and D.B. Burr, "Long-term fatigue behavior of compact bone at low strain magnitude and rate", Bone, 11(5), pp. 321-326, 1990.
51. J. Segurado, C. Gonzalez and J. LLorca, "A numerical investigation of the effect of particle clustering on the mechanical properties of composites", Acta Mater., 51(8), pp. 2355-2369, 2003.
52. I. Sevostianov and M. Kachanov, "Impact of the porous microstructure on the overall elastic properties of the osteonal cortical bone", J. Biomech., 33(7), pp. 881-888, 2000.
53. O.S. Sobelman, J.C. Gibeling, S.M. Stover, S.J. Hazelwood, O.C. Yeh, D.R. Shelton and R.B. Martin, "Do microcracks decrease or increase fatigue resistance in cortical bone?", J. Biomech., 37(9), pp. 1295-1303, 2004.
54. C.H. Turner, J. Rho, Y. Takano, T.Y. Tsui and G.M. Pharr, "The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques", J. Biomech., 32(4), pp. 437-441, 1999.
55. W.C. Van Buskirk and R.B. Ashman, "The elastic moduli of bone", Joint ASME-ASCE Applied Mechanics, in Mechanical Properties of Bone, Fluids Engineering and Bioengineering Conference, Boulder, CO 1981.
56. P.G. Van Der Varst and L.M. Mooren, "Comments on the paper 'Incompressibility in bone' by Mahanian and Piziali", J. Biomech., 19(2), pp. 175-177, 1986.
57. X. Wang and Q. Ni, "Determination of cortical bone porosity and pore size distribution using a low field pulsed NMR approach", J. Orthopaedic Research, 21(2), pp. 312-319, 2003.
58. J. Wood, S. Saha and R. Rao, "Non-homogenous strain distributions in bone using moiré interferometry", Proceedings of Society for Expermental Mechanics, pp. 989-992, 2001.