A homogenization model of the annulus fibrosus

Journal of Biomechanics

Volumn 38, Issue 8, 2005, Pages 1674-1684

  Yin, Luzhong ^a   Elliott, Dawn M ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Anisotropy; Annulus fibrosus; Finite element model; Homogenization; Strain energy

Indexed keywords

ELASTIC MODULI; ENERGY ABSORPTION; FIBER REINFORCED MATERIALS; FINITE ELEMENT METHOD; MICROSTRUCTURE; TISSUE; VOLUME FRACTION;

HOMOGENIZATION; SINGLE LAMELLA; TISSUE ENGINEERING; VOLUME ELEMENTS;

BIOMECHANICS;

ANNULAR FIBER; ARTICLE; FIBER; INTERVERTEBRAL DISK; INTERVERTEBRAL DISK DEGENERATION; MODEL; PREDICTION; PRIORITY JOURNAL; STRESS STRAIN RELATIONSHIP; STRUCTURE ACTIVITY RELATION; TENSILE STRENGTH; TISSUE ENGINEERING; TISSUE HOMOGENATE;

ANIMALS; ANISOTROPY; COMPRESSIVE STRENGTH; COMPUTER SIMULATION; ELASTICITY; HUMANS; INTERVERTEBRAL DISK; MODELS, BIOLOGICAL; STRESS, MECHANICAL; TENSILE STRENGTH;

EID: 20444489530     PISSN: 00219290     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jbiomech.2004.07.017     Document Type: Article

References (50)

1. R. Abeyaratne, and N. Triantafyllidis An investigation of localization in a porous elastic material using homogenization theory Journal of Applied Mechanics 51 1984 481 486
2. E.R. Acaroglu, J.C. Iatridis, L.A. Setton, and R.J. Foster Degeneration and aging affect the tensile behavior of human lumbar annulus fibrosus Spine 20 24 1995 2690 2701
3. Bendsoe Optimization of Structural Topology, Shape, and Material 1995 Springer Berlin
4. M.P. Bendsoe, and N. Kikuchi Generating optimal topologies in structural design using a homogenization method Computer Methods in Applied Mechanics and Engineering 71 1988 197 224
5. A. Bensoussan, J.-L. Lions, and G. Papanicolaou Asymptotic Analysis for Periodic Structures 1978 North-Holland Amsterdam
6. J.A. Buckwalter, V.C. Mow, S.D. Boden, and D.R. Eyre Intervertebral disk structure, composition, and mechanical function J.A. Buckwalter T.A. Einhorn S.R. Simon Orthopaedic Basic Science 2000 American Academy of Orthopaedic Surgeons Rosemont, IL 547 556
7. J.J. Cassidy, A. Hiltner, and E. Baer Hierarchical structure of the intervertebral disc Connective Tissue Research 23 1989 75 88
8. S. Ebara, J.C. Iatridis, L.A. Setton, and R.J. Foster Tensile properties of nondegenerate human lumbar annulus fibrosus Spine 21 4 1996 452 461
9. R. Eberlein, G.A. Holzapfel, and C.A.J. Schulze-Bauer An anisotropic model for annulus tissue and enhanced finite element analyses of intact lumbar disc bodies Computer Methods in Applied Mechanics and Engineering 00 2000 1 20
10. D.M. Elliott, and L.A. Setton A linear material model for fiber-induced anisotropy of the annulus fibrosus Journal of Biomechanical Engineering 122 2000 173 179
11. D.M. Elliott, and L.A. Setton Anisotropic and inhomogeneous tensile behavior of the human annulus fibrosus experimental measurement and material model predictions Journal of Biomechanical Engineering 123 2001 256 263
12. D.M. Elliott, and J. Sarver Validation of the mouse and rat disc as mechanical models of the human lumbar disc Spine 29 2004 713 722
13. M.J. Fagan, S. Julian, D.J. Siddall, and A.M. Mohsen Patient-specific spine models. Part 1 finite element analysis of the lumbar intervertebral disc - a material sensitivity study Proceedings of the Institute of Mechanical Engineering [H] 216 2002 299 314
14. Y. Fujita, N.A. Duncan, and J. Lotz Radial tensile properties of the lumbar annulus fibrosus are site and degeneration dependent Journal of Orthopaedic Research 15 1997 814 819
15. Y. Fujita, D.R. Wagner, A.A. Biviji, and N.A. Duncan Anisotropic shear behavior of the annulus fibrosus effect of harvest site and tissue prestrain Medical Engineering and Physics 22 5 2000 349 357
16. L.G. Gilbertson, V.K. Goel, W.Z. Kong, and J.D. Clausen Finite element methods in spine biomechanics research Critical Reviews in Biomedical Engineering 23 1995 411 473
17. V.K. Goel Biomechanics of disk herniation and related issues J.N. Weinstein S.L. Gordon Low Back Pain A Scientific and Clinical Overview 1996 American Academy of Orthopaedic Surgeons Rosemont, IL 289 304
18. V.K. Goel, B.T. Monroe, L.G. Gilbertson, and P. Brinckmann Interlaminar shear stresses and laminae separation in a disc finite element analysis of the L3-L4 motion segment subjected to axial compressive loads Spine 20 6 1995 689 698
19. S.J. Hollister, D.P. Fyhrie, K.J. Jepsen, and S.A. Goldstein Application of homogenization theory to the study of trabecular bone mechanics Journal of Biomechanics 24 9 1991 825 839
20. E.W. Hsu, and L.A. Setton Diffusion tensor microscopy of the intervertebral disc annulus fibrosus Magnetic Resonance in Medicine 41 5 1999 992 999
21. J.C. Iatridis, S. Kumar, R.J. Foster, and M. Weidenbaum Shear mechanical properties of human lumbar annulus fibrosus Journal of Orthopaedic Research 17 5 1999 732 737
22. S. Johnson, D. McNally, and M. Halliwell High-frequency ultrasound imaging of the intervertebral disc Ultrasound in Medicine and Biology 28 7 2002 939 947
23. R.M. Jones Mechanics of Composite Materials second ed. 1999 Taylor and Francis London
24. S.M. Klisch, and J.C. Lotz Application of a fiber-reinforced continuum theory to multiple deformations of the annulus fibrosus Journal of Biomechanics 32 1999 1027 1036
25. Y. Lanir Structure-function relations in mammalian tendon the effect of geometrical nonuniformity Journal of Bioengineering 2 1-2 1978 119 128
26. C.K. Lee, Y. Eun Kim, C.S. Lee, and Y.M. Hong Impact response of the intervertebral disc in a finite-element model Spine 25 19 2000 2431 2439
27. Y.M. Lu, W.C. Hutton, and V.M. Gharpuray The effect of fluid loss on the viscoelastic behavior of the lumbar intervertebral disc in compression Journal of Biomechanical Engineering 120 1 1998 48 54
28. H.A. Lynch, and D.M. Elliott Fiber-matrix interactions in a 3-D anisotropic strain energy model of tendon Transactions of the Orthopaedic Research Society 29 2004 855
29. D.A. MacKenna, S.M. Vaplon, and A.D. McCulloch Microstructural model of perimysial collagen fibers for resting myocardial mechanics during ventricular filling American Journal of Physiology 273 3, Part 2 1997 H1576 H1586
30. F. Marchand, and A.M. Ahmed Investigation of the laminate structure of lumbar disc annulus fibrosus Spine 15 5 1990 402 410
31. R.N. Natarajan, G.B. Andersson, A.G. Patwardhan, and S. Verma Effect of annular incision type on the change in biomechanical properties in a herniated lumbar intervertebral disc Journal of Biomechanical Engineering 124 2 2002 229 236
32. N. Ohno, D. Okumura, and H. Noguchi Microscopic symmetric bifurcation condition of cellular solids based on a homogenization theory of finite deformation Journal of the Mechanics and Physics of Solids 50 2002 1125 1153
33. M.M. Panjabi, and A.A. White Physical properties and functional biomechanics of the spine A.A. White M.M. Panjabi Clinical Biomechanics of the Spine 1990 Lippincott Philadelphia 1 84
34. A.A. Rao, and G.A. Dumas Influence of material properties on the mechanical behavior of the L5-S1 intervertebral disc in compression a nonlinear finite element study Journal of Biomedical Engineering 13 1991 139 151
35. E. Sanchez-Palencia, and A. Zaoui Homogenization Techniques for Composite Media 1987 Springer, Verlag Berlin
36. M.H. Schwartz, P.H. Leo, and J.L. Lewis Microstructural model for the elastic response of articular cartilage Journal of Biomechanics 27 7 1994 865 873
37. A. Shirazi-Adl On the fibre composite material models of disc annulus - comparison of predicted stresses Journal of Biomechanics 22 4 1989 357 365
38. A. Shirazi-Adl Nonlinear stress analysis of the whole lumbar spine in torsion - mechanics of facet articulation Journal of Biomechanics 27 3 1994 289 299
39. S.A. Shirazi-Adl, S.C. Shrivastava, and A.M. Ahmed Stress analysis of the lumbar disc-body unit in compression a 3D nonlinear finite element study Spine 9 2 1984 120 134
40. O. Sigmund Materials with prescribed constitutive parameters an inverse homogenization problem International Journal of Solids and Structures 31 1994 2313 2329
41. D.L. Skaggs, M. Weidenbaum, J.C. Iatridis, and A. Ratcliffe Regional variation in tensile properties and biochemical composition of the human lumbar annulus fibrosus Spine 19 12 1994 1310 1319
42. A.J.M. Spencer Deformations of Fibre-reinforced Materials 1972 Oxford University Press London
43. R.L. Spilker, D.M. Jakobs, and A.B. Schultz Material constants for a finite element model of the intervertebral disc with a fiber composite annulus Journal of Biomechanical Engineering 108 1986 1 11
44. K.K.U. Stellbrink Micromechanics of Composites Composite Properties of Fibre and Matrix Constituents 1996 Hanser Munich
45. H. Tsuji, N. Hirano, H. Ohshima, and H. Ishihara Structural variation of the anterior and posterior annulus fibrosus in the development of human lumbar intervertebral disc Spine 18 2 1993 204 210
46. M. Weidenbaum, J. Iatridis, L.A. Setton, and R.J. Foster Mechanical behavior of the intervertebral disc and the effects of degeneration J.N. Weinstein S.L. Gordon Low Back Pain A Scientific and Clinical Overview 1996 American Academy of Orthopaedic Surgeons Rosemont IL 557 582
47. H.C. Wu, and R.F. Yao Mechanical behavior of the human annulus fibrosus Journal of Biomechanics 9 1976 1 7
48. J.Z. Wu, and W. Herzog Elastic anisotropy of articular cartilage is associated with the microstructures of collagen fibers and chondrocytes Journal of Biomechanics 35 7 2002 931 942
49. L. Yin, and W. Yang Optimality criteria method for topology optimization under multiple constraints Computers and Structures 79 2001 1839 1850
50. L. Yin, W. Yang, and T. Guo Tunnel reinforcement via topology optimization International Journal for Numerical and Analytical Methods in Geomechanics 24 2000 201 213