Nonlinear finite element analysis of anular lesions in the L4/5 intervertebral disc

Journal of Biomechanics

Volumn 40, Issue 12, 2007, Pages 2744-2751

  Little, J P ^a   Adam, C J ^a   Evans, J H ^a   Pettet, G J ^a   Pearcy, M J ^a  

^a QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

Anular lesions; Degeneration; Finite element; Hyperelastic; Intervertebral disc

Indexed keywords

FINITE ELEMENT METHOD; HYDROSTATIC PRESSURE; MOTION ESTIMATION; PHYSIOLOGICAL MODELS; POLYNOMIAL APPROXIMATION;

ANULAR LESIONS; DEGENERATION; HYPERELASTIC STRAIN ENERGY EQUATION; INTERVERTEBRAL DISC;

BIOMECHANICS;

ANATOMY; ANULAR LIGAMENT; ARTICLE; BIOMECHANICS; COMPRESSIVE STRENGTH; ENERGY; FINITE ELEMENT ANALYSIS; HYDROSTATIC PRESSURE; INTERVERTEBRAL DISK DEGENERATION; LIGAMENT; LUMBAR DISK; MATHEMATICAL MODEL; MECHANICAL STRESS; MODEL; NONLINEAR SYSTEM; NUCLEUS PULPOSUS; PHYSIOLOGY; PRIORITY JOURNAL; RIGIDITY; ROTATION; YOUNG MODULUS;

ANIMALS; FINITE ELEMENT ANALYSIS; INTERVERTEBRAL DISK; LUMBOSACRAL REGION; MODELS, BIOLOGICAL; SHEEP; SPINAL CORD DISEASES; STRESS, MECHANICAL; WEIGHT-BEARING;

EID: 34547850253     PISSN: 00219290     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jbiomech.2007.01.007     Document Type: Article

References (83)

1. Acaroglu E.R., Iatridis J.C., Setton L.A., Foster R.J., Mow V.C., and Weidenbaum M. Degeneration and aging affect the tensile behaviour of human lumbar annulus fibrosus. Spine 20 (1995) 2690-2701
2. Adams M.A., and Dolan P. Spine biomechanics. Journal of Biomechanics 38 (2005) 1972-1983
3. Adams M.A., Freeman B.J., Morrison H.P., Nelson I.W., and Dolan P. Mechanical initiation of intervertebral disc degeneration. Spine 25 (2000) 1625-1636
4. Armstrong J.R. Lumbar Disc Lesions-Pathogenesis of Low Back Pain and Sciatica (1958), E & S Livingstone Ltd., Edinburgh
5. Belytschko T., Kulak R.F., Schultz A.B., and Galante J.O. Finite element stress analysis of an intervertebral disc. Journal of Biomechanics 7 (1974) 277-285
6. Betsch D.F., and Baer E. Structure and mechanical properties of rat tail tendon. Spine 11 (1986) 914-927
7. Bogduk N. The innervation of the lumbar spine. Spine 8 (1983) 286-293
8. Bogduk N. Clinical Anatomy of the Lumbar Spine and Sacrum (1997), Churchill Livingstone, New York
9. Broberg K.B. Slow deformation of intervertebral discs. Journal of Biomechanics 26 (1993) 501-512
10. Brown T., Hansen R.J., and Yorra A.J. Some mechanical tests on the lumbosacral spine with particular reference to the intervertebral discs. The Journal of Bone and Joint Surgery A39 (1957) 1135
11. Cassidy J.J., Hiltner A., and Baer E. Hierarchical structure of the intervertebral disc. Connective Tissue Research 23 (1989) 75-88
12. Chazal J., Tanguy A., Bourges M., Gaurel G., Escande G., Guillot M., and Vanneuville G. Biomechanical properties of spinal ligaments and a histological study of the supraspinal ligament in traction. Journal of Biomechanics 18 (1985) 167-176
13. Cossette J.W., Farfan H.F., Robertson G.H., and Wells R.V. The instantaneous centre of rotation of the third lumbar intervertebral joint. Journal of Biomechanics 4 (1971) 149-153
14. DiSilvestro M.R., Zhu Q., and Suh J.-K.F. Biphasic poroviscoelastic simulation of the unconfined compression of articular cartilage. II: effect of variable strain rates (technical brief). Journal of Biomechanical Engineering 123 (2001) 198-200
15. Eberlein R., Holzapfel G.A., and Frohlich M. Multi-segment FEA of the human lumbar spine including the heterogeneity of the annulus fibrosus. Computational Mechanics 34 (2004) 147-163
16. Elliot D.M., and Setton L.A. A linear material model for fiber-induced anisotropy of the anulus fibrosus. Journal of Biomechanical Engineering 122 (2000) 173-179
17. Eyre D., and Muir H. Types i and ii collagens in intervertebral disc. Interchanging radial distributions in annulus fibrosus. Biochemistry Journal 157 (1976) 267
18. Fagan, M.J., Gillespie, P., Julian, S., Siddall, D., Mohsen, A.M.M.A., 2001. A finite element model of a lumbar intervertebral disc: sensitivity to material property values. In: Proceedings of Fourth International Symposium on Computer Methods in Biomechanics and Biomedical Engineering, Rome, Italy.
19. Fagan M.J., Julian S., Siddall D.J., and Mohsen A.M. Patient-specific spine models. Part I: finite element analysis of the lumbar intervertebral disc-a material sensitivity study. Proceedings of Institute of Mechanical Engineers. Part H: Journal of Engineering in Medicine 216 (2002) 299-314
20. Goel V.K., Monroe B.T., Gilbertson L.G., Brinckmann P., and Nat R. Interlaminar shear stresses and laminae separation in a disc: finite element analysis of the l3-l4 motion segment subjected to axial compressive load. Spine 20 (1995) 689-698
21. Goto K., Tajima N., Chosa E., Totoribe K., Kuroki H., Arizumi Y., and Arai T. Mechanical analysis of the lumbar vertebrae in a three-dimensional finite element method model in which intradiscal pressure in the nucleus pulposus was used to establish the model. Journal of Orthopaedic Science 7 (2002) 243-246
22. Hilton, R.C., Ball, J., Benn, R., 1976. Vertebral endplate lesions (Schmor's nodes) in the dorsolumbar spine. Annals of the Rheumatic Diseases, 35, 127-132.
23. Hirsch, C., Schajowicz, F., 1953. Studies on structural changes in the lumbar annulus fibrosus. Acta Orthopaedica Scandinavica, 22, 184-231.
24. Higginson G.R., Litchfield M.R., and Snaith J. Load-displacement characteristics of articular cartilage. International Journal of Mechanical Sciences 18 (1976) 481-486
25. Holm S., Holm A.K., Ekstrom L., Karladani A., and Hansson T. Experimental disc degeneration due to endplate injury. Journal of Spinal Disorders and Techniques 17 (2004) 64-71
26. Humphrey J.D., and Yin F.C. A new constitutive formulation for characterizing the mechanical behaviour of soft tissues. Biophysical Journal 52 (1987) 563-570
27. Iatridis J.C., Kumar S., Foster R.J., Weidenbaum M., and Mow V.C. Shear mechanical properties of human lumbar annulus fibrosus. Journal of Orthopaedic Research 17 (1999) 732-737
28. Inoue H. Three-dimensional architecture of lumbar intervertebral discs. Spine 6 (1981) 139-146
29. Keller T.S., Spengler D.M., and Hansson T.H. Mechanical behaviour of the human lumbar spine. I. Creep analysis during static compressive loading. Journal of Orthopaedic Research 5 (1987) 467-478
30. Kumaresan S., Yoganandan N., Pintar F.A., and Maiman D.J. Finite element modelling of the cervical spine: role of intervertebral disc under axial and eccentric loads. Medical Engineering and Physics 21 (1999) 689-700
31. Li, S., 1994. Response of human intervertebral disc to prolonged axial loading and low-frequency vibration. Doctoral Dissertation, University of Illinois, Chicago, IL, USA.
32. Little, J.P., 2004. Finite element analysis of anular lesions in the intervertebral disc. Doctoral Thesis, Queensland University of Technology, Brisbane. Available from Australasian Digital Theses: 〈http://adt.library.qut.edu.au/adt-qut/public/adt-QUT20050517.14112 5/〉.
33. Malinsky J. The ontogenetic development of nerve terminations in the intervertebral discs of man. Acta Anatomica 38 (1959) 96-113
34. Marchand F., and Ahmed A. Investigation of the laminate structure of lumbar disc annulus fibrosus. Spine 15 (1990) 402-410
35. Markolf K.L., and Morris J.M. The structural components of the intervertebral disc: a study of their contributions to the ability of the disc to withstand compressive force. Journal of Bone and Joint Surgery A56 (1974) 675-687
36. McGill S.M., and Norman R.W. Partitioning of the dynamic l4/5 moment into disc, ligamentous and muscular components during lifting. Spine 11 (1986) 666-678
37. Meakin J.R., and Hukins D.W.L. Effect of removing the nucleus pulposus on the deformation of the annulus fibrosus during compression of the intervertebral disc. Journal of Biomechanics 33 (2000) 575-580
38. Meakin J.R., Redpath T.W., and Hukins D.W. The effect of partial removal of the nucleus pulposus from the intervertebral disc on the response of the human annulus fibrosus to compression. Clinical Biomechanics 16 (2001) 121-128
39. Mooney M. A theory of large elastic deformation. Journal of Applied Physics 11 (1940) 582-592
40. Morgan F.R. The mechanical properties of collagen fibres: stress-strain curves. Journal of the Society of Leather Trades' Chemists 44 (1960) 170-179
41. Nachemson A. Lumbar intradiscal pressure: experimental studies on post-mortem material. Acta Orthopaedica Scandinavica 43 (1960)
42. Nachemson A.L. Influence of spinal movement on the lumbar intradiscal pressure and on the tensile stresses in the annulus fibrosus. Acta Orthopaedica Scandinavica 33 (1963) 183-207
43. Nachemson A., and Evans J.H. Some mechanical properties of the 3rd lumbar interlaminar ligament (ligamentum flavum). Journal of Biomechanics 1 (1968) 211-220
44. Nachemson, A., 1992. Lumbar mechanics as revealed by lumbar intradiscal pressure measurements. In: Jayson, M.I.V. (Ed.), The Lumbar Spine and Back Pain. 4th ed. Churchill Livingstone, Edinburgh, pp. 157-171.
45. Natali A.N. A hyperelastic and almost incompressible material model as an approach to intervertebral disc analysis. Journal of Biomedical Engineering 13 (1991) 163-168
46. Natarajan R.N., Ke J.H., and Andersson G.B.J. A model to study the disc degeneration process. Spine 19 (1994) 259-265
47. Neumann P., Keller T.S., Ekstrom L., Perry L., Hansson T.H., and Spengler D.M. Mechanical properties of the human lumbar anterior longitudinal ligament. Journal of Biomechanics 25 (1992) 1185-1194
48. Ogden R.W. Large deformation isotropic elasticity-on the correlation of theory and experiment for incompressible rubberlike solids. Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences 326 (1972) 565-584
49. Oloyede A., and Broom N.D. A physical model for the time-dependent deformation of articular cartilage. Connective Tissue Research 29 (1993) 251-261
50. Oloyede A., Broom N.D., and Martinez J.B. Experimental factors governing the internal stress state of the intervertebral disc. Medical Engineering and Physics 20 (1998) 631-637
51. Oshima H., Ishihara H., Urban J.P.G., and Tsuji H. The use of coccygeal discs to study intervertebral disc metabolism. Journal of Orthopaedic Research 11 (1993) 332-338
52. Osti O.L., Vernon-Roberts B., and Fraser R.D. Anulus tears and intervertebral disc degeneration: an experimental study using an animal model. Spine 15 (1990) 762-767
53. Panjabi M., Brown M., Lindahl S., Irstam L., and Hermens M. Intrinsic disc pressure as a measure of integrity of the lumbar spine. Spine 13 (1988) 913-917
54. Panjabi M.M. The stabilizing system of the spine. Part ii. Neutral zone and instability hypothesis. Journal of Spinal Disorders 5 (1992) 390-396 [discussion 397]
55. Panjabi M.M., Greenstein G., Duranceau J., and Nolte L.P. Three-dimensional quantitative morphology of lumbar spinal ligaments. Journal of Spinal Disorders 4 (1991) 54-62
56. Pearcy M.J. Stereo radiography of lumbar spine motion. Acta Orthopaedica Scandinavica Supplementum 56 (1985)
57. Pearcy M.J., and Bogduk N. Instantaneous axes of rotation of the lumbar intervertebral joints. Spine 13 (1988) 1033-1041
58. Pintar F.A., Yoganandan N., Myers T., Elhagediab A., and Sances Jr. A. Biomechanical properties of human lumbar spine ligaments. Journal of Biomechanics 25 (1992) 1351-1356
59. Przybyla A., Pollintine P., Bedzinski R., and Adams M. Outer annulus tears have less effect than endplate fracture on stress distributions inside intervertebral discs: relevance to disc degeneration. Clinical Biomechanics (Bristol, Avon) 21 (2006) 1013-1019
60. Reid J.E., Meakin J.R., Robins S.P., Skakle J.M., and Hukins D.W. Sheep lumbar intervertebral discs as models for human discs. Clinical Biomechanics (Bristol, Avon) 17 (2002) 312-314
61. Reuber M., Schultz A., Denis F., and Spencer D. Bulging of lumbar intervertebral disks. Journal of Biomechanical Engineering 104 (1982) 187-192
62. Rivlin, R.S., 1984. Forty years of non-linear continuum mechanics. In: Proceedings of IX International Congress on Rheology, Acapulco, Mexico.
63. Rohlmann A., Zander T., Schmidt H., Wilke H.-J., and Bergmann G. Analysis of the influence of disc degeneration on the mechanical behaviour of a lumbar motion segment using the finite element method. Journal of Biomechanics 39 (2006) 2484-2490
64. Rolander S.D. Motion of the lumbar spine with special reference to the stabilizing effect of posterior fusion. Acta Orthopaedica Scandinavica 90 (1966) 1-144
65. Sato K., Kikuchi S., and Yonezawa T. In vivo intradiscal pressure measurement in healthy individuals and in patients with ongoing back problems. Spine 24 (1999) 2468-2474
66. Schmidt H., Heuer F., Simon U., Kettler A., Rohlmann A., Claes L., and Wilke H.-J. Application of a new calibration method for a three-dimensional finite element model of a human lumbar annulus fibrosus. Clinical Biomechanics 21 (2005) 337-344
67. Shirazi-Adl A., Shrivastava S.C., and Ahmed A.M. Stress analysis of the lumbar disc-body unit in compression-a three dimensional nonlinear finite element study. Spine 9 (1984) 120-134
68. Shirazi-Adl A., Ahmed A.M., and Shrivastava S.C. A finite element study of a lumbar motion segment subjected to pure sagittal plane moments. Journal of Biomechanics 19 (1986) 331-350
69. Shirazi-Adl A., Ahmed A.M., and Shrivastava S.C. Mechanical response of a lumbar motion segment in axial torque alone and combined with compression. Spine 11 (1986) 914-927
70. Sun D.N., and Leong K.W. A nonlinear hyperelastic mixture theory model for anisotropy, transport and swelling of annulus fibrosus. Annals of Biomedical Engineering 32 (2004) 92-102
71. Thompson R.E., Pearcy M.J., and Barker T.M. The mechanical effects of intervertebral disc lesions. Clinical Biomechanics (Bristol, Avon) 19 (2004) 448-455
72. Tibrewal S.B., and Pearcy M.J. Lumbar intervertebral disc heights in normal subjects and patients with disc herniation. Spine 10 (1985) 452-454
73. Tkaczuk H. Tensile properties of human lumbar longitudinal ligaments. Acta Orthopaedica Scandinavica Supplementum 115 (1968)
74. Tschoegl N.W. Constitutive equations for elastomers. Journal of Polymer Science A1 (1971) 1959-1970
75. Ueno K., and Liu Y.K. A three-dimensional nonlinear finite element model of lumbar intervertebral joint in torsion. Transactions of the ASME 109 (1987) 200-209
76. Urban J.P., and McMullin J.F. Swelling pressure of the lumbar intervertebral discs: influence of age, spinal level, composition, and degeneration. Spine 13 (1988) 179-187
77. Veronda D.R., and Westmann R.A. Mechanical characterisation of skin-finite deformations. Journal of Biomechanics 3 (1970) 111-124
78. Videman T., and Nurminen M. The occurrence of anular tears and their relation to lifetime back pain history: a cadaveric study using barium sulfate discography. Spine 29 (2004) 2668-2676
79. Virgin W.J. Experimental investigations into the physical properties of the intervertebral disc. Journal of Bone and Joint Surgery B33 (1951) 607-611
80. Wang J.-L., Parnianpour M., Shirazi-Adl A., and Engin A.E. Failure criterion of collagen fiber: viscoelastic behaviour simulated by using load control data. Theoretical and Applied Fracture Mechanics 27 (1997) 1-12
81. White A.A., and Panjabi M.M. Clinical Biomechanics of the Spine (1978), Lippincott, Philadelphia
82. Wu J., and Chen J. Clarification of the mechanical behaviour of spinal motion segments through a three-dimensional poroelastic mixed finite element model. Medical Engineering and Physics 18 (1996) 215-224
83. Yoshizawa H., O'Brien J.P., Thomas-Smith W., and Trumper M. The neuropathology of intervertebral discs removed for low-back pain. Journal of Pathology 132 (1980) 95-104