Material constants for a finite element model of the intervertebral disk with a fiber composite annulus

Spilker, R. L.; Jakobs, D. M.; Schultz, A. B.

Affiliations

¹Department of Mechanical Engineering, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy, N.Y. 12180

²Research Engineer, Danley Machine Company, Chicago, Ill, 60612

³Department of Mechanical Engineering and Engineering Mechanics, University of Michigan, Ann Arbor, Mich. 48109

Abstract

A simple axisymmetric finite element model of a human spine segment containing two adjacent vertebrae and the intervening intervertebral disk was constructed. The model incorporated four substructures: one to represent each of the vertebral bodies, the annulus fibrosus, and the nucleus pulposus. A semi-analytic technique was used to maintain the computational economies of a two-dimensional analysis when nonaxisymmetric loads were imposed on the model. The annulus material was represented as a layered fiber-reinforced composite. This paper describes the selection of material constants to represent the anisotropic layers of the annulus. It shows that a single set of material constants can be chosen so that model predictions of gross disk behavior under compression, torsion, shear, and moment loading are in reasonable agreement with the mean and range of experimentally measured disk behaviors. It also examines the effects of varying annular material propertie

Links

DOI: 10.1115/1.3138575

PubMed: 3959546

WoS: A1986A215400001

History

Received: 1983-06-01

Revised: 1985-08-21

Cited Works (14)

Year	Entry
1970	Yamada H. Strength of Biological Materials. Evans FG, ed. Baltimore, MD: Williams & Wilkins Company; 1970.
1980	Spilker RL. Mechanical behavior of a simple model of an intervertebral disk under compressive loading. J Biomech. 1980;13(10):895-901.
1979	Berkson MH, Nachemson A, Schultz AB. Mechanical properties of human lumbar spine motion segments, II: responses in compression and shear; influence of gross morphology. J Biomech Eng. February 1979;101(1):53-57.
1980	Hickey DS, Hukins DWL. Relation between the structure of the annulus fibrosus and the function and failure of the intervertebral disc. Spine. March–April 1980;5(2):106-116.
1979	Schultz AB, Warwick DN, Berkson MH, Nachemson AL. Mechanical properties of human lumbar spine motion segments, I: responses in flexion, extension, lateral bending, and torsion. J Biomech Eng. February 1979;101(1):46-52.
1974	Belytschko T, Kulak RF, Schultz AB, Galante JO. Finite element stress analysis of an intervertebral disc. J Biomech. May 1974;7(3):277-285.
1982	Somaratna N. Effects of Non-Axisymmetry on the Modelling Intervertebral Discs [Master's thesis]. University of Illinois at Chicago Circle; 1982.
1960	Nachemson A. Lumbar intradiscal pressure: experimental studies on post-mortem material. Acta Orthop Scand. 1960;31(suppl 43):1-104.
1978	Lin HS, Liu YK, Adams KH. Mechanical response of the lumbar intervertebral joint under physiological (complex) loading. J Bone Joint Surg. January 1978;60A(1):41-55.
1984	Shirazi-Adl SA, Shrivastava SC, Ahmed A. Stress analysis of the lumbar disc-body unit in compression: a three-dimensional nonlinear finite element study. Spine. March 1984;9(2):120-134.
1978	Lin HS, Lui YK, Ray G, Nikravesh P. Systems identification for material properties of the intervertebral joint. J Biomech. 1978;11(1-2):1-14.
1976	Wu H-C, Yao R-F. Mechanical behavior of the human annulus fibrosus. J Biomech. 1976;9(1):1-7.
1976	Kulak RF, Belytschko TB, Schultz AB, Galante JO. Nonlinear behavior of the human intervertebral disc under axial load. J Biomech. 1976;9(6):377-386.
1982	Reuber M, Schultz A, Denis F, Spencer D. Bulging of lumbar intervertebral disks. J Biomech Eng. August 1982;104(3):187-192.

Cited By (26)

Year	Entry
2004	Haug E, Choi H-Y, Robin S, Beaugonin M. Human models for crash and impact simulation. In: Ayache N, ed. Computational Models for the Human Body. Amsterdam, The Netherlands: Elsevier B.V; 2004:231-452. Ciarlet PG, ed. Handbook of Numerical Analysis; vol 12.
1990	Mow VC, Hou JS, Owens JM, Ratcliffe A. Biphasic and quasilinear viscoelastic theories for hydrated soft tissues. In: Mow VC, Ratcliffe A, Woo SL-Y, eds. Biomechanics of Diarthrodial Joints. Vol 1. New York, NY: Springer-Verlag; 1990:215-260.
1993	Fung YC. Biomechanics: Mechanical Properties of Living Tissues. 2nd ed. New York, NY: Springer-Verlag; 1993.
1999	Kumaresan S, Yoganandan N, Pintar FA. Finite element analysis of the cervical spine: a material property sensitivity study. Clin Biomech (Bristol, Avon). January 1999;12(1):41-53.
1989	Shirazi-Adl A. On the fibre composite material models of disc annulus: comparison of predicted stresses. J Biomech. 1989;22(4):357-365.
1997	Iatridis JC, Setton LA, Weidenbaum M, Mow VC. The viscoelastic behavior of the non-degenerate human lumbar nucleus pulposus in shear. J Biomech. October 1997;30(10):1005-1013.
1999	Arbogast KB, Margulies SS. A fiber-reinforced composite model of the viscoelastic behavior of the brainstem in shear. J Biomech. August 1999;32(8):865-870.
2006	Guerin HAL, Elliott DM. Degeneration affects the fiber reorientation of human annulus fibrosus under tensile load. J Biomech. 2006;39(8):1410-1418.
2000	Kumaresan S, Yoganandan N, Pintar FA, Maiman DJ, Kuppa S. Biomechanical study of pediatric human cervical spine: a finite element approach. J Biomech Eng. February 2000;122(1):60-71.
2000	Elliott DM, Setton LA. A linear material model for fiber-induced anisotropy of the anulus fibrosus. J Biomech Eng. April 2000;122(2):173-179.
2001	Elliott DM, Setton LA. Anisotropic and inhomogeneous tensile behavior of the human anulus fibrosus: experimental measurement and material model predictions. J Biomech Eng. June 2001;123(3):256-263.
1999	Iatridis JC, Kumar S, Foster RJ, Weidenbaum M, Mow VC. Shear mechanical properties of human lumbar annulus fibrosus. J Orthop Res. September 1999;17(5):732-737.
1995	Goel VK, Monroe BT, Gilbertson LG, Brinckmann P. Interlaminar shear stresses and laminae separation in a disc: finite element analysis of the L3-L4 motion segment subjected to axial compressive loads. Spine. March 15, 1995;20(6):689-698.
1996	Ebara S, Iatridis JC, Setton LA, Foster RJ, Mow VC, Weidenbaum M. Tensile properties of nondegenerate human lumbar anulus fibrosus. Spine. March 15, 1996;21(4):452-461.
1996	Iatridis JC, Weidenbaum M, Setton LA, Mow VC. Is the nucleus pulposus a solid or a fluid? mechanical behaviors of the nucleus pulposus of the human intervertebral disc. Spine. May 15, 1996;21(15):1174-1184.
1996	Iatridis JC. Biomechanics of the Anulus Fibrosus and Nucleus Pulposus of the Human Lumbar Intervertebral Disc and the Effects of Degeneration [PhD thesis]. Columbia University; 1996.
2012	Isaacs JL. Micromechanics of the Annulus Fibrosus: Role of Biomolecules in Mechanical Function [PhD thesis]. Drexel University; May 2012.
1999	Elliott DM. The Fiber-Induced Anisotropic Material Behaviors of the Anulus Fibrosus of the Intervertebral Disc in Tension [PhD thesis]. Duke University; 1999.
2001	Baer AE. The Micromechanical Environment of Intervertebral Disc Cells [PhD thesis]. Duke University; 2001.
1997	Kumaresan S. Clinical Studies of the Human Cervical Spine Using Finite Element Modeling [PhD thesis]. Marquette University; December 1997.
1991	Kasra M. Experimental and Finite Element Dynamic Response Analyses of a Human Lumbar Motion Segment [PhD thesis]. École polytechnique de Montréal; March 1991.
1999	Bass EC. Biaxial Nonlinear Elastic Response of the Human Lumbar Annulus Fibrosus and Its Role in the Determination of a Physiologically Relevant Constitutive Relation [PhD thesis]. Berkeley, CA: Berkeley, University of California; 1999.
2002	Wagner DR. A Mechanistic Strain Energy Function and Experimental Results for the Human Annulus Fibrosus [PhD thesis]. Berkeley, CA: Berkeley, University of California; 2002.
1988	Kim YE. An Analytical Investigation of Ligamentous Lumbar Spine Mechanics University of Iowa; May 1988.
2005	Guerin HAL. A Nonlinear Anisotropic Continuum Model of Human Annulus Fibrosus Mechanical Behavior [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 2005.
2006	Panzer MB. Numerical Modelling of the Human Cervical Spine in Frontal Impact [Master's thesis]. University of Waterloo; 2006.