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TECHNICAL PAPERS

Anisotropic and Inhomogeneous Tensile Behavior of the Human Anulus Fibrosus: Experimental Measurement and Material Model Predictions

[+] Author and Article Information
Dawn M. Elliott

Orthopaedic Research Laboratory, Department of Orthopaedic Surgery, Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104

Lori A. Setton

Department of Biomedical Engineering, Department of Surgery, Division of Orthopaedic Surgery, Duke University, Durham, NC 27708

J Biomech Eng 123(3), 256-263 (Dec 21, 2000) (8 pages) doi:10.1115/1.1374202 History: Received December 27, 1999; Revised December 21, 2000
Copyright © 2001 by ASME
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References

Coventry,  M. B., Ghormley,  R. K., and Kernohan,  J. W., 1945, “Intervertebral Disc—Its Microscopic Anatomy and Pathology—Part I: Anatomy, Development and Physiology.” J. Bone Joint Surg. Am., 27, No. 1, pp. 105–112.
Ayad, S., and Sandell, L. J., 1996, “Collagens of the Intervertebral Disc: Structure, Function, and Changes During Aging and Disease,” in: Low Back Pain: A Scientific and Clinical Overview, J. N. Weinstein and S. L. Gordon, eds., American Academy of Orthopaedic Surgeons, Rosemont, IL, pp. 539–556.
Bayliss, M. T., and Johnstone, B., 1992, “Biochemistry of the Intervertebral Disc,” in: The Lumbar Spine and Back Pain, M. I. V. Jayson and A. S. J. Dixon, eds., Churchill Liningstone, London, pp. 111–131.
Cassidy,  J. J., Hiltner,  A., and Baer,  E., 1989, “Hierarchical Structure of the Intervertebral Disc,” Connect. Tissue Res., 23, pp. 75–88.
Eyre,  D. R., 1979, “Biochemistry of the Intervertebral Disc,” Connect. Tissue Res., 8, pp. 227–291.
Marchand,  F., and Ahmed,  A. M., 1990, “Investigation of the Laminate Structure of Lumbar Disc Annulus Fibrosus,” Spine, 15, No. 5, pp. 402–410.
Acaroglu,  E. R., Iatridis,  J. C., Setton,  L. A., Foster,  R. J., , 1995, “Degeneration and Aging Affect the Tensile Behavior of Human Lumbar Annulus Fibrosus,” Spine, 20, No. 24, pp. 2690–2701.
Duncan, N. A., Ashford, F. A., and Lotz, J. C., 1996, “The Effect of Strain Rate on the Axial Stress–Strain Response of the Human Annulus Fibrosus in Tension and Compression: Experiment and Poroelastic Finite Element Predictions,” Advances in Bioengineering, ASME BED-Vol. 33, pp. 401–402.
Ebara,  S., Iatridis,  J. C., Setton,  L. A., Foster,  R. J., , 1996, “Tensile Properties of Nondegenerate Human Lumbar Anulus Fibrosus,” Spine, 21, No. 4, pp. 452–461.
Fujita,  Y., Duncan,  N. A., and Lotz,  J., 1997, “Radial Tensile Properties of the Lumbar Anulus Fibrosus Are Site and Degeneration Dependent,” J. Orthop. Res., 15, pp. 814–819.
Galante,  J., 1967, “Tensile Properties of the Human Lumbar Annulus Fibrosus,” Acta Orthop. Scand. Suppl., 100, pp. 1–91.
Elliott,  D. M., and Setton,  L. A., 2000, “A Linear Material Model for Fiber-Induced Anisotropy of the Anulus Fibrosus,” ASME J. Biomech. Eng., 122, pp. 173–179.
Goel,  V. K., Kim,  Y. E., Lim,  T. H., and Weinstein,  J. N., 1988, “Analytical Investigation of the Mechanics of Spinal Instrumentation,” Spine, 13, No. 9, pp. 1003–1011.
Klisch,  S. M., and Lotz,  J. C., 1999, “Application of a Fiber-Reinforced Continuum Theory to Multiple Deformations of the Annulus Fibrosus,” J. Biomech., 32, pp. 1027–1036.
Natarajan,  R. N., Ke,  J. H., and Andersson,  G. B. J., 1994, “A Model to Study the Disc Degeneration Process,” Spine, 19, No. 3, pp. 259–265.
Shirazi-Adl,  S. A., Shrivastava,  S. C., and Ahmed,  A. M., 1984, “Stress Analysis of the Lumbar Disc-Body Unit in Compression: A 3D Nonlinear Finite Element Study,” Spine, 9, No. 2, pp. 120–134.
Shirazi-Adl,  A., 1994, “Nonlinear Stress Analysis of the Whole Lumbar Spine in Torsion—Mechanics of Facet Articulation,” J. Biomech., 27, No. 3, pp. 289–299.
Spilker,  R. L., Jakobs,  D. M., and Schultz,  A. B., 1986, “Material Constants for a Finite Element Model of the Intervertebral Disc With a Fiber Composite Annulus,” ASME J. Biomech. Eng., 108, pp. 1–11.
Wu,  H. C., and Yao,  R. F., 1976, “Mechanical Behavior of the Human Annulus Fibrosus,” J. Biomech., 9, pp. 1–7.
Iatridis,  J. C., Setton,  L. A., Foster,  R. J., Rawlins,  B. A., , 1998, “Degeneration Affects the Anisotropic and Nonlinear Behaviors of Human Anulus Fibrosus in Compression,” J. Biomech., 31, pp. 535–544.
Fujita,  Y., Duncan,  N. A., and Lotz,  J. C., 1996, “Anisotropic Shear Behavior of the Annulus Fibrosus: Effect of Harvest Site and Tissue Prestrain,” Trans. Annu. Meet. — Orthop. Res. Soc., 21, p. 271.
Iatridis, J. C., Kumar, S., Krishnan, L., Rawlins, B. A., et al., 1996, “Shear Mechanical Behavior of the Human Lumbar Anulus Fibrosus and the Effects of Degeneration,” Advances in Bioengineering, ASME BED-Vol. 33, pp. 149–150.
Thompson,  J. P., Pearce,  R. H., Schechter,  M. T., Adams,  M. E., , 1990, “Preliminary Evaluation of a Scheme for Grading the Gross Morphology of the Human Intervertebral Disc,” Spine, 15, No. 5, pp. 411–415.
Elliott,  D. M., Guilak,  F., Vail,  T. P., Wang,  J. Y., , 1999, “Tensile Properties of Articular Cartilage Are Altered by Meniscectomy in a Canine Model of Osteoarthritis,” J. Orthop. Res., 17, No. 4, pp. 503–508.
Fung, Y. C., 1994, A First Course in Continuum Mechanics, 3rd ed., Prentice Hall, Englewood Cliffs, NJ.
Spencer, A. J. M., 1984, “Constitutive Theory for Strongly Anisotropic Solids,” Continuum Theory of the Mechanics of Fibre-Reinforced Composites, A. J. M. Spencer, ed., Springer-Verlag, New York, pp. 1–32.
Iatridis,  J. C., Kumar,  S., Foster,  R. J., Weidenbaum,  M., , 1999, “Shear Mechanical Properties of Human Lumbar Annulus Fibrosus,” J. Orthop. Res., 7, No. 5, pp. 732–737.
Elliott, D. M., and Setton, L. A., 1999, “Direct Measurement of a Complete Set of Orthotropic Material Properties for the Human Anulus Fibrosus in Tension,” Bioengineering Conference, ASME BED-Vol. 42, pp. 75–76.
Lai, W. M., Rubin, D., and Kremple, E., 1993, Introduction to Continuum Mechanics; Pergamon Press, New York.
Ting, T. C. T., 1996, Anisotropic Elasticity, Oxford University Press, New York.
Best,  B. A., Guilak,  F., Setton,  L. A., Zhu,  W., , 1994, “Compressive Mechanical Properties of the Human Anulus Fibrosus and Their Relationship to Biochemical Composition,” Spine, 19, No. 2, pp. 212–221.
Drost,  M. R., Willems,  P., Snijders,  H., Huyghe,  J. M. , 1995, “Confined Compression of Canine Annulus Fibrosus Under Chemical and Mechanical Loading,” ASME J. Biomech. Eng., 117, pp. 390–396.
Ateshian, G. A., and Soltz, M. A., 1999, “A Biphasic Conewise Linear Elasticity Model for Modeling Tension-Compression Nonlinearity in Articular Cartilage,” Bioengineering Conference, ASME BED-Vol. 42, pp. 69–70.
Li,  L. P., Soulhat,  J., Buschmann,  M. D., and Shirazi-Adl,  A., 1999, “Nonlinear Analysis of Cartilage in Unconfined Ramp Compression Using a Fibril Reinforced Poroelastic Model,” Clin. Biomech. (Bristol, Avon),14, No. 9, pp. 673–682.

Figures

Grahic Jump Location
Schematic of anterior AF showing the orientations of the samples prepared for tensile testing. Samples are shown for outer sites only. The coordinate system is related to the disc directions as follows: 1=circumferential, 2=axial, and 3=radial. For each Group “A”-“B”, “A” corresponds to the length of the sample along the direction of applied load and “B” corresponds to the width of the sample along which the transverse strain is measured.
Grahic Jump Location
Gray-scale, digital image of test sample and reference tab (R) for a representative sample. Box shows the approximate size and location that was imaged at higher magnification for optical strain analysis.
Grahic Jump Location
Schematic showing calculation of the strain tensor using the positions of the centroids of a triad of markers (shown as dots) from reference state, which were measured in the initial reference image, to the deformed state, measured in the subsequent images following uniaxial stretch of the sample.
Grahic Jump Location
Strain plots for a representative sample elongated along the axial direction (Group 2-1). Data points represent mean (SD) values at each applied grip strain for all triads on the sample surface; lines represent linear regressions, with R2 as shown. (TOP) Measured longitudinal and transverse Lagrangian strain. (BOTTOM) Poisson’s ratio for the same sample, calculated from strain measures.
Grahic Jump Location
Stress–strain behavior in three orientations for representative samples from the same anulus fibrosus. Line denotes model fit.
Grahic Jump Location
Predicted moduli as a function of fiber angle, ϕ, using average material properties from the outer sites. E1=circumferential orientation, E2=axial, and E3=radial. Y-bars=one standard deviation in experimental measures, X-bars=range of fiber angles reported by Cassidy et al. 4.
Grahic Jump Location
Fraction of total strain energy (W) at outer sites contributed by each term (Wi) in the quadratic strain energy function for (A) pure dilatation, and for simple tension in the (B) circumferential, (C) axial, (D) and radial directions. W5 and W9 are zero due to the model assumption of isotropy in shear.

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