Biaxial testing of human annulus fibrosus and its implications for a constitutive formulation

Annals of Biomedical Engineering

Volumn 32, Issue 9, 2004, Pages 1231-1242

  Bass, E C ^a,b   Ashford, F A ^a   Segal, M R ^c   Lotz, Jeffrey C ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Annulus; Biaxial behavior; Biomechanics; Intervertebral disc; Material properties; Mathematical model; Orthopedic bioengineering; Stress strain relations; Tension experiments

Indexed keywords

ANNULUS; ELASTIC MEMBRANES; OVERPARAMETERIZATION; STRAIN ENERGY;

APPROXIMATION THEORY; BIOMECHANICS; BIOMEDICAL ENGINEERING; HYSTERESIS; LAGRANGE MULTIPLIERS; MATHEMATICAL MODELS; PARAMETER ESTIMATION; POLYNOMIALS; STRESS ANALYSIS;

FIBROUS MEMBRANES;

ADULT; ALGORITHM; ANISOTROPY; ARTICLE; BIOLOGICAL MODEL; CADAVER; COMPARATIVE STUDY; COMPUTER SIMULATION; ELASTICITY; HUMAN; IN VITRO STUDY; INSTRUMENTATION; INTERVERTEBRAL DISK; LUMBAR VERTEBRA; MECHANICAL STRESS; METHODOLOGY; MIDDLE AGED; PHYSICAL EXAMINATION; PHYSIOLOGY; STIMULATION; TENSILE STRENGTH;

ADULT; ALGORITHMS; ANISOTROPY; CADAVER; COMPUTER SIMULATION; ELASTICITY; HUMANS; INTERVERTEBRAL DISK; LUMBAR VERTEBRAE; MIDDLE AGED; MODELS, BIOLOGICAL; PHYSICAL EXAMINATION; PHYSICAL STIMULATION; STRESS, MECHANICAL; TENSILE STRENGTH;

EID: 5444258585     PISSN: 00906964     EISSN: None     Source Type: Journal    
DOI: 10.1114/B:ABME.0000039357.70905.94     Document Type: Article

References (47)

1. Acaroglu, E. R., J. C. Iatridis, L. A. Setton, R. J. Foster, V. C. Mow, and M. Weidenbaum. Degeneration and aging affect the tensile behavior of human lumbar anulus fibrosus. Spine 20:2690-2701, 1995.
2. Bass, E. C. Biaxial Nonlinear Elastic Response of the Human Lumbar Annulus Fibrosus and Its Role in the Determination of a Physiologically Relevant Constitutive Relation. PhD Thesis, Mechanical Engineering, University of California at Berkeley, 1999.
3. Best, B. A., F. Guilak, L. A. Setton, W. Zhu, N. F. Saed, A. Ratcliffe, M. Weidenbaum, and V. C. Mow. Compressive mechanical properties of the human anulus fibrosus and their relationship to biochemical composition. Spine 19:212-221, 1994.
4. Best, B. A., L. A. Setton, F. Guilak, A. Ratcliffe, M. Weidenbaum, and V. C. Mow. Permeability and compressive stiffness of annulus fibrosus: Variation with site and composition. Trans. ORS 14:354, 1989.
5. Brinckmann, P. Injury of the annulus fibrosus and disc protrusions. An in vitro investigation on human lumbar discs. Spine 11:149-153, 1986.
6. Debes, J. C., and Y. C. Fung. Effect of temperature on the biaxial mechanics of excised lung parenchyma of the dog. J. Appl. Physiol. 73:1171-1180, 1992.
7. Debes, J. C., and Y. C. Fung. Biaxial mechanics of excised canine pulmonary arteries. Am. J. Physiol. 269:H433-H442, 1995.
8. Duncan, N. A., and J. C. Lotz. Experimental validation of a porohyperelastic finite element model of the annulus fibrosus. In: Computer Methods in Biomechanics & Biomedical Engineering - 2, edited by J. Middleton, M. L. Jones, and G. N. Pande. New York: Gordon and Breach, 1998, pp. 527-534.
9. Ebara, S., J. C. Iatridis, L. A. Setton, R. J. Foster, V. C. Mow, and M. Weidenbaum. Tensile properties of nondegenerate human lumbar anulus fibrosus. Spine 21:452-461, 1996.
10. Elliott, D. M., M. A. LeRoux, T. A. Laursen, and L. A. Setton. Formulation of a continuum anisotropic model for the anulus fibrosus in tension. Adv. Bioeng. 43:165-166, 1997.
11. "Elliott, D. M., and L. A. Setton. Anisotropic and inhomogeneous tensile behavior of the human anulus fibrosus: Experimental measurement and material model predictions. J. Biomech. Eng. 123:256-263, 2001.
12. Flynn, D. M., G. D. Peura, P. Grigg, and A. H. Hoffman. A finite element based method to determine the properties of planar soft tissus. J. Biomech. Eng. 120:202-210, 1998.
13. Fujita, Y., N. A. Duncan, and J. C. Lotz. Radial tensile properties of the lumbar annulus fibrosus are site and degeneration dependent J. Orthop. Res. 15:814-819, 1997.
14. Fung, Y. C., K. Fronek, and P. Patitucci. Pseudoelasticity of arteries and the choice of its mathematical expression. Am. J. Physiol. 237:H620-H631, 1979.
15. Galante, J. O. Tensile properties of the human lumbar annulus fibrosus. Acta Orthop. Scand. Suppl. 100:1-91, 1967.
16. Green, A. E., and J. E. Adkins. Large Elastic Deformations. Oxford: Clarendon Press, 1970, 324 pp.
17. Green, T. P., M. A. Adams, and P. Dolan. Tensile properties of the annulus fibrosus. Ii: Ultimate tensile strength and fatigue life. Eur. Spine J. 2:209-214, 1993.
18. Humphrey, J. D., R. K. Strumpf, and F. C. Yin. Biaxial mechanical behavior of excised ventricular epicardium. Am. J. Physiol. 259:H101-H108, 1990.
19. Humphrey, J. D., R. K. Strumpf, and F. C. Yin. Determination of a constitutive relation for passive myocardium: I. A new functional form. J. Biomech. Eng. 112:333-339, 1990.
20. Humphrey, J. D., R. K. Strumpf, and F. C. Yin. Determination of a constitutive relation for passive myocardium: II. Parameter estimation. J. Biomech. Eng. 112:340-346, 1990.
21. Humphrey, J. D., R. K. Strumpf, and F. C. Yin. A constitutive theory for biomembranes: Application to epicardial mechanics. J. Biomech. Eng. 114:461-466, 1992.
22. Humphrey, J. D., D. L. Vawter, and R. P. Vito. Quantification of strains in biaxially tested soft tissues. J. Biomech. 20:59-65, 1987.
23. James, A. G., A. Green, and G. M. Simpson. Strain-energy functions of rubber i: Characterization of gum vulcanates. J. Appl. Poly. Sci. 19:2033-2058, 1975.
24. Jones, D. F., and L. R. G. Treloar. The properties of rubber in pure homogeneous strain. J. Phys. D 8:1285-1304, 1975.
25. Kang, T., J. D. Humphrey, and F. C. Yin. Comparison of biaxial mechanical properties of excised endocardium and epicardium. Am. J. Physiol. 270:H2169-H2176, 1996.
26. Klisch, S. M., and J. C. Lotz. Application of a fiber-reinforced continuum theory to multiple deformations of the annulus fibrosus. J. Biomech. 32:1027-1036, 1999.
27. Lanir, Y., and Y. C. Fung. Two-dimensional mechanical properties of rabbit skin. Ii. Experimental results. J. Biomech. 7: 171-182, 1974.
28. Mansour, J. M., and V. C. Mow. The permeability of articular cartilage under compressive strain and at high pressures, J. Bone Joint Surg. [Am.] 58:509-516, 1976.
29. Marchand, F., and A. M. Ahmed. Mechanical properties and failure mechanisms of the lumbar disc annulus. Trans. ORS 14:355, 1989.
30. Markolf, K. L., and J. M. Morris. The structural components of the intervertebral disc. A study of their contributions to the ability of the disc to withstand compressive forces. J. Bone Joint Surg. [Am.] 56:675-687, 1974.
31. Ogden, R. W. Biaxial deformation of rubber-like solids: Comparison of theory and experiment. J. Phys. D 12:1463-1472, 1979.
32. Ogden, R. W. Non-Linear Elastic Deformations. Chichester, UK: Ellis Horwood, 1984, 532 pp.
33. Rivlin, R. S., and D. W. Saunders. Large elastic deformations of Isotropic materials: Vii. Experiments on the deformation of rubber. In: Collected Papers of R.S. Rivlin, edited by G. I. Barenblatt and D. D. Joseph. New York: Springer, 1997, 1997, pp. 157-194.
34. Sacks, M. S., and C. J. Chuong. Orthotropic mechanical properties of chemically treated bovine pericardium. Ann. Biomed. Eng. 26:892-902, 1998.
35. Shirazi-Adl, A., S. C. Shrivastava, and A. M. Ahmed. Stress analysis of the lumbar disc-body unit in compression. A three-dimensional nonlinear finite element study. Spine 9:120-134, 1984.
36. Skaggs, D. L., M. Weidenbaum, J. C. Iatridis, A. Ratcliffe, and V. C. Mow. Regional variation in tensile properties and biochemical composition of the human lumbar anulus fibrosus, Spine 19:1310-1319, 1994.
37. Stokes, I. A. Surface strain on human intervertebral discs. J. Orthop. Res. 5:348-355, 1987.
38. Thompson, J. P., R. H. Pearce, M. T. Schechter, M. E. Adams, I. K. Tsang, and P. B. Bishop. Preliminary evaluation of a scheme for grading the gross morphology of the human intervertebral disc. Spine 15:411-415, 1990.
39. Tong, P., and Y. C. Fung. The stress-strain relationship for the skin. J. Biomech. 9:649-657, 1976.
40. Vaishnav, R. N., J. T. Young, J. S. Janicki, and D. J. Patel. Nonlinear anisotropic elastic properties of the canine aorta. Biophys. J. 12:1008-1027, 1972.
41. Vangerko, H., and L. R. G. Treloar. The inflation and extension of rubber tube for biaxial strain studies. J. Phys. D 11:1969-1978, 1978.
42. Vawter, D. L., Y. C. Fung, and J. B. West. Constitutive equation of lung elasticity. J. Biomech. Eng. 101:38-45, 1979.
43. Vorp, D. A., K. R. Rajagopal, P. J. Smolinski, and H. S. Borovetz. Identification of elastic properties of homogeneous, orthotropic vascular segments in distension. J. Biomech. 28:501-512, 1995.
44. Wagner, D. R., and J. C. Lotz. Theoretical model and experimental results for the nonlinear elastic behavior of human annulus fibrosus. J. Orthop. Res., 22:901-909, 2004.
45. Waldman, S. D., and M. J. Lee. Boundary conditions during biaxial testing of planar connective tissues. Part 1: Dynamic behaviour. J. Mater. Sci. 13:933-938, 2002.
46. Wu, H. C., and R. F. Yao. Mechanical behavior of the human annulus fibrosus. J. Biomech. 9:1-7, 1976.
47. Yin, F. C., R. K. Strumpf, P. H. Hew, and S. L. Zeger. Quantification of the mechanical properties of noncontracting canine myocardium under simultaneous biaxial loading. J. Biomech. 20:577-589, 1987.