Skip to main content
SpringerLink
Log in

Mechanical Behavior of Annulus Fibrosus: A Microstructural Model of Fibers Reorientation

  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

Experimental uniaxial tensile tests have been carried out on annulus tissue samples harvested on pig and lamb lumbar intervertebral discs. When subjecting the samples to loading cycles, the stress–strain curves exhibit strong nonlinearities and hysteresis. This particular behavior results from the anisotropic microstructure of annulus tissue composed of woven oriented collagen fibers embedded in the extracellular matrix. During uniaxial tension, the collagen fibers reorient toward the loading direction increasing its global stiffness. To describe this behavior, we propose a heuristic two-dimensional rheological model based on three mechanical and one geometrical characteristics. The latter one is the fibers orientation angle becoming the key parameter that govern the macroscopic mechanical behavior. The experimental results are used to identify the physical properties associated with the rheological model, leading to an accurate representation of the stress–strain curve over a complete loading cycle. In this framework, the fibers reorientation can solely account for the rigidity increase while the hysteresis is associated with liquid viscous flows through the matrix. Based on this representation, unusual coupling effects between strains and fluid flows can be observed, that would significantly affect the cell nutrients transport mechanisms.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7

Similar content being viewed by others

References

  1. Accadbled, F., D. Ambard, J. S. de Gauzy, and P. Swider. A measurement technique to evaluate the macroscopic permeability of the vertebral end-plate. Med. Eng. Phys. 30:116–122, 2008.

    Article  PubMed  Google Scholar 

  2. Argoubi, M., and A. Shirazi-Adl. Poroelastic creep response analysis of a lumbar motion segment in compression. J. Biomech. 29:1331–1339, 1996.

    Article  PubMed  CAS  Google Scholar 

  3. Bass, E. C., F. A. Ashford, M. R. Segal, and J. C. Lotz. Biaxial testing of human annulus fibrosus and its implications for a constitutive formulation. Ann. Biomed. Eng. 32:1231–1242, 2004.

    Article  PubMed  CAS  Google Scholar 

  4. Best, B. A., F. Guilak, L. A. Setton, W. Zhu, F. Saed-Nejad, A. Ratcliffe, M. Weidenbaum, and V. C. Mow. Compressive mechanical properties of the human annulus fibrosus and their relationship to biochemical composition. Spine 19:212–221, 1994.

    Article  PubMed  CAS  Google Scholar 

  5. Bruehlmann, S. B., P. A. Hulme, and N. A. Duncan. In situ intercellular mechanics of the bovine outer annulus fibrosus subjected to biaxial strains. J. Biomech. 37:223–231, 2004.

    Article  PubMed  Google Scholar 

  6. Cassidy, J. J., A. Hiltner, and E. Baer. Hierarchical structure of the intervertebral disc. Connect. Tissue Res. 23:75–88, 1989.

    Article  PubMed  CAS  Google Scholar 

  7. Costi, J. J., I. A. Stokes, M. Gardner-Morse, J. P. Laible, H. M. Scoffone, and J. C. Iatridis. Direct measurement of intervertebral disc maximum shear strain in six degrees of freedom: motions that place disc tissue at risk of injury. J. Biomech. 40:2457–2466, 2007.

    Article  PubMed  CAS  Google Scholar 

  8. 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.

    Article  PubMed  CAS  Google Scholar 

  9. Eppell, S. J., B. N. Smith, H. Kahn, and R. Ballarini. Nano measurements with micro-devices: mechanical properties of hydrated collagen fibrils. J. R. Soc. Interface 3:117–121, 2006.

    Article  PubMed  CAS  Google Scholar 

  10. Ferguson, S. J., K. Ito, and L. P. Nolte. Fluid flow and convective transport of solutes within the intervertebral disc. J. Biomech. 37(2):213–221, 2004.

    Article  PubMed  Google Scholar 

  11. 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.

    Article  PubMed  CAS  Google Scholar 

  12. Grunhagen, T., G. Wilde, D. M. Soukane, S. A. Shirazi-Adl, and J. P. G. Urban. Nutrient supply and intervertebral disc metabolism. J. Bone Joint Surg. Am. 88 Suppl 2:30–35, 2006.

    Article  PubMed  Google Scholar 

  13. Guerin, H. A. L., and D. M. Elliott. Degeneration affects the fiber reorientation of human annulus fibrosus under tensile load. J. Biomech. 39:1410–1418, 2006.

    Article  PubMed  Google Scholar 

  14. Guerin, H. A. L., and D. M. Elliott. Quantifying the contributions of structure to annulus fibrosus mechanical function using a nonlinear, anisotropic, hyperelastic model. J. Orthop. Res. 25:508–516, 2007.

    Article  PubMed  Google Scholar 

  15. Holzapfel, G. A., F. Cacho, P. Elbischger, J. Rodriguez, and M. Doblare. A constitutive model for fibrous tissues considering collagen fiber crimp. Int. J. Nonlinear Mech. 42:391–402, 2007.

    Article  Google Scholar 

  16. Holzapfel, G. A., C. A. J. Schulze-Bauer, G. Feigl, and P. Regitnig. Single lamellar mechanics of the human lumbar annulus fibrosus. Biomech. Model. Mechanobiol. 3:125–140, 2005.

    Article  PubMed  CAS  Google Scholar 

  17. Iatridis, J. C., and I. ap Gwynn. Mechanisms for mechanical damage in the intervertebral disc annulus fibrosus. J. Biomech. 37:1165–1175, 2004.

    Article  PubMed  Google Scholar 

  18. Iatridis, J. C., S. Kumar, R. J. Foster, M. Weidenbaum, and V. C. Mow. Shear mechanical properties of human lumbar annulus fibrosus. J. Orthop. Res. 17:732–737, 2002.

    Article  Google Scholar 

  19. Iatridis, J. C., J. J. MacLean, M. O’Brien, and I. A. F. Stokes. Measurements of proteoglycan and water content distribution in human lumbar intervertebral discs. Spine 32:1493–1497, 2007.

    Article  PubMed  Google Scholar 

  20. Iatridis, J. C., J. J. MacLean, and D. A. Ryan. Mechanical damage to the intervertebral disc annulus fibrosus subjected to tensile loading. J. Biomech. 38:557–565, 2005.

    Article  PubMed  Google Scholar 

  21. Iatridis, J. C., L. Setton, M. Weidenbaum, and V. C. Mow. The viscoelastic behavior of the non-degenerate human lumbar nucleus pulposus in shear. J. Biomech. 30:1005–1013, 1997.

    Article  PubMed  CAS  Google Scholar 

  22. Johnstone, B., J. P. Urban, S. Roberts, and J. Menage. The fluid content of the human intervertebral disc. Comparison between fluid content and swelling pressure profiles of discs removed at surgery and those taken postmortem. Spine 17:412–416, 1992.

    Article  PubMed  CAS  Google Scholar 

  23. 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.

    Article  PubMed  CAS  Google Scholar 

  24. Magnier, C., O. Boiron, S. Wendling-Mansuy, P. Chabrand, and V. Deplano. Nutrient distribution and metabolism in the intervertebral disc in the unloaded state: a parametric study. J. Biomech. 42:100–108, 2009.

    Article  PubMed  Google Scholar 

  25. Marchand, F., and A. M. Ahmed. Investigation of the laminate structure of lumbar disc annulus fibrosus. Spine 15:402–410, 1990.

    Article  PubMed  CAS  Google Scholar 

  26. Riches, P. E., N. Dhillon, J. C. Lotz, A. W. Woods, and D. S. McNally. The internal mechanics of the intervertebral disc under cyclic loading. J. Biomech. 35:1263–1271, 2002.

    Article  PubMed  CAS  Google Scholar 

  27. Shirazi-Adl, S. A. Strain in fibers of a lumbar disc. Analysis of the role of lifting in producing disc prolapse. Spine 14:96–103, 1989.

    Article  PubMed  CAS  Google Scholar 

  28. 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 annulus fibrosus. Spine 19:1310–1319, 1994.

    Article  PubMed  CAS  Google Scholar 

  29. Smith, L. J., S. Byers, J. J. Costi, and N. L. Fazzalari. Elastic fibers enhance the mechanical integrity of the human lumbar anulus fibrosus in the radial direction. Ann. Biomed. Eng. 36:214–223, 2008.

    Article  PubMed  Google Scholar 

  30. Soukane, D. M., S. A. Shirazi-Adl, and J. P. G. Urban. Computation of coupled diffusion of oxygen, glucose and lactic acid in an intervertebral disc. J. Biomech. 40:2645–2654, 2007.

    Article  PubMed  Google Scholar 

  31. Tower, T. T., M. R. Neidert, and R. T. Tranquillo. Fiber alignment imaging during mechanical testing of soft tissues. Ann. Biomed. Eng. 30:1221–1233, 2002.

    Article  PubMed  Google Scholar 

  32. 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.

    Article  PubMed  Google Scholar 

  33. Yalta, A. T., and A. Y. Yalta. Gretl 1.6.0 and its numerical accuracy. J. Appl. Economet. 22:849–854, 2007.

    Article  Google Scholar 

  34. Yao, H., and W. Y. Gu. Three-dimensional inhomogeneous triphasic finite-element analysis of physical signals and solute transport in human intervertebral disc under axial compression. J. Biomech. 40:2071–2077, 2007.

    Article  PubMed  Google Scholar 

  35. Yao, H., M. A. Justiz, D. Flagler, and W. Y. Gu. Effects of swelling pressure and hydraulic permeability on dynamic compressive behavior of lumbar annulus fibrosus. Ann. Biomed. Eng. 30:1234–1241, 2002.

    Article  PubMed  Google Scholar 

  36. Yin, L., and D. M. Elliott. A homogenization model of the annulus fibrosus. J. Biomech. 38:1674–1684, 2005.

    Article  PubMed  Google Scholar 

  37. Yu, J., U. Tirlapur, J. Fairbank, P. Handford, S. Roberts, C. P. Winlove, Z. Cui, and J. P. G. Urban. Microfibrils, elastin fibres and collagen fibres in the human intervertebral disc and bovine tail disc. J. Anat. 210:460–471, 2007.

    Article  PubMed  Google Scholar 

Download references

Acknowledgment

This research was supported by the C.N.R.S (Projets Exploratoires Pluridisciplinaires) and the University of Montpellier II.

Author information

Authors and Affiliations

  1. Department of Mechanics and Civil Engineering, LMGC, UMR CNRS 5508, University of Montpellier 2, 34095, Montpellier Cedex 5, France

    D. Ambard & F. Cherblanc

Authors
  1. D. Ambard
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Cherblanc
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. Ambard.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ambard, D., Cherblanc, F. Mechanical Behavior of Annulus Fibrosus: A Microstructural Model of Fibers Reorientation. Ann Biomed Eng 37, 2256–2265 (2009). https://doi.org/10.1007/s10439-009-9761-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10439-009-9761-7

Keywords

Search

Navigation