Human annulus fibrosus material properties from biaxial testing and constitutive modeling are altered with degeneration

  • Grace D. O’Connell
  • Sounok Sen
  • Dawn M. ElliottEmail author
Original Paper


The annulus fibrosus (AF) of the intervertebral disk undergoes large and multidirectional stresses and strains. Uniaxial tensile tests are limited for measuring AF material properties, because freely contracting edges can prevent fiber stretch and are not representative of in situ boundary conditions. The objectives of this study were to measure human AF biaxial tensile mechanics and to apply and validate a constitutive model to determine material properties. Biaxial tensile tests were performed on samples oriented along the circumferential–axial and the radial–axial directions. Data were fit to a structurally motivated anisotropic hyperelastic model composed of isotropic extra-fibrillar matrix, nonlinear fibers, and fiber–matrix interactions (FMI) normal to the fibers. The validated model was used to simulate shear and uniaxial tensile behavior, to investigate AF structure–function, and to quantify the effect of degeneration. The biaxial stress–strain response was described well by the model (R 2 > 0.9). The model showed that the parameters for fiber nonlinearity and the normal FMI correlated with degeneration, resulting in an elongated toe-region and lower stiffness with degeneration. The model simulations in shear and uniaxial tension successfully matched previously published circumferential direction Young’s modulus, provided an explanation for the low values in previously published axial direction Young’s modulus, and was able to simulate shear mechanics. The normal FMI were important contributors to stress and changed with degeneration, therefore, their microstructural and compositional source should be investigated. Finally, the biaxial mechanical data and constitutive model can be incorporated into a disk finite element model to provide improved quantification of disk mechanics.


Biaxial tension Annulus fibrosus Continuum modeling Intervertebral disc Degeneration 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Grace D. O’Connell
    • 1
  • Sounok Sen
    • 1
  • Dawn M. Elliott
    • 1
    Email author
  1. 1.Department of Orthopaedic SurgeryUniversity of PennsylvaniaPhiladelphiaUSA

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