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J Biomech. 2014 Aug 22;47(11):2540-6. doi: 10.1016/j.jbiomech.2014.06.008. Epub 2014 Jun 17.

Validation and application of an intervertebral disc finite element model utilizing independently constructed tissue-level constitutive formulations that are nonlinear, anisotropic, and time-dependent.

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Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, 229 Towne Building, 220 South 33rd Street, Philadelphia, PA 19104, United States.
Biomedical Engineering Program, University of Delaware, 125 E. Delaware Ave, Newark, DE 19716, United States.
Department of Bioengineering, University of Pennsylvania, 210 South 33rd Street, Suite 240, Skirkanich Hall, Philadelphia, PA 19104, United States.
Penn State Hershey Bone and Joint Institute, Pennsylvania State University, Suite 2400, Building B, 30 Hope Drive, Hershey, PA 17033, United States.
Biomedical Engineering Program, University of Delaware, 125 E. Delaware Ave, Newark, DE 19716, United States. Electronic address:


Finite element (FE) models are advantageous in the study of intervertebral disc mechanics as the stress-strain distributions can be determined throughout the tissue and the applied loading and material properties can be controlled and modified. However, the complicated nature of the disc presents a challenge in developing an accurate and predictive disc model, which has led to limitations in FE geometry, material constitutive models and properties, and model validation. The objective of this study was to develop a new FE model of the intervertebral disc, to validate the model's nonlinear and time-dependent responses without tuning or calibration, and to evaluate the effect of changes in nucleus pulposus (NP), cartilaginous endplate (CEP), and annulus fibrosus (AF) material properties on the disc mechanical response. The new FE disc model utilized an analytically-based geometry. The model was created from the mean shape of human L4/L5 discs, measured from high-resolution 3D MR images and averaged using signed distance functions. Structural hyperelastic constitutive models were used in conjunction with biphasic-swelling theory to obtain material properties from recent tissue tests in confined compression and uniaxial tension. The FE disc model predictions fit within the experimental range (mean ± 95% confidence interval) of the disc's nonlinear response for compressive slow loading ramp, creep, and stress-relaxation simulations. Changes in NP and CEP properties affected the neutral-zone displacement but had little effect on the final stiffness during slow-ramp compression loading. These results highlight the need to validate FE models using the disc's full nonlinear response in multiple loading scenarios.


Annulus fibrosus; Biphasic; Biphasic-swelling; Cartilaginous endplate; Degeneration; Intervertebral disc; Nucleus pulposus

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