A comparison of cartilage stress-relaxation models in unconfined compression: QLV and stretched exponential in combination with fluid flow

Abstract

Cartilage exhibits nonlinear viscoelastic behaviour. Various models have been proposed to explain cartilage stress relaxation, but it is unclear whether explicit modelling of fluid flow in unconfined compression is needed. This study compared Fung's quasi-linear viscoelastic (QLV) model with a stretched-exponential model of cartilage stress relaxation and examined each of these models both alone and in combination with a fluid-flow model in unconfined compression. Cartilage explants were harvested from bovine calf patellofemoral joints and equilibrated in tissue culture for 5 days before stress-relaxation testing in unconfined compression at 5% nominal strain. The stretched exponential models fit as well as the QLV models. Furthermore, the average stretched exponential relaxation time determined by this model lies within the range of experimentally measured relaxation times for extracted proteoglycan aggregates, consistent with the hypothesis that the stretched exponential model represents polymeric mechanisms of cartilage viscoelasticity.

Keywords::

• cartilage
• flow-independent viscoelasticity
• stress relaxation
• polymer dynamics
• osteoarthritis

Acknowledgements

The authors are grateful to Professor A.H. Reddi for providing the cartilage samples and tissue-culture expertise and to J.P. Cunningham for optimisation advice. We thank S.J. Bornheimer and Anonymous Reviewer 2 for helpful suggestions with the manuscript. Funding was provided by NIH (AR050286) and the David Linn Chair in the UC Davis Medical Center Department of Orthopaedics.