New resource for the computation of cartilage biphasic material properties with the interpolant response surface method

Abstract

Cartilage material properties are important for understanding joint function and diseases, but can be challenging to obtain. Three biphasic material properties (aggregate modulus, Poisson's ratio and permeability) can be determined using an analytical or finite element model combined with optimisation to find the material properties values that best reproduce an experimental creep curve. The purpose of this study was to develop an easy-to-use resource to determine biphasic cartilage material properties. A Cartilage Interpolant Response Surface was generated from interpolation of finite element simulations of creep indentation tests. Creep indentation tests were performed on five sites across a tibial plateau. A least-squares residual search of the Cartilage Interpolant Response Surface resulted in a best-fit curve for each experimental condition with corresponding material properties. These sites provided a representative range of aggregate moduli (0.48–1.58 MPa), Poisson's ratio (0.00–0.05) and permeability (1.7 × 10^− 15–5.4 × 10^− 15 m⁴/N s) values found in human cartilage. The resource is freely available from https://simtk.org/home/va-squish.

Keywords:

• cartilage
• biphasic theory
• indentation testing

Acknowledgements

We gratefully acknowledge the input from Dr Robert Spilker (Rensselaer Polytechnic Institute) and Dr Kyriacos Athanasiou (Rice University). This study was funded by the following sources: VA Rehabilitation R&D Service (A2592R), Stanford Regenerative Medicine Training Grant (R90 DK071508-02), NIH (EB005790-01), NIH (EB002524-04), and a Bio-X Student Fellowship.