Hyperelastic parameter identification of human articular cartilage and substitute materials

Numerical simulations are a valuable tool in the field of tissue engineering for cartilage repair and can help to understand which mechanical properties affect the behavior of chondrocytes and contribute to the success or failure of surrogate materials as implants. However, special attention needs to be paid when identifying corresponding material parameters in order to provide reliable numerical predictions of the material's response. In this study, we identify hyperelastic material parameters for numerical simulations in COMSOL Multiphysics® v. 5.6 for human articular cartilage and two surrogate materials, commercially available ChondroFiller^liquid, and oxidized alginate-gelatin (ADA-GEL) hydrogels. We consider several hyperelastic isotropic material models and provide separate parameter sets for the unconditioned and the conditioned material response, respectively, based on previously generated experimental data including both compression and tension experiments. We compare a direct parameter identification approach assuming homogeneous deformation throughout the specimen and an inverse approach, where the experiments are simulated using a finite element model with realistic boundary conditions in COMSOL Multiphysics® v. 5.6. We demonstrate that it is important to consider both compression and tension data simultaneously and to use the inverse approach to obtain reliable parameters. The one-term Ogden model best represents the unconditioned response of cartilage, while the conditioned response of cartilage and ADA-GEL is equally well represented by the two-term Ogden and five-term Mooney-Rivlin models. The five-term Mooney-Rivlin model is also most suitable to model the unconditioned response of ADA-GEL. For ChondroFiller^liquid, we suggest using the five-term Mooney-Rivlin or two-term Ogden model for the unconditioned and the two-term Ogden model for the conditioned material response. These results will help to choose appropriate material models and parameters for simulations of whole joints or to advance mechanical-stimulation assisted cartilage tissue engineering in the future.