Hyperelastic modeling of location-dependent human distal femoral cartilage mechanics

Knee articular cartilage exhibits complex mechanical behavior, even under high strain rates, which poses a challenge to developing accurate and efficient cartilage models. In particular, the tissue׳s stress–strain response is non-linear and the stiffness of the response is location-dependent. Hyperelastic models such as those of Alan Gent and others have increasingly found use in soft tissue biomechanics. Recently, a hyperelastic statistical chain network model representing the transverse isotropy of the collagen matrix in the superficial tangential zone has been developed. The model successfully simulated the 100% strain/s unconfined compression response of human proximal tibial cartilage. Moreover, spatial variations in the tangent modulus to the nominal stress–strain curve taken at 10% strain were reflected in the variability of a single parameter of the model. Given the success of the model, we desired to determine whether these outcomes are equally applicable to healthy human distal femoral cartilage so that a complete model of tibiofemoral joint cartilage can be developed. The transversely isotropic model was employed along with two other hyperelastic chain network models to determine which model best simulated unconfined compression data for healthy distal femoral cartilage. The transversely isotropic model fit the data excellently (R2=0.999). The model was subsequently simplified to depend on a single parameter and reapplied to the dataset. The modified model maintained an excellent fit to the data (R2=0.999), and its single parameter varied in a statistically similar regional pattern (p<0.05) to the experimentally-obtained elastic modulus of the tissue. Outcomes suggest that this model is suitable for modeling the spatially-varying, non-linear mechanics of healthy human distal femoral cartilage. Implementation of this constitutive relation within computational models of the knee will provide novel insight into the relationship between joint mechanics, cartilage loading, and knee osteoarthritis development.