Evaluation of hyperelastic models for the non-linear and non-uniform high strain-rate mechanics of tibial cartilage

Abstract

Accurate modeling of the high strain-rate response of healthy human knee cartilage is critical to investigating the mechanism(s) of knee osteoarthritis and other cartilage disorders. Osteoarthritis has been suggested to originate from regional shifts in joint loading during walking and other high strain-rate physical activities. Tibial plateau cartilage under compression rates analogous to walking exhibits a non-linear and location-dependent mechanical response. A constitutive model of cartilage that efficiently predicts the non-linear and non-uniform high strain-rate mechanics of tibial plateau cartilage is important for computational studies of osteoarthritis development. A transversely isotropic hyperelastic statistical chain model has been developed. The model's ability to simulate the 1-strain/s unconfined compression response of healthy human tibial plateau articular cartilage has been assessed, along with two other hyperelastic statistical chain models. The transversely isotropic model exhibited a superior fit to the non-linear stress–strain response of the cartilage. Furthermore, the model maintained its predictive capability after being reduced from four degrees of freedom to one. The remaining material constant of the model, which represented the local collagen density of the tissue, demonstrated a regional dependence in close agreement with physiological variations in collagen density and cartilage modulus in human knees. The transversely isotropic eight-chain network of freely jointed chains with a regionally-dependent material constant represents a novel and efficient approach for modeling the complex response of human tibial cartilage under high strain-rate compression. The anisotropy and microstructural variations of the cartilage matrix dictate the model's response, rendering it directly applicable to computational modeling of the human knee.