Hyperelastic constitutive modeling of healthy and enzymatically mediated degraded articular cartilage

This research demonstrates a systematic curve fitting approach for acquiring parametric values of hyperelastic constitutive models for both healthy and enzymatically mediated degenerated cartilage to facilitate finite element modeling of cartilage. Several widely used phenomenological hyperelastic constitutive models were tested to adequately capture the changes in cartilage mechanics that vary with the differential/unequal abundance of matrix metalloproteinases (MMPs). Trauma and physiological conditions result in an increased production of collagenases (MMP-1) and gelatinases (MMP-9), which impacts the load-bearing ability of cartilage by significantly deteriorating its extracellular matrix (ECM). The material parameters in the constitutive equation of each hyperelastic model are significant for developing a comprehensive computational interpretation of MMP mediated degenerated cartilage. Stress-strain responses obtained from indentation test were fitted with selected Ogden, polynomial, reduced polynomial, and van der Waals hyperelastic constitutive models by optimizing their adjustable parameters (material constants). The goodness of fit of the 2^nd order reduced polynomial and van der Waals model exhibited the closest data fitting with the experimental stress-strain distributions of healthy and degraded articular cartilage. The coefficient of the shear modulus for the 2^nd order reduced polynomial decreased gradually by 21.9% to 80.1% with more enzymatic degradation of collagen fibril due to the relative abundance of MMP-1 (collagenases), and 28.5% to 69.2% for the van der Waals model. Our findings showed that the major materials coefficients of the models were reduced in the degenerated cartilages, and the reduction varied differentially with the relative abundance of MMPs-1 and 9, correlating the severity of degeneration. This work advances the understanding of cartilage mechanics and offers insights into the impact of biochemical (enzymatic) effects on cartilage degradation.