A depth dependent transversely isotropic micromechanic model of articular cartilage

Articular cartilage owing to the variation of collagen fibers orientation through its zones has been indicated to have depth dependent mechanical properties. The aim of this study was to present an innovative micromechanics model to predict the depth dependent mechanical properties of articular cartilage as a function of collagen fibers and proteoglycan matrix mechanical properties, collagen fibers volume fraction as well as angle toward cartilage surface. The variation of collagen fibers angle toward the cartilage surface as a function of cartilage depth was computed using the micromechanics model. This function showed that the collagen fibers parallel to the cartilage surface in the superficial zone have a nonlinear angle variation in the transition zone and become perpendicular to cartilage surface in the deep zone. Depth dependent elastic modulus in perpendicular to cartilage surface plane direction was calculated using presented micromechanics model and variation function of the collagen fibers' angle. The results revealed a suitable agreement with that of the experimental measurements in different samples at different ages and races (R-2 = 0.944). The results also showed that the elastic and aggregate modules perpendicular to the cartilage surface plane in the deep zone were 25.8 and 26.3 times higher than that of the superficial zone, respectively. These findings have implications not only for computing the depth dependent mechanical properties of any type of articular cartilage at different ages and races, but also of potential ability for developing a depth dependent transversely isotropic biphasic model to predict the accurate mechanical behavior of articular cartilage.