Transversely isotropic micromechanics model to determine effect of collagen fibre angle in mechanical properties of articular cartilage

Owing to a variation of collagen fibres orientation through the zones of articular cartilage, it shows a depth dependent transversely isotropic mechanical behaviour. This study characterised the role of collagen fibre angle toward cartilage surface phi on the mechanical properties of articular cartilage with an innovative micromechanics (multi-direction composite - MDC) model. The role of collagen fibres, their volume fraction as well as angle phi in all zones of articular cartilage, was embedded into the MDC model. Variation of collagen fibre angle toward the cartilage surface as a function of cartilage depth was calculated. According to this function, collagen fibres are parallel to cartilage surface in superficial zone, have a nonlinear angle variation in transition zone and become perpendicular to the cartilage surface in the deep zone. The results revealed that owing to constancy of the mechanical properties of articular cartilage components and slight variation of fibres volume fraction through the depth of cartilage, variations of collagen fibre angle phi has the most important role in depth dependent variation of the mechanical properties of the articular cartilage. As elastic modulus parallel to cartilage surface is decreased by increasing the fibre angle qua radial elastic modulus in superficial zone is 10.2 times greater than deep zone, but elastic modulus perpendicular to cartilage surface is increased by increasing the fibre angle qua axial elastic modulus in superficial zone is 28.3 times smaller than deep zone.