Depth-Dependent Strain Calculations of Anisotropic Fibril Structures in Articular Cartilage

The mechanical response of articular cartilage (AC) under compression is anisotropic and depth-dependent. AC is osmotically active, and its intrinsic osmotic swelling pressure is balanced by its collagen fibril network. This mechanism requires the collagen fibers be under a state of tensile pre-strain. A simple mathematical model is used to describe collagen fibril mechanics in articular cartilage under 1D axial compression (perpendicular-to-surface direction). The collagen fibers are in pre-strain (swelling stress) which depends upon the concentration of proteoglycans (fixed charged density, FCD) as well as the intrinsic stiffness of collagen fibrils against swelling stress. The stiffness is introduced as an anisotropic modulus that varies with fibril orientation through the depth. The collagen fibers are stiffer to stretch parallel to their length than perpendicular to it; when combined with depth-varying FCD, the model successfully predicts the typical depth-dependent trends of zone-specific tissue strains and displacements (both decreasing with depth) in the loading direction. In general, the model supports the hypothesis that the mechanical properties of cartilage are not only dependent upon proteoglycans but also the pre-strained collagen fibril network, which is crucial for the mechanical functionality of articular cartilage