## 3 Biomechanics of Articular Cartilage
### Mechanical Properties of Articular Cartilage  
AC is a biphasic tissue characterised by a complex layered structure in which the mechanical behaviour depends on the distribution of collagen, proteoglycans and water. In their work, [PERSON] et al. [51] consider the following key mechanical parameters of AC: aggregate modulus, Young's modulus in compression and tension, and Poisson's ratio. The aggregate modulus (H\({}_{\text{A}}\)) is a parameter describing the stiffness of the AC in mechanical equilibrium during compression, when all the load is carried by the solid matrix and the SF flow ceases [51]. This is a key parameter in two- or three-phase AC models, reflecting tissue resistance to volume deformation [122]. For a healthy AC, the values of this parameter range from 0.1 to 2.0 MPa, while the values can increase with the depth of the AC [165]. The high H\({}_{\text{A}}\) value is related to the high concentration of proteoglycans and negative charges, which, by retaining water, increase the resistance to compression [120]. The compressive Young's modulus (E\({}_{\text{C}}\)) is a parameter that determines the linear elasticity of AC under compressive loading, which can be determined from indentation tests or uniaxial compression tests [124]. The value of this parameter depends on factors such as the water content, collagen structure and layer depth, as the surface layer shows greater deformability than the deep layers [169]. The tensile Young's modulus (E\({}_{\text{t}}\)) shows higher values than in compression, as the network of collagen fibres plays a key role in tension [153]. Depending on the layer and the direction relative to the collagen system, the values of this parameter can be in the range of 5-25 MPa at equilibrium [170]. It has been shown that E\({}_{\text{t}}\) values can be more than twice as high in the direction following the fibre orientation as opposed to the perpendicular direction [171]. The values of this parameter decrease with age or during the progression of degenerative diseases [154]. The parameter describing the lateral expansion of tissue under compression or stretching in AC is the Poisson's ratio (v) [172]. The Poisson's ratio is a reflection of the deformation capacity of the AC in response to mechanical loads. Changes in the value of this parameter can be related to degenerative processes. During the course of osteoarthritis of the joint, there is a reduction in elasticity and impaired SF flow, which has a direct impact on \(\upsilon\). Hydraulic permeability (\(k\)) is a parameter describing the ability of AC to allow SF to pass through its porous structure under the action of a pressure gradient [173]. [PERSON] et al. [173] used indentation tests under creep conditions to determine \(k\), obtaining values in the range of 0.44 \(\times\) 10\({}^{-15}\) m\({}^{4}\)/N\(\cdot\)s. for femoral condyle cartilage, to 1.42 \(\times\) 10\({}^{-15}\) m\({}^{4}\)/N\(\cdot\)s for patellar sulcus cartilage. Tensile strength is a parameter referring to the maximum stress the AC is capable of withstanding before breaking in tension [154]. [PERSON] et al. [154] used bovine cartilage in their study and showed that tensile strength increases with age in the deeper layers but decreases in the superficial layers. To determine the elasticity of AC in equilibrium during tension, the equilibrium tensile modulus (E\({}_{\text{eq}}\)) is used. [PERSON] et al. [174] showed a significant increase in this parameter with age, which is influenced by the increased collagen content and its cross-linking. The composite shear modulus (G) is used to characterise the response of AC to shear loads in the dynamic range, taking into account elastic and viscous components. Oscillatory shear tests were used in the studies by [PERSON] et al. [175], which showed the sensitivity of this parameter to changes in the structure of the extracellular matrix, especially to the degradation of proteoglycans. Equilibrium shear modulus (G\({}_{\text{eq}}\)) refers to the elasticity of AC in response to long-term shear loading.