An analysis of the effects of depth-dependent aggregate modulus on articular cartilage stress-relaxation behavior in compression

An accurate description of the mechanical environment around chondrocytes embedded within their dense extracellular matrix (ECM) is essential for the study of mechano-signal transduction mechanism(s) in explant experiments. New methods have been developed to determine the inhomogeneous strain distribution throughout the depth of the ECM during compression (Schinagl et al., 1996, Annals of Biomedical Engineering 24, 500–512; Schinagl et al 1997. Journal of Orthopaedics Research 15, 499–506) and the corresponding depth-dependent aggregate modulus distribution (Wang and Mow, 1998. Transactions of the Orthopaedics Research Society 23, 484; Chen and Sah, 1999. Transactions of the Orthopaedics Research Society 24, 635). These results provide the motivation for the current investigation to assess the influence of tissue inhomogeneity on the chondrocyte milieu in situ, e.g. stress, strain, fluid velocity and pressure fields within articular cartilage. To describe this inhomogeneity, we adopted the finite deformation biphasic constitutive law developed by Holmes and Mow (1990 Journal of Biomechanics 23, 1145–1156). Our calculations show that the mechanical environment inside an inhomogeneous tissue differs significantly from that inside a homogeneous tissue. Furthermore, our results indicate that the need to incorporate an inhomogeneous aggregate modulus, or an anisotropy, into the biphasic theory to describe articular cartilage depends largely on the motivation for the study.