Multiphoton microscope measurement-based biphasic multiscale analyses of knee joint articular cartilage and chondrocyte by using visco-anisotropic hyperelastic finite element method and smoothed particle hydrodynamics method

Summary The articular cartilage of a knee joint has a variety of functions including dispersing stress and absorbing shock in the tissue, and lubricating the surface region of cartilage. The metabolic activity of chondrocytes under the cyclic mechanical stimulations regenerates the morphology and function of tissues. Hence, the stress evaluation of the chondrocyte is vital subject to assess the regeneration cycle in the normal walking condition, and predict the injury occurrence in the accidents. Further, the threshold determination of stress for the chondrocytes activation is valuable for development of regenerative bio-reactor of articular cartilage. In this study, in both macro- and micro-scale analyses, the dynamic-explicit finite element method was employed for the solid phase and the smoothed particle hydrodynamics (SPH) method was used for the fluid phase. In the homogenization procedure, the representative volume element (RVE) for the micro-scale finite element model was derived by using the Multi-Photon Microscope (MPM) measured 3D structure comprising three different layers: surface, middle, and deep layers. The layers had different anisotropic structural and rigidity characteristics because of the collagen fiber orientation. In both micro- and macro-scale FE analyses, the visco-anisotropic hyperelastic constitutive law was used. Material properties were identified by experimentally determined stress–strain relationships of three layers. With respect to the macro- and micro-scale SPH models for non-Newtonian viscous fluid, the previous observation results of interstitial fluid and proteoglycan were used to perform parameter identifications. Biphasic multi-scale FE and SPH analyses were conducted under normal walking conditions. Therefore, the hydrostatic and shear stresses occurring in the chondrocytes caused by the compressive load and shear viscous flow were evaluated. These stresses will be used to design an ex-vivo “bio-reactor” to regenerate the damaged articular cartilage, where chondrocytes are seeded in the culture chamber. To know the stress occurred on and in the chondrocytes is vitally important not only to understand the normal metabolic activity of the chondrocyte, but also to develop a bio-reactor of articular cartilage regeneration as the knee joint disease treatment.