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

• Published in: International journal for numerical methods in biomedical engineering Vol. 33; no. 11
• Main Authors: Nakamachi, Eiji, Noma, Tomohiro, Nakahara, Kaito, Tomita, Yoshihiro, Morita, Yusuke
• Format: Journal Article
• Language: English
• Published: England Wiley Subscription Services, Inc 01.11.2017
• Subjects: Anisotropy; articular cartilage; Biomechanical Phenomena; Bioreactors; biphasic multiscale analysis; Cartilage; Cartilage (articular); Cartilage, Articular - anatomy & histology; Cartilage, Articular - physiology; chondrocyte; Chondrocytes; Chondrocytes - cytology; Collagen; Computational fluid dynamics; Elasticity; Fiber orientation; Finite Element Analysis; Finite element method; Fluid flow; Fluid mechanics; Humans; Hydrodynamics; hyperelastic constitutive law; Iron; Knee; Knee Joint - anatomy & histology; Knee Joint - physiology; Lubrication; Mathematical analysis; Mathematical models; Medical treatment; Metabolism; Microscopy - methods; Models, Biological; Multiscale analysis; Regeneration; Rigidity; Smooth particle hydrodynamics; smoothed particle hydrodynamics method; Stress; Stress, Mechanical; Stress-strain relationships; Stresses; Tissues; Viscous flow; Viscous fluids; Walking; articular cartilage; chondrocyte; finite element method; smoothed particle hydrodynamics method; biphasic multiscale analysis; hyperelastic constitutive law
• DOI: 10.1002/cnm.2864
• ISSN: 2040-7939; 2040-7947

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 a 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 bioreactor of articular cartilage. In this study, in both macroscale and microscale analyses, the dynamic explicit finite element (FE) method was used 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 for the microscale finite element model was derived by using the multiphoton microscope measured 3D structure comprising 3 different layers: surface, middle, and deep layers. The layers had different anisotropic structural and rigidity characteristics because of the collagen fiber orientation. In both macroscale and microscale FE analyses, the visco‐anisotropic hyperelastic constitutive law was used. Material properties were identified by experimentally determined stress‐strain relationships of 3 layers. With respect to the macroscale and microscale SPH models for non‐Newtonian viscous fluid, the previous observation results of interstitial fluid and proteoglycan were used to perform parameter identifications. Biphasic multiscale 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 bioreactor 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 bioreactor of articular cartilage regeneration as the knee joint disease treatment. We developed a biphasic multiscale analysis code to evaluate the stress occurred in the chondrocyte cell of articular cartilage to elucidate the metabolic activity for regeneration and the injury. We determined RVE for microscale FE models by using MPM measured results. We evaluated stresses in the chondrocyte caused by the normal compressive loading. Our numerical code can be applied for accurate stress evaluations by using more detail experimental results for material properties identification.