Visco-Anisotropic Hyperelastic Finite Element Analysis of Knee Joint Considering Deformation Induced Anisotropy Evolution of Meniscus

Abstract

Recently, the observation technology of micro structure has made great progress, and then collagen fiber orientation of meniscus can be measured accurately. This makes it possible to evaluate the stress in knee joint by considering the collagen fiber orientations at the micro scale. In this study, we developed visco-isotropic/anisotropic hyperelastic constitutive equations (Iso-VHE/Aniso-VHE) for menisci, which can reflect the initial collagen fiber orientations and their deformation induced rotations. Subsequently, we constructed a finite element (FE) model of normal human knee joint by using the magnetic resonance (MR) tomography images. The FE analysis with the proposed constitutive equations and FE model clarifies the reinforcement effect of collagen fibers on mechanical characteristics of knee joint. Our computational prediction clarified that the stress concentration occurred on the contact parts of articular cartilages of femur and tibia, which met the tendency of the experimental results. Furthermore, the maximum compressive stresses evaluated by Aniso-VHE always showed a lower value as compared with Iso-VHE. This suggested that the anisotropy of meniscal collagen fibers relieved the stress concentration and lowered the maximum value. Therefore, our proposed FE analysis was proved to have a potential to reveal the functions of meniscus and knee joint.