Évaluation de modèles biphasiques linéaires pour la caractérisation mécanique de la plaque de croissance

ABSRACT: The growth plate is a cartilaginous tissue that has a time dependant mechanical behavior in creep or relaxation like a viscoelastic material. The growth plate's mechanical properties are generally obtained by using a biphasic poroelastic model to curve-t relaxation responses in Unconned Compression (UC) or Conned Compression (CC). According to the biphasic poroelastic models, the growth plate is a homogenous tissue. It is however composed of chondrocytes distributed within an extracellular matrix and has 3 histological zones: the reserve, the proliferative and the hypertrophic zones. Furthermore, the form, volume fraction and chondrocyte dispersion varies in each of the three histological zones. A recent study has shown that the horizontal orientation of the collagen bers within the reserve zone's extracellular matrix is dierent from that of the proliferative and hypertrophic zones. Each zone's mechanical behavior is similar to an isotropic transverse behavior as revealed by a biomechanics study. This study's rst objective was to evaluate the Biphasic PoroElastic model (BPE) for the reserve and proliferative zones' mechanical characterization and the Transversely Isotropic Biphasic PoroElastic model (TIBPE) for the reserve zone. The second objective was to verify if the apparent transversely isotropic behavior of the proliferative zone is related to its chondrocytes alignment. Random generation algorithms were developed in order to generate Finite Element Models (FEMs) representing the detailed microstructure of the reserve and proliferative zones. To evaluate the BPE, the reserve and proliferative zones detailed models had an extracellular matrix that obeyed the BPE whereas the evaluation of the TIBPE was conducted with reserve zone's detailed models with an extracellular matrix that obeyed the TIBPE. As a rst approximation, the chondrocytes were assumed isotropically linear elastic in all models. To obtain the reserve and proliferative zones eective mechanical behavior, Representative Volume Elements (RVEs) were dened for relaxation in both UC and CC. Axisymmetric models obeying the BPE were optimized to simultaneously curve-t the RVEs' responses in UC and CC for each zone which extracellular matrix behavior obeyed the BPE. In order to evaluate the TIBPE, an axisymmetric model obeying the TIBPE was optimized to simultaneously curve-t the reserve zone's RVEs' responses in UC and CC for an extracellular matrix obeying the TIBPE. The previously optimized axisymmetric model obeying the TIBPE was then used to predict the mechanical behavior of a RVE under a new mechanical loading.