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

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-fit relaxation responses in Unconfined Compression (UC) or Confined 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 fibers within the reserve zone's extracellular matrix is different 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 first 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 first approximation, the chondrocytes were assumed isotropically linear elastic in all models. To obtain the reserve and proliferative zones effective mechanical behavior, Representative Volume Elements (RVEs) were defined for relaxation in both UC and CC. Axisymmetric models obeying the BPE were optimized to simultaneously curve-fit 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-fit 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.

Results showed that the BPE was not able to predict the mechanical behavior of the reserve and proliferative zones modeled with an extracellular matrix obeying the BPE and isotropically linear elastic chondrocytes. The results of the simultaneous curve-fitting with the TIBPE gave good results. However, the optimized TIBPE was not able to predict the mechanical behavior for another loading. When the proliferative zone was modeled with an extracellular matrix obeying the BPE, their responses was not like a transversely isotropic behavior.

The curve-fittings' results with the BPE and the TIBPE suggest that a new behavior law could be developed to predict the mechanical behavior of the growth plate. Moreover, the chondrocytes alignment in the proliferative zone can not explain the apparent transversely isotropic behavior of this zone, suggesting that this behavior is related to the collagen fibers' orientation. This study had some limitations. The principal limitations were that the extracellular matrix's permeability was considered constant, the small deformations formulation of the biphasic models were used and the chondrocytes were modeled as an isotropically linear elastic material. For the methodology, the user had to manipulate several files and different softwares to obtain the RVEs and the optimization process could be improved.