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

RÉSUMÉ: La plaque de croissance est un tissu cartilagineux dont le comportement mecanique en fluage ou en relaxation de contrainte est dependant du temps, tel celui d'un materiau visco elastique. Les proprietes mecaniques de la plaque de croissance sont generalement obtenues par le recalage de courbes d'essais de relaxation de contrainte en Compression Non Connee (CNC) ou Compression Connee (CC) avec un modele biphasique poroelastique. Cependant, les modeles biphasiques poroelastiques supposent que la plaque de croissance est un tissu homogene alors que ce tissu cartilagineux est compose de chondrocytes repartis dans une matrice extracellulaire et est histologiquement divisee selon trois zones, soit les zones de reserve, proliferative et hypertrophique. De plus, la forme, la fraction volumique et la dispersion des chondrocytes dierent entre chacune des trois zones histologiques. Une etude recente a permis d'observer que l'orientation horizontale des bres de collagene dans la matrice extracellulaire de la zone de reserve diere de celle dans les zones proliferative et hypertrophique. Une etude biomecanique revele egalement que le comportement mecanique de chaque zone s'apparente a un comportement isotrope transverse. La presente etude avait pour premier objectif d'evaluer le modele biphasique poroelastique (Biphasic PoroE- lastic model (BPE)) pour la caracterisation mecanique des zones de reserve et proliferative et le modele biphasique poroelastique isotrope transverse (Transversely Isotropic Biphasic PoroElastic model (TIBPE)) pour la zone de reserve. Le deuxieme objectif etait de verier si le comportement isotrope transverse apparent de la zone proliferative pouvait s'expliquer par l'organisation de ses chondrocytes. Des algorithmes de generation aleatoire ont d'abord ete developpes an de creer des Mod eles d'Elements Finis (MEFs) representant la microstructure detaillee de la zone de reserve et de la zone proliferative. Pour evaluer le BPE, les modeles detailles des zones de reserve et proliferative ont ete representes par une matrice extracellulaire obeissant au BPE alors que, pour evaluer le TIBPE, la matrice extracellulaire des modeles detailles de la zone de reserve obeissait au TIBPE. Les proprietes mecaniques de la matrice extracellulaire ont ete determinees a partir d'une etude de microindentation et d'une etude de caracterisation de la plaque de croissance et de ses trois zones. Comme premiere approximation, les chondrocytes ont ete representes par un comportement isotrope elastique lineaire dans tous les modeles. Les proprietes mecaniques des chondrocytes ont, de leur c^ote, ete determinees a partir d'etudes d'aspiration par micropipette.

Abstract

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.