Extraction et analyse comparative des propriétés mécaniques intrinsèques des plaques de croissance porcines à quatre stades développementaux

The objective of this study is to extract the intrinsic mechanical properties of the porcine growth plate at four developmental stages in order to characterize the biomechanical sensitivity of growth plates as a function of developmental stage.

In previous experiments, porcine growth plate explants at four developmental stages (newborn, four, eight and 18 weeks) were tested in unconfined compression under stress relaxation. These explants were subjected to a deformation of 1.5x10^-3 s^-1 until equilibrium; corresponding to relaxation criteria of 0.05 g/min. Experimental data obtained from these experiments were modeled with a transversely isotropic biphasic mathematical model which is described by the transverse and out-of-plane permeabilities (k₁, k₃), Young‘s moduli (E₁, E ₃), and Poisson‘s ratios (ν₂₁, ν₃₁). The out-of-plane Young‘s modulus (E₃) was determined experimentally and the out-of-plane permeability (k₃) was not studied as it is only determined from confined compression. Extraction of the four remaining mechanical properties (k1, E₁, ν₂₁, ν ₃₁) was done by curve fitting experimental curves with this mathematical model using an optimization algorithm. In order to improve graphical correlation with experimental curves, a sensitivity study was done to determine the mechanical properties that have the greatest effect on the behaviour of this model, with the goal of potentially modifying the error function. A procedure to extract intrinsic mechanical properties was developed for curve fitting using a global optimization algorithm and a new error function based the relative error and the maximal stress. The criteria necessary for the use of this algorithm were determined though a rigorous process that evaluated their performance with analytical and experimental curves. Using this curve fitting procedure, mechanical properties were extracted for all samples, at all developmental ages method 1), as well as for the average experimental curve at each stage (method 2).

The results of this study indicate that intrinsic mechanical properties vary nonlinearly with developmental stage. Overall, flexibility and permeability increase, in conjunction with a continuous decrease in thickness of the complete growth plate. Marked differences observed at the four week stage lead to the separation of this stage into two distinct subgroups: (a) and (b). In contrast to global trends, group (a) is characterized by an increase in stiffness (E ₁, E₃) and a reduction in permeability (k₁) of the growth plate, a particularity which has yet to be explained. The curve fitting procedure developed for extracting mechanical properties provided very good graphical correlation. Method 1 shows that there are significant differences between developmental stages for the Young‘s moduli and transverse permeability. However, this method does not produce good curve fits with average experimental curves. Method 2 provides good curve fits and shows significant differences between developmental stages with respect to maximum and equilibrium stress, but it is not capable of discerning which properties are responsible for these differences. Consequently, both methods of extracting mechanical properties should be used, as considered separately, they do not provide a comprehensive analysis. Together, these two methods provide a complete representation of average mechanical behaviour and significant differences between mechanical stages, as well as the trends and differences for individual mechanical properties. The large variation of values obtained for permeability using the two extraction methods suggests that this property should be measured experimentally.

The hypothesis of the study, stating that the flexibility and permeability of the growth plate increases with developmental stage, due to a decrease in thickness of the reserve zone, characterized as the stiffest and largest zone at the newborn stage, is therefore partially confirmed. This global trend is observed, but one of the developmental stages shows the opposite. This observation shows that the mechanical behaviour of the growth plate is not constant and can change markedly depending on the stage attainted at the point in time. (Abstract shortened by UMI.)