Extraction and Comparative Analysis of the Intrinsic Mechanical Properties of Porcine Growth Plates at Four Developmental Stages [English translation]

Bone growth is a process regulated by hormones, nutrition, genetics and mechanical forces. When excessive, mechanical forces have key implications in the progression of infantile and juvenile musculoskeletal deformities, where marked progression is clinically observed during periods of rapid growth, notably, the juvenile and adolescent growth spurts. Longitudinal growth of long bones and vertebrae occurs in growth plates, which are divided into three distinct histological zones (reserve, proliferative and hypertrophic). Previous studies have investigated the biomechanical behaviour of growth plates and its histological zones, but no study has characterized the variation of this behaviour with developmental stage. 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 .5×10-3 s-1 until equilibrium; corresponding to relaxat ion criteria of 0.05 g/min. Experimental data obtained from t hese 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, E3), 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 propert ies (k1, E 1, ν21, ν31) was d one 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 f or 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). Statistical analyses were done in order to determine the variation of mechanical properties as a function of developmental st age and to determine if there were significant differences between stages for each property. Graphical analyses allowed for the determination of global trends regarding the variation of mechanical behaviour between stages, as well as the resulting significant differences. The results of this study indicate that intrinsic mechanical properties vary nonlinearly with developmental stage. Overall, flexibility and permeability increase, in conjunction w ith 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, g roup (a) is characterized by an increase in stiffness (E1, 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 correlatio n. 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 provide s good curve f its 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 mechanic al 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 we ll 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. Information on the weights and growth rates of the pigs used in the study at the different developmental stages would have been beneficial for this project . In addition, samples at more advanced growth stages, such as puberty and maturity, could not be obtained. In return, this is the first study to determine the variation of the biomechanical behaviour of growth plates as a function of developmental stage for the same animal and bone model . The results of the study provide information on the relationship between mechanical behaviour and the growth variations at certain developmental stages. 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. A future study with samples of the growth plate and its anatomical zones from later developmental stages, with parameters such as weight, growth rate and hormone concentr ation would allow for a more explicit characterization of the biomechanical sensitivity of growth plates as a function of developmental stage. The characterization of growth plate biomechanical behaviour during these periods is useful for the development o f new techniques and approaches in the treatment of progressive musculoskeletal deformities. Keywords: growth plate, unconfined compression, developmental stage, mechanical properties, transversely isotropic, biphasic model, differential evolution