No abstract

As a determinant of skeletal fragility, the organic matrix is responsible for the post-yield and creep behavior of bone and for its toughness, while the mineral apatite acts on stiffness. Specific to the fibula and ulna in children, greenstick fractures show a plastic in vivo mechanical behavior before bone fracture. During growth, the immature form of collagen enzymatic cross-links gradually decreases, to be replaced by the mature form until adolescence, subsequently remaining constant throughout adult life. However, the link between the cortical bone organic matrix and greenstick fractures in children remains to be explored. Here, we sought to determine: 1) whether plastic bending fractures can occur in vitro, by testing cortical bone samples from children's fibula and 2) whether the post-yield behavior (ωp plastic energy) of cortical bone before fracture is related to total quantity of the collagen matrix, or to the quantity of mature and immature enzymatic cross-links and the quantity of non-enzymatic cross-links. We used a two-step approach; first, a 3-point microbending device tested 22 fibula machined bone samples from 7 children and 3 elderly adults until fracture. Second, biochemical analysis by HPLC was performed on the sample fragments. When pooling two groups of donors, children and elderly adults, results show a rank correlation between total energy dissipated before fracture and age and a linear correlation between plastic energy dissipated before fracture and ratio of immature/mature cross-links. A collagen matrix with more immature cross-links (i.e. a higher immature/mature cross-link ratio) is more likely to plastically deform before fracture. We conclude that this ratio in the sub-nanostructure of the organic matrix in cortical bone from the fibula may go some way towards explaining the variance in post-yield behavior. From a clinical point of view, therefore, our results provide a potential explanation of the presence of greenstick fractures in children.

Finite-difference time domain (FDTD) numerical simulations coupled to real experimental data were used to investigate the propagation of 1 MHz pure bulk wave propagation through models of cortical bone microstructures. Bone microstructures were reconstructed from three-dimensional high resolution synchrotron radiation microcomputed tomography (SR-muCT) data sets. Because the bone matrix elastic properties were incompletely documented, several assumptions were made. Four built-in bone matrix models characterized by four different anisotropy ratios but the same Poisson's ratios were tested. Combining them with the reconstructed microstructures in the FDTD computations, effective stiffness coefficients were derived from simulated bulk-wave velocity measurements. For all the models, all the effective compression and shear bulk wave velocities were found to decrease when porosity increases. However, the trend was weaker in the axial direction compared to the transverse directions, contributing to the increase of the effective anisotropy. On the other hand, it was shown that the initial Poisson's ratio value may substantially affect the variations of the effective stiffness coefficients. The present study can be used to elaborate sophisticated macroscopic computational bone models incorporating realistic CT-based macroscopic bone structures and effective elastic properties derived from muCT-based FDTD simulations including the cortical porosity effect.