Distribution of mesoscale elastic properties and mass density in the human femoral shaft

Abstract

Cortical bone properties are determined by tissue composition and structure at several hierarchical length scales. In this study, the spatial distribution of micro- and mesoscale elastic properties within a human femoral shaft has been investigated. Microscale tissue degree of mineralization (DMB), cortical vascular porosity Ct.Po and the average transverse isotropic stiffness tensor C^Micro of cylindrical-shaped samples (diameter: 4.4 mm, N = 56) were obtained from cortical regions between 20 and 85% of the total femur length and around the periphery (anterior, medial, posterior and lateral quadrants) by means of synchrotron radiation µCT (SRµCT) and 50-MHz scanning acoustic microscopy (SAM). Within each cylinder, the volumetric bone mineral density (vBMD) and the mesoscale stiffness tensor C^Meso were derived using a numerical homogenization approach. Moreover, microelastic maps of the axial elastic coefficient c₃₃ measured by SAM at distinct cross-sectional locations along the femur were used to construct a 3-D multiscale elastic model of the femoral shaft. Variations of vBMD (6.1%) were much lower than the variations of mesoscale elastic coefficients (11.1–21.3%). The variation of DMB was only a minor predictor for variations of the mesoscale elastic properties (0.05 ≤ R²≤ 0.34). Instead, variations of the mesoscale elastic properties could be explained by variations of cortical porosity and microscale elastic properties. These data were suitable inputs for numerical evaluations and may help to unravel the relations between structure and composition on the elastic function in cortical bone.

• Acoustic microscopy
• bone
• density
• elasticity
• homogenization
• microstructure
• porosity
• synchrotron radiation micro-CT

Declaration of interest

This work has been conducted within the European Associated Laboratory “Ultrasound Based Assessment of Bone” (ULAB) and was supported by the Deutsche Forschungsgemeinschaft (SPP 1420, grant Ra1380/7) and the ESFR Long Term Proposal MD239. All authors have no conflict of interest.