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 ≤ R(2) ≤ 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.

Elasticity–density and viscoelasticity–density relationships at the tibia mid-diaphysis assessed from resonant ultrasound spectroscopy measurements

“…Simple homogenization models of cortical bone assuming a bone matrix with fixed properties and a cylindrical porosity of variable volume fraction (Granke et al 2011;Parnell et al 2012;Hellmich et al 2008) are consistent with this observation. However, there are evidences that the variation of elastic coefficients is not only due to the varying porosity only but also to variations of the stiffness of the bone matrix (Rho et al 2002;Granke et al 2011;Rohrbach et al 2015). The bone matrix should be less stiff (younger) and more porous when remodeling is more intense and stiffer and less porous when remodeling is less intense.…”

Associations between femoral 3D curvature and sagittal imbalance of spine

“…Studies showed that knee flexion is usually the later CMs and is more often recruited in prolonged and severe sagittal malalignment in subjects with severely degenerative spine when spinal and pelvic compensations are inadequate to restore proper postural balance 4,33–35 . The regional heterogeneity of femoral shaft nature was revealed by previous studies, where posterior region exhibited the highest porosity, smallest density, and lowest stiffness values 36 . Zhang et al discovered that femoral bowing was negatively associated with femoral cortical thickness and significantly increased in the aging process.…”

Estimation of Thickness and Speed of Sound in Cortical Bone Using Multifocus Pulse-Echo Ultrasound

“…To approve the in vivo feasibility of the multifocus imaging technique, the implementation of the aforementioned phase-aberration corrections, more sophisticated algorithms for the detection of the bone surface, eventually in combination with edge-enhancing image filters are required. Moreover, the method can only be applied with the imaging plane parallel to the plane of transverse isotropy, i.e., the radial direction perpendicular to the long bone axes [40]. Potential measurement regions are shaft regions, in which the cortical thickness is not much smaller than 1 mm, and the geometry is approximately plate-shaped, e.g., the medial portion of the tibia.…”