Constitutive relationships of fabric, density, and elastic properties in cancellous bone architecture

Abstract

The hypothesis that trabecular morphology can predict the elastic properties of cancellous bone has only partly been verified and no predictive analytical model is currently available. Such models are becoming increasingly relevant as the resolution levels of three-dimensional scanning techniques approach the size of trabeculae. This study took advantage of micro-finite-element methods and tested the aforementioned hypothesis in normal cancellous bone material collected at six anatomical locations from 56 individuals. Numerical analysis was based on high-resolution three-dimensional computer reconstructions of cancellous bone specimens from which the complete elastic characteristics and trabecular morphology, represented by three different fabric measures (the mean intercept length and two volume-based ones), were calculated. Each fabric measure was analyzed individually using the tensorial relationships derived by Cowin (Mech Mater 4:137-147; 1985). Models for both stiffness and compliance entries were developed. The models based on stiffness entries could explain 93.4%-95.6% of the variance, whereas those based on compliance entries could explain 89.2%-89.4%. When using the former model, the MIL (mean intercept length measure) performed slightly better than the two volume-based measures, VO (volume orientation) and SVD (star volume distribution), with 23% less remaining variance. The high correlations found strongly support the hypothesis and increase the hope that, on the basis of information on trabecular morphology, it will be possible to obtain considerably better estimates of bone quality in vivo compared with the rough two-dimensional density measurements used today. (Bone 25:481-486; 1999) © 1999 by Elsevier Science Inc. All rights reserved.

In Vivo Assessment of Architecture and Micro-Finite Element Analysis Derived Indices of Mechanical Properties of Trabecular Bone in the Radius

“…The measures of mechanical anisotropy and the shear moduli showed that the structural anisotropy measures such as MIL1/MIL3 improved the adjusted correlation coefficient significantly. These results in vivo are consistent with results seen in vitro by Ulrich et al [11] and Kabel et al [12]. Using higher-resolution mCT images of specimens of trabecular bone, both groups of investigators found improvements in the finite element derived mechanical properties with the inclusion of structural measures.…”

“…The directional mechanics of bone may potentially play an important role in predicting biomechanics, as has been shown in vitro [6,11,12], and hence these properties and their relative changes may be useful for fracture prediction and assessing response to therapy. In this study, using a stepwise multiple regression model, we found that App BV/TV clearly explained 73-83% of the variation in elastic moduli and shear moduli, but other measures of bone structure such as App TbSp and TbN increased the adjusted correlation coefficient with the mechanical measures.…”

Connectivity and the elastic properties of cancellous bone

“…2,3,29 Including anisotropy, however, the correlation improves the explanatory capacity further (up to 92%). 10,15,24,30,31,33 Evidently, these results suggest that the value of connectivity density as an additional explanatory variable might be rather limited.…”

Gracility of the modernHomo sapiensskeleton is the result of decreased biomechanical loading

“…The results of these studies suggest that relative trabecular bone volume in the axial skeleton and lower limbs is significantly lower in modern humans compared with quadrupeds, despite the legs and vertebral column bearing a higher proportion of body mass and peak substrate reaction forces during bipedal locomotion (25)(26)(27). The high positive correlation between BV/TV and bone material properties (28)(29)(30)(31)(32) suggests that trabecular bone in the human lower limb and vertebral column is less stiff than in other primates. Ongoing debates aimed at enhancing our understanding of bone adaptation, skeletal health, and the prevention and treatment of osteoporosis would be greatly enhanced by the determination of the primary factors underlying the relatively gracile skeleton of living humans.…”