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.