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

The hypothesis that trabecular morphology can predict the elastic propertie s of cancellous bone has only partly been verified and no predictive analyt ical model is currently available. Such models are becoming increasingly re levant as the resolution levels of three-dimensional scanning techniques ap proach the size of trabeculae, This study took advantage of micro-finite-el ement methods and tested the aforementioned hypothesis in normal cancellous bone material collected at six anatomical locations from 56 individuals. N umerical analysis was based on high-resolution three-dimensional computer r econstructions 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 tensor ial 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 forme r model, the MIL (mean intercept length measure) performed slightly better than the two volume-based measures, VO (volume orientation) and SVD (star v olume distribution), with 23% less remaining variance. The high correlation s found strongly support the hypothesis and increase the hope that, on the basis of information on trabecular morphology, it will be possible to obtai n considerably better estimates of bone quality in vivo compared with the r ough two-dimensional density measurements used today. (C) 1999 by Elsevier Science Inc. All rights reserved.