A review of morphology-elasticity relationships in human trabecular bone: theories and experiments

In the perspective of predicting mechanical from morphological properties of human trabecular bone, the theoretical and experimental relationships between volume fraction, fabric and elastic properties were reviewed.Five data sets of human trabecular bone and two data sets of idealized cells were obtained from various investigators and analyzed statistically with one isotropic and four anisotropic models. For each model, multiple linear regressions were performed to fit the components of both the compliance and the stiffness tensors using volume fraction and in some cases fabric. The adjusted coefficients of determination of the regressions and the average relative errors of the reported versus the predicted tensor norms were calculated. The three anisotropic models that implied a log transformation of the data showed the best results. Excluding the idealized cell data, the adjusted coefficients of determination of these models ranged from 0.80 to 0.95 for the compliance and from 0.80 to 0.94 for the stiffness tensors, while the average relative errors varied between 16% and 55% for the compliance and between 25% and 62% for the stiffness data. The use of volume fraction alone in the isotropic model decreased the adjusted coefficients of determination by 0.03-0.25 and increased the average relative errors by 5-27%. This review confirms the potential of morphology-elasticity relationships for estimation of elastic properties of human trabecular bone using peripheral quantitative computed tomography or magnetic resonance imaging, but emphasizes the need for standardized measurements of mechanical properties at both continuum and tissue level.