The effects of side-artifacts on the elastic modulus of trabecular bone

Determining accurate density-mechanical property relationships for trabecular bone is critical for correct characterization of this important structure-function relation. When testing any excised specimen of trabecular bone, an unavoidable experimental artifact originates from the sides of the specimen where peripheral trabeculae lose their vertical load-bearing capacity due to interruption of connectivity, a phenomenon denoted here as the 'side-artifact'. We sought in this study to quantify the magnitude of such side-artifact errors in modulus measurement and to do so as a function of the trabecular architecture and specimen size. Using parametric computational analysis of high-resolution micro-CT-based finite-element models of cores of elderly human vertebral trabecular bone, a specimen-specific correction factor for the side-artifact was quantified as the ratio of the side-artifact-free apparent modulus (Etrue) to the apparent modulus that would be measured in a typical experiment (Emeasured). We found that the width over which the peripheral trabeculae were mostly unloaded was between 0.19 and 0.58 mm. The side-artifact led to an underestimation error in Etrue of over 50% in some specimens, having a mean (+/-SD) of 27+/-11%. There was a trend for the correction factor to linearly increase as volume fraction decreased (p=0.001) and as mean trabecular separation increased (p<0.001). Further analysis indicated that the error increased substantially as specimen size decreased. Two methods used for correcting for the side-artifact were both successful in bringing Emeasured into statistical agreement with Etrue. These findings have important implications for the interpretation of almost all literature data on trabecular bone mechanical properties since they indicate that such properties need to be adjusted to eliminate the substantial effects of side-artifacts in order to provide more accurate estimates of in situ behavior.