Finite-element modeling of trabecular bone: comparison with mechanical testing and determination of tissue modulus

We combined three techniques--mechanical testing, three-dimensional imaging, and finite-element modeling--to distinguish between the contributions of architecture and tissue modulus to mechanical function in human trabecular bone. The objectives of this study were 2-fold. The first was to assess the accuracy of micromechanical modeling of trabecular bone using high-contrast x-ray images of the trabecular architecture. The second was to combine finite-element calculations with mechanical testing to infer an average tissue modulus for the specimen. Specimens from five human L1 vertebrae were mechanically tested along the three anatomic axes. The specimens were then imaged by synchrotron x-ray tomography, and the elastic moduli of each specimen were calculated from the tomographic image by finite-element modeling. We found that 23-microm tomographic images resolved sufficient structural detail such that the calculated anisotropy in the elastic modulus was within the uncertainties of the experimental measurements in all cases. The tissue modulus of each specimen was then estimated by comparing the calculated mean stiffness of the specimen, averaged over the three anatomical directions, with the experimental measurement. The absolute values of the experimental elastic constants could be fitted, again within the uncertainties of the experimental measurements, by a single tissue modulus of 6.6 GPa, which was the average tissue modulus of the five specimens. These observations suggest that a combination of mechanical testing, three-dimensional imaging, and finite-element modeling might enable the physiological variations in tissue moduli to be determined as a function of age and gender.