Characterization of human cancellous bone specimens in terms of Biot's theory

The goal of this study is to compare experimental ultrasonic results to the predictions of the macroscopic Biot's model of wave propagation in cancellous bones. Biot's model has been applied by a number of investigators with moderate success, mainly because of difficulty in the measurements of many input parameters of the model. In our study, both structural and mechanical properties of cancellous bone were measured or evaluated individually for each specimen and were used as input data for derivation of frequency dependent ultrasonic parameters (frequency-dependent attenuation coefficient and phase velocity), accordingly to Biot's theory. The experiments were performed on 31 human pure trabecular bone specimens taken from human proximal femurs. The phase velocity and attenuation coefficient of the first arriving signal were measured in the frequency range from 0.4 to 1.2 MHz. The most important findings are that Biot's predictions do not correlate well with ultrasonic experimental data. In particular, no velocity dispersion is predicted by Biot's theory, in contrast with experiments where positive or negative velocity dispersion has been found depending on the specimens. The values predicted for the attenuation coefficient are two orders of magnitude lower than measured values and the discrepancy between theory and experiments increases when the porosity decreases. Biot's theory assumes long wavelengths compared to the typical dimension of heterogeneities and therefore does not account for important physical interactions such as scattering which is known to be a major source of energy loss in cancellous bone. Another possible source of discrepancy is the essential anisotropy of bone architecture. Both scattering and anisotropy were not taken into account in the Biot's model and studies performed within this paper.