Simulation of Ultrasound Propagation Through Three-Dimensional Trabecular Bone Structures: Comparison with Experimental Data

We present a direct comparison between numerical simulation of wave propagation, performed through 28 volumes of trabecular bone, and the corresponding experimental data obtained on the same specimens. The volumes were reconstructed from high resolution synchrotron microtomography experiments and were used as the input geometry in a three-dimensional (3D) finite-difference simulation tool developed in our laboratory. The version of the simulation algorithm that was used accounts for propagation in both the saturating fluid and bone, and does not take absorption into account. This algorithm has been validated in a previous paper [Bossy et al.: Med. Biol. 50 (2005) 5545] for simulation of wave propagation through trabecular bone. Two quantitative ultrasound parameters were studied at 1 MHz for both simulated and experimental signals: the normalized slope of the frequency dependent attenuation coefficient (also called normalized broadband ultrasound attenuation (nBUA) in the medical field), and the phase velocity at the center frequency. We show that the simulated and experimental nBUA are in close agreement, especially for the high porosity specimens. For specimens with a low porosity (or a high solid volume fraction), the simulation systematically underestimate the experimentally observed nBUA. This result suggests that the relative contribution of scattering and absorption to nBUA may vary with the bone volume fraction. A linear relationship is found between experimental and simulated phase velocity. Simulated phase velocity is found to be slightly higher than the experimental one, but this may be explained by the choice of material properties used for the simulation.