The acoustic properties of bovine cancellous (spongy) bone have been experimentally studied in vitro by the pulse transmission technique. Fast and slow longitudinal waves have been clearly identified when the acoustic wave propagates parallel to the direction of the trabeculae. Propagation speeds and attenuation of the fast and slow waves were observed in the frequency range of 0.5-5 MHz. Theoretical discussion is given to Biot's theory and the propagation of sound waves in fluid-saturated porous media.

This paper presents the experimental results on the acoustic anisotropy in bovine cancellous bone. The propagation of both fast and slow longitudinal waves in bovine cancellous bone was experimentally examined in relation to the structural anisotropy, or the trabecular arrangement. Propagation speeds of the fast and slow waves were measured as a function of the propagation angle to the trabecular alignment, and theoretically estimated by use of Biot's theory for an isotropic medium.

The propagation of ultrasonic pulse waves in bovine cancellous bone has been numerically analyzed in two dimensions by using two finite-difference time-domain (FDTD) methods: the commonly used elastic FDTD method and an FDTD method extended with Biot's theory for a porous elastic solid saturated with viscous fluid. Both FDTD results were compared with the results of previous experiments by Hosokawa and Otani [J. Acoust. Soc. Am. 101, 558-562 (1997)], in which the Biot's fast and slow longitudinal waves were clearly identified. It was difficult to analyze both the fast and slow waves with the elastic FDTD method because of the inadequate 2D model of cancellous bone. On the other hand, in Biot's FDTD results that consider the pore fluid motion relative to the solid frame, both waves could be clearly observed. The experimental and simulated values of the speeds of these waves were in good agreement. Using the modified Biot's FDTD equations containing the possible attenuations for the fast wave other than the viscous loss due to the pore fluid motion, the amplitude ratio of the slow wave to the fast wave largely increased with the porosity, which also agrees with the experimental results.

Ultrasonic wave propagation in water-saturated bovine cancellous (spongy) bone has been experimentally studied in vitro by a pulse transmission technique. The propagation of fast and slow longitudinal waves in bovine cancellous bone [rf:1] is examined in relation to porosity using Biot's and Wyllie's equations to estimate the measured speeds versus porosity. In the high porosity range, the trabecular structure influences the propagation of the fast and slow waves in cancellous bone.

The manner by which the trabecular microstructure affects the propagation of ultrasound waves through cancellous bone is numerically investigated by finite difference time-domain (FDTD) simulation. Sixteen 3-D numerical models of 6.45 x 6.45 x 6.45 mm with a voxel size of 64.5 microm are reconstructed using a 3-D microcomputed tomographic (microCT) image taken from a bovine cancellous bone specimen of approximately 20 x 20 x 9 mm. All cancellous bone models have an oriented trabecular structure, and their trabecular elements are gradually eroded to increase the porosity using an image processing technique. Three erosion procedures are presented to realize various changes in the trabecular microstructure with increasing porosity. FDTD simulations of the ultrasound pulse waves propagating through the cancellous bone models at each eroded step are performed in 2 cases of the propagations parallel and perpendicular to the major trabecular orientation. The propagation properties of the wave amplitudes and propagation speeds are derived as a function of the porosity, and their variability due to the trabecular microstructure is revealed. To elucidate an effect of the microstructure, the mean intercept length (MIL), which is a microstructural parameter, is introduced, and the correlations of the propagation properties with the MILs of the trabecular elements and pore spaces are investigated.