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.

In previous studies, two longitudinal waves, the fast and slow waves, were observed in cancellous bone. The propagation speed of the fast wave increases with bone density and that of the slow wave remains almost constant. The attenuation constant of the fast wave is much higher than that of the slow wave and is independent of bone density, but the attenuation constant of the slow wave increases with bone density. In the present study, experimental results on ultrasonic waves transmitted through cancellous bone show that the fast wave amplitude increases proportionally and the slow wave amplitude decreases inversely with bone density. The dependence of the fast wave amplitude on bone density cannot be explained by the attenuation constant. The ultrasonic wave propagation path through cancellous bone is modeled to specify the causality between ultrasonic wave parameters and bone density. Then bone density and bone elasticity are quantitatively formulated.

Ultrasonic waves in cancellous bone change dramatically depending on its structural complexity. One good example is the separation of an ultrasonic longitudinal wave into fast and slow waves during propagation. In this study, we examined fast wave propagation in cancellous bone obtained from the head of the bovine femur, taking the bone structure into consideration. We investigated the wave propagation perpendicular to the bone axis and found the two-wave phenomenon. By rotating the cylindrical cancellous bone specimen, changes in the fast wave speed due to the rotation angle then were observed. In addition to the ultrasonic evaluation, the structural anisotropy of each specimen was measured by X-ray micro-computed tomography (CT). From the CT images, we obtained the mean intercept length (MIL), degree of anisotropy (DA), and angle of insonification relative to the trabecular orientation. The ultrasonic and CT results showed that the fast wave speed was dependent on the structural anisotropy, especially on the trabecular orientation and length. The fast wave speeds always were higher for propagation parallel to the trabecular orientation. In addition, there was a strong correlation between the DA and the ratio between maximum and minimum speeds (V(max)/V(min)) (R(2) = 0.63).

We study the dynamics of a three-dimensional laser bullet propagating inside a nonlinear saturable medium. We show that an increase of the pump parameter destabilizes the bullet and leads to its destruction through oscillations with increasing amplitude. We propose an inhomogeneous and anisotropic external excitation mechanism leading to a stable oscillating bullet. By varying the frequency of the external excitation, a stable quasi-in-phase or quasi-antiphase internal state can be reached.