Ultrasonic wave propagation in stereo-lithographical bone replicas.

Predictions of a modified anisotropic Biot-Allard theory are compared with measurements of pulses centered on 100 kHz and 1 MHz transmitted through water-saturated stereo-lithographical bone replicas. The replicas are 13 times larger than the original bone samples. Despite the expected effects of scattering, which is neglected in the theory, at 100 kHz the predicted and measured transmitted waveforms are similar. However, the magnitude of the leading negative edge of the waveform is overpredicted, and the trailing parts of the waveforms are not predicted well. At 1 MHz, although there are differences in amplitudes, the theory predicts that the transmitted waveform is almost a scaled version of that incident in conformity with the data.

Predictions of angle dependent tortuosity and elasticity effects on sound propagation in cancellous bone.

The anisotropic pore structure and elasticity of cancellous bone cause wave speeds and attenuation in cancellous bone to vary with angle. Previously published predictions of the variation in wave speed with angle are reviewed. Predictions that allow tortuosity to be angle dependent but assume isotropic elasticity compare well with available data on wave speeds at large angles but less well for small angles near the normal to the trabeculae. Claims for predictions that only include angle-dependence in elasticity are found to be misleading. Audio-frequency data obtained at audio-frequencies in air-filled bone replicas are used to derive an empirical expression for the angle-and porosity-dependence of tortuosity. Predictions that allow for either angle dependent tortuosity or angle dependent elasticity or both are compared with existing data for all angles and porosities.