Acoustic wave propagation in bovine cancellous bone is experimentally and theoretically investigated in the frequency range of 0.5-1 MHz. The phase velocity, attenuation coefficient, and broadband ultrasonic attenuation (BUA) of bovine cancellous bone are measured as functions of frequency and porosity. For theoretical estimation, the Modified Biot-Attenborough (MBA) model is employed with three new phenomenological parameters: the boundary condition, phase velocity, and impedance parameters. The MBA model is based on the idealization of cancellous bone as a nonrigid porous medium with circular cylindrical pores oriented normal to the surface. It is experimentally observed that the phase velocity is approximately nondispersive and the attenuation coefficient linearly increases with frequency. The MBA model predicts a slightly negative dispersion of phase velocity linearly with frequency and the nonlinear relationships of attenuation and BUA with porosity. The experimental results are in good agreement with the theoretical results estimated with the MBA model. It is expected that the MBA model can be usefully employed in the field of clinical bone assessment for the diagnosis of osteoporosis.
Correlations between acoustic properties and bone density were investigated in the 12 defatted bovine cancellous bone specimens in vitro. Speed of sound (SOS) and broadband ultrasonic attenuation (BUA) were measured in three different frequency bandwidths from 0.5 to 2 MHz using three matched pairs of transducers with the center frequencies of 1, 2.25, and 3.5 MHz. The relative orientation between ultrasonic beam and bone specimen was the mediolateral (ML) direction of the bovine tibia. SOS shows significant linear positive correlation with apparent density for all three pairs of transducers. However, BUA shows relatively weak correlation with apparent density. SOS and BUA are only weakly correlated with each other. The linear combination of SOS and BUA in a multiple regression model leads to a significant improvement in predicting apparent density. The correlations among SOS, BUA, and bone density can be effectively and clearly represented in the three-dimensional space by the multiple regression model. These results suggest that the frequency range up to 1.5 MHz and the multiple regression model in the three-dimensional space can be useful in the osteoporosis diagnosis.
This study aims to apply the modified Biot-Attenborough (MBA) model to predict the dependence of phase velocity on porosity in cancellous bone. The MBA model predicted that the phase velocity decreases nonlinearly with porosity. The optimum values for input parameters of the MBA model, such as compressional speed cm of solid bone and phase velocity parameter s2, were determined by comparing the prediction with the previously published measurements in human calcaneus and bovine cancellous bones. The value of the phase velocity parameter s2=1.23 was obtained by curve fitting to the experimental data only for 53 human calcaneus samples with a compressional speed cm=2500 m/s of solid bone. The root-mean-square error (rmse) of the curve fit was 15.3 m/s. The optimized value of s2 for all 75 cancellous bone samples (53 human and 22 bovine samples) was 1.42 with the rmse of 55 m/s. The latter fit was obtained by using cm=3200 m/s. Although the MBA model relies on empirical parameters determined from the experimental data, it is expected that the model can be usefully employed as a practical tool in the field of clinical ultrasonic bone assessment.
Bubble density was estimated with a subharmonic acoustic wave generated in bubbly water. The subharmonic acoustic wave can be easily generated due to the nonlinearity of bubbly water if the frequency of primary acoustic wave is double of the bubble resonance frequency and the driving acoustic pressure amplitude exceeds a certain threshold value. The frequency of primary acoustic wave was varied from 200 kHz to 500 kHz while the bubble resonance radius at subharmonic frequency was from 12 um to 28 um. The pressure level of the subharmonic acoustic wave linearly increased as the driving acoustic pressure amplitude increased. With the subharmonic pressure level, the bubble density was estimated from nonlinear bubble oscillation equation [Yu. A. Ilinskii and E. A. Zabolotskaya, J. Acoust. Soc. Am. 92, 2837–2841 (1992)]. The estimated bubble densities were also compared with those from a linear conventional acoustic bubble sizing method. Bubble sizing with subharmonic acoustic wave seems to be easily utilized for the diagnosis of sandy sediment with bubbles.
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