The goal of this study is to model the frequency dependence of the ultrasonic backscatter coefficient in cancellous bone. A twofold theoretical approach has been adopted: the analytical theoretical model of Faran for spherical and cylindrical elastic scatterers, and the scattering model for weakly scattering medium in which the backscatter coefficient is related to the autocorrelation function of the propagating medium. The ultrasonic backscatter coefficient was measured in 19 bone specimens (human calcaneae) in the frequency range of 0.4-1.2 MHz. The autocorrelation function was computed from the three-dimensional (3D) microarchitecture measured using synchrotron radiation microtomography. Good agreement was found between the frequency dependence of the experimental (f3.38+/-0.31) and autocorrelation modeled (f3.48+/-0.26) backscatter coefficients. The results based on Faran theory (cylindrical Faran model: f2.89+/-0.06 and spherical Faran model: f3.91+/-0.04) show qualitative agreement with experimental data. The good prediction obtained by modeling the backscatter coefficient using the autocorrelation function of the medium opens interesting prospects for the investigation of the influence of bone microarchitecture on ultrasonic scattering.

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Abstruct-The acquisition and interpretation of in vivo ultrasonic measurements in tissue encounter problems associated with limited access to the region of interest, intermixed scattering structures with different characteristic dimensions, and systemdependent effects. This work addresses these problems by adapting and testing a technique for measuring the absolute attennation and the absolute backscatter coefficient (effective backscatter cross section per unit volume of material), as a function of frequency, in a single-transducer backscatter configuration. The frequency-dependent attenuation and backscatter coefficients of a tissue-mimicking gelatin phantom containing a random distribution of two populations of scatterers were measured. Three transducers with different center frequencies and focusing characteristics were used in order to verify that system-dependent effects were removed by the technique and to investigate the change in the measured parameters across a broad range of frequencies (2 to 60 MHz). A spherical autocorrelation model was applied to measurements of the backscatter coefficient in order to estimate the size of scatterers. Measurements demonstrate that the backscatter and attenuation properties of a mixture of two distinct intermixed scatterer-size populations change as a function of the frequency range across which the model is applied. Comparison of both the magnitude and the frequency dependence of the experimental results with the theoretical prediction of the backscatter coefficient showed good agreement.

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