Numerical investigation of the frequency dependence of ultrasonic backscatter in trabecular bone

The goal of this study was 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 (1951) 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 calcaneus) in the frequency range of 0.4-1.2 MHz. The autocorrelation function was computed from the 3D microarchitecture measured using synchrotron radiation microtomography. Good agreement was found between the frequency dependence of the experimental (f^3.38±0.31) and autocorrelation modeled (f^3.48±0.26) backscatter coefficients. The results based on Faran theory (cylindrical Faran model: f^2.89±0.06 and spherical Faran model: f^3.91±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