Prediction of frequency-dependent ultrasonic backscatter in cancellous bone using statistical weak scattering model.

The goal of this study was to propose a model for the ultrasonic frequency-dependent backscatter coefficient in cancellous bone. This model allows us to address the inverse problem and to predict the mean trabecular thickness. A weak scattering model is used and the backscatter coefficient is expressed in terms of an autocorrelation function of the medium. Different autocorrelation functions (Gaussian, exponential and densely populated media) were used to compute the backscatter coefficient and comparison is made with experimental data for 19 specimens and for frequency ranging from 0.4 to 1.2 MHz. For each specimen, a nonlinear regression was performed and the mean trabecular thickness is estimated. Experimental data and theoretical predictions were averaged over the 19 specimens. A good agreement between experimental data and predictions was found for both the magnitude and the frequency-dependence of the backscatter coefficient. We also found a good agreement between the experimental mean trabecular thickness (Tb. Th = 130 +/- 6.5 micro m) derived from the analysis of bone 3-D microarchitecture using high-resolution microtomography and theoretical predictions (d(Gauss) = 140 +/- 10 micro m, d(exponential) = 153 +/- 12.5 micro m and d(dense) = 138 +/- 6.5 micro m). These results open interesting prospects for the estimation of the mean trabecular thickness from in vivo measurements.