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

The goal of this study is to propose a model for the ultrasonic frequency-dependent backscatter coefficient in cancellous bone. A weak scattering model is used. It allows us to address the inverse problem and to predict the mean trabecular thickness. The backscatter coefficient is expressed in terms of an autocorrelation function of the medium. Comparison is made with experimental data for 19 specimens and for frequency ranging from 0.4 to 1.2 MHz. For each specimen a non-linear regression is performed and the mean trabecular thickness is estimated. Experimental data and theoretical predictions are 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 μm) derived from the analysis of bone 3-D micro-architecture using high resolution micro-tomography and theoretical predictions (d_Gauss = 140±10 μm, d_exponential=153±12.5 μm). These results open interesting prospects for the estimation of the mean trabecular thickness from in vivo measurements.