Measurements of attenuation and backscattering in trabecular bones over a large frequency range

In order to understand the propagation of ultrasound through trabecular bones, measurements of attenuation and backscattering coefficients were performed. Attenuation was measured on 14 human calcanei, over a large frequency bandwidth (0.2–1.7 MHz). The experimental attenuation coefficient values were modeled with a nonlinear power fit α(f)=a0+a1fn. The attenuation coefficient was found to increase as f1.09±0.3. A highly significant relationship was noted between a1 and BMD. No correlation was found between n and BMD. The backscatter coefficient was measured in 19 bones specimen in the frequency range 0.4–1.2 MHz. The experimental frequency dependence was found to be f3.4±0.3. A twofold theoretical approach was then adopted. The analytical model of Faran for spherical and cylindrical elastic cylinders showed a qualitative agreement with experimental data. A better agreement was found with a weak scattering medium model, where the backscatter coefficient is related to the autocorrelation function of the propagating medium. These results first open interesting prospects for the investigation of the influence of bone microarchitecture on ultrasonic scattering; second it seems to indicate that scattering is not the main mechanism of ultrasonic attenuation, because of the two different frequency dependencies, as confirmed by a numerical fit (absorption + scattering).