Frequency variation of ultrasonic attenuation coefficient of cancellous bone between 0.2 and 2.0 MHz

The goal was to evaluate the frequency dependence of ultrasonic attenuation coefficient α(f) in cancellous bone and to compare it to site-matched measurements of bone mineral density (BMD). Estimates of α(f) were obtained in immersion, in the through-transmit mode, by scanning 14 human bone specimens (calcaneus), using successively 3 pairs of focused transducers with center frequency of 0.5, 1.0, and 2.25 MHz respectively in order to cover an extended frequency range from 0.2 to 2.0 MHz. Then, the attenuation coefficient was assumed to obey a simple power law α₀+α1fⁿ. The coefficients of the model were calculated using a non linear power fit least-squares calculations with respect to frequency over the 0.2-1.7 MHz bandwidth (resulting from the combination of the individual frequency bandwidth of each pair of transducers). The ultrasonic parameters n and α₁ were compared to site-matched BMD values measured using X-ray quantitative computed tomography. On the average, the attenuation coefficient was found to increase as f^1.1±0.3 (mean±SD). Although, n was on the average close to 1, the values ranged from 0.4 to 2.2. A highly significant relationship was noted between α₁ and BMD (r²=0.75, p<10^-4 ). No correlation was found between n and BMD. This frequency dependence of the attenuation coefficient has still to be validated by a theoretical model. However, these findings suggest the potential importance of additional parameters (besides the slope of the attenuation coefficient) for bone characterization