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Dependences of the attenuation and the backscatter coefficients on the frequency and the porosity in bovine trabecular bone: Application of the binary mixture model

The present study aims to investigate the dependences of the attenuation and the backscatter coefficients on the frequency and the porosity in bovine trabecular bone in vitro. The frequencydependent attenuation and backscatter coefficients were measured in 22 bovine femoral trabecular bone samples over a frequency range from 1.4 to 3.0 MHz by using a pair of transducers with a diameter of 12.7 mm and a center frequency of 2.25 MHz. The binary mixture model for ultrasonic scattering in trabecular bone, in which trabecular bone is assumed to be an isotropic binary mixture composed of a bone matrix and marrow, was applied to predict the measurements. The experimental results showed that the attenuation and the backscatter coefficients increased with increasing frequency from 1.4 to 3.0 MHz and decreased with increasing porosity from 66.9 to 91.5%. The predictions of the binary mixture model showed good agreements with the measurements, suggesting that scattering may be the dominant attenuation mechanism in dense bovine trabecular bone at frequencies from 1.4 to 3.0 MHz.