Ultrasonic non-destructive characterization of trabecular bone: Experimental and theoretical prediction of the ultrasonic attenuation

The objective of this study is to model the attenuation of ultrasonic waves as they propagate through the trabecular bone. Trabecular bone is assumed to be constituted of a binary mixture of a bone matrix and a saturating fluid (marrow or water). The disturbances to which it is subjected are supposed to be of low amplitude. The attenuation due to absorption is determined by using the analytical model of Biot. The attenuation due to scattering, which is caused by solids trabeculae, is determined by means of the scattering model used in the case of soft biological tissues and formulated for binary mixtures with fluctuations of velocity and density. A qualitative and quantitative evaluation of the attenuation due to absorption and scattering is performed. Experimentally, the attenuation of ultrasound has been measured by transmission through 10 bone samples (resulting from the bovine femur bone, which has been defatted and saturated with water), with porosity ranges between 40% and 70%. These measurements have been done at a frequency range between 0.1 and 1.0 MHz. The model used in this study seems to give satisfactory results compared to experimental ones. These results show that the density fluctuations contribute significantly to the phenomenon of attenuation and cannot thus be neglected. This study also shows the important contribution of the scattering phenomenon to the ultrasonic attenuation process through the porous bones. It confirms the strong dependence of the attenuation with respect to the size of the scatterer, its porosity and the frequency. The accurate assessment of the ultrasonic attenuation through the trabecular bone allows predicting the bone pathology and particularly permits better diagnosis of bone fragility.