Frequency-dependent analysis of ultrasound apparent absorption coefficient in multiple scattering porous media: application to cortical bone.

The effect of matrix viscoelastic absorption on frequency-dependent attenuation in porous structures mimicking simplified cortical bone is addressed in this numerical study. An apparent absorption is defined to quantify the difference between total attenuation (resulting from both absorption and scattering) and attenuation exclusively due to scattering. A power-law model is then used to describe the frequency-dependent apparent absorption as a function of pore diameter and density. The frequency response of the studied porous structures to a Gaussian pulse is studied to determine the frequency range over which the system can be considered linear. The results show that for low scattering regimes (normalized frequency $<$ 0.80), the system and its apparent absorption can be considered linear. Hence, the total attenuation coefficient results from the summation of scattering and absorption coefficients. However, for highly scattering regimes, the system can no longer be considered linear and the apparent absorption vs. frequency deviates from a linear trend. As the pore density increases, the apparent absorption coefficient increases as well.