The Role of Microarchitecture on Absorption and Scattering of Ultrasound Waves in Trabecular Bone

Abstract

Biot's theory of wave propagation in porous media predicts the genesis of two waves -fast and slow- due to the in-phase and out of phase motion of the solid and fluid constituents of the porous medium. In Biot's theory, the loss of energy (attenuation) of both fast and slow waves is modeled to occur due to absorption and dispersion processes. However, Biot's approach does not take into account the effect of the pore microstructure on the elastic scattering of fast and slow waves. Scattering of elastic waves generally to the loss of energy associated to the change in direction of the wave ray as a consequence of inhomogeneities in the medium. The directionality of pore microarchitecture was recently introduced into the linear anisotropic poroelastic wave propagation theory (Cowin and Cardoso 2011, Cardoso and Cowin, 2011) using the fabric tensor -a quantitative stereological measure of the degree of structural anisotropy of bone. This recent approach thus allows investigating the relationship between the fabric tensor and directional-dependent attenuation of elastic waves in anisotropic porous media. In particular, the contribution of both absorption and scattering on the attenuation of the fast and slow waves in anisotropic porous media was investigated. The absorption and scattering attenuation processes are compared, finding the scattering to be the dominating mechanism of attenuation for ultrasound waves in the 1MHz range of frequency.