Measurements of ultrasound velocity and attenuation in numerical anisotropic porous media compared to Biot’s and multiple scattering models

Abstract

This article quantitatively investigates ultrasound propagation in numerical anisotropic porous media with finite-difference simulations in 3D. The propagation media consist of clusters of ellipsoidal scatterers randomly distributed in water, mimicking the anisotropic structure of cancellous bone. Velocities and attenuation coefficients of the ensemble-averaged transmitted wave (also known as the coherent wave) are measured in various configurations. As in real cancellous bone, one or two longitudinal modes emerge, depending on the micro-structure. The results are confronted with two standard theoretical approaches: Biot's theory, usually invoked in porous media, and the Independent Scattering Approximation (ISA), a classical first-order approach of multiple scattering theory. On the one hand, when only one longitudinal wave is observed, it is found that at porosities higher than 90% the ISA successfully predicts the attenuation coefficient (unlike Biot's theory), as well as the existence of negative dispersion. On the other hand, the ISA is not well suited to study two-wave propagation, unlike Biot's model, at least as far as wave speeds are concerned. No free fitting parameters were used for the application of Biot's theory. Finally we investigate the phase-shift between waves in the fluid and the solid structure, and compare them to Biot's predictions of in-phase and out-of-phase motions.

Ultrasonic evaluation of intact, healing and osteoporotic long bones

“…However, when only one longitudinal wave was observed and for porosities higher than 90%, the ISA successfully predicted the attenuation coefficient, as well as negative dispersion. This was not the case in the Biot's theory (Mézière et al 2014). …”

“…Then, this model was modified assuming a lattice structure of regularly-spaced parallel trabeculae, trabeculae positioned sufficiently randomly and trabeculae positioned quasi-periodically (Kitamura et al 1998, Kitamura et al 1996, Wear 1999, Ta et al 2008. In (Mézière et al 2014), 3D numerical models were developed representing clusters of ellipsoidal scatterers randomly distributed in water. Finite-difference simulations were performed to study ultrasonic propagation in anisotropic porous media.…”

An iterative fullwave simulation approach to multiple scattering in media with randomly distributed microbubbles

“…To predict the velocity using the ISA, we conducted a reference simulation with no scatterers and another simulation with a single scatterer (bubble) to calculate the normalized forward scattering intensity. From this, the effective wave number for a given volume fraction of scatterers can be evaluated (Mézière et al 2014), which gives access to the phase velocity and attenuation.…”

New perspectives in echographic diagnosis of osteoporosis on hip and spine

“…Consequently, it is quite difficult the proper interpretation of specific literature-reported studies that did not find a clear diagnostic value for calcaneal QUS devices (24,27). However, further work in this field is ongoing and interesting experimental studies aimed at elucidating the mentioned interaction mechanisms are being continuously published (65)(66)(67)(68)(69)(70). Although the most common QUS devices employ the described through transmission approach to provide parameters such as broadband US attenuation (BUA), speed of sound (SOS) and stiffness index (STI), some recent papers reported the potential of US backscatter as a new approach to osteoporosis diagnosis (34).…”