Simulations of ultrasound propagation in random arrangements of elliptic scatterers: Occurrence of two longitudinal waves

Abstract

Ultrasound propagation in clusters of elliptic (two-dimensional) or ellipsoidal (three-dimensional) scatterers randomly distributed in a fluid is investigated numerically. The essential motivation for the present work is to gain a better understanding of ultrasound propagation in trabecular bone. Bone microstructure exhibits structural anisotropy and multiple wave scattering. Some phenomena remain partially unexplained, such as the propagation of two longitudinal waves. The objective of this study was to shed more light on the occurrence of these two waves, using finite-difference simulations on a model medium simpler than bone. Slabs of anisotropic, scattering media were randomly generated. The coherent wave was obtained through spatial and ensemble-averaging of the transmitted wavefields. When varying relevant medium parameters, four of them appeared to play a significant role for the observation of two waves: (i) the solid fraction, (ii) the direction of propagation relatively to the scatterers orientation, (iii) the ability of scatterers to support shear waves, and (iv) a continuity of the solid matrix along the propagation. These observations are consistent with the hypothesis that fast waves are guided by the locally plate/bar-like solid matrix. If confirmed, this interpretation could significantly help developing approaches for a better understanding of trabecular bone micro-architecture using ultrasound.

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

“…We observed similar results, at least qualitatively, in 2D and in 3D. Four conditions were necessary to observe the two waves in our simple models: The first two points are consistent with previous observations 120 in real cancellous bone [11, chap.11], justifying a posteriori [23]. In the rest of the present article, the simulation of propagation along the main direction in a binary medium made of bone and water with a 50% solid fraction ( Fig.1a) will be referred to as the "reference simulation".…”

“…We now move to the case where two compressional waves 329 propagate. Previous work by our group showed that the two 330 waves could be observed in the case of an ultrasound propaga-331 tion along the main direction and for an appropriate range of 332 solid fraction, from 30% to 70% [23] (Fig.1) wave. Fig.4 shows the resulting attenuation coefficients and ve- For all three cases, ultrasound propagation was set perpendicular to the direction of anisotropy so that only one wave could be observed.…”

“…In the last ten years, numerical studies have been intensively used, both in real bone structures derived from X-ray computed tomography [19,20,21] or in numerically synthesized media [22]. Our approach here is based on the synthesis of numerical random and biphasic structures, previously described in [23]: elliptic (2D) or ellipsoidal (3D) scatterers were randomly distributed in a fluid to form a slab of random medium. In this previous work, we had qualitatively studied the occurrence of the fast and slow waves depending on simple statistical medium parameters using a finite-difference time-domain (FDTD) tool 1 to simulate the propagation of elastic waves.…”

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).…”

Ultrasound Transit Time Spectroscopy in Complex Media - Applications and Relationship with Phase Interference

“…Hosokawa & Otani, 1998). They concluded that the relative motion of the solid-fluid substance is the main reason for the observation of slow wave and this statement was numerically confirmed by Haiat et al (Haïat, Padilla, Peyrin, & Laugier, 2008) and by Meziere et al (Mézière, Muller, Dobigny, Bossy, & Derode, 2013). Nevertheless, one in-vivo experiment has been performed on trabecular bone at the distal end of the radius supporting the observation of the two longitudinal signals (Yamamoto et al, 2009).…”