Comparison between independent and multiple scattering models to predict velocity dispersion in trabecular bone.

Abstract

Transverse transmission devices are used clinically to assess fracture risk. However, the physical interaction between trabecular bone and ultrasound remains unclear. Unlike most soft tissues, negative values of velocity dispersion have been measured in trabecular bone. The origin of negative dispersion is still a matter of debate. The aim of this paper is to propose a model predicting the frequency dependence of phase velocity as well as its physical determinants. A two‐dimensional homogenization model accounting for the coupling of independent scattering effects with viscoelastic absorption is employed to calculate the dependence of phase velocity on frequency, bone volume fraction (BV/TV), and trabecular thickness (TbTh). A simple biphasic description of TB in which the trabeculae are assumed to be identical and parallel cylinders are considered. The first step of the method is to compute the attenuation coefficient in the entire frequency range using a suitable decomposition via Bessel functions. Then, the Kramers–Kronig relationships are used to derive the frequency dependence of phase velocity. The results obtained assuming, independent scattering are compared with a model accounting for multiple scattering [Haiat et al., J. Acoust. Soc. Am. (2008)], which is shown to be in better agreement with experimental results obtained in the literature.