Influence of viscoelasticity on the ultrasonic wave propagation in cortical bone: Application to the axial transmission technique.

Abstract

Cortical bone quality is assessed in clinical practice using axial transmission (AT) devices. Cortical bone and the surrounding soft tissues are attenuating media, which might affect the results obtained with AT devices. Following the work of in Haiat et al. [J. Acoust. Soc. Am. (2009)] which considers the elastic case, the aim of this work is to evaluate the effect of anisotropic heterogeneous dissipative phenomena occurring in bone and in soft tissues on the ultrasonic response of the bone structure. A two‐dimensional finite element time‐domain method is derived to model transient wave propagation in a three‐layer medium composed of an inhomogeneous transverse isotropic viscoelastic (Kelvin–Voigt description) solid layer sandwiched between two dissipative acoustic fluid layers. Bone viscoelasticity is assumed to be heterogeneous and a constant spatial gradient of viscoelastic properties is considered for two values of bone thicknesses corresponding to relatively thick and thin bones. The results allow the derivation of a contributing depth (CD) for a thick bone width. For a gradient of viscoelasticity, CD≅1.6 mm, for a gradient of C11, CD≅0.6 mm, and for a gradient of mass density, CD≅1 mm. [The Agence Nationale de la Recherche (Contract No. no BLAN06‐2 144779) is acknowledged.]