This work deals with the ultrasonic wave propagation in the cortical layer of long bones which is known as being a functionally-graded anisotropic material coupled with fluids. The motivation arises from mechanical modeling of the ultrasound axial transmission technique in vivo for cortical long bone which is known as being a functionally-graded anisotropic material. | Vietnam Journal of Mechanics, VAST, Vol. 33, No. 4 (2011), pp. 225 – 243 SIMULATION OF TRANSIENT ULTRASONIC WAVE PROPAGATION IN FLUID-LOADED HETEROGENEOUS CORTICAL BONE Vu Hieu Nguyen, Salah Naili Université Paris-Est, France Abstract. This work deals with the ultrasonic wave propagation in the cortical layer of long bones which is known as being a functionally-graded anisotropic material coupled with fluids. The motivation arises from mechanical modeling of the ultrasound axial transmission technique in vivo for cortical long bone which is known as being a functionally-graded anisotropic material. The proposed method is based on a combined Laplace-Fourier transform which substitutes a problem defined by partial differential equations into a system of differential equations established in the frequency-wavenumber domain. In the spectral domain, as radiation conditions may be exactly introduced in the infinite fluid halfspaces, only the heterogeneous solid layer needs to be analyzed using finite element method. Several numerical tests are presented showing very good performance of the proposed approach. Keywords: Spectral finite element, transient wave, ultrasound, anisotropic, vibroacoustic, cortical bone, axial transmission. 1. INTRODUCTION In recent years, quantitative ultrasound (QUS) has demonstrated its promising potential in assessment of in vivo bone characteristics. An advantage of QUS over X-ray techniques is its ability to give some information about the elastic properties and defects of bones. Moreover, ultrasound is non-ionizing and the ultrasonic apparatus is relatively inexpensive and can be made portable. For measuring in vivo properties of cortical long bones, a so-called "axial transmission" (AT) technique has been developed [1]. The axial transmission technique uses a set of ultrasonic transducers (transmitters and receivers) placed on a line in contact with the skin along the bone axial axis. The transmitter emits an ultrasound pulse wave .
