Ultrasonic wave propagation in cancellous and cortical bone: Prediction of some experimental results by Biot’s theory

Abstract

Pulse transmission ultrasound was used to determine the longitudinal wave speed along the direction of trabecular alignment in 32 water-saturated anisotropic tibial bovine cancellous bone samples and in one cortical bone sample also from the bovine tibia. These results are compared to published ultrasound wave-speed data obtained from bovine femoral specimens. Nonlinear regression was used to fit Biot's theory to the data. The correlation coefficient for regression analysis between the experimental ultrasound velocities and the velocities predicted by Biot's theory was r = 0.78.

Wave propagation in stereo-lithographical (STL) bone replicas at oblique incidence

“…Values of n 1 = 1.23 and n 2 = 2.35 are chosen by Lee et al [2] to be consistent with the work of Williams [16].…”

“…(2) for h =0°and 90°respectively with values deduced from air-filled replicas of known porosity [13]. Values of r and k are found by solving the resulting simultaneous equations.To allow for elastic anisotropy, Williams [16] suggests that the dependence of skeletal frame modulus (Young's modulus, E b , Bulk Modulus, K b , and rigidity modulus, l b ) in terms of bone volume fraction (1-u) and the Young's modulus of the solid material of the frame (E s ) are given…”

“…The elastic moduli of the bone replicas made of resin have been taken to be equal to the elastic modulus of resin which is 6.04 GPa (DSM Somos) and is smaller than the elastic modulus of real bone which is 20 GPa (Williams [16]). Assuming that the permeability of the bone is 5 Â 10 À9 m 3 (McKelvie and Palmer [9]), the permeability of bone replicas has been taken to be 169 (i.e.…”

A numerical study of ultrasonic response of random cortical bone plates

“…In recent years, the development of quantitative ultrasound methods (QUS) to asses mechanical behaviors of bone tissue is a key issue [1][2][3]. It has been shown that speed of sound (SOS) and broadband ultrasound attenuation (BUA) provided valuable information about bone structure in clinical assessment [4].…”

Fabric dependence of quasi-waves in anisotropic porous media

“…Isotropic poroelasticity theory has been used for many years to analyze wave propagation in cancellous bone (Williams, 1992;Otani, 1997, 1998;Haire and Langton, 1999;Kaczmarek et al, 2002;Fellah et al, 2004;Wear et al, 2005;Pakula et al, 2008;Fellah et al, 2008;Sebaa et al, 2008;Cardoso et al, 2008), and just recently the role of microarchitecture has been included in poroelasticity theory through the fabric tensor (Cowin and Cardoso, 2011). Most clinical ultrasound densitometers depend on empirical relationships between the speed of sound (SOS), broadband ultrasound attenuation (BUA), and bone density in order to assess bone loss.…”