Simulation of fast and slow wave propagations through cancellous bone using three-dimensional elastic and Biot’s trabecular models

Abstract

The propagation of ultrasonic pulse waves in cancellous (trabecular) bone was numerically simulated by using three-dimensional finite-difference time-domain (FDTD) methods. In previous research [A. Hosokawa, J. Acoust. Soc. Am. 118, 1782–1789 (2005)], two two-dimensional FDTD models, the commonly used elastic FDTD model and an FDTD model based on Biot’s theory for elastic wave propagation in an isotropic fluid-saturated porous medium, were used to simulate the fast and slow longitudinal waves propagating through cancellous bone in the direction parallel to the main trabecular orientation. In the present study, the extended three-dimensional viscoelastic and Biot’s anisotropic models were developed to investigate the effect of trabecular structure on the fast and slow wave propagations. Using the viscoelastic model of the trabecular frame comprised of numerous pore spaces in the solid bone, the effect of the trabecular irregularity, that is the scattering effect, on both the fast and slow waves could be investigated. The effect of the anisotropic viscous resistance of the fluid in the trabecular pore spaces on the slow wave could be considered using Biot’s anisotropic model.