FDTD simulations of ultrasonic wave propagation in the cortical bone with heterogeneity

Abstract

The ultrasonic axial transmission (AT) technique is known to assess the cortical bone of femur and tibia. After the first application of the finite difference time domain (FDTD) method [1], the wave propagation in bone has been discussed by both simulation and experimental studies. The wave propagation depends on the wave velocity, bone geometry (curvature, cortical thickness), anisotropy, heterogeneity, etc. In this study, we have investigated the ultrasonic wave propagation in the cortical bone with heterogeneity (stiffness distribution) by FDTD method. Using the stiffness distribution of bovine cortical bone, experimentally measured by Yamato and Nakatsuji [2], [3], wave propagation of one cycle of sinusoidal wave at 0.5~1 MHz was investigated, assuming cuboid samples. The wave velocities inside the bone were higher than those of the bone surfaces. The complex propagating waves were slightly concentrated at the bone surface. The results indicate that the stiffness distribution is also an important factor to understand the wave propagation. [1] E. Bossy et al., J. Acoust. Soc. Am. 115 , 2314 (2004). [2] Y. Yamato et al., Jpn. J. Appl. Phys. 47, 4096 (2008). [3] T. Nakatsuji et al., Jpn. J. Appl. Phys. 50, 07HF18 (2011).