The effect of the heterogeneity of the long cortical bone is an important factor when applying the axial transmission technique. In this study, the axial longitudinal wavevelocity distributions in specimens from the mid-shaft of a bovine femur were measured, in the MHz range. Bilinear interpolation and the piecewise cubic Hermite interpolating polynomial method were used to construct three-dimensional (3D) axial velocity models with a resolution of 40 μm. By assuming the uniaxial anisotropy of the bone and using the results of previous experimental studies [Yamato, Matsukawa, Yanagitani, Yamazaki, Mizukawa, and Nagano (2008b). Calcified Tissue Int. 82, 162–169; Nakatsuji, Yamamoto, Suga, Yanagitani, Matsukawa, Yamazaki, and Matsuyama (2011). Jpn. J. Appl. Phys. 50, 07HF18], the distributions of all elastic moduli were estimated to obtain a 3D heterogeneous bone model and a uniform model. In the heterogeneous model, moduli at the surface were smaller than those inside the model. The elasticfinite-difference time-domain method was used to simulate axial ultrasonicwave propagation in these models. In the heterogeneous model, the wavefront of the first arriving signal (FAS) was dependent on the heterogeneity, and the FAS velocity depended on the measured position. These phenomena were not observed in the uniform model.
