Simulation study of ultrasound propagation in anisotropic and heterogeneous cortical bone model

Ultrasound propagation in the heterogeneous long cortical bone was studied. First, ring shaped specimens were obtained from the mid-shaft of a bovine radius. The longitudinal wave velocity distribution of each specimen was measured in the MHz range. Then, using the bilinear interpolation and the piecewise cubic Hermite interpolating method, a 3D axial velocity model was created with the resolution of 40 μm. Assuming the uniaxial anisotropy of the bone,1,2 distributions of all elastic moduli of the initial 3D heterogeneous model were estimated. At the surface of the model, the elastic moduli were smaller than those of the inside parts. Elastic finite-difference time-domain method was used to simulate axial ultrasonic wave propagation in the model. The initial model and the thinner model, where the inner part of the cortical bone was removed, were compared. The wave front of the first arriving signal (FAS) depended on the heterogeneity in the model. However, the effects of removal on the arrival time of the FAS was not obvious. 1. Y. Yamato, et al. (2008). Calcif. Tissue Int. 82, 162-169. 2. T. Nakatsuji, et al. (2011). Jpn. J. Appl. Phys. 50, 07HF18.