Variations in reflection properties of fast and slow longitudinal waves in cancellous bone with boundary condition

Fast and slow longitudinal waves propagating in cancellous bone can reflect at the boundaries of the cortical bone and bone marrow layers, but the reflection properties of these waves have not significantly been clarified. The purpose of this study is to numerically investigate the variations in the reflection coefficients with the boundary condition. The reflected waveforms at normal incidence to the boundaries of a 100% bone (cortical bone) and a 0% bone (water) layers were simulated using a finite-difference time-domain (FDTD) method with microcomputed tomographic (μCT) models of bovine cancellous bone. The reflection coefficients were calculated by comparing with the simulated waveform for the model with an artificial absorbing boundary. The reflection coefficient of the fast wave increased with the cancellous bone porosity in the case of the 100% bone boundary but was almost constant in the case of the 0% bone boundary. On the other hand, the reflection coefficient of the slow wave increased slightly with the porosity in the case of the 100% bone boundary but decreased greatly in the case of the 0% bone boundary. It was considered that the reflection properties of the fast and slow waves could be affected by the conversions between these waves at the boundary.