Numerical investigation of reflections of fast and slow longitudinal waves at a boundary between cancellous bone and cortical bone

As in vivo cancellous bone is generally surrounded by cortical bone, ultrasound waves propagating in the bone can reflect at the boundary of cortical bone. In this study, the ultrasound reflection properties were numerically investigated using finite-difference time-domain (FDTD) simulations with microcomputed tomographic (μCT) models of bovine cancellous bone. The reflected waveforms at normal incidence to the boundary surface between the cancellous bone and cortical bone layers were simulated. By comparing with the waveform in the case of an absorbing boundary, the reflection properties were derived. When the boundary surface was perpendicular to the main orientation of the trabecular network in cancellous bone, both reflections of the fast and slow longitudinal waves could be clearly observed. In the porosity range of 0.53-0.86, the reflection coefficients of the fast and slow waves increased linearly from 0.27 to 0.48 and from 0.49 to 0.65, respectively. When the boundary surface was parallel, only a single wave reflection was observed. The reflection coefficient increased linearly from 0.23 to 0.62, which was between the coefficients of the fast and slow waves.