Numerical investigation of reflection properties of fast and slow longitudinal waves in cancellous bone: Variations with boundary medium

Abstract

The purpose of this study is to numerically investigate the basic reflection properties of fast and slow longitudinal waves propagating in cancellous bone in the direction parallel to the strong orientation of the trabecular network. Finite-difference time-domain simulations with microcomputed tomographic models of bovine cancellous bone were performed to calculate the reflected waveforms at the boundary layers of 100–0% bones. The reflection coefficients of the fast and slow waves were derived by comparing with the waveform simulated for the cancellous bone model with an artificial absorbing boundary. For the fast wave, the reflection coefficients were positive at the boundaries of the 100 and 80% bone layers, but negative at the other boundaries. Moreover, the reflection coefficient at the 100% bone boundary increased with cancellous bone porosity. As the density of the boundary layer decreased, the porosity dependence became weaker, and the reflection coefficient at the 0% bone boundary was almost constant. For the slow wave, at the 100% bone boundary, the reflection coefficient increased with porosity but decreased at the other boundaries. These variations could be associated with the degrees of conversions between the fast and slow waves.