3-D numerical simulations of wave propagation in trabecular bone predicts existence of the Biot fast compressional wave

Abstract

Trabecular bone is a poroelastic medium in which the propagation of two longitudinal waves (fast and slow) has been observed. The 3-D finite-difference time-domain simulations neglecting absorption coupled to 3-D microstructural models of 34 trabecular bone reconstructed from synchrotron radiation microtomography are shown to be suitable to predict both types of compressional wave in the three orthogonal directions. The influence of bone volume fraction (BV/TV) on the existence of the fast and slow waves was studied using a dedicated iterative image processing algorithm (dilation, erosion) in order to modify all 34 initial 3-D microstructures. An automatic criteria aiming at determining the existence of both wave modes was developed from the analysis of the transmitted signals in the frequency domain. For all samples, the fast wave disappears when bone volume fraction decreases. Both propagation modes were observed for BV/TV superior to a critical value for 2, 13, and 17 samples according to the direction of propagation. Above this critical value, the velocity of the fast (slow) wave increases (decreases) with BV/TV, consistent with Biot’s theoretical predictions. This critical value decreases when the degree of anisotropy increases, showing coupling between structural anisotropy and the existence of the fast wave.