Microstructural simulation of ultrasonic wave propagation through vertebral bone samples

The use of ultrasound as an alternative diagnostic ldquoscreeningrdquo tool for osteoporosis has extensively been studied. One ultrasound parameter that has shown promise is the speed-of-sound (SOS) as it has been correlated experimentally to bone strength. Unfortunately, to date, a complete mechanical understanding of these findings is still missing. The aim of this study was therefore to look into the direction dependency of SOS, and the possibility to predict the microstructure starting from SOS. Fifteen human trabecular bone samples (4times4times4 mm
³
) from the lumbar spine were acquired; the samples had been scanned using micro-CT (resolution 14 micron) in order to obtain the 3D representation of their trabecular bone architecture. Three-dimensional numerical simulations were subsequently performed on all samples using a finite element (FE) approach (ANSYS, Inc) based on the general equations of motion. As such, SOS could be estimated. Additionally, the apparent elastic modulus E
_S
was calculated directly from the FE model. All simulations were performed at a frequency of 1 MHz in the three main directions of the bone sample (resulting in 45 simulations): anterior-posterior (AP), medio-lateral (ML) and cranio-caudal (CC). Two groups can be distinguished when the relationship between ES and SOS is studied. The first group contains the measurements in the CC direction. They display high velocity values and a wide range of elastic moduli. The calculations in the transverse directions (AP and ML) are situated in the second group. This group is characterized by low values of the structural elastic moduli and a wide range of velocities. The direction dependency of these results could be understood by a simple model of trabecular bone. For the lumbar spine, this simple model has main trabeculae in the CC direction and smaller struts, arranged randomly connecting the main trabeculae, in the AP and ML direction. The simulated velocity is the velocity of the fastest wave through the bone sample, i.e., the wave that covers the shortest distance through the trabeculae. From these results can be concluded that ultrasonic wave propagation is direction dependent and this dependency can help in the characterization of the strength of the trabecular bone.