Effect of porosity distribution in the propagation direction on ultrasound waves through cancellous bone

Cancellous bone is a porous material composed of numerous trabecular elements, and its porosity changes according to its position within a bone. In this study, the effect of porosity distribution in the propagation direction on ultrasound waves through cancellous bone was numerically investigated using finite-difference time-domain (FDTD) simulations. Fifty-four numerical models of cancellous bone were reconstructed from 3-D X-ray microcomputed tomographic (μCT) images at 6 positions in a bovine femoral bone. To generate trabecular structures with distinct porosity distributions, 3 erosion procedures were performed in which the trabecular elements in each cancellous bone model were eroded. In one procedure, erosion was uniformly distributed over the whole spatial region of the cancellous bone model, but in the other 2 procedures, the spatial distribution of erosion was changed in a specific direction. Fast and slow waves propagating through the 3-D μCT cancellous bone models in the porosity-distributed direction were simulated using the viscoelastic FDTD method. The wave amplitudes and propagation speeds of the fast and slow waves were measured for the cancellous bone models eroded by each procedure, and the effect of porosity distribution was investigated in terms of change in the trabecular microstructure. The results suggest that both wave amplitudes increased when porosity distribution was low and when trabecular structure was more uniform, but that the speed of the fast wave increased when porosity distribution was high and when longer trabecular elements were present.