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

Cancellous bone is a porous material composed of numerous trabecular elements and its porosity changes with position in the bone. In this study, the effect of the porosity distribution in the propagation direction on ultrasound waves through cancellous bone has been numerically investigated using finite difference time-domain (FDTD) simulations with three-dimensional (3-D) microcomputed tomographic (¿CT) models of bovine cancellous bone having an oriented trabecular structure. To generate the trabecular structures with distinct porosity distributions, 3 erosion procedures, in which the trabecular elements in each cancellous bone model were eroded, were used. In one procedure, the erosion was uniformly distributed in the whole spatial region of the cancellous bone model and, in the other procedures, the spatial distribution of the erosion was changed in the direction of the trabecular orientation. For ultrasound propagation in the porosity-distributed direction, pulse waveforms propagating through the 3-D ¿CT cancellous bone models were simulated by the viscoelastic FDTD method. The wave amplitude and propagation speed were measured for the cancellous bone models eroded by each procedure, and the effect of the porosity distribution was investigated with the trabecular structure.