Development of a numerical cancellous bone model for finite-difference time-domain simulations of ultrasound propagation

The trabecular frame in cancellous bone has numerous porous spaces of various sizes and shapes. Their continual arrangement changes with position in the bone. Assuming that the complicated pore space is the aggregation of spherical pores, in this study, the trabecular structure was analyzed using a three-dimensional (3-D) X-ray microcomputed tomography (muCT) image. Analysis involved a 3-D cancellous bone model developed for numerical simulations of ultrasound propagation. In this model, the trabecular structure was simplified by regularly arranging spherical pores in a solid bone. Using a viscoelastic, finite-difference, time-domain (FDTD) method with the simplified cancellous bone model, ultrasound pulse waveforms propagating through cancellous bone were simulated in two cases of the propagations parallel and perpendicular to the main trabecular orientation. The porosity dependences of the propagation properties, attenuation, and propagation speed were derived from the simulated waveforms. Comparisons with simulated results using the realistic cancellous bone model reconstructed from a 3-D muCT image, assisted to further validate this simplified model.