Numerical analysis of variability in ultrasound propagation properties induced by trabecular microstructure in cancellous bone

Abstract

The manner by which the trabecular microstructure affects the propagation of ultrasound waves through cancellous bone is numerically investigated by finite difference time-domain (FDTD) simulation. Sixteen 3-D numerical models of 6.45 x 6.45 x 6.45 mm with a voxel size of 64.5 microm are reconstructed using a 3-D microcomputed tomographic (microCT) image taken from a bovine cancellous bone specimen of approximately 20 x 20 x 9 mm. All cancellous bone models have an oriented trabecular structure, and their trabecular elements are gradually eroded to increase the porosity using an image processing technique. Three erosion procedures are presented to realize various changes in the trabecular microstructure with increasing porosity. FDTD simulations of the ultrasound pulse waves propagating through the cancellous bone models at each eroded step are performed in 2 cases of the propagations parallel and perpendicular to the major trabecular orientation. The propagation properties of the wave amplitudes and propagation speeds are derived as a function of the porosity, and their variability due to the trabecular microstructure is revealed. To elucidate an effect of the microstructure, the mean intercept length (MIL), which is a microstructural parameter, is introduced, and the correlations of the propagation properties with the MILs of the trabecular elements and pore spaces are investigated.

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

“…To generate the trabecular structures with distinct porosity distributions (or variations), 3 erosion procedures using an image processing technique [10]- [12] were applied to the cancellous bone models. In erosion procedure I, the erosion of the trabecular elements, that is the transformations of the points from the trabecular to pore parts, was performed in macroscopically uniform at every position.…”

“…In all procedures, the weakly oriented trabecular elements were more largely eroded than the strongly oriented elements because, in the actual bone, the minor trabecular elements, to which large loads are not usually applied, firstly disappear with increasing the porosity (or progressing the condition of osteoporosis). Then, the weighted erosion procedure, which was the same with the procedure in [12], was used, and the trabecular elements in the y-direction of the weak trabecular orientation were mainly eroded. The erosion was continued until the averaged porosity over the whole region in the cancellous bone model decreased by 0.05 (5%).…”

“…A numerical model with a total region of 11.97 × 5.7 × 5.7 mm was used for FDTD simulation [12], [13] of ultrasound propagation through the cancellous bone model in the porositydistributed direction (or x-direction). In this simulation model, the transmitting and receiving flat surfaces with a diameter of 5.7 mm were placed on the y-z planes at x = 0 and 11.97 mm and water regions were set between each surface and the cancellous bone model.…”

“…The spatial interval was 57 μm and the time interval was 4 ns. Table I lists the physical parameter values of bovine cancellous bone used in the simulations (referred to [12], in which it was assumed that the pore spaces in the bone were filled with not water but bone marrow). A pulse waveform propagating through each of the eroded cancellous bone models was simulated, and the wave amplitude and propagation speed were measured.…”

The speed of sound through trabecular bone predicted by Biot theory

“…In recent studies, finite-difference time domain (FDTD) method have been employed for simulating two waves propagated in cancellous bone (Bossy et al, 2005;Hosokawa, 2010;Nagatani et al, 2006). The same as fabric tensor, the mean intercept length (MIL), is introduced, and the correlations of the propagation properties with the MILs of the trabecular elements and pore spaces are investigated (Hosokawa, 2009). Also using the same method, the attenuation for the fast and slow waves due to the pore fluid motion are observed (Hosokawa, 2005), which are also shown in Cowin and Cardoso (2011).…”