Atsushi Hosokawa

Influences of Trabecular Structure on Ultrasonic Wave Propagation in Bovine Cancellous Bone

Ultrasonic wave propagation in water-saturated bovine cancellous (spongy) bone has been experimentally studied in vitro by a pulse transmission technique. The propagation of fast and slow longitudinal waves in bovine cancellous bone [rf:1] is examined in relation to porosity using Biots and Wyllies equations to estimate the measured speeds versus porosity. In the high porosity range, the trabecular structure influences the propagation of the fast and slow waves in cancellous bone.

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.

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.

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

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 6.45times6.45times6.45 mm with a voxel size of 64.5 mum are reconstructed using a 3-D microcomputed tomographic (muCT) image taken from a bovine cancellous bone specimen of approximately 20times20times9 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.

Numerical investigation of ultrasound refraction caused by oblique orientation of trabecular network in cancellous bone

Ultrasound propagation through cancellous bone can be greatly affected by the trabecular structure. In the present study, the ultrasound propagation for the oblique orientation of the trabecular network was numerically investigated using 3-D finite-difference time-domain (FDTD) simulations. The models of cancellous bone were reconstructed from X-ray microcomputed tomographic (μCT) images of a bovine bone. Cancellous bone models with various orientations of the trabecular network were realized by cutting the μCT images rotated from 0 to 90°. Ultrasound waveforms propagating through these cancellous bone models were simulated while changing the receiving position. The refraction of the ultrasound wave for the oblique angle of the main orientation was investigated on the basis of the variation in the arrival time and peak amplitude. As the propagation direction approached the direction parallel to the main orientation, the arrival time of the first peak became less and the peak amplitude became smaller. This means that the wave of the first peak, which corresponded to a fast wave, propagated in the direction perpendicular to the main orientation. In addition, a strong correlation between the first-peak amplitude and the arrival time was observed in the porosity range of 0.68 to 0.85, in which the slope of the amplitude with respect to time increased linearly with porosity.

Influence of Minor Trabecular Elements on Fast and Slow Wave Propagations through Cancellous Bone

Fast and slow longitudinal waves could propagate through cancellous bone in the direction parallel to the trabecular orientation; therefore, the major trabecular elements in the propagation direction are closely related to both the fast and slow wave propagations. To clarify in detail how the trabecular microstructure can be related to these waves, in this study, the influence of minor trabecular rods and pore spaces perpendicular to major trabecular plates was investigated using cancellous bone phantoms developed on the basis of a stratified model. In both experimental and simulated results, both waves were disturbed by trabecular rods and pore spaces. Moreover, it was investigated by simulation using realistic cancellous bone models via two erosion procedures whether the disturbance of both wave propagations due to minor trabecular elements could be induced in the real bone.

Effect of trabecular irregularity on fast and slow wave propagations through cancellous bone

Cancellous bone is composed of a porous network of trabeculae, with soft tissues (mostly bone marrow) in the pore spaces. The propagation phenomena of ultrasonic waves in cancellous bone largely depend on this complicated trabecular structure, and fast and slow longitudinal waves can propagate through cancellous bone in the direction parallel to the trabecular orientation. In a previous paper [A. Hosokawa: Jpn. J. Appl. Phys. 45 (2006) 4697], it was suggested that the irregularity in the trabecular structure could affect both the fast and slow wave propagations. To investigate the effect of trabecular irregularity in detail, in this study, the fast and slow wave propagations through cancellous bone were numerically simulated using the viscoelastic finite-difference time-domain (FDTD) method. The simulated results showed that the two waves could easily propagate through a regular trabecular structure. It was also shown that the porosity dependences of their propagation properties were closely related to trabecular irregularity.

Ultrasonic pulse waves propagating through cancellous bone phantoms with aligned pore spaces

To elucidate the propagation phenomena of ultrasonic waves in cancellous bone related to trabecular structure, pulse waves propagating through three cancellous bone phantoms with different skeletal frames have been experimentally observed using a water-immersion ultrasonic technique. Skeletal frames with regularly aligned pore spaces were formed to imitate the orthotropic trabecular structure, using wire gauzes, punched plates and honeycomb ceramics. The propagations of the fast and slow waves, which were clearly observed in the direction of the trabecular alignment of cancellous bone, were investigated with the frames structures of these phantoms.

A generalized harmonic analysis of ultrasound waves propagating in cancellous bone

Two longitudinal waves, called fast and slow waves, can be observed in ultrasound signals propagating through in vitro cancellous bone. From the propagation properties of both the fast and slow waves, an estimation of the bone status can be made. However, in in vivo measurements, a wide overlap of the fast and slow waves in the time domain is generally observed. In this study, a derivation of the characteristics of the fast and slow waves was attempted using a generalized harmonic analysis. From the results of this analysis, the times of the leading edges, frequencies, and amplitudes of the fast and slow waves were derived. These derived characteristics were scarcely influenced by the noise when the noise level was low. When the noise level was high, the derived frequencies and amplitudes were influenced by the noise, but the times of leading edges generally were not.

Numerical investigation of reflection properties of fast and slow longitudinal waves in cancellous bone: Variations with boundary medium

The purpose of this study is to numerically investigate the basic reflection properties of fast and slow longitudinal waves propagating in cancellous bone in the direction parallel to the strong orientation of the trabecular network. Finite-difference time-domain simulations with microcomputed tomographic models of bovine cancellous bone were performed to calculate the reflected waveforms at the boundary layers of 100–0% bones. The reflection coefficients of the fast and slow waves were derived by comparing with the waveform simulated for the cancellous bone model with an artificial absorbing boundary. For the fast wave, the reflection coefficients were positive at the boundaries of the 100 and 80% bone layers, but negative at the other boundaries. Moreover, the reflection coefficient at the 100% bone boundary increased with cancellous bone porosity. As the density of the boundary layer decreased, the porosity dependence became weaker, and the reflection coefficient at the 0% bone boundary was almost constant. For the slow wave, at the 100% bone boundary, the reflection coefficient increased with porosity but decreased at the other boundaries. These variations could be associated with the degrees of conversions between the fast and slow waves.