Elastic Finite-difference Time-domain Method Research Articles

Effect of inconsistency of irradiation conditions of acoustic radiation force caused by tissue structure on shear wave velocity evaluation

Previous studies have shown that shear wave elastography of liver tissue can be unstable due to factors such as uncertainties in the acoustic radiation force (ARF) irradiation due to the influence of tissues near the surface and the complexity of the liver’s structure and its physical properties. This study aims to verify the influence of near-surface tissues on ARF and the effect of tissue structure on shear wave propagation and shear wave velocity (SWV) evaluation using wave propagation simulations by the elastic finite-difference time domain method. It is found that the ARF becomes weakly focused on multiple locations due to refraction of longitudinal waves by near-surface tissues, and multiple shear waves of small amplitude are propagated. However, a macroscopic SWV assessment, as in clinical practice, reduces the influence of near-surface tissues because the microscopic assessment results are averaged over the near-surface tissues.

Piezoelectric finite-difference time-domain simulations of piezoelectric signal generated in cancellous bone by ultrasound irradiation

Bone formation can be driven by mechanical loads applied to the bone. By taking advantage of this mechanism, the accelerated healing of bone fracture using low-intensity pulsed ultrasound (LIPUS) has been medically practiced. Bone can behave as a piezoelectric material, and the piezoelectric effects are considered to accompany the bone formation. However, the piezoelectric properties in bone, particularly in cancellous bone with a porous structure, at ultrasound frequencies are too complex to easily clarify. In such a case, numerical simulations can be helpful because they enable visualization in the "black box." Numerical simulations by an elastic finite-difference time-domain (FDTD) method have been widely performed to investigate ultrasound behaviors in bone. In this study, the elastic FDTD method with piezoelectric constitutive equations (PE-FDTD method) was used to simulate the piezoelectric signals generated in water-saturated cancellous bone by ultrasound irradiation. The cubic cancellous bone model was reconstructed from the x-ray microtomographic image. The piezoelectric signal waveforms when an ultrasound burst wave was irradiated in three orthogonal directions were calculated, together with the ultrasound signal waveforms propagated through cancellous bone. From the calculated results, the effect of the trabecular orientation was investigated.

Study on ultrasonic wave propagation in equine leg bone for screening bucked shin.

For simple, safe, portable, and inexpensive evaluation suitable for leg bone diseases of racehorses in the field, an ultrasonic measurement technique was applied to evaluate wave velocities. A digital model of the third metacarpal bone with the bucked shin was fabricated using high-resolution peripheral quantitative computerized tomography data of a racehorse. This model was anisotropic and heterogeneous, and was constructed using the measured ultrasonic wave velocities in the bone. With this model, ultrasonic wave propagation along the bone axis was simulated using the elastic finite-difference time-domain method. We found two main waves with different propagation velocities. The fast-waves showed a wave velocity close to the longitudinal wave in the axial direction. However, the apparent velocities changed dramatically owing to bone surface irregularities (changes of the shape) in the area of bucked shin. The slow-waves showed a wave velocity close to the shear wave, which was unaffected by the bone surface irregularities. The simple comparison of different wave behaviors may be a suitable parameter for the initial in vivo screening of bucked shin in the legs of racehorses, which can be performed in the field.

Verification of the influence of liver microstructure on the evaluation of shear wave velocity

Previous studies have shown that evaluation results of shear wave elastography were unstable due to factors such as liver structure and complexity of physical properties. The present study attempts to verify the influence of liver microstructure (fat droplets and fibrous tissue) on the shear wave and shear wave velocity (SWV) evaluation using a shear wave propagation simulation by the elastic finite-difference time-domain method. It was found that disruption of the shear wave causes variations in the SWV of the liver around fat droplets, and the SWV of the fibrous tissue depends on the shear wave propagation direction and the tissue shape. In a nonalcoholic steatohepatitis liver, which contains fat and fiber, the influences of these two tissues are synergistically reflected in the SWV evaluation.

Fast decomposition of two ultrasound longitudinal waves in cancellous bone using a phase rotation parameter for bone quality assessment: Simulation study

Ultrasound signals that pass through cancellous bone may be considered to consist of two longitudinal waves, which are called fast and slow waves. Accurate decomposition of these fast and slow waves is considered to be highly beneficial in determination of the characteristics of cancellous bone. In the present study, a fast decomposition method using a wave transfer function with a phase rotation parameter was applied to received signals that have passed through bovine bone specimens with various bone volume to total volume (BV/TV) ratios in a simulation study, where the elastic finite-difference time-domain method is used and the ultrasound wave propagated parallel to the bone axes. The proposed method succeeded to decompose both fast and slow waves accurately; the normalized residual intensity was less than -19.5 dB when the specimen thickness ranged from 4 to 7 mm and the BV/TV value ranged from 0.144 to 0.226. There was a strong relationship between the phase rotation value and the BV/TV value. The ratio of the peak envelope amplitude of the decomposed fast wave to that of the slow wave increased monotonically with increasing BV/TV ratio, indicating the high performance of the proposed method in estimation of the BV/TV value in cancellous bone.

Simulation study of axial ultrasound transmission in heterogeneous cortical bone model

Ultrasound propagation in a heterogeneous cortical bone was studied. Using a bovine radius, the longitudinal wave velocity distribution in the axial direction was experimentally measured in the MHz range. The bilinear interpolation and piecewise cubic Hermite interpolation methods were applied to create a three-dimensional (3D) precise velocity model of the bone using experimental data. By assuming the uniaxial anisotropy of the bone, the distributions of all elastic moduli of a 3D heterogeneous model were estimated. The elastic finite-difference time-domain method was used to simulate axial ultrasonic wave propagation. The wave propagation in the initial model was compared with that in the thinner model, where the inner part of the cortical bone model was removed. The wave front of the first arriving signal (FAS) slightly depended on the heterogeneity in each model. Owing to the decrease in bone thickness, the propagation behavior also changed and the FAS velocity clearly decreased.

Simulation study of axial ultrasonic wave propagation in heterogeneous bovine cortical bone.

The effect of the heterogeneity of the long cortical bone is an important factor when applying the axial transmission technique. In this study, the axial longitudinal wave velocity distributions in specimens from the mid-shaft of a bovine femur were measured, in the MHz range. Bilinear interpolation and the piecewise cubic Hermite interpolating polynomial method were used to construct three-dimensional (3D) axial velocity models with a resolution of 40 μm. By assuming the uniaxial anisotropy of the bone and using the results of previous experimental studies [Yamato, Matsukawa, Yanagitani, Yamazaki, Mizukawa, and Nagano (2008b). Calcified Tissue Int. 82, 162-169; Nakatsuji, Yamamoto, Suga, Yanagitani, Matsukawa, Yamazaki, and Matsuyama (2011). Jpn. J. Appl. Phys. 50, 07HF18], the distributions of all elastic moduli were estimated to obtain a 3D heterogeneous bone model and a uniform model. In the heterogeneous model, moduli at the surface were smaller than those inside the model. The elastic finite-difference time-domain method was used to simulate axial ultrasonic wave propagation in these models. In the heterogeneous model, the wavefront of the first arriving signal (FAS) was dependent on the heterogeneity, and the FAS velocity depended on the measured position. These phenomena were not observed in the uniform model.

Simulation study of ultrasound propagation in anisotropic and heterogeneous cortical bone model

Ultrasound propagation in the heterogeneous long cortical bone was studied. First, ring shaped specimens were obtained from the mid-shaft of a bovine radius. The longitudinal wave velocity distribution of each specimen was measured in the MHz range. Then, using the bilinear interpolation and the piecewise cubic Hermite interpolating method, a 3D axial velocity model was created with the resolution of 40 μm. Assuming the uniaxial anisotropy of the bone,1,2 distributions of all elastic moduli of the initial 3D heterogeneous model were estimated. At the surface of the model, the elastic moduli were smaller than those of the inside parts. Elastic finite-difference time-domain method was used to simulate axial ultrasonic wave propagation in the model. The initial model and the thinner model, where the inner part of the cortical bone was removed, were compared. The wave front of the first arriving signal (FAS) depended on the heterogeneity in the model. However, the effects of removal on the arrival time of the FAS was not obvious. 1. Y. Yamato, et al. (2008). Calcif. Tissue Int. 82, 162-169. 2. T. Nakatsuji, et al. (2011). Jpn. J. Appl. Phys. 50, 07HF18.

Finite-difference time-domain simulations of piezoelectric effect in bone under ultrasound irradiation

To understand the piezoelectricity in bone at ultrasound frequencies, numerical simulations of piezoelectric effect under ultrasound irradiation was performed using an elastic finite-difference time-domain method with piezoelectric constitutive equations (PE-FDTD method). First, the effect of piezoelectricity on ultrasound wave propagation in a piezoelectric material was investigated with consideration of conductivity. Ultrasound pulsed waveforms propagating through piezoelectric ceramics, whose piezoelectric parameter values were known, were investigated by the PE-FDTD simulations. In the simulated results, the ultrasound speed in the ceramics increased with piezoelectricity, and the ultrasound attenuation caused by the piezoelectricity increased with conductivity. The simulated waveforms were in good agreement with the experimental waveforms, which demonstrated the validity of the PE-FDTD simulations. Next, the piezoelectric effect on ultrasound wave propagation in cortical bone was simulated. The piezo...

Numerical simulation of piezoelectric effect of bone under ultrasound irradiation

The piezoelectric effect of bone under ultrasound irradiation was numerically simulated using an elastic finite-difference time-domain method with piezoelectric constitutive equations (PE-FDTD method). First, to demonstrate the validity of the PE-FDTD method, the ultrasound propagation in piezoelectric ceramics was simulated and then compared with the experimental results. The simulated and experimental waveforms propagating through the ceramics were in good agreement. Next, the piezoelectric effect of human cortical bone on the ultrasound propagation was investigated by PE-FDTD simulation. The simulated result showed that the difference between the waveforms propagating through the bone without and with piezoelectricity was negligible. Finally, the spatial distributions of the electric fields in a human femur induced by ultrasound irradiation were simulated. The electric fields were changed by a bone fracture, which depended on piezoelectric anisotropy. In conclusion, the PE-FDTD method is considered to be useful for investigating the piezoelectric effect of bone.

Simulation of ultrasound propagation through bovine cancellous bone using elastic and Biot’s finite-difference time-domain methods

The propagation of ultrasonic pulse waves in bovine cancellous bone has been numerically analyzed in two dimensions by using two finite-difference time-domain (FDTD) methods: the commonly used elastic FDTD method and an FDTD method extended with Biot's theory for a porous elastic solid saturated with viscous fluid. Both FDTD results were compared with the results of previous experiments by Hosokawa and Otani [J. Acoust. Soc. Am. 101, 558-562 (1997)], in which the Biot's fast and slow longitudinal waves were clearly identified. It was difficult to analyze both the fast and slow waves with the elastic FDTD method because of the inadequate 2D model of cancellous bone. On the other hand, in Biot's FDTD results that consider the pore fluid motion relative to the solid frame, both waves could be clearly observed. The experimental and simulated values of the speeds of these waves were in good agreement. Using the modified Biot's FDTD equations containing the possible attenuations for the fast wave other than the viscous loss due to the pore fluid motion, the amplitude ratio of the slow wave to the fast wave largely increased with the porosity, which also agrees with the experimental results.