Elastic Finite-difference Time-domain 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.

Numerical simulation and machine learning based analysis of the ultrasonic waveform propagating in bone tissue

Since bone has a complex structure, it is difficult to analytically understand the behavior of the ultrasound although it is useful for bone quality diagnosis. Our group, therefore, had been working on simulating ultrasound propagation inside bone models. In this paper, the results of the neural network based bone analysis using waveforms derived by the 3-D elastic FDTD (finite-difference time domain) simulation will be presented as well as its basis and some representative results of the FDTD method applied for the bone assessment. Since the FDTD simulation only requires the 3-D geometry of the model and the acoustic parameters (density, speed of longitudinal wave and shear wave) of the media, it has been very useful for evaluating each effect of a certain acoustic parameter or the bone geometry such as bone density, respectively, in addition to the purpose of visually understanding the wave behavior inside the model including the propagation path. Moreover, thanks to the recent powerful computational resource, it is now realized to prepare a huge number of waveforms for machine learning by using FDTD method. As a result, it was shown that the neural network can estimate the bone density better than the traditional method. (Grant: JSPS KAKENHI 16K01431.)

Numerical simulation of the ultrasonic propagation in bone tissue

Since bone has a complex structure, it is difficult to model analytically the behavior of ultrasound propagating in bone although ultrasound is useful for the diagnosis of not only bone density but also bone quality. Our group, therefore, had been working on simulating ultrasound propagation inside cancellous bones and models with cortical bones using actual mammal bones. In this paper, the basis and the results of the 3-D elastic FDTD (finite-difference time domain) method will be presented. The FDTD simulation only requires the 3-D geometry of the model and the distribution of acoustic parameters (density, speed of longitudinal wave, and shear wave) of the media such as bone and bone marrow, so that the effect of the each acoustic parameter or the geometry (e.g., BV/TV) can be easily investigated by changing these values. In addition, the effect of the frequency-dependent absorption caused by the viscosity and the piezoelectricity of bone also can be considered in the viscoelastic FDTD and the piezoelastic FDTD, respectively. The effects of these characteristics are not negligible. Moreover, thanks to the recent progress of the PC resource, a real-size simulation of human radius model is realized. Some preliminary data will also be presented. [JSPS KAKENHI 16K01431.]

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.

Study on coupled analysis for compact acoustic systems using finite-difference time-domain method based on Kirchhoff-Love plate theory and elastic wave

In this paper, we propose a coupled analysis method for compact acoustic systems (e.g., micro speakers, electret condenser microphones) using finite-difference time-domain (FDTD) method based on the Kirchhoff-Love plate theory and elastic wave. Acoustic systems are usually analyzed through any numerical analysis technique based on wave propagation. However, an exact frequency response is rarely obtained for compact acoustic systems. This is because the standard FDTD method cannot treat the change of the frequency response due to the air viscosity and cannot also treat the wave propagation in a solid. Thus, we cannot obtain exact frequency responses for compact acoustic systems through the analysis of coupled fluid-solid model based on standard FDTD method. In order to solve these problems, we utilize a coupled analysis method based on Kirchhoff-Love plate theory and elastic wave FDTD method considering air viscosity. The analysis method models diaphragm and voice coil as a two-dimensional plate model base...

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.

Propagation of two longitudinal waves in a cancellous bone with the closed pore boundary

Ultrasound propagation in cancellous bone (porous media) under the condition of closed pore boundaries was investigated. A cancellous bone and two plate-like cortical bones obtained from a racehorse were prepared. A water-immersion ultrasound technique in the MHz range and a three-dimensional elastic finite-difference time-domain (FDTD) method were used to investigate the waves. The experiments and simulations showed a clear separation of the incident longitudinal wave into fast and slow waves. The findings advance the evaluation of bones based on the two-wave phenomenon for in vivo assessment.

Numerical and experimental study on the wave attenuation in bone – FDTD simulation of ultrasound propagation in cancellous bone

In cancellous bone, longitudinal waves often separate into fast and slow waves depending on the alignment of bone trabeculae in the propagation path. This interesting phenomenon becomes an effective tool for the diagnosis of osteoporosis because wave propagation behavior depends on the bone structure. Since the fast wave mainly propagates in trabeculae, this wave is considered to reflect the structure of trabeculae. For a new diagnosis method using the information of this fast wave, therefore, it is necessary to understand the generation mechanism and propagation behavior precisely. In this study, the generation process of fast wave was examined by numerical simulations using elastic finite-difference time-domain (FDTD) method and experimental measurements. As simulation models, three-dimensional X-ray computer tomography (CT) data of actual bone samples were used. Simulation and experimental results showed that the attenuation of fast wave was always higher in the early state of propagation, and they gradually decreased as the wave propagated in bone. This phenomenon is supposed to come from the complicated propagating paths of fast waves in cancellous bone.

Effects of bone marrow on the ultrasonic propagation in the cancellous bone ‐ Comparative study on experiment and simulation

Longitudinal ultrasonic wave in cancellous bone separates into fast and slow waves depending on the bone structure. This phenomenon seems useful for the diagnosis of osteoporosis. In this study, we have investigated the influences of soft tissue (bone marrow) in the cancellous bone on the propagation of waves, in order to investigate the mechanism of this phenomenon. First, we have experimentally investigated the temperature dependence of longitudinal wave velocity and attenuation in bovine bone marrow, using a conventional ultrasonic pulse method. We used the ultrasonic wave at 1MHz. Then, we simulated the wave propagation in cancellous bone. For simulation, we used the 3 dimensional elastic FDTD (Finite Difference Time Domain) method. Here, we used the X‐ray CT pictures of actual cancellous bone obtained from the head of left bovine femur as the bone model. By changing the velocity and the attenuation values in the soft tissue among trabeculae from those of marrow to the water, we have found the changes in the waveforms of both fast and slow waves. This indicates the changes in both wave properties, due to the properties of soft tissue.

Estimation of received pulse from sea bottom with a transition layer using elastic finite difference time domain method

Recently, ocean acoustic thermometry is being planned in shallow water. Characteristics of sound propagation in shallow water are influenced by bottom media because sound propagation is affected by acoustic boundary conditions of the water-sediment interface. To investigate characteristics of sound propagation in shallow water, it is necessary to develop an accurate numerical method to model sound propagation. Elastic finite difference time domain method (elastic FDTD) is very accurate and is useful for range-dependent models in shallow water. Therefore, we calculate the sound waveform reflected from the sea bottom with a transition layer in shallow water using elastic FDTD. It is assumed that a 1.5-kHz transducer is placed at 50-m depth. The influence of the sea bottom with the transition layer is calculated for a 400-m range. To determine the influence of thickness of the transition layer to sound propagation, we calculate sound pulses as transition layers of varying thickness. Results show that fluctuation of the pulse amplitude depends on the transition layer thickness if the thickness is greater than one wavelength. A sea bottom with a transition layer clearly affects sound propagation in shallow water.

Simulation of fast and slow wave propagations through cancellous bone using three-dimensional elastic and Biot’s trabecular models

The propagation of ultrasonic pulse waves in cancellous (trabecular) bone was numerically simulated by using three-dimensional finite-difference time-domain (FDTD) methods. In previous research [A. Hosokawa, J. Acoust. Soc. Am. 118, 1782–1789 (2005)], two two-dimensional FDTD models, the commonly used elastic FDTD model and an FDTD model based on Biot’s theory for elastic wave propagation in an isotropic fluid-saturated porous medium, were used to simulate the fast and slow longitudinal waves propagating through cancellous bone in the direction parallel to the main trabecular orientation. In the present study, the extended three-dimensional viscoelastic and Biot’s anisotropic models were developed to investigate the effect of trabecular structure on the fast and slow wave propagations. Using the viscoelastic model of the trabecular frame comprised of numerous pore spaces in the solid bone, the effect of the trabecular irregularity, that is the scattering effect, on both the fast and slow waves could be investigated. The effect of the anisotropic viscous resistance of the fluid in the trabecular pore spaces on the slow wave could be considered using Biot’s anisotropic model.

Acoustic Defect-Mode Waveguides Fabricated in Sonic Crystal: Numerical Analyses by Elastic Finite-Difference Time-Domain Method

A novel acoustic waveguide composed of a line of single defects in a sonic crystal is shown to have desirable properties for acoustic circuits. The absence of a scatterer, i.e., a single defect or a point defect, in artificial crystals such as photonic crystals and phononic crystals leads to some localized resonant modes around the defect. Single defects in a sonic crystal made of acrylic resin cylinders in air are shown in this paper to have resonant modes or defect modes, which are excited successively to form a mode guided along a line of defects. Both a straight waveguide and a sharp bending waveguide composed of lines of single defects are shown equally to have a good transmission with small reflections at the inlet as well as at the outlet within the full band gap of the sonic crystal. Their advantages over conventional line-defect waveguides are clearly shown by their transmission versus frequency characteristics and also by typical examples of their spatial acoustic field distribution. On the basis of these properties, coupled defect-mode waveguides are investigated, and a high mode-coupling ratio is obtained. Defect-mode waveguides in a sonic crystal are expected to be desirable elements for functional acoustic circuits. The results of the elastic finite difference time domain (FDTD) method used as a tool of numerical calculation are also investigated and precisely compared with the experimental band gaps.

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.