Ultrasonic pulse waves in cancellous bone analyzed by finite-difference time-domain methods

The trabecular frame of cancellous bone has a high degree of porosity, anisotropy and inhomogeneity. The propagation of ultrasonic waves in cancellous bone is significantly affected by the trabecular structure. In this paper, two two-dimensional finite-difference time-domain (FDTD) methods, which were the popular viscoelastic FDTD method for a viscoelastic medium and Biot's FDTD method for a fluid-saturated porous medium, have been applied to numerically analyze the ultrasonic pulse waves propagating through bovine cancellous bone in the directions parallel and perpendicular to the trabecular alignment. The Biot's fast and slow longitudinal waves, which were identified in previous experiments for the propagation parallel to the trabecular orientation, could be analyzed using Biot's FDTD method rather than the viscoelastic FDTD method. For the single wave propagation in the perpendicular direction, on the other hand, the viscoelastic FDTD result was found to be in more good agreement with the experimental result.     

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.     

Non-iterative bi-directional wave propagation method for treating reflections

We describe a bi-directional wave propagation method based on the split-step non-paraxial collocation method. The method is non-iterative and does not require any matrix inversion or diagonalization. The method is applied to reflections from waveguide discontinuities, terminations as well as multilayer reflecting structures. The results obtained compare very well with those obtained using computationally intensive methods such as the finite element method (FEM) and the finite-difference time-domain (FDTD) method.     

In vitro estimation of fast and slow wave parameters of thin trabecular bone using space-alternating generalized expectation-maximization algorithm

In testing cancellous bone using ultrasound, two types of longitudinal Biot’s waves are observed in the received signal. These are known as fast and slow waves and their appearance depend on the alignment of bone trabeculae in the propagation path and the thickness of the specimen under test (SUT). They can be used as an effective tool for the diagnosis of osteoporosis because wave propagation behavior depends on the bone structure. However, the identification of these waves in the received signal can be difficult to achieve.In this study, ultrasonic wave propagation in a 4 mm thick bovine cancellous bone in the direction parallel to the trabecular alignment is considered. The observed Biot’s fast and slow longitudinal waves are superimposed; which makes it difficult to extract any information from the received signal. These two waves can be separated using the space alternating generalized expectation maximization (SAGE) algorithm. The latter has been used mainly in speech processing.In this new approach, parameters such as, arrival time, center frequency, bandwidth, amplitude, phase and velocity of each wave are estimated. The B-Scan images and its associated A-scans obtained through simulations using Biot’s finite-difference time-domain (FDTD) method are validated experimentally using a thin bone sample obtained from the femoral-head of a 30 months old bovine.     

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.     

二次变换法估计骨小梁的间距

平均骨小梁间距作为松质骨微结构的重要表征参数,其值可作为诊断骨质疏松的重要参考信息。提出将二次变换法运用于骨小梁间距的估算,探究其运用于骨小梁间距估算的可行性。通过散射元仿真、时域有限差分法仿真和离体松质骨实验所得到松质骨背散射信号进行分析,同时以自回归倒谱法(AR倒谱法)、反向滤波-自回归倒谱法(反向滤波-AR倒谱法)、自适应滤波-自回归倒谱法(自适应滤波-AR倒谱法)和简易反向滤波跟踪(SIFT)算法作为对比方法进行分析,通过对比证明了其可行性和相比于其他方法的优越性。结果表明,不管是利用仿真实验还是牛胫骨的离体实验所得信号估算骨小梁间距,二次变换法比其他算法具有更强的测量稳定性和准确性。      

Investigation of the effects of tensile strain on optical properties of ZnO nanowire

In this paper, the effects of mechanical tensile strain on optical properties of ZnO nanowire before and after embedding ZnS nanowire were investigated by simulation. Finite element modeling (FEM) software package ABAQUS and three-dimensional (3D) finite-difference time-domain (FDTD) methods were furnished to analyze the problems numerically, including the nonlinear mechanical behavior and optical properties of the sample, respectively. The physical deformation model was imported into the FDTD to investigate optical properties of ZnO nanowire under mechanical tensile strain. Besides, the stress-strain curve via tensile experimental was compared with stress-strain curve that was obtained from finite element modeling. The results disclosed that the mechanical strain was demonstrated to play an important role in determining the optical properties of ZnO nanowire such as absorption coefficient and optical density.     

A hybrid FDTD-Rayleigh integral computational method for the simulation of the ultrasound measurement of proximal femur

The development of novel quantitative ultrasound (QUS) techniques to measure the hip is critically dependent on the possibility to simulate the ultrasound propagation. One specificity of hip QUS is that ultrasounds propagate through a large thickness of soft tissue, which can be modeled by a homogeneous fluid in a first approach. Finite difference time domain (FDTD) algorithms have been widely used to simulate QUS measurements but they are not adapted to simulate ultrasonic propagation over long distances in homogeneous media. In this paper, an hybrid numerical method is presented to simulate hip QUS measurements. A two-dimensional FDTD simulation in the vicinity of the bone is coupled to the semi-analytic calculation of the Rayleigh integral to compute the wave propagation between the probe and the bone. The method is used to simulate a setup dedicated to the measurement of circumferential guided waves in the cortical compartment of the femoral neck. The proposed approach is validated by comparison with a full FDTD simulation and with an experiment on a bone phantom. For a realistic QUS configuration, the computation time is estimated to be sixty times less with the hybrid method than with a full FDTD approach.     

LED光学传播的有限元研究

有限时域差分(FDTD)广泛应用于提高发光二极管(LED)芯片外量子效率.这种方法是针对波导结构的一种分析计算,对于激光器是有效的,但是对LED很难模拟其有源层多种模式出射的情况.应用有限元电磁场分析方法对LED进行光学建模并对光子晶体结构的外量子效率进行了计算.特别在对光源的处理上,使用了点光源球面波来进行分析并且考...     

Numerical simulation of electromagnetic acoustic transducers using distributed point source method

In spite of many advances in analytical and numerical modeling techniques for solving different engineering problems, an efficient solution technique for wave propagation modeling of an electromagnetic acoustic transducer (EMAT) system is still missing. Distributed point source method (DPSM) is a newly developed semi-analytical technique developed since 2000 by Placko and Kundu (2007) [12] that is very powerful and straightforward for solving various engineering problems, including acoustic and electromagnetic modeling problems. In this study DPSM has been employed to model the Lorentz type EMAT with a meander line and flat spiral type coil. The problem of wave propagation has been solved and eddy currents and Lorentz forces have been calculated. The displacement field has been obtained as well. While modeling the Lorentz force the effect of dynamic magnetic field has been considered that most current analyses ignore. Results from this analysis have been compared with the finite element method (FEM) based predictions. It should be noted that with the current state of knowledge this problem can be solved only by FEM.     

骨小梁材料特性对超声背散射信号的影响

基于时域有限差分法(FDTD)建立了松质骨的超声背散射仿真系统,研究了骨小梁材料特性对超声背散射信号的影响。首次得到松质骨中的超声背散射系数(BSC)和积分背散射系数(IBC)随骨小梁材料参数(密度、拉梅常数、黏度系数及声阻抗系数)的变化关系。研究结果表明,IBC随骨小梁密度的增加而增加;BSC和IBC随拉梅常数的增加而增加、随第一黏度系数的增加而近似线性地减小,第二黏度的变化对背散射信号的影响很小;背散射参数随阻抗系数的增加而减小。说明松质骨中的超声背散射特性不仅受骨矿密度(BMD)和骨微结构的影响,还与骨小梁的材料参数密切相关。研究结果有利于理解松质骨中超声的背散射特性,对松质骨骨质状况的评价有一定帮助。      

Effect of trabecular bone material properties on ultrasonic backscattering signals

In this study, ultrasonic backscattering signals in cancellous bones were obtained by finite difference time domain （FDTD） simulations, and the effect of trabecular material properties on these signals was analyzed. The backscatter coefficient （BSC） and integrated backscatter coefficient （IBC） were numerically investigated for varying trabecular bone material properties, including density, Lame coefficients, viscosities, and resistance coefficients. The results show that the BSC is a complex function of trabecular bone density, and the IBC increases as density increases. The BSC and IBC increase with the first and second Lame coefficients. While not very sensitive to the second viscosity of the trabeculae, the BSC and IBC decrease as the first viscosity and resistance coefficients increase. The results demonstrate that, in addition to bone mineral density （BMD） and microarchitecture, trabecular material properties significantly influence ultrasonic backseattering signals in cancellous bones. This research furthers the understanding of ultrasonic backscattering in cancellous bones and the characterization of cancellous bone status.     

Time-Resolved Reflectance of an Optical Pulse in Adult Heads Based on the Finite Difference Time Domain (FDTD) Analysis

Time-resolved reflectance of an optical pulse in adult head models including non-scattering cerebrospinal fluid (CSF) has been analyzed by the finite difference time domain (FDTD) analysis formulated by the authors. Averaged light intensity and mean time of flight dependences on the source-detector separations calculated by the FDTD analysis are in good agreement with previous experiments, hybrid finite element method (FEM) and Monte Carlo calculations, which justify the FDTD analysis. Based on the analysis, time-resolved reflectance sensitivities to detect optical property changes in brain have been analyzed. As a result, it has been become clear that the sensitivities to detect absorption changes of brain are enhanced in time-resolved reflectance compared to the sensitivities in averaged light intensity, whereas the sensitivities to detect scattering property changes of brain are almost the same in time-resolved reflectance and in averaged light intensity. © 2005 The Optical Society of Japan     

Ultrasonic wave propagation in cancellous and cortical bone: prediction of some experimental results by Biot's theory.

Pulse transmission ultrasound was used to determine the longitudinal wave speed along the direction of trabecular alignment in 32 water-saturated anisotropic tibial bovine cancellous bone samples and in one cortical bone sample also from the bovine tibia. These results are compared to published ultrasound wave-speed data obtained from bovine femoral specimens. Nonlinear regression was used to fit Biot's theory to the data. The correlation coefficient for regression analysis between the experimental ultrasound velocities and the velocities predicted by Biot's theory was r = 0.78.     

3D modeling and testing of transient temperature in selective laser sintering (SLS) process

In the process of rapid prototyping by the method of selective laser sintering (SLS), transient temperature has direct effect upon the sintering performance. In the present work, a model is developed in order to generate 3D transient temperature field. It uses Al₂O₃ coated ceramic powder and involves the finite element method (FEM) variation of thermal properties and solid–liquid two-phase interface. A high-speed charge coupled device (CCD) image temperature measurement system is used to generate for testing. The obtained test results validates the simulation data and implies that the proposed modeling method is useful in simulating the transient sintering temperature specially when the correct thermal properties and key factors of two-phase interface are main concerns. The performance characteristics of the reasonable sintering parameters are predicted by the proposed modeling method.     

高斯波束在双负媒质中的传播特性分析

 提出了一种基于Drude色散媒质模型的2维TM模时域有限差分法，数值模拟了高斯波束从自由空间垂直入射和斜入射到双负媒质(介电常数和磁导率同时为负)平板后的折射现象，并给出了平板内外的电场强度分布。模拟结果显示：垂直入射时，双负媒质平板对高斯波束具有汇聚作用，通过改变媒质的折射率，可以控制高斯波束通过组合平板的传播时间而不发生衰减；斜入射时，折射波束与入射波束均位于法线的同一侧，高斯波束在双负媒质与空气交界面处发生了负折射。     

横观各向同性材料中激光超声谱有限元数值模拟

研究了横观各向同性材料中激光超声波的传播特征．基于谱有限元方法,建立了横观各向同性材料中激光超声的数值模型．利用谱有限元方法模拟脉冲激光作用于材料上产生超声波及其传播的过程．讨论了横观各向同性薄板的各向异性及各向同性平面内超声波的传播特征,并分析了材料厚度的变化对产生超声波模态的影响．     

横观各向同性材料中激光超声谱有限元数值模拟

研究了横观各向同性材料中激光超声波的传播特征.基于谱有限元方法,建立了横观各向同性材料中激光超声的数值模型.利用谱有限元方法模拟脉冲激光作用于材料上产生超声波及其传播的过程.讨论了横观各向同性薄板的各向异性及各向同性平面内超声波的传播特征,并分析了材料厚度的变化对产生超声波模态的影响.     

Influence of transparent coating thickness on thermoelastic force source and laser-generated ultrasound waves

A numerical model is established to investigate the influence of transparent coating thickness on the laser-generated thermoelastic force source and ultrasound waves in the coating-substrate system by using the finite element method (FEM). Taking into account the effects of thermal diffusion, the finite width and duration of the laser source, as well as the temperature dependence of material properties, the transient temperature distributions are obtained firstly. Applying this temperature field to structure analyses as thermal loading, the thermoelastic stress field and laser-generated ultrasound wave in the specimen are obtained. The generation and propagation of the laser thermoelastically induced stress field and ultrasonic waves in coating-substrate system are presented in detail. The influence of transparent coating thickness on the transient temperature distribution, thermoelastic force source and the laser-generated ultrasound waveforms is investigated. The numerical results indicate that the thermoelastic force source and laser-generated ultrasound waveform are strongly affected by the coating thickness due to the constraint of coating. This method can provide insight into the generation and propagation of the laser-generated stress field in coating-substrate system consisting of a transparent coating and an opaque metallic substrate. It provides theoretical basics to optimize ultrasonic signal generation in particular applications and invert the physical and geometrical parameter of the coating-substrate system more accurately in the experiment.     

Analysis of Two-Dimensional Thin Structures (from Micro- to Nano-Scales) Using the Singular Boundary Method

This study investigates the applicability of the singular boundary method (SBM), a recent developed meshless boundary collocation method, for the analysis of two-dimensional (2D) thin structural problems. The troublesome nearly-singular kernels, which are crucial in the applications of SBM to thin shapes, are dealt with efficiently by using a non-linear transformation technique. Promising SBM results with only a small number of boundary nodes are obtained for thin structures with the thickness-to-length ratio is as small as 1E-9, which is sufficient for modeling most thin layered coating systems as used in smart materials and micro-electro-mechanical systems. The advantages, disadvantages and potential applications of the proposed method, as compared with the finite element (FEM) and boundary element methods (BEM), are also discussed.