Ultrasonic slow waves in air-saturated cancellous bone

This paper describes preliminary observations of ultrasonic wave propagation in air-saturated defatted cancellous bone from the human vertebra. Using a broadband pulse transmission system, attenuation and phase velocity were measured over a wide frequency range (100 kHz-1 MHz). The observed behaviour was consistent with that expected for the decoupled slow wave predicted by Biot's theory. Velocity was lower than that of free air, and there was marked frequency-dependent attenuation and velocity dispersion. The tortuosity (alpha) of the trabecular microstructure was estimated from the high frequency limit of the dispersion curve, with a mean value of alpha = 1.040 +/- 0.004 obtained in five specimens. Ultrasonic measurements in air represent a valuable new approach, capable of yielding parameters that directly characterise bone structure. Furthermore, they may give useful insights into wave propagation in bone in vivo, where the trabecular framework is saturated with marrow fat rather than air.     

Analysis of femtosecond optical pulse propagation in one-dimensional nonlinear photonic crystals using finite-difference time-domain method

In this paper, we have used the finite-difference time-domain (FDTD) method to analyze the optical pulse propagation in a nonlinear, one-dimensional photonic crystal (1DPC). Hyperbolic secant pulses with various carrier wavelengths are utilized in this study. In a nonlinear regime, a 1DPC introduces a photonic band-gap whose central wavelength and width depend on the input pulse intensity. In the present work, three different cases are considered. These correspond to the carrier wavelengths of the incident pulses being out of, near to, and partially in the band-gap. For each case, the effect of nonlinearity on pulse propagation is investigated. Also, we have analyzed the two-frequency regime, in which each of the two pulses has a different carrier frequency (wavelength). This kind of study can be done directly with FDTD without any further computational burden but it is somewhat complicated using nonlinear coupled-mode equations (NLCME) and nonlinear Schrödinger equation (NLSE), which require separate treatments for each carrier wavelength.     

Ultrasonic wave propagation in human cancellous bone: application of Biot theory

Ultrasonic wave propagation in human cancellous bone is considered. Reflection and transmission coefficients are derived for a slab of cancellous bone having an elastic frame using Biot's theory modified by the model of Johnson et al. [J. Fluid Mech. 176, 379-402 (1987)] for viscous exchange between fluid and structure. Numerical simulations of transmitted waves in the time domain are worked out by varying the modified Biot parameters. The variation is applied to the governing parameters and is about 20%. From this study, we can gain an insight into the sensitivity of each physical parameter used in this theory. Some parameters play an important role in slow-wave wave form, such as the viscous characteristic length lambda and pore fluid bulk modulus Kf. However, other parameters play an important role in the fast-wave wave form, such as solid density rhos and shear modulus N. We also note from these simulations that some parameters such as porosity phi, tortuosity alpha(infinty), thickness, solid bulk modulus Ks, and skeletal compressibility frame Kb, play an important role simultaneously in both fast and slow wave forms compared to other parameters which act on the wave form of just one of the two waves. The sensitivity of the modified Biot parameters with respect to the transmitted wave depends strongly on the coupling between the solid and fluid phases of the cancellous bone. Experimental results for slow and fast waves transmitted through human cancellous bone samples are given and compared with theoretical predictions.     

Mode-coupling analysis of three-dimensional microdisk resonators by the finite-difference time-domain technique

Quality factor enhancement due to mode coupling is observed in a three-dimensional microdisk resonator. The microdisk, which is vertically sandwiched between air and a substrate, with a radius of 1 microm, a thickness of 0.2 microm, and a refractive index of 3.4, is considered in a finite-difference time-domain (FDTD) numerical simulation. The mode quality factor of the fundamental mode HE71 decreases with an increase of the refractive index of the substrate, n(sub), from 2.0 to 3.17. However, the mode quality factor of the first-order mode HE72 reaches a peak value at n(sub) = 2.7 because of the mode coupling between the fundamental and the first-order modes. The variation of mode field distributions due to the mode coupling is also observed. This mechanism may be used to realize high-quality-factor modes in microdisks with high-refractive-index substrates.     

利用时域有限差分法模拟介质纳米波导的导波特性

利用时域有限差分法模拟介质纳米波导的导波性质,研究了不同结构波导中的光传输特性.结果表明,通过设计合适的纳米波导结构,可以达到纳米尺度下导波和滤波的目的.     

Determining attenuation properties of interfering fast and slow ultrasonic waves in cancellous bone

Previous studies have shown that interference between fast waves and slow waves can lead to observed negative dispersion in cancellous bone. In this study, the effects of overlapping fast and slow waves on measurements of the apparent attenuation as a function of propagation distance are investigated along with methods of analysis used to determine the attenuation properties. Two methods are applied to simulated data that were generated based on experimentally acquired signals taken from a bovine specimen. The first method uses a time-domain approach that was dictated by constraints imposed by the partial overlap of fast and slow waves. The second method uses a frequency-domain log-spectral subtraction technique on the separated fast and slow waves. Applying the time-domain analysis to the broadband data yields apparent attenuation behavior that is larger in the early stages of propagation and decreases as the wave travels deeper. In contrast, performing frequency-domain analysis on the separated fast waves and slow waves results in attenuation coefficients that are independent of propagation distance. Results suggest that features arising from the analysis of overlapping two-mode data may represent an alternate explanation for the previously reported apparent dependence on propagation distance of the attenuation coefficient of cancellous bone.     

Ultrasonic backscatter characterization of cancellous bone using a general Nakagami statistical model

The goal of this study is to analyze the statistics of the backscatter signal from bovine cancellous bone using a Nakagami model and to evaluate the feasibility of Nakagami-model parameters for cancellous bone characterization. Ultrasonic backscatter measurements were performed on 24 bovine cancellous bone specimens in vitro and the backscatter signals were compensated for the frequency-dependent attenuation prior to the envelope detection. The statistics of the backscatter envelope were modeled using the Nakagami distribution. Our results reveal that the backscatter envelope mainly followed pre-Rayleigh distributions, and the deviations of the backscatter envelope from Rayleigh distribution decreased with increasing bone density. The Nakagami shape parameter(i.e., m) was significantly correlated with bone densities(R = 0.78–0.81, p 0.001) and trabecular microstructures(|R| = 0.46–0.78, p 0.05). The scale parameter(i.e.,?) and signal-to-noise ratio(SNR) also yielded significant correlations with bone density and structural features. Multiple linear regressions showed that bone volume fraction(BV/TV) was the main predictor of the Nakagami parameters,and microstructure produced significantly independent contribution to the prediction of Nakagami distribution parameters,explaining an additional 10.2% of the variance at most. The in vitro study showed that statistical parameters derived with Nakagami model might be useful for cancellous bone characterization, and statistical analysis has potential for ultrasonic backscatter bone evaluation.     

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.     

Auxiliary differential equation: efficient implementation in the finite-difference time-domain method

An efficient algorithm for modeling dispersive media in finite-difference time-domain methods is presented. It is based on the auxiliary differential equation method for treatment of Lorentz media with an arbitrary number of relaxations. The algorithm shows excellent accuracy of second order in time and space and is efficient in both memory requirements and computational effort.     

Ultrasonic characterization of human cancellous bone using the Biot theory: inverse problem

This paper concerns the ultrasonic characterization of human cancellous bone samples by solving the inverse problem using experimental transmitted signals. The ultrasonic propagation in cancellous bone is modeled using the Biot theory modified by the Johnson et al. model for viscous exchange between fluid and structure. The sensitivity of the Young modulus and the Poisson ratio of the skeletal frame is studied showing their effect on the fast and slow wave forms. The inverse problem is solved numerically by the least squares method. Five parameters are inverted: the porosity, tortuosity, viscous characteristic length, Young modulus, and Poisson ratio of the skeletal frame. The minimization of the discrepancy between experiment and theory is made in the time domain. The inverse problem is shown to be well posed, and its solution to be unique. Experimental results for slow and fast waves transmitted through human cancellous bone samples are given and compared with theoretical predictions.     

Acoustic analysis of the vocal tract during vowel production by finite-difference time-domain method

The vocal tract shape is three-dimensionally complex. For accurate acoustic analysis, a finite-difference time-domain method was introduced in the present study. By this method, transfer functions of the vocal tract for the five Japanese vowels were calculated from three-dimensionally reconstructed magnetic resonance imaging (MRI) data. The calculated transfer functions were compared with those obtained from acoustic measurements of vocal tract physical models precisely constructed from the same MRI data. Calculated transfer functions agreed well with measured ones up to 10 kHz. Acoustic effects of the piriform fossae, epiglottic valleculae, and inter-dental spaces were also examined. They caused spectral changes by generating dips. The amount of change was significant for the piriform fossae, while it was almost negligible for the other two. The piriform fossae and valleculae generated spectral dips for all the vowels. The dip frequencies of the piriform fossae were almost stable, while those of the valleculae varied among vowels. The inter-dental spaces generated very small spectral dips below 2.5 kHz for the high and middle vowels. In addition, transverse resonances within the oral cavity generated small spectral dips above 4 kHz for the low vowels.     

时域有限差分法在建筑声学中的应用及前景

介绍了声波方程的基本差分格式及稳定条件、数值色散、吸收边界条件等数值计算理论，例举了前人用时域有限差分法对噪声传播过程的模拟和室内声学中座椅吸声低谷效应模拟的模拟结果。本文指出，由于时域有限差分法的特点使其具有在模拟脉冲响应方而的特别优势，因而，应用这一技术研究厅堂的声学特性，尤其是低频特性，将有重要意义。     

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.     

声学中用于时域有限差分法的一种高效吸收边界

本文提出一种用于声场时域有限差分法(FDTD)的高效吸收边界条件。通过伪逆矩阵对截断边界附近网格线之间的转移矩阵作最小二乘估计,所得到的吸收边界条件性能明显优于多种常用方法。新方法的数值计算效率高,算法稳定。对点源辐射,尖劈衍射和圆柱体散射问题的FDTD数值计算结果显示了这种方法的优异性能。     

Optical absorption modeling of thermal infrared detectors by use of the finite-difference time-domain method

The optical absorption of thin-film thermal infrared detectors was calculated as a function of wavelength, pixel size, and area fill factor by use of the finite-difference time-domain (FDTD) method. The results indicate that smaller pixels absorb a significantly higher percentage of incident energy than larger pixels with the same fill factor. A polynomial approximation to the FDTD results was derived for use in system models.     

Subpixel smoothing for conductive and dispersive media in the finite-difference time-domain method

Staircasing of media properties is one of the intrinsic problems of the finite-difference time-domain method, which reduces its accuracy. There are different approaches for solving this problem, and the most successful of them are based on correct approximation of inverse permittivity tensor epsilon(-1) at the material interface. We report an application of this tensor method for conductive and dispersive media. For validation, comparisons with analytical solutions and various other subpixel smoothing methods are performed for the Mie scattering from a small sphere.     

Investigation of three-pulse photon echo in thick crystal using finite-difference time-domain method

This paper investigates the phenomenon of three-pulse photon echo in thick rare-earth ions doped crystal whose thickness is far larger than 0.002 cm which is adopted in previous works.The influence of thickness on the three-pulse photon echo's amplitude and efficiency is analyzed with the Maxwell-Bloch equations solved by finite-difference timedomain method.We demonstrate that the amplitude of three-pulse echo will increase with the increasing of thickness and the optimum thickness to generate three-pulse photon echo is 0.3 cm for Tm~(3+):YAG when the attenuation of the input pulse is taken into account.Meanwhile,we find the expression 0.09 exp(α'L),which is previously employed to describe the relationship between echo's efficiency and thickness,should be modified as 1.3 · 0.09 exp(2.4 ·α'L) with the propagation of echo considered.     

Effective optical response of silicon to sunlight in the finite-difference time-domain method

The frequency dependent dielectric permittivity of dispersive materials is commonly modeled as a rational polynomial based on multiple Debye, Drude, or Lorentz terms in the finite-difference time-domain (FDTD) method. We identify a simple effective model in which dielectric polarization depends both on the electric field and its first time derivative. This enables nearly exact FDTD simulation of light propagation and absorption in silicon in the spectral range of 300-1000 nm. Numerical precision of our model is demonstrated for Mie scattering from a silicon sphere and solar absorption in a silicon nanowire photonic crystal.     

色散介质电磁特性时域有限差分分析的Newmark方法

根据Debye模型、Drude模型和Lorentz模型3种常见色散介质模型频域极化率的特点,利用频域到时域的转换关系jω→?/?t,将极化矢量P与电场强度E的频域关系转换成时域内关于P的二阶微分方程,其对3种色散介质模型皆适用,具有统一的形式.然后采用相比于中心差分具有更高精度的Newmark两步算法(Newmark-β-γ法)求解该方程,进而得到E→P的递推公式,再结合本构关系得到D→E的时域递推式.实现了色散介质电磁场量的时域有限差分迭代计算.数值计算结果表明该方法是适用于3种色散介质模型的通用算法,并且相比于移位算子时域有限差分方法等以中心差分为基础的离散方案具有更高的计算精度.