FDTD simulation of finite-amplitude pressure and temperature fields for biomedical ultrasound.

Full wave simulations provide a valuable tool for studying the spatial and temporal nature of an acoustic field. One method for producing such simulations is the finite-difference time-domain (FDTD) method. This method uses discrete differences to approximate derivatives in the governing partial differential equations. We used the FDTD method to model the propagation of finite-amplitude sound in a homogeneous thermoviscous fluid. The calculated acoustic pressure field was then used to compute the transient temperature rise in the fluid; the heating results from absorption of acoustic energy by the fluid. As an example, the transient temperature field was calculated in biological tissue in response to a pulse of focused ultrasound. Enhanced heating of the tissue from finite-amplitude effects was observed. The excess heating was attributed to the nonlinear generation of higher-frequency harmonics which are absorbed more readily than the fundamental. The effect of nonlinear distortion on temperature rise in tissue was observed to range from negligible at 1 MPa source pressure to an 80% increase in temperature elevation at 10 MPa source pressure.     

Modeling of nonlinear ultrasound propagation in tissue from array transducers

A computationally efficient model capable of simulating finite-amplitude ultrasound beam propagation in water and in tissue from phased linear arrays and other transducers of arbitrary quasiplanar geometry is described. It is based on a second-order operator splitting approach [Tavakkoli et al., J. Acoust. Soc. Am. 104, 2061-2072 (1998)], with a fractional step-marching scheme, whereby the effects of diffraction, attenuation, and nonlinearity can be computed independently over incremental steps. This approach is an extension to that of Christopher and Parker [J. Acoust. Soc. Am. 90, 507-521; 90, 488-499 (1991)], wherein linear and nonlinear effects are propagated separately over incremental steps, and the computation of the diffractive substeps are based on an angular spectrum technique with a modified sampling scheme for accurate and efficient implementation of diffractive propagation from nonradially symmetric sources. Results of the model are compared with published data. Predicted field profiles for nonlinear propagation in tissue from realistic array transducers using the pulse inversion method are presented.     

Propagation of acoustic pulses in material with hysteretic nonlinearity

Evolution equations for propagation of both unipolar and bipolar acoustic pulses are derived by using hysteretic stress-strain relationships. Hysteretic stress-strain loops that incorporate quadratic nonlinearity are derived by applying the model of Preisach-Mayergoyz space for the characterization of structural elements in a micro-inhomogeneous material. Exact solutions of the nonlinear evolution equations predict broadening in time and reduction in amplitude of a unipolar finite-amplitude acoustic pulse. In contrast with some earlier theoretical predictions, the transformation of the pulse shape predicted here satisfies the law of "momentum" conservation (the "equality of areas" law in nonlinear acoustics of elastic materials). A bipolar pulse of nonzero momentum first transforms during its propagation into a unipolar pulse of the same duration. This process occurs in accordance with the "momentum" conservation law and without formation of shock fronts in the particle velocity profile.     

Nonlinear pulsed ultrasound beams radiated by rectangular focused diagnostic transducers

A numerical model for simulating nonlinear pulsed beams radiated by rectangular focused transducers, which are typical of diagnostic ultrasound systems, is presented. The model is based on a KZK-type nonlinear evolution equation generalized to an arbitrary frequency-dependent absorption. The method of fractional steps with an operator-splitting procedure is employed in the combined frequency-time domain algorithm. The diffraction is described using the implicit backward finite-difference scheme and the alternate direction implicit method. An analytic solution in the time domain is employed for the nonlinearity operator. The absorption and dispersion of the sound speed are also described using an analytic solution but in the frequency domain. Numerical solutions are obtained for the nonlinear acoustic field in a homogeneous tissue-like medium obeying a linear frequency law of absorption and in a thermoviscous fluid with a quadratic frequency law of absorption. The model is applied to study the spatial distributions of the fundamental and second harmonics for a typical diagnostic ultrasound source. The nonlinear distortion of pulses and their spectra due to the propagation in tissues are presented. A better understanding of nonlinear propagation in tissue may lead to improvements in nonlinear imaging and in specific tissue harmonic imaging. Published in Russian in Akusticheskiĭ Zhurnal, 2006, Vol. 52, No. 4, pp. 560–570. This article was translated by the authors.     

Modeling the propagation of nonlinear three-dimensional acoustic beams in inhomogeneous media

A three-dimensional model of the forward propagation of nonlinear sound beams in inhomogeneous media, a generalized Khokhlov-Zabolotskaya-Kuznetsov equation, is described. The Texas time-domain code (which accounts for paraxial diffraction, nonlinearity, thermoviscous absorption, and absorption and dispersion associated with multiple relaxation processes) was extended to solve for the propagation of nonlinear beams for the case where all medium properties vary in space. The code was validated with measurements of the nonlinear acoustic field generated by a phased array transducer operating at 2.5 MHz in water. A nonuniform layer of gel was employed to create an inhomogeneous medium. There was good agreement between the code and measurements in capturing the shift in the pressure distribution of both the fundamental and second harmonic due to the gel layer. The results indicate that the numerical tool described here is appropriate for propagation of nonlinear sound beams through weakly inhomogeneous media.     

Increase in the efficiency of the shear wave generation in gelatin due to the nonlinear absorption of a focused ultrasonic beam

Experimental results and theoretical estimates are presented to demonstrate the prospects of using the acoustic nonlinearity of a gel-like medium for increasing the efficiency of the shear wave generation in it by a pulsed ultrasonic beam. The experiment is based on the propagation of a focused beam of longitudinal acoustic waves at a frequency of 1.1 MHz in a gelatin sample and on the detection of shear waves by the optical method [1]. It is demonstrated that the amplitude of the shear wave excited by a nonlinear acoustic pulse can be increased by an order of magnitude owing to the formation of shock fronts in the profile of this pulse.     

Counterpropagation of waves with shock fronts in a nonlinear tissue-like medium

A numerical model for describing the counterpropagation of one-dimensional waves in a nonlinear medium with an arbitrary power law absorption and corresponding dispersion is developed. The model is based on general one-dimensional Navier-Stokes equations with absorption in the form of a time-domain convolution operator in the equation of state. The developed algorithm makes it possible to describe wave interactions in the presence of shock fronts in media like biological tissue. Numerical modeling is conducted by the finite difference method on a staggered grid; absorption and sound speed dispersion are taken into account using the causal memory function. The developed model is used for numerical calculations, which demonstrate the absorption and dispersion effects on nonlinear propagation of differently shaped pulses, as well as their reflection from impedance acoustic boundaries.     

Model equation for strongly focused finite-amplitude sound beams

A model equation that describes the propagation of sound beams in a fluid is developed using the oblate spheroidal coordinate system. This spheroidal beam equation (SBE) is a parabolic equation and has a specific application to a theoretical prediction on focused, high-frequency beams from a circular aperture. The aperture angle does not have to be small. The theoretical background is basically along the same analytical lines as the composite method (CM) reported previously [B. Ystad and J. Berntsen, Acustica 82, 698-706 (1996)]. Numerical examples are displayed for the amplitudes of sound pressure along and across the beam axis when sinusoidal waves are radiated from the source with uniform amplitude distribution. The primitive approach to linear field analysis is readily extended to the case where harmonic generation in finite-amplitude sound beams becomes significant due to the inherent nonlinearity of the medium. The theory provides the propagation and beam pattern profiles that differ from the CM solution for each harmonic component.     

有限长号筒中非线性声传播的数值模拟研究

研究了大振幅活塞声源经有限长号筒向外辐射声波的非线性声学问题。采用具有频散保持特性的高精度计算格式求解了适用于变截面管道的一维非线性声场模型,并考虑到声波的非线性畸变及管口处的声反射,加入了宽频时域声阻抗边界条件。宽频阻抗模型的共轭复数系数采用优化拟合方法近似求解,并采用递推卷积算法快速求解出时域声阻抗。在弱非线性条件下模拟指数形号筒中的声传播取得了与已有实验相一致的结果,表明模型能够描述声波非线性畸变带来的宽频特性。进而采用本模型数值模拟了大振幅活塞声源在双曲形、锥形、指数形和正弦形号筒中的非线性声传播问题,结果表明号筒出口声压级受活塞振动速度、频率以及号筒形状的影响,并分析讨论了波形畸变与号筒几何形状之间的关系。      

Locally conformal method for acoustic finite-difference time-domain modeling of rigid surfaces

The finite-difference time-domain method is a simple but powerful numerical method for simulating full-wave acoustic propagation and scattering. However, the method can demand a large amount of computational resources. Traditionally, continuously curved boundaries are represented in a stair-step fashion and thus accurately modeling scattering from a boundary will require a finer discretization than would otherwise be necessary for modeling propagation in a homogeneous medium. However, a fine discretization might not be practical due to limited computational resources. A locally conformal technique is presented here for modeling acoustic scattering from continuously curved rigid boundaries. This technique is low cost, simple to implement, and gives better results for the same grid discretization than the traditional stair-step representation. These improvements can be traded for a coarser discretization which reduces the computational burden. The improved accuracy of this technique is demonstrated for a spherical scatterer.     

聚焦超声波在层状生物媒质中的二次谐波声场的理论与实验研究

基于Khokhlov-Zabolotkaya-Kuznetsov(KZK)方程，在频域提出了聚焦超声波在层状生物媒质中传播的理论模型，该模型计及生物媒质的吸收、非线性和边界，同时考虑声源的衍射对声传播的影响.数值研究了聚焦超声波的基波和二次谐波在层状生物媒质中的声传播，并与实验结果相比较.研究结果表明，此方法可以有效地描述聚焦超声波在层状生物媒质中的二次谐波声场. 关键词： 聚焦超声波 层状生物媒质 二次谐波     

室温条件下掺铒光纤中光脉冲群速可控特性的研究

利用相干布居振荡技术在介质吸收光谱上产生烧孔，孔宽大约为基态粒子数恢复时间的倒数. 由增益理论分析得到不同抽运光功率对介质吸收状态的影响. 在介质的吸收区域，振荡导致光脉冲经历饱和吸收，脉冲传输延迟；在介质的增益区域，振荡又导致光脉冲经历增益饱和，脉冲传输超前. 应用此技术在掺铒光纤中实现了光速人为可控. 在掺铒光纤晶体中观测到了最慢为2.857×10³m/s的光速减慢传输，相应感生群折射率为10.5×10⁴. 根据布居振荡效应及增益理论，由速率方程出发，得到了 关键词： 光谱烧孔 相干布居振荡 饱和吸收 慢光     

Numerical simulation of nonlinear propagation of sound waves in a finite horn

Nonlinear acoustic propagation generated by a piston in a finite horn is numerically studied.A quasi-one-dimensional nonlinear model with varying cross-section uses high-order low-dispersion numerical schemes to solve the governing equation.Because of the nonlinear wave distortion and reflected sound waves at the mouth,broadband time-domain impedance boundary conditions are employed.The impedance approximation can be optimized to identify the complex-conjugate pole-residue pairs of the impedance functions,which can be calculated by fast and efficient recursive convolution.The numerical results agree very well with experimental data in the situations of weak nonlinear wave propagation in an exponential horn,it is shown that the model can describe the broadband characteristics caused by nonlinear distortion.Moreover,finite-amplitude acoustic propagation in types of horns is simulated,including hyperbolic,conical,exponential and sinusoidal horns.It is found that sound pressure levels at the horn mouth are strongly affected by the horn profiles,the driving velocity and frequency of the piston.The paper also discusses the influence of the horn geometry on nonlinear waveform distortion.     

Characterization of high intensity focused ultrasound transducers using acoustic streaming

A new approach for characterizing high intensity focused ultrasound (HIFU) transducers is presented. The technique is based upon the acoustic streaming field generated by absorption of the HIFU beam in a liquid medium. The streaming field is quantified using digital particle image velocimetry, and a numerical algorithm is employed to compute the acoustic intensity field giving rise to the observed streaming field. The method as presented here is applicable to moderate intensity regimes, above the intensities which may be damaging to conventional hydrophones, but below the levels where nonlinear propagation effects are appreciable. Intensity fields and acoustic powers predicted using the streaming method were found to agree within 10% with measurements obtained using hydrophones and radiation force balances. Besides acoustic intensity fields, the streaming technique may be used to determine other important HIFU parameters, such as beam tilt angle or absorption of the propagation medium.     

介质参数对受激布里渊散射脉宽压缩的影响

 利用KrF激光和SF₆介质从理论和实验上研究了声子寿命和增益系数等介质参数对SBS脉宽压缩比和能量反射率的影响。理论上采用一维瞬态模型对SBS过程进行数值模拟，考虑了瞬态过程、介质吸收以及泵浦耗空的影响，计算了SBS介质不同参数对脉冲压缩影响的规律。实验表明，在实验参数的变化范围内声子寿命越短、增益系数越小，越有利于脉宽压缩。在0.68MPa下，脉宽压缩比达到8。数值模拟了声子寿命和介质增益系数单独变化时对SBS过程影响的规律，发现在声子寿命和增益系数同时变化时，SBS对泵浦脉冲的压缩有最佳点。     

Time-domain simulation of acoustic wave propagation and interaction with flexible structures using Chebyshev collocation method

A time-domain Chebyshev collocation (ChC) method is used to simulate acoustic wave propagation and its interaction with flexible structures in ducts. The numerical formulation is described using a two-dimensional duct noise control system, which consists of an expansion chamber and a tensioned membrane covering the side-branch cavity. Full coupling between the acoustic wave and the structural vibration of the tensioned membrane is considered in the modelling. A systematic method of solution is developed for the discretized differential equations over multiple physical domains. The time-domain ChC model is tested against analytical solutions under two conditions: one with an initial state of wave motion; the other with a time-dependent acoustic source. Comparisons with the finite-difference time-domain (FDTD) method are also made. Results show that the time-domain ChC method is highly accurate and computationally efficient for the time-dependent solution of duct acoustic problems. For illustrative purposes, the time-domain ChC method is applied to investigate the acoustic performance of three typical duct noise control devices: the expansion chamber, the quarter wavelength resonator and the drum silencer. The time-dependent simulation of the sound-structure interaction in the drum silencer reveals the delicate role of the membrane mass and tension in its sound reflection capability.     

Modeling of acoustic wave propagation in time-domain using the discontinuous Galerkin method – A comparison with measurements

Simulations of acoustic wave propagation in time-domain are presented. In the simulations, the discontinuous Galerkin method for spatial derivatives and the low-storage Runge–Kutta approach for time derivatives are used. Three different simulation cases are studied. First, the directivity of loudspeaker is simulated. In the second case, acoustic wave propagation in free space is studied using a short pulse. In the last case, acoustic wave scattering from a metallic cylinder is simulated. All simulation results are compared with measurement results. The measurements for the acoustic wave scattering from the metallic cylinder are made in 2D planes using an automated measurement system. Comparison between the simulation and measurement results are made both temporally and spatially and a good agreement between the simulation and measurement results is found. The results suggest that the discontinuous Galerkin method coupled with the low-storage Runge–Kutta approach is a viable tool for modeling acoustic wave propagation in the time-domain.     

一种简化的分析光纤布拉格光栅的时域有限差分束传输法

提出了一种便于分析光纤布拉格光栅(FBG)、基于强制边界条件的简化TD-FD-BPM模型.采用交替隐式法(ADIM)和综合道格拉斯(GD)法,离散化时域束传输方程,获得比普通差分格式低二阶的误差。提出并采用强制边界条件,简化了光波导分析中边界处理问题.重点讨论和确定了在此条件下激励源位置、脉冲形状和径向分布函数、连续波激励条件等.在修正的正弦脉冲激励情况下,通过离散傅利叶变换,直接得到较为理想的短FBG反射谱.此法可减少数值计算时间,直观反映光脉冲传输.     

非线性对大气介质中阵列聚焦声场分布影响的研究

基于时域有限差分算法将大气中近似到二阶微小项的非线性声波波动方程进行离散化,得到了模拟采用的差分波动方程.在此基础上,数值模拟了初始声压强弱不同的5个点声源组成的线阵列垂直或斜向辐射的连续正弦波在大气中传播时二维声场的分布情况.将线性条件下的模拟结果与非线性条件下的模拟结果进行比较后发现:弱非线性会对声场的分布和阵列聚焦增益产生一定的影响,使声场分布波形比线性条件下的声场分布波形更加靠近阵列,聚焦效果变差;强非线性会使波形发生更严重畸变,这是由于产生了基频以外的其他频率声波引起的;非线性对斜向传播时声场分布的影响与垂直传播时的影响效果基本相同,但由于斜向辐射时的声波几何扩展造成的轴向声压衰减要大于垂直辐射时的轴向声压衰减,因此聚焦增益和强非线性的影响都将小于垂直辐射时的情况.     

Experimental study of nonlinear dust acoustic solitary waves in a dusty plasma

The excitation and propagation of finite-amplitude low-frequency solitary waves are investigated in an argon plasma impregnated with kaolin dust particles. A nonlinear longitudinal dust acoustic solitary wave is excited by pulse modulating the discharge voltage with a negative potential. It is found that the velocity of the solitary wave increases and the width decreases with the increase of the modulating voltage, but the product of the solitary wave amplitude and the square of the width remains nearly constant. The experimental findings are compared with analytic soliton solutions of a model Korteveg-de Vries equation.