多层介质中超声相控阵声场仿真*

由于良好的声束偏转与聚焦特性,超声相控阵已经广泛应用于多层固体介质的缺陷检测。当超声束经过多层介质时,由于反射、透射以及模式转换的存在,多种声束存在于这种结构中,使得声场分析变得复杂。为了提高多层介质检测的准确性,有必要对超声声场的分布规律进行深入地了解。该文结合高斯声束等效点源模型以及射线追踪法,给出了相控阵声源在多层固体介质中激发声场的仿真方法,并且模拟计算了一维线型相控阵在楔块-铝-黄铜-钢四层固体介质中的辐射声场。通过对不同延时法则的计算,实现了声波在这种复杂介质中的偏转与聚焦,进而研究了不同焦点处聚焦声场的分布。结果表明:相控阵方法能使聚焦点处的声场幅值增大,能量集中,提高了检测分辨率;不同聚焦点处声场聚焦效果不同,实际检测时应根据检测区域结构及位置特点,合理放置相控阵换能器。与瑞利积分法的比较表明,该文的仿真方法适用于多层介质相控阵声场的计算。     

Quantitative estimation of ultrasound beam intensities using infrared thermography-Experimental validation

Infrared (IR) thermography is a technique that has the potential to rapidly and noninvasively determine the intensity fields of ultrasound transducers. In the work described here, IR temperature measurements were made in a tissue phantom sonicated with a high-intensity focused ultrasound (HIFU) transducer, and the intensity fields were determined using a previously published mathematical formulation relating intensity to temperature rise at a tissue/air interface. Intensity fields determined from the IR technique were compared with those derived from hydrophone measurements. Focal intensities and beam widths determined via the IR approach agreed with values derived from hydrophone measurements to within a relative difference of less than 10%, for a transducer with a gain of 30, and about 13% for a transducer with a gain of 60. At axial locations roughly 1 cm in front (pre-focal) and behind (post-focal) the focus, the agreement with hydrophones for the lower-gain transducer remained comparable to that in the focal plane. For the higher-gain transducer, the agreement with hydrophones at the pre-focal and post-focal locations was around 40%.     

Characterization of HIFU transducers designed for sonochemistry application: Acoustic streaming

Cavitation distribution in a High Intensity Focused Ultrasound sonoreactors (HIFU) has been extensively described in the recent literature, including quantification by an optical method (Sonochemiluminescence SCL). The present paper provides complementary measurements through the study of acoustic streaming generated by the same kind of HIFU transducers. To this end, results of mass transfer measurements (electrodiffusional method) were compared to optical method ones (Particle Image Velocimetry). This last one was used in various configurations: with or without an electrode in the acoustic field in order to have the same perturbation of the wave propagation. Results show that the maximum velocity is not located at the focal but shifted near the transducer, and that this shift is greater for high powers. The two cavitation modes (stationary and moving bubbles) are greatly affect the hydrodynamic behavior of our sonoreactors: acoustic streaming and the fluid generated by bubble motion. The results obtained by electrochemical measurements show the same low hydrodynamic activity in the transducer vicinity, the same shift of the active focal toward the transducer, and the same absence of activity in the post-focal axial zone. The comparison with theoretical Eckart’s velocities (acoustic streaming in non-cavitating media) confirms a very high activity at the “sonochemical focal”, accounted for by wave distortion, which induced greater absorption coefficients. Moreover, the equivalent liquid velocities are one order of magnitude larger than the ones measured by PIV, confirming the enhancement of mass transfer by bubbles oscillation and collapse close to the surface, rather than from a pure streaming effect.     

A derating method for therapeutic applications of high intensity focused ultrasound

Current methods of determining high intensity focused ultrasound (HIFU) fields in tissue rely on extrapolation of measurements in water assuming linear wave propagation both in water and in tissue. Neglecting nonlinear propagation effects in the derating process can result in significant errors. A new method based on scaling the source amplitude is introduced to estimate focal parameters of nonlinear HIFU fields in tissue. Focal values of acoustic field parameters in absorptive tissue are obtained from a numerical solution to a KZK-type equation and are compared to those simulated for propagation in water. Focal wave-forms, peak pressures, and intensities are calculated over a wide range of source outputs and linear focusing gains. Our modeling indicates, that for the high gain sources which are typically used in therapeutic medical applications, the focal field parameters derated with our method agree well with numerical simulation in tissue. The feasibility of the derating method is demonstrated experimentally in excised bovine liver tissue.     

格子玻尔兹曼方法对不同张角聚焦声束的建模

高强度聚焦超声(HIFU)是一种新型的无创治疗肿瘤新技术,其中换能器声场数值计算能够为HIFU治疗提供重要的依据。传统非线性KZK和SBE模型广泛应用于换能器声场数值计算,但依然存在某些不足。我们采用一种介观尺度的新型流体力学方法,即格子Boltzmann方法(LBM),基于2维9离散速度(D2Q9)格子构建了轴对称多弛豫参数LBM模型,并通过调节弛豫参数分析其对模型的影响;利用该模型对两个具有不同张角的球面聚焦换能器的声场进行数值模拟,并与KZK和SBE模型的计算结果进行比较。结果表明LBM模型能够很好地描述超声波的激发和传播机制,从流体力学的角度描述聚焦声场的分布,具有清晰的物理意义,且计算过程不受换能器张角的限制,在换能器声场的理论分析和模拟计算及其在HIFU治疗中的应用有着积极的意义。      

Measurements of harmonic profiles of a bounded ultrasonic beam in a liquid medium

The acoustic field of a bounded finite-amplitude beam is governed by competing mechanisms such as medium non-linearity, interference, and attenuation. An analytic determination of the distribution of sonic energy in the individual harmonic components is often not reliable; consequently an experimental mapping of those harmonic components may be more appropriate. An experimental method is presented here which involves a miniature hydrophone probe which has been frequency calibrated for each harmonic component using a light diffraction technique. Measurements (made across the sound field) of the acoustic amplitude of the first three harmonic components are presented.     

New Techniques and Designs of Focusing Piezoelectric Transducers for Ultrasonic Diagnostics and Therapy

New techniques of forming high intensity focused ultrasound (HIFU) fields using dynamic focusing and harmonic multifrequency excitation are developed for ultrasonic diagnostics and therapy. New designs of HIFU transducers based on high-performance composite materials are developed and studied. Finite-element and finite-difference simulations of HIFU transducers and processes of ultrasonic wave propagation in biological tissues are performed. The parameters of piezoceramic materials, piezoelements, and the acoustic fields of focusing ultrasonic transducers are measured. Experiments are performed on biological tissues ex vivo that confirm the efficiency, selectivity, and safety of the developed HIFU transducers and techniques of forming acoustic fields.     

大气风场和温度对无线电声波探测系统探测高度影响的数值研究

从声波扰动介质中的电波波动方程出发, 使用时域有限差分(FDTD)方法, 结合声波传播的FDTD 模型, 构建了描述声波和电波相互作用的数值模型, 并运用该模型分析风场和温度对无线电声波探测系统的探测高度的影响. 数值模拟结果表明: 温度与风场剖面的存在改变声波和电波散射回波的传播轨迹; 温度梯度剖面主要影响声波的传播速度, 风场剖面导致作为电波散射体的声波波阵面的偏移, 降低电波散射回波的强度并改变回波路径, 使得接收数据减少, 限制无线电声波探测系统的探测高度; 在强风背景下, 若降低声波散射体高度, 电波散射回波“聚束点”的偏移会有较大的改善, 但同时意味着探测高度的降低. 为了改善风场背景下无线电声波探测系统的探测高度, 可以使用双基地雷达或者增大接收天线面积等方法来实现.     

Fluid dynamics phenomena induced by power ultrasounds

Propagation of power ultrasound (from 20 to 800 kHz) through a liquid inside a cylindrical reactor initiates acoustic cavitation and also fluid dynamics phenomena such as free surface deformation, convection, acoustic streaming, etc. Mathematical modelling is performed as a new approach to predict where active bubbles are and how intense cavitation is. A calculation based on fluid dynamics equations is undertaken using computational fluid dynamics code; this is of great interest because such code provides not only the pressure field but also velocity and temperature fields. The link between the acoustic pressure and the cavitation field is clearly established. Moreover, the pressure profile near a free surface allows one to predict the shape of the acoustic fountain. The influence of the acoustic fountain on the wave propagation is shown to be important. The convective flow inside a reactor is numerically obtained and agrees well with particle image velocity measurements. Non-linearities arising from the dissipation of the acoustic wave are computed and lead to the calculation of the acoustic streaming. The superimposed velocity field (convective flow and acoustic streaming) succeeds in simulating the bubble behaviour at 500 kHz, for instance.     

Nonlinear absorption in biological tissue for high intensity focused ultrasound

In recent years the propagation of the high intensity focused ultrasound (HIFU) in biological tissue is an interesting area due to its potential applications in non-invasive treatment of disease. The base principle of these applications is the heat effect generated by ultrasound absorption. In order to control therapeutic efficiency, it is important to evaluate the heat generation in biological tissue irradiated by ultrasound. In his paper, based on the Khokhlov-Zabolotkaya-Kuznetsov (KZK) equation in frequency-domain, the numerical simulations of nonlinear absorption in biological tissues for high intensity focused ultrasound are performed. We find that ultrasound thermal transfer effect will be enhanced with the increasing of initial acoustic intensity due to the high harmonic generation. The concept of extra absorption factor is introduced to describe nonlinear absorption in biological tissue for HIFU. The theoretical results show that the heat deposition induced by the nonlinear theory can be nearly two times as large as that predicated by linear theory. Then, the influence of the diffraction effect on the position of the focus in HIFU is investigated. It is shown that the sound focus moves toward the transducer compared with the geometry focus because of the diffraction of the sound wave. The position of the maximum heat deposition is shifted to the geometry focus with the increase of initial acoustic intensity because the high harmonics are less diffraction. Finally, the temperature in the porcine fat tissue changing with the time is predicated by Pennes' equation and the experimental results verify the nonlinear theoretical prediction.     

Theoretical framework for quantitatively estimating ultrasound beam intensities using infrared thermography

In the characterization of high-intensity focused ultrasound (HIFU) systems, it is desirable to know the intensity field within a tissue phantom. Infrared (IR) thermography is a potentially useful method for inferring this intensity field from the heating pattern within the phantom. However, IR measurements require an air layer between the phantom and the camera, making inferences about the thermal field in the absence of the air complicated. For example, convection currents can arise in the air layer and distort the measurements relative to the phantom-only situation. Quantitative predictions of intensity fields based upon IR temperature data are also complicated by axial and radial diffusion of heat. In this paper, mathematical expressions are derived for use with IR temperature data acquired at times long enough that noise is a relatively small fraction of the temperature trace, but small enough that convection currents have not yet developed. The relations were applied to simulated IR data sets derived from computed pressure and temperature fields. The simulation was performed in a finite-element geometry involving a HIFU transducer sonicating upward in a phantom toward an air interface, with an IR camera mounted atop an air layer, looking down at the heated interface. It was found that, when compared to the intensity field determined directly from acoustic propagation simulations, intensity profiles could be obtained from the simulated IR temperature data with an accuracy of better than 10%, at pre-focal, focal, and post-focal locations.     

声波作用下球形颗粒外声流分布的数值模拟

综合考虑声学边界层内的热损失和黏性损失,建立处于平面驻波声压波节位置二维球形颗粒外声流计算模型,利用分离时间尺度的数值方法对颗粒外声流流场特征进行模拟。将模拟结果与相应的解析解和实验结果对比,验证了数值模拟的可靠性。在此基础上,研究了雷诺数Re和斯特劳哈尔数Sr对球形颗粒声学边界层内二阶声流流场结构、涡流强度及范围的影响规律。结果表明,随Sr和Re增大,声学边界层内的涡流结构尺度呈指数形式减小,其涡流尺度与颗粒直径D和激励频率f成反比,与流体介质运动黏度v成正比;且满足低Sr和高Re的声振系统可形成范围较大、更强烈的声流运动。该数值方法可用于对任意物理模型外声流特性的评估。      

超声相控阵在多层媒质中的声场模式优化

针对超声在多层媒质中的传播特性,引入相位补偿因子并结合遗传算法, 提出了一种可对多层媒质进行声聚焦控制的方法.利用该方法对16×16二维超声相控阵在多层生物媒质中的多焦点声场模式进行了仿真,计算了生物媒质不同厚度层和不同吸收系数时的声场. 结果表明:该方法能优化多焦点声场模式,抑制旁瓣,提高声场增益,将声强最大限度地聚焦在目标区域内; 改变生物组织不同层的厚度和不同层的吸收系数,焦点位置不发生变化,但焦域内的声强会有所变化.     

微泡对高强度聚焦超声声压场影响的仿真研究*

微泡对高强度聚焦超声(HIFU)治疗焦域具有增效作用,而HIFU治疗中不同声学条件下微泡对HIFU形成声压场的影响尚不清楚。本文基于气液混合声波传播方程、Keller气泡运动方程、时域有限差分(FDTD)法和龙格-库塔(RK)法数值仿真研究输入声压、激励频率、气泡初始空隙率和气泡初始半径对HIFU形成声压场的影响。研究结果表明,随着输入声压的增大,焦点处声压升高但焦点处最大声压与输入声压的比值减小,焦点位置几乎不变;随着激励频率和气泡初始半径的增大,焦点处声压升高且焦点位置向远离换能器方向移动;随着气泡初始空隙率的增大,焦点处声压降低且焦点位置向换能器方向移动。     

Magnetic resonance imaging of acoustic streaming: absorption coefficient and acoustic field shape estimation

In this study, magnetic resonance imaging (MRI) is used to visualize acoustic streaming in liquids. A single-shot spin echo sequence (HASTE) with a saturation band perpendicular to the acoustic beam permits the acquisition of an instantaneous image of the flow due to the application of ultrasound. An average acoustic streaming velocity can be estimated from the MR images, from which the ultrasonic absorption coefficient and the bulk viscosity of different glycerol-water mixtures can be deduced. In the same way, this MRI method could be used to assess the acoustic field and time-average power of ultrasonic transducers in water (or other liquids with known physical properties), after calibration of a geometrical parameter that is dependent on the experimental setup.     

A comparative evaluation of three hydrophones and a numerical model in high intensity focused ultrasound fields

The pressure fields of two different high intensity focused ultrasound (HIFU) transducers operated in burst mode were measured at acoustical power levels of 25 and 50 W (continuous wave equivalent) with three different hydrophones: A fiber-optic displacement sensor, a commercial HIFU needle hydrophone, and a prototype of a membrane hydrophone with a protective coating against cavitation effects. Additionally, the fields were modeled using a freely available simulations software package. The measured waveforms, the peak pressure profiles, as well as the spatial-peak temporal-average intensities from the different devices and from the modeling are compared and possible reasons for differences are discussed. The results clearly show that reliable pressure measurements in HIFU fields remain a difficult task concerning both the reliability of the measured values and the robustness of the sensors used: Only the fiber-optic hydrophone survived all four exposure regimes and the measured spatial-peak temporal-average intensities varied by a factor of up to 1.5 between the measurements and the modeling and between the measurements among themselves.     

Parabolic equation for nonlinear acoustic wave propagation in inhomogeneous moving media

A new parabolic equation is derived to describe the propagation of nonlinear sound waves in inhomogeneous moving media. The equation accounts for diffraction, nonlinearity, absorption, scalar inhomogeneities (density and sound speed), and vectorial inhomogeneities (flow). A numerical algorithm employed earlier to solve the KZK equation is adapted to this more general case. A two-dimensional version of the algorithm is used to investigate the propagation of nonlinear periodic waves in media with random inhomogeneities. For the case of scalar inhomogeneities, including the case of a flow parallel to the wave propagation direction, a complex acoustic field structure with multiple caustics is obtained. Inclusion of the transverse component of vectorial random inhomogeneities has little effect on the acoustic field. However, when a uniform transverse flow is present, the field structure is shifted without changing its morphology. The impact of nonlinearity is twofold: it produces strong shock waves in focal regions, while, outside the caustics, it produces higher harmonics without any shocks. When the intensity is averaged across the beam propagating through a random medium, it evolves similarly to the intensity of a plane nonlinear wave, indicating that the transverse redistribution of acoustic energy gives no considerable contribution to nonlinear absorption. Published in Russian in Akusticheskiĭ Zhurnal, 2006, Vol. 52, No. 6, pp. 725–735. This article was translated by the authors.     

Tracking sperm whale (Physeter macrocephalus) dive profiles using a towed passive acoustic array

A passive acoustic method is presented for tracking sperm whale dive profiles, using two or three hydrophones deployed as either a vertical or large-aperture towed array. The relative arrival times between the direct and surface-reflected acoustic paths are used to obtain the ranges and depths of animals with respect to the array, provided that the hydrophone depths are independently measured. Besides reducing the number of hydrophones required, exploiting surface reflections simplifies automation of the data processing. Experimental results are shown from 2002 and 2003 cruises in the Gulf of Mexico for two different towed array deployments. The 2002 deployment consisted of two short-aperture towed arrays separated by 170 m, while the 2003 deployment placed an autonomous acoustic recorder in tandem with a short-aperture towed array, and used ship noise to time-align the acoustic data. The resulting dive profiles were independently checked using single-hydrophone localizations, whenever multipath reflections from the ocean bottom could be exploited to effectively create a large-aperture vertical array. This technique may have applications for basic research and for real-time mitigation for seismic airgun surveys.     

Impact of cavitation on lesion formation induced by high intensity focused ultrasound

High intensity focused ultrasound(HIFU) has shown a great promise in noninvasive cancer therapy. The impact of acoustic cavitation on the lesion formation induced by HIFU is investigated both experimentally and theoretically in transparent protein-containing gel and ex vivo liver tissue samples. A numerical model that accounts for nonlinear acoustic propagation and heat transfer is used to simulate the lesion formation induced by the thermal effect. The results showed that lesions could be induced in the samples exposed to HIFU with various acoustic pressures and pulse lengths. The measured areas of lesions formed in the lateral direction were comparable to the simulated results, while much larger discrepancy was observed between the experimental and simulated data for the areas of longitudinal lesion cross-section. Meanwhile,a series of stripe-wiped-off B-mode pictures were obtained by using a special imaging processing method so that HIFUinduced cavitation bubble activities could be monitored in real-time and quantitatively analyzed as the functions of acoustic pressure and pulse length. The results indicated that, unlike the lateral area of HIFU-induced lesion that was less affected by the cavitation activity, the longitudinal cross-section of HIFU-induced lesion was significantly influenced by the generation of cavitation bubbles through the temperature elevation resulting from HIFU exposures. Therefore, considering the clinical safety in HIFU treatments, more attention should be paid on the lesion formation in the longitudinal direction to avoid uncontrollable variation resulting from HIFU-induced cavitation activity.     

Modeling nonlinear ultrasound propagation in heterogeneous media with power law absorption using a k-space pseudospectral method

The simulation of nonlinear ultrasound propagation through tissue realistic media has a wide range of practical applications. However, this is a computationally difficult problem due to the large size of the computational domain compared to the acoustic wavelength. Here, the k-space pseudospectral method is used to reduce the number of grid points required per wavelength for accurate simulations. The model is based on coupled first-order acoustic equations valid for nonlinear wave propagation in heterogeneous media with power law absorption. These are derived from the equations of fluid mechanics and include a pressure-density relation that incorporates the effects of nonlinearity, power law absorption, and medium heterogeneities. The additional terms accounting for convective nonlinearity and power law absorption are expressed as spatial gradients making them efficient to numerically encode. The governing equations are then discretized using a k-space pseudospectral technique in which the spatial gradients are computed using the Fourier-collocation method. This increases the accuracy of the gradient calculation and thus relaxes the requirement for dense computational grids compared to conventional finite difference methods. The accuracy and utility of the developed model is demonstrated via several numerical experiments, including the 3D simulation of the beam pattern from a clinical ultrasound probe.