Numerical modeling of microbubble backscatter to optimize ultrasound particle image velocimetry imaging: initial studies

We have developed a promising non-invasive ultrasound-based method for performing particle image velocimetry (PIV) in vivo. This method, termed echo PIV, provides multi-component blood velocity data with good (2 ms) temporal resolution. The method takes advantage of the non-linear ultrasound backscatter characteristics of small gas-filled microbubbles (ultrasound contrast) that are seeded into the blood stream. In this study, we use a numerical model to explore potential areas to focus future work in echo PIV.

Ultrasound backscatter from encapsulated microbubbles was modeled using a modified Rayleigh–Plesset equation (Church model, 1995), taking into account the protein/lipid shell layer as a thick, mass-conserving incompressible fluid surrounded by incompressible blood-like fluid. The equation of motion was solved numerically to characterize the fundamental and second harmonic components of the backscattered pressure. Results show a significant advantage in using the second harmonic component for echo PIV, especially for small bubble sizes less than 3 μm in diameter at 2.2 MHz frequency. The effect of the shell thickness ranging from 10 to 500 nm on the vibration amplitude of the bubble was examined and it is shown that the presence of the shell requires mechanical index (MI)>0.2 of incident pressure amplitude to improve bubble detectability. Analysis of the effect of pulse length shows a tradeoff between axial resolution (short pulse length) and bubble detectability (longer pulse length) will most likely be required. The effect of varying MI between 0.1 and 0.6 was also studied at a center frequency of 2.2 MHz and the results indicate that the resonance of the second harmonic is maximized for bubbles with diameter of approximately 2.75 μm. Bubble non-linearities at MI>0.2 induced a resonant frequency shift away from the integer multiple of the incident frequency in the second harmonic backscatter. For a given bubble size, there is a combination of optimal incident frequency and mechanical index range that maximizes the ratio of the second harmonic compared to the fundamental. This resonant frequency decreases with increasing bubble radius. Further, a narrow bandwidth pulse is shown to increase signal strength. Both of these effects may cause conflict with factors governing spatial resolution. Optimization of the incident frequency, microbubble size and mechanical index to enhance bubble detectability will depend on the particular clinical application. These theoretical predictions provide further understanding of the physics behind our echo PIV technique, and should be useful for guiding the design of echo PIV systems.     

Bernoulli excitation and detection of gas bubbles.

A simple method is proposed for detecting and sizing bubbles in pipeline fluid flow. This is based on changing the pressure of the fluid, which in turn excites volume oscillations in the bubble. If the change in pressure is of sufficient brevity and magnitude, the transient distortion results in excitation of the bubble into radiative oscillation at its natural frequency. In a moving fluid, the Bernoulli equation predicts that such a pressure change can be achieved through a suitable gradient in the flow velocity. In the experiments described here, this is achieved by altering the cross-sectional area of the pipe in which the fluid is flowing. We demonstrate the efficacy of this excitation method and, by detecting the radiated sound using a nearby hydrophone, determine the size of individual bubbles from their characteristic oscillation frequency.     

Nonlinear oscillation and acoustic scattering of bubbles

The scattered acoustic pressure and scattered cross section of bubbles is studied using the scattered theory of bubbles. The nonlinear oscillations of bubbles and the scattering acoustic fields of a spherical bubble cluster are numerically simulated based on the bubble dynamic and fluid dynamic. The influences of the interaction between bubbles on scattering acoustic field of bubbles are researched. The results of numerical simulation show that the oscillation phases of bubbles are delayed to a certain extent at different positions in the bubble cluster, but the radii of bubbles during oscillation do not differ too much at different positions. Furthermore, directivity of the acoustic scattering of bubbles is obvious. The scattered acoustic pressures of bubbles are different at the different positions inside and outside of the bubble cluster. The scattering acoustic fields of a spherical bubble cluster depend on the driving pressure amplitude, driving frequency, the equilibrium radii of bubbles, bubble number and the radius of the spherical bubble cluster. These theoretical predictions provide a further understanding of physics behind ultrasonic technique and should be useful for guiding ultrasonic application.     

The acoustic emissions of cavitation bubbles in stretched vortices

Pairs of unequal strength, counter-rotating vortices were produced in order to examine the inception, dynamics, and acoustic emission of cavitation bubbles in rapidly stretching vortices. The acoustic signatures of these cavitation bubbles were characterized during their inception, growth, and collapse. Growing and collapsing bubbles often produced a sharp, broadband, pop sound. The spectrum of these bubbles, and the peak resonant frequency can generally be related to quiescent flow bubble dynamics and corresponding resonant frequencies. However, some elongated cavitation bubbles produced a short tonal burst, or chirp, with frequencies on the order of a few kilohertz. Theses frequencies are too low to be related to resonant frequencies of a bubble in a quiescent flow. Instead, the frequency content of the acoustic signal during bubble inception and growth is related to the volumetric oscillations of the bubble while it interacted with vortical flow that surrounds the bubble (i.e., the resonant frequency of the vortex-bubble system). A relationship was determined between the observed peak frequency of the oscillations, the highly stretched vortex properties, and the water nuclei content. It was found that different cavitation spectra could relate to different flow and fluid properties and therefore would not scale in the same manner.     

Influence of bubble clustering on multibubble sonoluminescence

Influence of clustering of cavitation bubbles on multibubble sonoluminescence (MBSL) in standing wave fields is studied through measurement of MBSL intensity with a photomultiplier tube and observation of corresponding bubble behavior with a high-speed video camera and an intensified charge-coupled device one. It is clarified that, when the SL is quenched suddenly at excessive ultrasonic power, the behavior of bubbles clearly changes; the bubbles which form dendritic branches of filaments change into clusters due to the secondary Bjerknes force. The cluster is composed of several bubbles surrounded by many tiny bubbles, in which bubbles repeatedly coalesce and fragment, and run away from pressure antinodes. When the clusters are broken up by forced fluid motion, the quenching of MBSL is suppressed.     

Nonlinear effects in the dynamics of clouds of bubbles

This paper presents a spectral analysis of the response of a fluid containing bubbles to the motions of a wall oscillating normal to itself. First, a Fourier analysis of the Rayleigh-Plesset equation is used to obtain an approximate solution for the nonlinear effects in the oscillation of a single bubble in an infinite fluid. This is used in the approximate solution of the oscillating wall problem, and the resulting expressions are evaluated numerically in order to examine the nonlinear effects. Harmonic generation results from the nonlinearity. It is observed that the bubble natural frequency remains the dominant natural frequency in the volume oscillations of the bubbles near the wall. On the other hand, the pressure perturbations near the wall are dominated by the first and second harmonics present at twice the natural frequency while the pressure perturbation at the natural frequency of the bubble is inhibited. The response at the forcing frequency and its harmonics is explored along with the variation with amplitude of wall oscillation, void fraction, and viscous and surface tension effects. Splitting and cancellation of frequencies of maximum and minimum response due to enhanced nonlinear effects are also observed.     

Nonlinear oscillations of gas bubbles in viscoelastic fluids

Nonlinear oscillations of gas bubbles in viscoelastic fluids of a three-constant Oldroyd model are theoretically investigated. The equation of motion for a bubble in a viscoelastic fluid subject to a pulsating pressure, and the pressure equation at the bubble wall are obtained. By numerical calculations on these equations, the effects of relaxation time and retardation time on frequency response curves, and the relation between the maximum pressure at the bubble wall and the initial radius of the bubble are clarified.     

两个等径蛋白质气泡在Bingham流体中振动特性

利用黏弹性膜构成的蛋白质气泡有限变形方程,并考虑一个气泡在Bingham流体中振动产生的Bjerknes力对另一个气泡振动特性的影响,建立了两个等径蛋白质气泡在Bingham流体中振动的非线性方程.利用数值计算方法求解该方程,结果表明,增加Bingham流体的塑性黏度,蛋白质气泡振幅衰减速度加快,振动周期增加,频率减小;当两个气泡间的距离减小时,气泡振动频率会增加,振幅衰减速度加快;初始半径小的气泡振动频率高,振幅衰减快,而且振动的频率和振幅衰减的速率越大;与单个气泡相比,两个蛋白质气泡在Bingham流体中振动时,振动具有更高的振动频率,而且振幅衰减速度更快.     

The role of the bubble–bubble interaction on radial pulsations of bubbles

Using a model that with or without considering the interaction between bubbles through the radiated pressure waves, numerical simulations of cavitation bubbles have been performed in order to study the effect of the bubble–bubble interaction on radial pulsations of bubbles. Comparing the results obtained by with or without considering the bubble–bubble interaction, it is suggested that the suppression or enlargement property of expansion ratios of bubbles due to the bubble–bubble interaction largely depends on the ultrasound parameters, the ambient bubble radii, the distances between bubbles and the number of bubbles (in multi-bubble environment, the last two aspects can be expressed using the coupling strength). The frequency response curve of expansion ratio decreases and shifts to left due to the bubble–bubble interaction and the larger the coupling strength is, the more the left-shifting is.     

气泡在内置交错矩形肋管道中自由上升的FTM直接数值模拟

采用直接数值模拟的FTM（Front-Tracking Method）方法研究在重力作用下单气泡在竖直内置矩形肋管内的自由上升.选择矩形肋的肋高、肋距与方管宽度的比值作为管道几何特征值,用莫顿数作为流体特征参数,分析不同肋高、肋距及莫顿数情况下的气泡自由上升,研究不同几何特征及流体参数对气泡运动轨迹的影响.研究表明：在矩形肋片的影响下气泡上升时形状不对称,存在水平方向位移,表现为"蛇形"上升.这种现象与管道几何结构及气泡周围流体性质有关,肋高越大,现象越明显;气泡周围流体的粘度越小,水平方向位移越大.     

In-situ synchrotron X-ray imaging of ultrasound (US)-generated bubbles: Influence of US frequency on microbubble cavitation for membrane fouling remediation

Gaining an in-depth understanding of the characteristics and dynamics of ultrasound (US)--generated bubbles is crucial to effectively remediate membrane fouling. The goal of present study is to conduct in-situ visualization of US-generated microbubbles in water to examine the influence of US frequency on the dynamics of microbubbles. This study utilized synchrotron in-line phase contrast imaging (In-line PCI) available at the biomedical imaging and therapy (BMIT) beamlines at the Canadian Light Source (CLS) to enhance the contrast of liquid/air interfaces at different US frequencies of 20, 28 and 40 KHz at 60 Watts. A high-speed camera was used to capture 2,000 frames per second of the bubble cavitation generated in water under the ultrasound influence. Key parameters at the polychromatic beamlines were optimized to maximize the phase contrast of gas/liquid of the microbubbles with a minimum size of 5.5 µm. ImageJ software was used to analyze the bubble characteristics and their behavior under the US exposure including the microbubble number, size, and fraction of the total area occupied by the bubbles at each US frequency. Furthermore, the bubble characteristics over the US exposure time and at different distances from the transducer were studied. The qualitative and quantitative data analyses showed that the microbubble number or size did not change over time; however, it was observed that most bubbles were created at the middle of the frames and close to the US field. The number of bubbles created under the US exposure increased with the frequency from 20 kHz to 40 kHz (about 4.6 times). However, larger bubbles were generated at 20 kHz such that the average bubble radius at 20 kHz was about 6.8 times of that at 40 kHz. Microbubble movement/traveling through water was monitored, and it was observed that the bubble velocity increased as the frequency was increased from 20 kHz to 40 kHz. The small bubbles moved faster, and the majority of them traveled upward towards the US transducer location. The growth pattern (a correlation between the mean growth ratio and the exposure time) of bubbles at 20 kHz and 60 W was obtained by tracking the oscillation of 22 representative microbubbles over the 700 ms of imaging. The mean growth ratio model was also obtained.     

导电流体中气泡径向振动行为的磁场控制

液态金属中气泡行为是磁流体力学的重要方面。为对磁场条件下导电流体中气泡动力学行为作全面理解,基于磁流体动力学方法建立了磁场条件下导电流体中气泡径向振动的无量纲化动力学方程,数值研究了磁场对导电流体中气泡径向非线性振动稳定性、泡内温度、泡内气压及液体空化阈值的影响。结果显示:磁场增强了气泡非线性振动的稳定性,随着磁场增强且当作用在泡上的电磁力与惯性力数量级可比时,气泡运动为稳定的周期性振动;同时,磁场引起泡内温度、泡内压力及液体空化阈值变化。研究表明,可用磁场调节和控制液态金属中气泡的运动使其满足工程应用需求。     

Acoustic noise spectra under hydrothermal conditions

Acoustic noise spectra were studied for the first time in overheated water using sonohydrothermal reactor operating at 20 kHz ultrasound in the temperature range from 25 to 200 °C at the autogenic pressure of 1–14 bar. The obtained results highlighted a dominating role of stable cavitation during ultrasonic treatment of hot water. Heating of sonicated water results in the formation of large number of nonlinearly oscillating bubbles synchronous with the driving frequency. At 200 °C, the acoustic spectra also display strong subharmonic and multiple ultraharmonic bands. Moreover, cavitation bubbles formed at 200 °C exhibit chaotic and random motions. It has been shown that the addition of TiO₂ nanoparticles to hydrothermal water heated at 200 °C allows to eliminate subharmonic/ultraharmonic bands and stochastic oscillations as well. This effect was assigned to Pickering-like bubble stabilization due to the particle accumulation at the bubble surface.     

Effect of an elastic wall on the dynamics of an encapsulated microbubble: A simulation study

The purpose of the present simulation study is to reveal how confining surfaces with different mechanical properties affect the acoustic response of a contrast agent microbubble. To this end, numerical simulations are carried out for three types of walls: a plastic (OptiCell) wall, an aluminium wall, and a biological tissue. For each wall, the behaviour of contrast microbubbles of three sizes is investigated. The spectral characteristics of the scattered pressure produced by the microbubbles are compared for two cases: the bubble oscillates far away from the wall and the same bubble oscillates in the immediate vicinity of the wall. The results of the simulations allow one to make the following main conclusions. The effect of the OptiCell wall on the acoustic bubble response is stronger than that of the aluminium and tissue walls. Changes in the bubble response near the wall are stronger when bubbles are excited above their resonance frequency. Considering changes in the fundamental and the 2nd harmonic with respect to the peak values of these components at different bubble radii, it is found that the changes are stronger for smaller bubbles and that the changes in the 2nd harmonic are stronger than those in the fundamental. These results allow one to gain an insight into conditions under which the effect of an elastic wall on the acoustic response of a contrast agent microbubble is easier to be detected.     

采用遗传算法对压力脉动过程中气泡模型参数的辨识

流动液体中的压力变化会引起气泡和气穴的产生及破灭,而气泡和气穴又会对液体的流动产生影响及压力变化.为了合理预测流控系统瞬态压力脉动过程中气泡和气穴的体积变化及其对脉动传播过程的影响,基于气泡溶解和析出的物理过程,建立了压力脉动过程中气泡和气穴产生及破灭的数学模型,并提出采用遗传算法对气泡模型中初始气泡体积、气体溶解和析出时间常数进行参数辨识.以一段液压油管路为研究对象,对管路中伴随气泡和气穴的瞬态压力脉动过程进行仿真及实验研究.利用仿真及实验结果,验证了采用遗传算法对气泡模型进行参数辨识的可行性. 关键词： 气泡 气穴 压力脉动 参数辨识     

The acoustic signature of bubbles fragmenting in sheared flow

Measurements of the sound of bubbles fragmenting in fluid shear are presented and analyzed. The frequency, amplitude, and decay rate of the acoustic emissions from 1.8-mm-radius bubbles fragmenting between opposed fluid jets have been determined. A broad band of frequencies (1.8 to 30 kHz) is observed with peak pressure amplitudes in the range of 0.03 to 2 Pa. While the peak pressure amplitudes show no significant scaling with frequency, the frequency dependence of the decay rates is consistent with the sum of thermal and acoustic radiation losses.     

冲击加载下铝中氦泡和孔洞的塑性变形特征研究

通过分子动力学模拟研究了在相同冲击加载强度下单晶铝中氦泡和孔洞的塑性变形特征,结果发现氦泡和孔洞的塌缩是由发射剪切型位错环引起的,而没有观测到棱锥型位错环发射. 氦泡和孔洞周围的位错优先成核位置基本一致,但是氦泡周围发射的位错环数目比孔洞多,位错环发射速度明显比孔洞快. 且氦泡和孔洞被冲击波先扫过部分比后扫过部分发射位错困难. 通过滑移面上的分解应力分析发现,氦泡和孔洞周围塑性特征的差别是由于氦泡内压引起最大分解应力分布改变造成的. 氦泡和孔洞被冲击波先后扫过部分塑性不对称是因为冲击波扫过时引起形状变化, 关键词： 分子动力学 冲击波 氦泡 孔洞     

球状泡群内气泡的耦合振动

振动气泡形成辐射场影响其他气泡的运动, 故多气泡体系中气泡处于耦合振动状态. 本文在气泡群振动模型的基础上, 考虑气泡间耦合振动的影响, 得到了均匀球状泡群内振动气泡的动力学方程, 以此为基础分析了气泡的非线性声响应特征. 气泡间的耦合振动增加了系统对每个气泡的约束, 降低了气泡的自然共振频率, 增强了气泡的非线性声响应. 随着气泡数密度的增加, 振动气泡受到的抑制增强; 增加液体静压力同样可抑制泡群内气泡的振动, 且存在静压力敏感区(1–2 atm, 1 atm=1.01325×10⁵ Pa); 驱动声波对气泡振动影响很大, 随着声波频率的增加, 能够形成空化影响的气泡尺度范围变窄. 在同样的声条件、泡群尺寸以及气泡内外环境下, 初始半径小于5 μm 的气泡具有较强的声响应. 气泡耦合振动会削弱单个气泡的空化影响, 但可延长多气泡系统空化泡崩溃发生的时间间隔和增大作用范围, 整体空化效应增强.     

超声场中气泡融合的影响因素分析

采用高速摄影机对不同声压和频率作用下接触气泡的融合时间进行了实验研究,运用实验和数值计算相结合的方法分析了次Bjerknes力和最大径向振动速度对气泡融合时间的影响,结果表明在不同的超声声压和频率作用下,气泡的融合时间会随着次Bjerknes力和最大径向振动速度的增大而增大,对两个因素进行对比分析得到次Bjerknes力是影响气泡融合的关键因素。     

气泡体积分数对沙质沉积物低频声学特性的影响

由于有机物质分解等原因,实际的海底沉积物中存在气泡,气泡的存在会显著影响沉积物低频段的声学特性,因此研究气泡对沉积物低频段声速的影响机理具有重要意义.考虑到外场环境的不可控性,在室内水池中搭建了大尺度含气非饱和沙质沉积物声学特性获取平台,在有界空间中应用多水听器反演方法首次获取了含气非饱和沙质沉积物300—3000 Hz频段内的声速数据(79—142 m/s),并同时利用双水听器法获取了同一频段的数据(112—121 m/s).在声波频率远低于沉积物中最大气泡的共振频率时,根据等效介质理论,将孔隙水和气泡等效为一种均匀流体,改进了水饱和等效密度流体近似模型.模型揭示了气泡对沉积物低频段声学特性的影响规律,理论上解释了沉积物中声速的降低.通过分析模型预报声速对模型参数的敏感性,根据测量得到的声速分布反演得到了沉积物不同区域的气泡体积分数,气泡体积分数从1.07%变化到2.81%.改进的模型为沉积物中气泡体积分数估计提供了一种新方法.