Numerical investigation of the inertial cavitation threshold by dual-frequency excitation in the fluid and tissue

Inertial cavitation thresholds, which are defined as bubble growth by 2-fold from the equilibrium radius, by two types of ultrasonic excitation (at the classical single-frequency mode and dual-frequency mode) were calculated. The effect of the dual-frequency excitation on the inertial cavitation threshold in the different surrounding media (fluid and tissue) was studied, and the paramount parameters (driving frequency, amplitude ratio, phase difference, and frequency ratio) were also optimized to maximize the inertial cavitation. The numerical prediction confirms the previous experimental results that the dual-frequency excitation is capable of reducing the inertial cavitation threshold in comparison to the single-frequency one at the same output power. The dual-frequency excitation at the high frequency (i.e., 3.1 + 3.5 MHz vs. 1.1 + 1.3 MHz) is preferred in this study. The simulation results suggest that the same amplitudes of individual components, zero phase difference, and large frequency difference are beneficial for enhancing the bubble cavitation. Overall, this work may provide a theoretical model for further investigation of dual-frequency excitation and guidance of its applications for a better outcome.     

The effects of coupling and bubble size on the dynamical-systems behaviour of a small cluster of microbubbles

This study endeavours to apply a theoretical model for predicting the dynamics of a bubble cluster of various sizes, within which each bubble may assume different initial conditions from other bubbles in the cluster. The resulting system of coupled Keller-Miksis-Parlitz equations are solved numerically, and the effects of coupling and bubble size on bubble cluster dynamics are examined for a given set of ultrasound parameters. It has been found that the effects of coupling are significant, and a bubble cluster's bifurcation characteristics and route to chaos can be altered by inter-bubble interactions. This gives rise to the possibility of suppressing the chaotic oscillations of microbubbles by varying bubble cluster size. Small equilibrium radii bubbles have little influence on the dynamics of neighbouring bubbles in a cluster via coupling. Furthermore, a bubble system consisting of smaller-sized bubbles transitions from order to chaos at lower driving pressure amplitudes.     

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.     

超声药物释放空化动力学行为研究

以直径1 μm的脂质体为空化研究对象,从修正的Rayleigh空化方程入手,研究机械系数(MI)对300 kHz和1 MHz超声作用时空化效应的影响。脂质体的药物释放以超声作用前后脂质体中钙黄绿素的荧光强度为量度。模拟结果表明:在微泡振荡过程中,由超声波驱动产生的负向最大泡壁运动速度促使微泡半径从最大快速减小接近于零,微泡积聚到最大能量。对于300 kHz和1 MHz的激励超声,存在一个拐点(MI)值,当MI小于接近0.4时,1 MHz微泡半径变化幅度强于300 kHz;当MI>0.4时,300 kHz微泡半径变化幅度强于1 MHz。这一结果预示在此范围内,300 kHz的药物释放效果好于1 MHz。本研究为超声空化效应研究及超声药物释放应用提供了理论依据。     

Biological effect of paramecium in diffused ultrasonic fields

Since the cell structure or biophysical reaction includes in the interaction between ultrasound and living matter. When multi-cell creature is exposed to ultrasound, this reaction will lead the biological effect becomes complex. Therefore, in this paper, a single cell creature is chosen to study the biological effects induced by ultrasound exposure. The paramecium, which possesses many features typical of higher-order animal cells, was considered an appropriate choice for this study. The ability shown by ultrasound in promoting and/or accelerating many reactions has been shown to be a useful field. The growth phase of paramecium by using the ultrasound irradiation is an important parameter in this study. In our experiment, the exponential and stationary phases were employed. Three important factors must be taken into account when an ultrasonic biological reaction is investigated: the medium system, the bubbles' field, and the acoustic field. The medium system involves the physical parameters of the medium field. The bubbles' field includes the reacting bubble size of the liquid and the resonance frequency of the reaction bubbles. The oscillation of the cells in response to the ultrasound radiation is simulated using Rayleigh-Plesset's bubble activation theory. The resonance frequency of the unicellular creature is then calculated. The acoustic field is about using the diffuse field theory of Sabine to create a uniform sound field for the radiation experiment. The resonance frequency of the paramecium vacuole is among 0.54-1.09 MHz. When the 0.25 and 0.5 MHz frequencies of ultrasound was irradiated in the stationary phase of the paramecium, the relative growth rate was about 20% lower than that of unexposed sample. Therefore, the phenomenon of inhibition and destruction appeared during irradiation. The exponential phase of the paramecium samples appear to be different when irradiated with 1 MHz ultrasound. As can be seen in the results, the maximum relative growth rate was increasing 18% with 1 MHz ultrasound exposure.     

Spatial-temporal dynamics of cavitation bubble clouds in 1.2 MHz focused ultrasound field

Cavitation bubbles have been recognized as being essential to many applications of ultrasound. Temporal evolution and spatial distribution of cavitation bubble clouds induced by a focused ultrasound transducer of 1.2 MHz center frequency are investigated by high-speed photography. It is revealed that at a total acoustic power of 72 W the cavitation bubble cloud first emerges in the focal region where cavitation bubbles are observed to generate, grow, merge and collapse during the initial 600 μs. The bubble cloud then grows upward to the post-focal region, and finally becomes visible in the pre-focal region. The structure of the final bubble cloud is characterized by regional distribution of cavitation bubbles in the ultrasound field. The cavitation bubble cloud structure remains stable when the acoustic power is increased from 25 W to 107 W, but it changes to a more violent form when the acoustic power is further increased to 175 W.     

弹性微管内气泡的非线性受迫振动

将弹性管壁视为膜弹性结构, 探索在外部声场作用下弹性微管内液柱-气泡-管壁构成耦合振动系统的非线性特征. 利用逐级近似法对系统非线性共振频率、基频和三倍频振动幅值响应、 分频激励共振机理等进行了理论分析. 基频和三倍频振动的幅-频响应数值结果表明: 气泡的轴向共振和管壁共振不能同时出现; 两垂直方向的振动均表现出幅值响应多值性, 进而可能引起系统的不稳定声响应; 三倍频振动在低频区的声响应强于高频区. 关键词： 弹性微管 受迫振动 非线性振动 气泡声响应     

High frequency attenuation measurements of lipid encapsulated contrast agents

A number of recent studies have indicated the potential of ultrasound contrast agent imaging at high ultrasound frequencies. However, the acoustic properties of microbubbles at frequencies above 10 MHz remain poorly understood at present. In this study we characterize the high frequency attenuation properties of (1) BR14, (2) BR14 that has been mechanically filtered (1 and 2 microm pore sizes) to exclude larger bubbles, and (3) the micron to submicron agent BG2423. A narrowband pulse-echo substitution method is employed with a series of four transducers covering the frequency range from 2 to 50 MHz. For BR14, attenuation decreases rapidly from 2 to 10 MHz and then more gradually from 10 to 50 MHz. For 2 microm filtration, the attenuation peaks between 10 and 15 MHz. For 1 microm filtration, attenuation continues to rise until 50 MHz. The agent BG2423 exhibits a diffuse attenuation peak in the range of 15-25 MHz and remains high until 50 MHz. These results demonstrate a strong influence of bubble size on high frequency attenuation curves, with bubble diameters of 1-2 microm and below having more pronounced acoustic activity at frequencies above 10 MHz.     

Sound scattering and localized heat deposition of pulse-driven microbubbles

The sound scattering of free microbubbles released from strongly driven ultrasound contrast agents with brittle shell (e.g., Sonovist) is studied numerically. At high peak pressure of the driving pulses, the bubbles respond nonlinearly with cross sections pronouncedly larger than in the linear case; a large portion of the energy is radiated into high frequency ultrasound. Subsequent absorption of these high frequencies in the surrounding liquid (blood) diminishes the effective scattering cross section drastically. The absorption results in highly localized heating, with a substantial temperature rise within the first few microm from the bubble surface. The maximum heating in 1 microm distance is strongly dependent on driving pressure. Temperature elevations of more than 100 K can be achieved for amplitudes of Pa approximately 30 atm, which coincides with the highest pressures used in ultrasound diagnostics. The perfectly spherical collapses assumed here occur rarely, and the heating is highly localized and transient (approximately 10 micros). Therefore, a thermal hazard would only be expected at driving pressures beyond the diagnostic range.     

Thresholds for cavitation produced in water by pulsed ultrasound

The threshold for transient cavitation produced in water by pulsed ultrasound was measured as a function of pulse duration and pulse repetition frequency at both 0.98 and 2.30 MHz. The cavitation events were detected with a passive acoustic technique which relies upon the scattering of the irradiation field by the bubble clouds associated with the events. The results indicate that the threshold is independent of pulse duration and acoustic frequency for pulses longer than approximately 10 acoustic cycles. The threshold increases for shorter pulses. The cavitation events are likely to be associated with bubble clouds rather than single bubbles.     

Theoretical prediction of the scattering of spherical bubble clusters under ultrasonic excitation

Due to the nonlinear vibration of ultrasound contrast agent bubbles, a nonlinear scattered sound field will be generated when bubbles are driven by ultrasound. A bubble cluster consists of numerous bubbles gathering in a spherical space. It has been noted that the forward scattering of a bubble cluster is larger than its backscattering, and some studies have experimentally found the angular dependence of a bubble cluster’s scattering signal. In this paper, a theory is proposed to explain the difference of acoustic scattering at different directions of a bubble cluster when it is driven by ultrasound, and predicts the angular distribution of scattered acoustic pressure under different parameters. The theory is proved to be correct under circumstances of small clusters and weak interactions by comparing theoretical results with numerical simulations. This theory not only sheds light on the physics of bubble cluster scattering, but also may contribute to the improvement of ultrasound imaging technology, including ultrasonic harmonic imaging and contrast-enhanced ultrasonography.     

Erratum: transient pulsations of small gas bubbles in water [J. Acoust. Soc. Am. 84, 985-998 (1988)] [corrected and republished

Transient behavior of small gas bubbles in a liquid set into violent motion by ultrasonic pressure waves is of interest because of widespread use of microsecond pulses in diagnostic ultrasound. Such pulses contain only a few pressure cycles and the transient pulsations of bubbles set in motion by such pulses would determine the bubble-ultrasound interaction. A computer study has been made to obtain a global representation of the pulsation amplitudes R (t) of small gas bubbles (nuclei) in water during the first few cycles of a cw ultrasonic pressure. One objective was to obtain a better understanding of cavitation phenomena where many nuclei with initial radii Rn from 0.1-20 microns are set in motion at pressures ranging from 0.5-5 bars and at frequencies from 0.5-10 MHz. Results allowed construction of surfaces showing the relative bubble amplitude R/Rn as a function of Rn and of the time t/TA, where TA is the acoustic period. One finding is that, in the range of peak pressures found in diagnostic pulses, transient cavities would be generated during the first pressure cycle from nuclei with initial radii as small as a few microns (micron). Nuclei that grow into transient cavities in the first pressure cycle are here called "prompt" nuclei. At a specified pressure, the size range of radii Rn in which they occur decreases with increasing frequency. At 5 bars, the range of Rn for prompt nuclei is 0.166-11.35 microns at 0.5 MHz and vanishes at 10 MHz.     

Shape stability of a gas bubble in a soft solid

Predicting the onset of non-spherical oscillations of bubbles in soft matter is a fundamental cavitation problem with implications to sonoprocessing, polymeric materials synthesis, and biomedical ultrasound applications. The shape stability of a bubble in a Kelvin-Voigt viscoelastic medium with nonlinear elasticity, the simplest constitutive model for soft solids, is analytically investigated and compared to experiments. Using perturbation methods, we develop a model reducing the equations of motion to two sets of evolution equations: a Rayleigh-Plesset-type equation for the mean (volume-equivalent) bubble radius and an equation for the non-spherical mode amplitudes. Parametric instability is predicted by examining the natural frequency and the Mathieu equation for the non-spherical modes, which are obtained from our model. Our theoretical results show good agreement with published experiments of the shape oscillations of a bubble in a gelatin gel. We further examine the impact of viscoelasticity on the time evolution of non-spherical mode amplitudes. In particular, we find that viscosity increases the damping rate, thus suppressing the shape instability, while shear modulus increases the natural frequency, which changes the unstable mode. We also explain the contributions of rotational and irrotational fields to the viscoelastic stresses in the surroundings and at the bubble surface, as these contributions affect the damping rate and the unstable mode. Our analysis on the role of viscoelasticity is potentially useful to measure viscoelastic properties of soft materials by experimentally observing the shape oscillations of a bubble.     

非球形包膜微泡近场局部高压研究

基于流体力学,导出了超声驱动下的非球形包膜微泡的外部流体压强的解析表达式.数值模拟表明,虽然包膜微泡的非球形状对远场流体压强没有明显影响,但会造成近场局部位置有极大的流体压强,其明显高于同等条件下的球形包膜微泡周围相应位置上的流体压强.这一现象对包膜微泡的实际应用,如强超声治疗、靶向给药和细胞微穿孔等有着重要的意义.随着驱动频率向包膜微泡本征频率的靠近或微泡偏离球形程度的增大,所产生的近场局部高压也越大.     

Multi-time scale characterization of acoustic droplet vaporization and payload release of phase-shift emulsions using high-speed microscopy

Acoustic droplet vaporization (ADV) is the phase-transitioning of perfluorocarbon emulsions, termed phase-shift emulsions, into bubbles using focused ultrasound. ADV has been utilized in many biomedical applications. For localized drug release, phase-shift emulsions with a bioactive payload can be incorporated within a hydrogel to yield an acoustically-responsive scaffold (ARS). The dynamics of ADV and associated drug release within hydrogels are not well understood. Additionally, emulsions used in ARSs often contain high molecular weight perfluorocarbons, which is unique relative to other ADV applications. In this study, we used ultra-high-speed brightfield and fluorescence microscopy, at frame rates up to 30 million and 0.5 million frames per second, respectively, to elucidate ADV dynamics and payload release kinetics in fibrin-based ARSs containing phase-shift emulsions with three different perfluorocarbons: perfluoropentane (PFP), perfluorohexane (PFH), and perfluorooctane (PFO). At an ultrasound excitation frequency of 2.5 MHz, the maximum expansion ratio, defined as the maximum bubble diameter during ADV normalized by the initial emulsion diameter, was 4.3 ± 0.8, 4.1 ± 0.6, and 3.6 ± 0.4, for PFP, PFH, PFO emulsions, respectively. ADV yielded stable bubble formation in PFP and PFH emulsions, though the bubble growth rate post-ADV was three orders of magnitudes slower in the latter emulsion. Comparatively, ADV generated bubbles in PFO emulsions underwent repeated vaporization/recondensation or fragmentation. Different ADV-generated bubble dynamics resulted in distinct release kinetics in phase-shift emulsions carrying fluorescently-labeled payloads. The results provide physical insight enabling the modulation of bubble dynamics with ADV and hence release kinetics, which can be used for both diagnostic and therapeutic applications of ultrasound.     

Bubble nonlinear dynamics and stimulated scattering process

A complete understanding of the bubble dynamics is deemed necessary in order to achieve their full potential applications in industry and medicine. For this purpose it is first needed to expand our knowledge of a single bubble behavior under different possible conditions including the frequency and pressure variations of the sound field. In addition, stimulated scattering of sound on a bubble is a special effect in sound field, and its characteristics are associated with bubble oscillation mode. A bubble in liquid can be considered as a representative example of nonlinear dynamical system theory with its resonance, and its dynamics characteristics can be described by the Keller–Miksis equation. The nonlinear dynamics of an acoustically excited gas bubble in water is investigated by using theoretical and numerical analysis methods. Our results show its strongly nonlinear behavior with respect to the pressure amplitude and excitation frequency as the control parameters, and give an intuitive insight into stimulated sound scattering on a bubble. It is seen that the stimulated sound scattering is different from common dynamical behaviors, such as bifurcation and chaos, which is the result of the nonlinear resonance of a bubble under the excitation of a high amplitude acoustic sound wave essentially. The numerical analysis results show that the threshold of stimulated sound scattering is smaller than those of bifurcation and chaos in the common condition.     

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.     

The impact of methanol mass transport on its conversion for the production of hydrogen and oxygenated reactive species in sono-irradiated aqueous solution

This study aims principally to assess numerically the impact of methanol mass transport (i.e., evaporation/condensation across the acoustic bubble wall) on the thermodynamics and chemical effects (methanol conversion, hydrogen and oxygenated reactive species production) of acoustic cavitation in sono-irradiated aqueous solution. This effect was revealed at various ultrasound frequencies (from 213 to 1000 kHz) and acoustic intensities (1 and 2 W/cm²) over a range of methanol concentrations (from 0 to 100%, v/v). It was found that the impact of methanol concentration on the expansion and compression ratios, bubble temperature, CH₃OH conversion and the molar productions inside the bubble is frequency dependent (either with or without consideration of methanol mass transport), where this effect is more pronounced when the ultrasound frequency is decreased. Alternatively, the decrease in acoustic intensity decreases clearly the effect of methanol mass transport on the bubble sono-activity. When methanol mass transfer is eliminated, the decrease of the bubble temperature, CH₃OH conversion and the molar yield of the bubble with the rise of methanol concentration was found to be more amortized as the wave frequency is reduced from 1 MHz to 213 kHz, compared to the case when the mass transport of methanol is taken into account. Our findings indicate clearly the importance of incorporating the evaporation and condensation mechanisms of methanol throughout the numerical simulations of a single bubble dynamics and chemical activity.     

含气泡液体中气泡振动的研究

研究了含气泡液体中单个气泡在驱动声场一定情况下的振动过程. 让每次驱动声场作用的时间特别短, 使气泡半径发生微小变化后再将其变化反馈到气泡群对驱动声场的散射作用中去, 从而可以得到某单个气泡周围受气泡散射影响后的声场, 接着再让气泡在该声场作用下做短时振动, 如此反复. 通过这样的方法, 研究了液体中单个气泡的振动情况并对其半径变化进行了数值模拟, 结果发现, 在液体中含有大量气泡的情况下, 某单个气泡的振动过程明显区别于液体中只有一个气泡的情况. 由于大量气泡和驱动声场的相互作用, 使气泡半径的变化存在多种不同的振动情况, 在不同的气泡大小和含量的情况下, 半径变化过程分别表现为: 在平衡位置附近振荡的过程; 周期性的空化过程; 一次空化过程后保持某一大小振荡的过程; 增长后维持某一大小振荡的过程等. 所以, 对于含气泡液体中气泡振动的研究, 在驱动声场一定的情况下, 必须考虑气泡含量的因素. 关键词： 含气泡液体 超声空化 散射 数值模拟