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.     

Optical and acoustic monitoring of bubble cloud dynamics at a tissue-fluid interface in ultrasound tissue erosion

Short, high-intensity ultrasound pulses have the ability to achieve localized, clearly demarcated erosion in soft tissue at a tissue-fluid interface. The primary mechanism for ultrasound tissue erosion is believed to be acoustic cavitation. To monitor the cavitating bubble cloud generated at a tissue-fluid interface, an optical attenuation method was used to record the intensity loss of transmitted light through bubbles. Optical attenuation was only detected when a bubble cloud was seen using high speed imaging. The light attenuation signals correlated well with a temporally changing acoustic backscatter which is an excellent indicator for tissue erosion. This correlation provides additional evidence that the cavitating bubble cloud is essential for ultrasound tissue erosion. The bubble cloud collapse cycle and bubble dissolution time were studied using the optical attenuation signals. The collapse cycle of the bubble cloud generated by a high intensity ultrasound pulse of 4-14 micros was approximately 40-300 micros depending on the acoustic parameters. The dissolution time of the residual bubbles was tens of ms long. This study of bubble dynamics may provide further insight into previous ultrasound tissue erosion results.     

流体控制方程的超声空化泡动力学模拟*

本文基于流体动力学控制方程和VOF模型,在FLUENT 14.5软件环境下对超声空化泡进行数值模拟。首先研究了超声空化泡一个周期内的形态变化,并且利用空化泡形态变化的最大面积、最小面积、膨胀时间、收缩时间等数值结果分析超声参数对空化效果的影响。同时探究了双频超声作用下空化泡运动的变化,计算结果表明:在其他条件相同的情况下,在1~5MPa范围内,超声声压幅值为3MPa时空化效果最好;当超声频率大于20kHz时,空化效果随着超声频率的增大而降低。对于频率相同的双频超声,较声压幅值为其两倍的单频超声有更好的空化效果;对于频率不同的双频超声,空化效果受到频率差的影响。     

The interaction of shockwaves with a vapour bubble in boiling histotripsy: The shock scattering effect

Boiling histotripsy is a High Intensity Focused Ultrasound (HIFU) technique which uses a number of short pulses with high acoustic pressures at the HIFU focus to induce mechanical tissue fractionation. In boiling histotripsy, two different types of acoustic cavitation contribute towards mechanical tissue destruction: a boiling vapour bubble and cavitation clouds. An understanding of the mechanisms underpinning these phenomena and their dynamics is therefore paramount to predicting and controlling the overall size of a lesion produced for a given boiling histotripsy exposure condition. A number of studies have shown the effects of shockwave heating in generating a boiling bubble at the HIFU focus and have studied its dynamics under boiling histotripsy insonation. However, not much is known about the subsequent production of cavitation clouds that form between the HIFU transducer and the boiling bubble. The main objective of the present study is to examine what causes this bubble cluster formation after the generation of a boiling vapour bubble. A numerical simulation of 2D nonlinear wave propagation with the presence of a bubble at the focus of a HIFU field was performed using the k-Wave MATLAB toolbox for time domain ultrasound simulations, which numerically solves the generalised Westervelt equation. The numerical results clearly demonstrate the appearance of the constructive interference of a backscattered shockwave by a bubble with incoming incident shockwaves. This interaction (i.e., the reflected and inverted peak positive phase from the bubble with the incoming incident rarefactional phase) can eventually induce a greater peak negative pressure field compared to that without the bubble at the HIFU focus. In addition, the backscattered peak negative pressure magnitude gradually increased from 17.4 MPa to 31.6 MPa when increasing the bubble size from 0.2 mm to 1.5 mm. The latter value is above the intrinsic cavitation threshold of –28 MPa in soft tissue. Our results suggest that the formation of a cavitation cloud in boiling histotripsy is a threshold effect which primarily depends (a) the size and location of a boiling bubble, and (b) the sum of the incident field and that scattered by a bubble.     

High-speed observation of cavitation bubble clouds near a tissue boundary in high-intensity focused ultrasound fields

Cavitation bubble clouds generated near a tissue boundary by high-intensity focused ultrasound (HIFU) were studied using high-speed photography. In all, 171 image series were captured during the initial 100 ms of continuous HIFU exposure, which showed that cavitation bubble clouds at the tissue boundary organized into two structures - “cone-shape bubble cloud structure” recorded in 146 image series and “crown-shape bubble cloud structure” recorded in 18 image series. The remaining 7 image series showed the interchanging of these two structures. It was found that when cavitation bubbles first appeared at the tissue boundary, they developed to cone-shape bubble cloud. The cone-shape bubble cloud structure was characterized by a nearly fixed tip in front of the tissue boundary. When the cavitation bubbles initially appeared away from the tissue boundary they evolved into a crown-shape bubble cloud. Deformation of tissue boundary was shown in all the recorded image series.     

Effects of acoustic parameters on bubble cloud dynamics in ultrasound tissue erosion (histotripsy)

High intensity pulsed ultrasound can produce significant mechanical tissue fractionation with sharp boundaries ("histotripsy"). At a tissue-fluid interface, histotripsy produces clearly demarcated tissue erosion and the erosion efficiency depends on pulse parameters. Acoustic cavitation is believed to be the primary mechanism for the histotripsy process. To investigate the physical basis of the dependence of tissue erosion on pulse parameters, an optical method was used to monitor the effects of pulse parameters on the cavitating bubble cloud generated by histotripsy pulses at a tissue-water interface. The pulse parameters studied include pulse duration, peak rarefactional pressure, and pulse repetition frequency (PRF). Results show that the duration of growth and collapse (collapse cycle) of the bubble cloud increased with increasing pulse duration, peak rarefactional pressure, and PRF when the next pulse arrived after the collapse of the previous bubble cloud. When the PRF was too high such that the next pulse arrived before the collapse of the previous bubble cloud, only a portion of histotripsy pulses could effectively create and collapse the bubble cloud. The collapse cycle of the bubble cloud also increased with increasing gas concentration. These results may explain previous in vitro results on effects of pulse parameters on tissue erosion.     

声场中水力空化泡的动力学特性

以水为工作介质,考虑了液体黏性、表面张力、可压缩性及湍流作用等情况,对文丘里管反应器中空化泡在声场作用下的动力学行为特性进行了数值研究.分析了超声波频率、声压及喉径比对空化泡运动特性以及空化泡崩溃时所形成泡温以及压力脉冲的影响.结果表明,超声将水力空化泡运动调制成稳态空化,有利于增强空化效果. 关键词： 超声波 水力空化 湍流 气泡动力学     

Numerical simulations of stable cavitation bubble generation and primary Bjerknes forces in a three-dimensional nonlinear phased array focused ultrasound field

We present a model developed for studying the generation of stable cavitation bubbles and their motion in a three-dimensional volume of liquid with axial symmetry under the effect of finite-amplitude phased array focused ultrasound. The density of bubbles per unit volume is determined by a nonlinear law which is a threshold-dependent function of the negative acoustic pressure reached in the liquid, in which nuclei are initially distributed. The nonlinear mutual interaction of ultrasound and bubble oscillations is modeled by a nonlinear coupled differential system formed by the wave and a Rayleigh-Plesset equations, for which both the pressure and the bubble oscillation variables are unknown. The system, which accounts for nonlinearity, dispersion, and attenuation due to the bubbles, is solved by numerical approximations. The nonlinear acoustic pressure field is then used to evaluate the primary Bjerknes force field and to predict the subsequent motion of bubbles. In order to illustrate the procedure, a medium-high and a low ultrasonic frequency configurations are assumed. Simulation results show where bubbles are generated, the nonlinear effects they have on ultrasound, and where they are relocated. Despite many physical restrictions and thanks to its particularities (two nonlinear coupled fields, bubble generation, bubble motion), the numerical model used in this work gives results that show qualitative coherence with data observed experimentally in the framework of stable cavitation and suggest their usefulness in some application contexts.     

硫酸中多气泡声致发光光谱

非线性声波方程与气泡脉动方程联立, 可以描述声空化云中的声场以及任何一个气泡的脉动过程,为数值计算空化场问题提供了理论框架.计算的声压分布变化可以用来计算单气泡动力学,了解任何位置处气泡发光过程以及气泡内气体温度和压强变化等. 对浓硫酸中氙气泡空化云的计算定性符合实验观测, 只有钠原子线谱的计算结果相比实验观测有些出入.     

Spatio-temporal dynamics of cavitation bubble clouds in a low frequency reactor: comparison between theoretical and experimental results.

The propagation of ultrasound through a liquid induces the growth of inceptions and germs into bubbles. In a low frequency reactor, fragmentary transient bubbles emerge due to the acoustic driving. They violently collapse in one cycle and fragment into many smaller bubbles than in turn cavitate. This violent collapse is responsible for the mechanical effects of ultrasounds effects. The latter bubbles gather in a ball-shaped cloud and migrate to pressure antinodes. During their migration, their nonexplosive collapses mainly contribute to activate chemical reactions by producing OH. radicals. Mathematical modelling is performed as a new approach to predict the bubbles field. Through numerical simulation, we determinate emergence sites of mechanically active cavitation bubbles. Calculus are compared with aluminium foil degradation. The modelling of bubble migration allow us to have an insight on the privileged sites of the chemical reactions. Validation of the modelling is made through direct comparison with chemiluminescence photo. All experiments and computations are made in a 28.2 kHz sonoreactor.     

双泡超声空化计算分析

将由速度势叠加原理得到的双泡超声空化动力学微分方程归一化,通过matlab语言编程计算,分析了水中空化泡的线度、双泡间距、声压幅值、声波频率等因素对空化过程的影响. 在双泡超声空化动力学微分方程中引入双频超声,探讨了双泡双频超声问题. 研究表明泡的线度是决定空化特性的主要因素,声压幅值对空化特性的影响最大,其次是超声波的频率;双泡间的相互作用影响空化特性,这种影响随双泡间距的增大而减弱;双频超声对双泡空化特性的影响有限,这种影响在两超声分量的声压幅值相等时较强. 关键词： 超声空化 双泡 双频超声     

Effects of adjacent bubble on spatiotemporal evolutions of mechanical stresses surrounding bubbles oscillating in tissues

The cavitation dynamics and mechanical stress in viscoelastic tissues, as the primary mechanisms of some ultrasound therapies, are extremely complex due to the interactions of cavitation bubble with adjacent bubbles and surrounding tissues. Therefore, the cavitation dynamics and resultant mechanical stress of two-interacting bubbles in the viscoelastic tissues are numerically investigated, especially focusing on the effects of the adjacent bubble. The results demonstrate that the mechanical stress is highly dependent on the bubble dynamics. The compressive stress and tensile stress are generated at the stage of bubble expansion and collapse stage, respectively. Furthermore, within the initial parameters examined in this paper, the effects of the adjacent bubble will distinctly suppress the radial expansion of the small bubble and consequently lead its associated stresses to decrease. Owing to the superimposition of two stress fields, the mechanical stresses surrounding the small bubble in the direction of the neighboring bubble are smaller than those in other directions. For two interacting cavitation bubbles, the suppression effects of the nearby bubble on both the cavitation dynamics and the stresses surrounding the small bubble increase as the ultrasound amplitude and the initial radius of the large bubble increase, whereas they decrease with the inter-bubble distance increasing. Moreover, increasing the tissue viscoelasticity will reduce the suppression effects of the nearby bubble, except in instances where the compressive stress and tensile stress first increase and then decrease with the tissue elasticity and viscosity increasing respectively. This study can provide a further understanding of the mechanisms of cavitation-associated mechanical damage to the adjacent tissues or cells.     

亚临界水中超声激励空化泡动力学分析

考察亚临界水中压力和温度对超声空化泡动力学的影响。应用非线性Rayleigh-Plesset方程模拟空化泡运动过程,并利用Matlab软件编程求数值解,用碘量法测定超声在亚临界水中的声空化产额。结果表明:当亚临界水的压力相似文献   

Numerical investigation on acoustic cavitation characteristics of an air-vapor bubble: Effect of equation of state for interior gases

The cavitation dynamics of an air-vapor mixture bubble with ultrasonic excitation can be greatly affected by the equation of state (EOS) for the interior gases. To simulate the cavitation dynamics, the Gilmore-Akulichev equation was coupled with the Peng–Robinson (PR) EOS or the Van der Waals (vdW) EOS. In this study, the thermodynamic properties of air and water vapor predicted by the PR and vdW EOS were first compared, and the results showed that the PR EOS gives a more accurate estimation of the gases within the bubble due to the less deviation from the experimental values. Moreover, the acoustic cavitation characteristics predicted by the Gilmore-PR model were compared to the Gilmore-vdW model, including the bubble collapse strength, the temperature, pressure and number of water molecules within the bubble. The results indicated that a stronger bubble collapse was predicted by the Gilmore-PR model rather than the Gilmore-vdW model, with higher temperature and pressure, as well as more water molecules within the collapsing bubble. More importantly, it was found that the differences between both models increase at higher ultrasound amplitudes or lower ultrasound frequencies while decreasing as the initial bubble radius and the liquid parameters (e.g., surface tension, viscosity and temperature of the surrounding liquid) increase. This study might offer important insights into the effects of the EOS for interior gases on the cavitation bubble dynamics and the resultant acoustic cavitation-associated effects, contributing to further optimization of its applications in sonochemistry and biomedicine.     

Synchrotron X-ray imaging of the onset of ultrasonic horn cavitation

High-power ultrasonic horns operating at low frequency are known to generate a cone-shaped cavitation bubble cloud beneath them. The exact physical processes resulting in the conical structure are still unclear mainly due to challenges associated with their visualization. Herein, we address the onset of the cavitation cloud by exploiting high-speed X-ray phase contrast imaging. It reveals that the cone formation is not immediate but results from a three-step phenomenology: (i) inception and oscillation of single bubbles, (ii) individual cloud formation under splitting or lens effects, and (iii) cloud merging leading to the formation of a bubble layer and, eventually, to the cone structure due to the radial pressure gradient on the horn tip.     

Effect of static pressure on acoustic energy radiated by cavitation bubbles in viscous liquids under ultrasound

The effect of static pressure on acoustic emissions including shock-wave emissions from cavitation bubbles in viscous liquids under ultrasound has been studied by numerical simulations in order to investigate the effect of static pressure on dispersion of nano-particles in liquids by ultrasound. The results of the numerical simulations for bubbles of 5 μm in equilibrium radius at 20 kHz have indicated that the optimal static pressure which maximizes the energy of acoustic waves radiated by a bubble per acoustic cycle increases as the acoustic pressure amplitude increases or the viscosity of the solution decreases. It qualitatively agrees with the experimental results by Sauter et al. [Ultrason. Sonochem. 15, 517 (2008)]. In liquids with relatively high viscosity (～200 mPa s), a bubble collapses more violently than in pure water when the acoustic pressure amplitude is relatively large (～20 bar). In a mixture of bubbles of different equilibrium radius (3 and 5 μm), the acoustic energy radiated by a 5 μm bubble is much larger than that by a 3 μm bubble due to the interaction with bubbles of different equilibrium radius. The acoustic energy radiated by a 5 μm bubble is substantially increased by the interaction with 3 μm bubbles.     

Ultrasound line-by-line scanning method of spatial–temporal active cavitation mapping for high-intensity focused ultrasound

This paper presented an ultrasound line-by-line scanning method of spatial–temporal active cavitation mapping applicable in a liquid or liquid filled tissue cavities exposed by high-intensity focused ultrasound (HIFU). Scattered signals from cavitation bubbles were obtained in a scan line immediately after one HIFU exposure, and then there was a waiting time of 2 s long enough to make the liquid back to the original state. As this pattern extended, an image was built up by sequentially measuring a series of such lines. The acquisition of the beamformed radiofrequency (RF) signals for a scan line was synchronized with HIFU exposure. The duration of HIFU exposure, as well as the delay of the interrogating pulse relative to the moment while HIFU was turned off, could vary from microseconds to seconds. The feasibility of this method was demonstrated in tap-water and a tap-water filled cavity in the tissue-mimicking gelatin–agar phantom as capable of observing temporal evolutions of cavitation bubble cloud with temporal resolution of several microseconds, lateral and axial resolution of 0.50 mm and 0.29 mm respectively. The dissolution process of cavitation bubble cloud and spatial distribution affected by cavitation previously generated were also investigated. Although the application is limited by the requirement for a gassy fluid (e.g. tap water, etc.) that allows replenishment of nuclei between HIFU exposures, the technique may be a useful tool in spatial–temporal cavitation mapping for HIFU with high precision and resolution, providing a reference for clinical therapy.     

Translation of cavitation bubble near the different walls

The interaction between spherical cavitation bubble and flat wall is transformed into that between the real bubble and imaging bubble by the method of images. Firstly, we investigate the dynamics of real bubble and matched, inversed or mis-matched imaging bubble driven by a small amplitude ultrasound, revealing the characteristics of the interaction between cavitation bubble and rigid, soft and impedance walls. Then, we emphatically study the dynamics of real bubble and mis-matched imaging bubble driven by a finite amplitude ultrasound, and the interaction characteristics between cavitation bubble and real impedance wall are revealed. The results show that the cavitation bubble is always close to the rigid wall and far away from the soft wall; For the impedance wall, whether the cavitation bubble is far away or close depends on the specific wall parameters. Moreover, the direction and magnitude of bubble's translation velocity can be changed by adjusting the driving parameters. Understanding the interaction between cavitation bubble and impedance wall is of great significance for efficient application of ultrasonic cavitation.     

Cavitation clouds created by shock scattering from bubbles during histotripsy

Histotripsy is a therapy that focuses short-duration, high-amplitude pulses of ultrasound to incite a localized cavitation cloud that mechanically breaks down tissue. To investigate the mechanism of cloud formation, high-speed photography was used to observe clouds generated during single histotripsy pulses. Pulses of 5-20 cycles duration were applied to a transparent tissue phantom by a 1-MHz spherically focused transducer. Clouds initiated from single cavitation bubbles that formed during the initial cycles of the pulse, and grew along the acoustic axis opposite the propagation direction. Based on these observations, we hypothesized that clouds form as a result of large negative pressure generated by the backscattering of shockwaves from a single bubble. The positive-pressure phase of the wave inverts upon scattering and superimposes on the incident negative-pressure phase to create this negative pressure and cavitation. The process repeats with each cycle of the incident wave, and the bubble cloud elongates toward the transducer. Finite-amplitude propagation distorts the incident wave such that the peak-positive pressure is much greater than the peak-negative pressure, which exaggerates the effect. The hypothesis was tested with two modified incident waves that maintained negative pressure but reduced the positive pressure amplitude. These waves suppressed cloud formation which supported the hypothesis.     

Designing and characterizing a multi-stepped ultrasonic horn for enhanced sonochemical performance

The commonly used ultrasonic horn generates localized cavitation below its converging tip resulting in a dense bubble cloud near the tip and limiting diffusion of reactive components into the bubble cloud or reactive radicals out of the bubble cloud. To improve contact between reactive components, a novel ultrasonic horn design was developed based on the principles of the dynamic wave equation. The horn, driven at 20 kHz, has a multi-stepped design with a cone-shaped tip increasing the energy-emitting surface areas and creating multiple reactive zones. Through different physical and chemical experiments, performance of the horn was compared to a typical horn driven at 20 kHz. Hydrophone measurements showed high acoustic pressure areas around the horn neck and tip. Sonochemiluminescence experiments verified multiple cavitation zones consistent with hydrophone readings. Calorimetry and dosimetry results demonstrated a higher energy efficiency (31.3%) and a larger hydroxyl radical formation rate constant (0.36 μM min⁻¹) compared to typical horns. In addition, the new horn degraded naphthalene faster than the typical horn tested. The characterization results demonstrate that the multi-stepped horn configuration has the potential to improve the performance of ultrasound as an advanced oxidation technology by increasing the cavitation zone in the solution.