The dependence of ultrasound contrast agents backscatter on acoustic pressure: theory versus experiment

Experimental investigations have not fully explored the interaction between ultrasound beams and microbubble contrast agents. Moreover theoretical investigations have not solved the problem of the microbubble oscillation. A simple in-vitro system based on a commercial scanner (ATL UM9) was used to insonate (3 MHz transmission) diluted contrast suspensions of Definity and Quantison at different acoustic pressures (0.27-1.52 MPa). The experimental data were referred to a blood mimicking fluid in order to extract an estimate of their scattering cross-section. The results were compared with the solutions of the three main bubble oscillatidn models, Rayleigh-Plesset, Herring and Gilmore. Non-linear solutions of the above models were produced numerically using the Mathematica Package Software. The experiments showed that both agents provided a linear increase in scattering cross-section with increasing acoustic pressure. The thick shelled Quantison provided an increasing number of scatterers with increasing acoustic pressure, which proved that free bubbles leaked out of the shell. At high acoustic pressures both Quantison and Definity scattering cross-sections were almost identical, and were probably that of a free bubble. The Rayleigh-Plesset model provided a scattering cross-section almost independent of acoustic pressure. On the contrary the scattering cross-sections calculated by the Herring and Gilmore models solutions displayed a definite dependence on acoustic pressure of an order higher than one, which is slightly higher than the order of dependence exhibited by the experimental data. However, the increase of the experimentally measured scattering cross-section with acoustic pressure was sharper than the calculated one by the above two models. This is most probably due to the fact that the models simulated damped and not free bubble oscillations. In conclusion the Rayleigh-Plesset model was inadequate in describing the bubble oscillations even at small diagnostic acoustic pressures. The Herring and Gilmore models could simulate the dependence of the scattering cross-section of encapsulated microbubbles on acoustic pressure. However the contribution of free bubble oscillations has still to be modelled.     

Ultrasonic bubbles in medicine: influence of the shell

Ultrasound contrast agents consist of microscopically small bubbles encapsulated by an elastic shell. These microbubbles oscillate upon ultrasound insonification, and demonstrate highly nonlinear behavior, ameliorating their detectability. (Potential) medical applications involving the ultrasonic disruption of contrast agent microbubble shells include release-burst imaging, localized drug delivery, and noninvasive blood pressure measurement. To develop and enhance these techniques, predicting the cracking behavior of ultrasound-insonified encapsulated microbubbles has been of importance. In this paper, we explore microbubble behavior in an ultrasound field, with special attention to the influence of the bubble shell. A bubble in a sound field can be considered a forced damped harmonic oscillator. For encapsulated microbubbles, the presence of a shell has to be taken into account. In models, an extra damping parameter and a shell stiffness parameter have been included, assuming that Hooke's Law holds for the bubble shell. At high acoustic amplitudes, disruptive phenomena have been observed, such as microbubble fragmentation and ultrasonic cracking. We analyzed the occurrence of ultrasound contrast agent fragmentation, by simulating the oscillating behavior of encapsulated microbubbles with various sizes in a harmonic acoustic field. Fragmentation occurs exclusively during the collapse phase and occurs if the kinetic energy of the collapsing microbubble is greater than the instantaneous bubble surface energy, provided that surface instabilities have grown big enough to allow for break-up. From our simulations it follows that the Blake critical radius is not a good approximation for a fragmentation threshold. We demonstrated how the phase angle differences between a damped radially oscillating bubble and an incident sound field depend on shell parameters.     

Oscillations of polymeric microbubbles: effect of the encapsulating shell

A model for the oscillation of gas bubbles encapsulated in a thin shell has been developed. The model depends on viscous and elastic properties of the shell, described by thickness, shear modulus, and shear viscosity. This theory was used to describe an experimental ultrasound contrast agent from Nycomed, composed of air bubbles encapsulated in a polymer shell. Theoretical calculations were compared with measurements of acoustic attenuation at amplitudes where bubble oscillations are linear. A good fit between measured and calculated results was obtained. The results were used to estimate the viscoelastic properties of the shell material. The shell shear modulus was estimated to between 10.6 and 12.9 MPa, the shell viscosity was estimated to between 0.39 and 0.49 Pas. The shell thickness was 5% of the particle radius. These results imply that the particles are around 20 times more rigid than free air bubbles, and that the oscillations are heavily damped, corresponding to Q-values around 1. We conclude that the shell strongly alters the acoustic behavior of the bubbles: The stiffness and viscosity of the particles are mainly determined by the encapsulating shell, not by the air inside.     

Effect of coupled oscillations on microbubble behavior

Ultrasound contrast agents are encapsulated microbubbles whose nonlinear acoustic scattering signatures have been the foundation of their use in diagnostic imaging. The coupled oscillations of microbubbles along their lines of center are investigated theoretically using radial equations in the monopole approximation and an energy balance, which is obtained for the system. Coupled microbubble pairs of different initial radii are investigated numerically relative to the normal modes for the linearized system. For microbubble pairs of different size bubbles driven below the mode of the smaller bubble and above the mode of the larger bubble, it is shown that oscillations of the smaller agent are affected substantially more by the coupling than those of the larger one. For separation distances of 10 and 500 microns, a difference of approximately 10 dB occurs in the second harmonic output of a 1.0-micron radius agent coupled with a 2.2-micron radius agent forced at 2.0 MHz and 0.3 MPa. The subharmonic spectral peak is shown to decrease approximately 19 dB for the coupling of 1.5- and 2.2-micron radius agents at 10- and 500-micron distances under the same acoustic forcing conditions. These coupling effects on the radiated pressure and its spectral power are highlighted for contrast agent imaging applications.     

声场中空化气泡的耦合振动及形状不稳定性的研究

计算了两个具有非球形扰动的气泡所组成系统的能量,并基于Lagrange方程得到了有声相互作用的非球形气泡的动力学方程和形状稳定性方程,研究了声场中非球形气泡间相互作用力对非球形气泡的形状不稳定性和气泡形状模态振幅的影响.研究结果表明声场中具有非球形扰动的气泡之间的耦合方式有两种:形状耦合模式和径向耦合模式,气泡之间的耦合方式取决于气泡形状扰动模态.由形状耦合及径向耦合产生的气泡之间的相互作用力能够改变单个气泡的形状不稳定及形状模态振幅,具体影响因素取决于声场驱动条件、气泡形状模态、相邻气泡的初始半径.     

超声造影剂微泡非线性动力学响应的机理及相关应用

随着生命科学及现代医学的发展, 一体化无创精准诊疗已经日益成为人们关注的焦点问题, 而关于超声造影剂微泡的非线性效应的相关机理、动力学建模及其在超声医学领域中的应用研究也得到了极大的推动. 本文对下列课题进行了总结和讨论, 包括: 1)基于Mie散射技术和流式细胞仪对造影剂微泡参数进行定征的一体化解决方案; 2)通过对微泡包膜的黏弹特性进行非线性修正, 构建新的包膜微泡动力学模型; 3)探索造影剂惯性空化阈值与其包膜参数之间的相关性; 以及4)研究超声联合造影剂微泡促进基因/药物转染效率并有效降低其生物毒性的相关机理.     

多层膜磁性微泡的非线性声振动特性

超顺磁性氧化铁纳米粒子与造影剂微泡结合形成磁性微泡,用于产生多模态造影剂,以增强医学超声和磁共振成像.将装载有纳米磁性颗粒的微泡包膜层看作由磁流体膜与磷脂膜组合而成的双层膜结构,同时考虑磁性纳米颗粒体积分数a对膜密度及黏度的影响,从气泡动力学基本理论出发,构建多层膜结构磁性微泡非线性动力学方程.数值分析了驱动声压和频率等声场参数、颗粒体积分数、膜层厚度以及表面张力等膜壳参数对微泡声动力学行为的影响.结果表明,当磁性颗粒体积分数较小且a≤0.1时,磁性微泡声响应特性与普通包膜微泡相似,微泡的声频响应与其初始尺寸和驱动压有关;当驱动声场频率f为磁性微泡共振频率f0的2倍(f=2f0)时,微泡振动失稳临界声压最低;磁性颗粒的存在抑制了泡的膨胀和收缩但抑制效果非常有限;磁性微泡外膜层材料的表面张力参数K及膜层厚度d也会影响微泡的振动,当表面张力参数及膜厚取值分别为0.2—0.4 N/m及50—150 nm时,可观察到气泡存在不稳定振动响应区.     

Microbubble spectroscopy of ultrasound contrast agents

A new optical characterization of the behavior of single ultrasound contrast bubbles is presented. The method consists of insonifying individual bubbles several times successively sweeping the applied frequency, and to record movies of the bubble response up to 25 million frames/s with an ultrahigh speed camera operated in a segmented mode. The method, termed microbubble spectroscopy, enables to reconstruct a resonance curve in a single run. The data is analyzed through a linearized model for coated bubbles. The results confirm the significant influence of the shell on the bubble dynamics: shell elasticity increases the resonance frequency by about 50%, and shell viscosity is responsible for about 70% of the total damping. The obtained value for shell elasticity is in quantative agreement with previously reported values. The shell viscosity increases significantly with the radius, revealing a new nonlinear behavior of the phospholipid coating.     

Stability analysis of ultrasound thick-shell contrast agents

The stability of thick shell encapsulated bubbles is studied analytically. 3-D small perturbations are introduced to the spherical oscillations of a contrast agent bubble in response to a sinusoidal acoustic field with different amplitudes of excitation. The equations of the perturbation amplitudes are derived using asymptotic expansions and linear stability analysis is then applied to the resulting differential equations. The stability of the encapsulated microbubbles to nonspherical small perturbations is examined by solving an eigenvalue problem. The approach then identifies the fastest growing perturbations which could lead to the breakup of the encapsulated microbubble or contrast agent.     

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.     

Resonance behaviors of encapsulated microbubbles oscillating nonlinearly with ultrasonic excitation

The resonance behaviors of a few lipid-coated microbubbles acoustically activated in viscoelastic media were comprehensively examined via radius response analysis. The size polydispersity and random spatial distribution of the interacting microbubbles, the rheological properties of the lipid shell and the viscoelasticity of the surrounding medium were considered simultaneously. The obtained radius response curves present a successive occurrence of linear resonances, nonlinear harmonic and sub-harmonic resonances with the acoustic pressure increasing. The microbubble resonance is radius-, pressure- and frequency-dependent. Specifically, the maximum bubble expansion ratio at the main resonance peak increases but the resonant radius decreases as the ultrasound pressure increases, while both of them decrease with the ultrasound frequency increasing. Moreover, compared to an isolated microbubble case, it is found that large microbubbles in close proximity prominently suppress the resonant oscillations while slightly increase the resonant radii for both harmonic and subharmonic resonances, even leading to the disappearance of the subharmonic resonance with the influences increasing to a certain degree. In addition, the results also suggest that both the encapsulating shell and surrounding medium can substantially dampen the harmonic and subharmonic resonances while increase the resonant radii, which seem to be affected by the medium viscoelasticity to a greater degree rather than the shell properties. This work offers valuable insights into the resonance behaviors of microbubbles oscillating in viscoelastic biological media, greatly contributing to further optimizing their biomedical applications.     

Oscillating bubble concentration and its size distribution using acoustic emission spectra

New method has been proposed for the estimation of size and number density distribution of oscillating bubbles in a sonochemical reactor using acoustic emission spectra measurements. Bubble size distribution has been determined using Minnaert's equation [M. Minnaert, On musical air bubbles and sound of running water, Philanthr. Mag. 16 (1933) 235], i.e., size of oscillating bubble is inversely related to the frequency of its volume oscillations. Decomposition of the pressure signal measured by the hydrophone in frequency domain of FFT spectrum and then inverse FFT reconstruction of the signal at each frequency level has been carried out to get the information about each of the bubble/cavity oscillation event. The number mean radius of the bubble size is calculated to be in the range of 50-80mum and it was not found to vary much with the spatial distribution of acoustic field strength of the ultrasound processor used in the work. However, the number density of the oscillating bubbles and the nature of the distribution were found to vary in different horizontal planes away from the driving transducer surface in the ultrasonic bath. A separate set of experiments on erosion assessment studies were carried out using a thin aluminium foil, revealing a phenomena of active region of oscillating bubbles at antinodal points of the stationary waves, identical to the information provided by the acoustic emission spectra at the same location in the ultrasonic bath.     

Contributions to the acoustic excitation of bubbles released from a nozzle

It has recently been demonstrated that air bubbles released from a nozzle are excited into volume mode oscillations by the collapse of the neck of air formed at the moment of bubble detachment. A pulse of sound is caused by these breathing mode oscillations, and the sound of air-entraining flows is made up of many such pulses emitted as bubbles are created. This paper is an elaboration on a JASA-EL paper, which examined the acoustical excitation of bubbles released from a nozzle. Here, further details of the collapse of a neck of air formed at the moment of bubble formation and its implications for the emission of sound by newly formed bubbles are presented. The role of fluid surface tension was studied using high-speed photography and found to be consistent with a simple model for neck collapse. A re-entrant fluid jet forms inside the bubble just after detachment, and its role in acoustic excitation is assessed. It is found that for slowly-grown bubbles the jet does make a noticeable difference to the total volume decrease during neck collapse, but that it is not a dominant effect in the overall acoustic excitation.     

Resonance frequency of microbubbles: effect of viscosity

The transmitted frequency at which a gas bubble of millimeter or submillimeter size oscillates resonantly in a low-viscosity liquid is approximately equal to the undamped natural frequency (referred to as the Minnaert frequency if surface tension effects are disregarded). Based on a theoretical analysis of bubble oscillation, this paper shows that such an approximation cannot be validated for microbubbles used in contrast-enhanced ultrasound imaging. The contrast-agent microbubbles represent either encapsulated bubbles of size less than 10 microm or free (nonencapsulated) bubbles of submicron size. The resonance frequency of the microbubbles deviates significantly from the undamped natural frequency over the whole range of microbubble sizes due to the increased viscous damping coefficient. The difference between these two frequencies is shown to have a tremendous impact on the resonant backscatter by the microbubbles. In particular, the first and second harmonics of the backscattered signal from the microbubbles are characterized by their own resonance frequencies, equal to neither the microbubble resonance frequency nor the undamped natural frequency.     

Using light scattering to measure the response of individual ultrasound contrast microbubbles subjected to pulsed ultrasound in vitro

Light scattering was used to measure the radial pulsations of individual ultrasound contrast microbubbles subjected to pulsed ultrasound. Highly diluted Optison or Sonazoid microbubbles were injected into either a water bath or an aqueous solution containing small quantities of xanthan gum. Individual microbubbles were insonified by ultrasound pulses from either a commercial diagnostic ultrasound machine or a single element transducer. The instantaneous response curves of the microbubbles were measured. Linear and nonlinear microbubble oscillations were observed. Good agreement was obtained by fitting a bubble dynamics model to the data. The pulse-to-pulse evolution of individual microbubbles was investigated, the results of which suggest that the shell can be semipermeable, and possibly weaken with subsequent pulses. There is a high potential that light scattering can be used to optimize diagnostic ultrasound techniques, understand microbubble evolution, and obtain specific information about shell parameters.     

High-speed imaging of ultrasound driven cavitation bubbles in blind and through holes

The interest in application of ultrasonic cavitation for cleaning and surface treatment processes has increased greatly in the last decades. However, not much is known about the behavior of cavitation bubbles inside the microstructural features of the solid substrates. Here we report on an experimental study on dynamics of acoustically driven (38.5 kHz) cavitation bubbles inside the blind and through holes of PMMA plates by using high-speed imaging. Various diameters of blind (150, 200, 250 and 1000 µm) and through holes (200 and 1000 µm) were investigated. Gas bubbles are usually trapped in the holes during substrate immersion in the liquid thus preventing their complete wetting. We demonstrate that trapped gas can be successfully removed from the holes under ultrasound agitation. Besides the primary Bjerknes force and acoustic streaming, the shape oscillations of the trapped gas bubble seem to be a driving force for bubble removal out of the holes. We further discuss the bubble dynamics inside microholes for water and Cu²⁺ salt solution. It is found that the hole diameter and partly the type of liquid media influences the number, size and dynamics of the cavitation bubbles. The experiments also showed that a large amount of the liquid volume inside the holes can be displaced within one acoustic cycle by the expansion of the cavitation bubbles. This confirmed that ultrasound is a very effective tool to intensify liquid exchange processes, and it might significantly improve micro mixing in small structures. The investigation of the effect of ultrasound power on the bubble density distribution revealed the possibility to control the cavitation bubble distribution inside the microholes. At a high ultrasound power (31.5 W) we observed the highest bubble density at the hole entrances, while reducing the ultrasound power by a factor of ten shifted the bubble locations to the inner end of the blind holes or to the middle of the through holes.     

Spatio-temporal dynamics of an encapsulated gas bubble in an ultrasound field

Coupled equations describing the radial and translational dynamics of an encapsulated gas bubble in an ultrasound field are derived by using the Lagrangian formalism. The equations generalize Church's theory by allowing for the translation motion of the bubble and radiation losses due to the compressibility of the surrounding liquid. The expression given by Church for the inner bubble radius corresponding to the unstrained state of the bubble shell is also refined, assuming that the shell can be of arbitrary thickness and impermeable to gas. Comparative linear analysis of the radial equation is carried out relative to Church's theory. It is shown that there are substantial departures from predictions of Church's theory. The proposed model is applied to evaluate radiation forces exerted on encapsulated bubbles and their translational displacements. It is shown that in the range of relatively high frequencies encapsulated bubbles are able to translate more efficiently than free bubbles of the equivalent size.     

Collective bubble dynamics near a surface in a weak acoustic standing wave field

The transport of bubbles to a neighboring surface is very important in surface chemistry, bioengineering, and ultrasonic cleaning, etc. This paper proposes a multi-bubble transport method by using an acoustic standing wave field and establishes a model that explains the multi-bubble translation by expressing the balance between Bjerknes forces and hydrodynamic forces on a bubble in a liquid medium. Results indicated that the influence of primary Bjerknes force, secondary Bjerknes force, and buoyancy force on the bubble translation depends on the position of the target bubble in the acoustic field. Moreover, it was found that increasing the size of a bubble or pressure amplitude can accelerate the bubble motion and enhance the bubble-bubble interaction. The secondary Bjerknes force between two bubbles can switch from an attractive one when they oscillate in phase to a repulsive one when the bubble oscillations are out of phase. These findings provide an insight into the multi-bubble translation near a surface and can be applied to future bubble motion control studies, especially in drug delivery, sonoporation, and ultrasonic cleaning.     

Dynamics of a bubble cluster in an acoustic field

A mathematical model describing the dynamics of clustered gas bubbles under the effect of an acoustic field is presented. The proposed model is used as the basis for an analytical study of small bubble oscillations in monodisperse and polydisperse clusters and for a numerical study of nonlinear bubble oscillations under high-amplitude external pressures. The following effects are found to occur in a polydisperse cluster: a synchronization of the collapse phases of bubbles with different radii and a collapse intensification for bubbles of one size in the presence of bubbles of another size. These effects are explained by the interaction between bubbles of different radii in the cluster.     

Effect of ultrasonic frequency and surfactant addition on microcapsule destruction

In a previous study, we found that cavitation bubbles cause the ultrasonic destruction of microcapsules containing oil in a shell made of melamine resin. The cavitation bubbles can be smaller or larger than the resonance size; smaller bubbles cause Rayleigh contraction, whereas larger bubbles are not involved in the sonochemical reaction. The activity in and around the bubble (e.g., shear stress, shock wave, microjet, sonochemical reaction, and sonoluminescence) varies substantially depending on the bubble size. In this study, we investigated the mechanism of the ultrasonic destruction of microcapsules by examining the correlations between frequency and microcapsule destruction rate and between microcapsule size and cavitation bubble size. We evaluated the bubbles using multibubble sonoluminescence and the bubble size was changed by adding a surfactant to the microcapsule suspension. The microcapsule destruction was frequency dependent. The main cause of microcapsule destruction was identified as mechanical resonance, although the relationship between bubble size and microcapsule size suggested that bubbles smaller than or equal to the microcapsule size may also destroy microcapsules by applying shear stress locally.