Forced linear oscillations of microbubbles in blood capillaries

A theoretical investigation of the forced linear oscillations of a gas microbubble in a blood capillary, whose radius is comparable in size to the bubble radius is presented. The natural frequency of oscillation, the thermal and viscous damping coefficients, the amplitude resonance, the energy resonance, as well as the average energy absorbed by the system, bubble plus vessel, have been computed for different kinds of gas microbubbles, containing air, octafluropropane, and perflurobutane as a function of the bubble radius and applied frequency. It has been found that the bubble behavior is isothermal at low frequencies and for small bubbles and between isothermal and adiabatic for larger bubbles and higher frequencies, with the viscous damping dominating over the thermal damping. Furthermore, the width of the energy resonance is strongly dependent on the bubble size and the natural frequency of oscillation is affected by the presence of the vessel wall and position of the bubble in the vessel. Therefore, the presence of the blood vessel affects the way in which the bubble absorbs energy from the ultrasonic field. The motivation of this study lies in the possibility of using gas microbubbles as an aid to therapeutic focused ultrasound treatments.     

I. Formation and rise of a bubble stream in a viscous liquid

The continuous emission of gas bubbles from a single ejection orifice immersed in a viscous fluid is considered. We first present a semi empirical model of spherical bubble growth under constant flow conditions to predict the bubble volume at the detachment stage. In a second part, we propose a physical model to describe the rise velocity of in-line interacting bubbles and we derive an expression for the net viscous force acting on the surrounding fluid. Experimental results for air/water-glycerol systems are presented for a wide range of fluid viscosity and compared with theoretical predictions. An imagery technique was used to determine the bubble size and rise velocity. The effects of fluid viscosity, gas flow rate, orifice diameter and liquid depth on the bubble stream dynamic were analyzed. We have further studied the effect of large scale recirculation flow and the influence of a neighbouring bubble stream on the bubble growth and rising velocity. Received: 23 July 1997 / Revised: 16 December 1997 / Accepted: 11 May 1998     

Study on bubble formation in non-Newtonian fluids by laser image technique

A laser image system for studying bubble formation at the orifice submerged in liquid was established. The process of bubble formation can be directly visualized and real-time recorded through computer by means of He–Ne laser as light source using the beam expanding and light amplification technique. The behaviors of bubble formation in polyacrylamide (PAM) aqueous solutions were investigated at temperature 293.15 K and orifice diameters 1, 1.5 and 2 mm, respectively, the chamber volume was 90 cm³ and the gas flowrate from 0.1 to 0.6 cm³/s. The influences of mass concentration of solution and orifice diameter on bubble detachment volume were investigated experimentally and the results show that bubble detachment volume increases with solution concentration and orifice diameter in the experimental range of this work.     

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.     

Modeling non-spherical oscillations and stability of acoustically driven shelled microbubbles

The oscillation and destruction of microbubbles under ultrasound excitation form the basis of contrast enhanced ultrasound imaging and microbubble assisted drug and gene delivery. A typical microbubble has a size of a few micrometers and consists of a gas core encapsulated by a shell. These bubbles can be driven into surface mode oscillations, which not only contribute to the measured acoustic signal but can lead to bubble destruction. Existing models of surface model oscillations have not considered the effects of a bubble shell. In this study a model was developed to study the surface mode oscillations in shelled bubbles. The effects of shell viscosity and elasticity on the surface mode oscillations were modeled using a Boussinesq-Scriven approach. Simulation was conducted using the model with various bubble sizes and driving acoustic pressures. The occurrence of surface modes and the number of ultrasound cycles needed for the occurrence were calculated. The simulation results show a significant difference between shelled bubbles and shell free bubbles. The shelled bubbles have reduced surface mode amplitudes and a narrower bubble size range within which these modes develop compared to shell free bubbles. The clinical implications were also discussed.     

On the mass of the liquid attached to a moving bubble separated from the electrode surface by a spark discharge

The mechanism of detachment and motion of gas bubbles from the GaAs surface, initiated by a spark discharge in an aqueous electrolyte, is investigated. The model proposed for the displacement of bubbles in the liquid is based on the theory of the formation of a water ram pressed by a gaseous inclusion out of the compacted layer of the liquid as a result of action of the compression wave produced by a spark discharge. The effect of the size and temperature of a gas bubble on the geometrical parameters of the water ram is considered. The lifetime of the water ram is determined from the pressure drop at the leading edge of the compression wave.     

Estimation of mechanical properties of a viscoelastic medium using a laser-induced microbubble interrogated by an acoustic radiation force

An approach to assess the mechanical properties of a viscoelastic medium using laser-induced microbubbles is presented. To measure mechanical properties of the medium, dynamics of a laser-induced cavitation microbubble in viscoelastic medium under acoustic radiation force was investigated. An objective lens with a 1.13 numerical aperture and an 8.0 mm working distance was designed to focus a 532 nm wavelength nanosecond pulsed laser beam and to create a microbubble at the desired location. A 3.5 MHz ultrasound transducer was used to generate acoustic radiation force to excite a laser-induced microbubble. Motion of the microbubble was tracked using a 25 MHz imaging transducer. Agreement between a theoretical model of bubble motion in a viscoelastic medium and experimental measurements was demonstrated. Young's modulii reconstructed using the laser-induced microbubble approach were compared with those measured using a direct uniaxial method over the range from 0.8 to 13 kPa. The results indicate good agreement between methods. Thus, the proposed approach can be used to assess the mechanical properties of a viscoelastic medium.     

竖直环形通道内液氮自然循环沸腾可视化实验研究

采用基于高速摄像手段的可视化方法研究了竖直环形通道内的液氮自然循环沸腾过程,建立了汽泡脱离直径及汽泡脱离频率的实验关联式,以新建方程结合双流体模型进行了数值计算。与实验数据的对比表明,建立的实验关联式对于液氮自然循环沸腾过程中的汽泡脱离直径及汽泡脱离频率具有很好的预测精度。     

The problems of the upward monodispersed microbubble flow in a vertical tube

The paper presents the first experimental results concerning the wall shear stress in an upward monodispersed microbubble flow in vertical tube. A bubble generator using a microfluid focusing technique was designed to produce monodispersed submillimeter bubbles. The experimental results allow to think that there is an optimal size of the bubbles and the optimal gas fraction in the bubble sublayer that provide the maximal mass transfer coefficient beween the flow and the tube wall.     

超声对近壁微气泡溃灭过程的影响*

近壁微气泡溃灭特性的深入研究对靶向给药和基因治疗等技术具有较好的指导作用。该文基于数值模拟技术,采用有限体积法结合流体体积模型对超声作用下的近壁微气泡溃灭特性进行了研究,分析了超声对近壁微气泡溃灭动力学过程的影响。结果表明气泡溃灭最大射流速度与近壁距离无量纲参数在1.1~1.6范围内时成正比,与超声频率在10~60 Hz范围内时成正比,与气泡初始半径在50~100μm范围内时成反比;近壁气泡的二次溃灭最大射流速度大于一次溃灭,二次溃灭的作用更加明显。超声参数对近壁气泡溃灭过程存在较大影响,该研究为超声在医学上的应用提供了依据。     

Gas bubble fragmentation in an ultrasonic field

A model system consisting of a thin layer of vacuum-deposited metallic aluminium on a glass microscope slide was developed to demonstrate the effectiveness of cavitational activity (occurring within the cooling water supply of a dental ultrasonic descaler operating at 25 kHz) in the removal of particulate matter from solid surfaces. The pattern of particulate matter removal using this model system demonstrated both the mechanism of bubble activity and the erosive nature of microbubbles.Non-resonant bubbles were formed by surface wave activity and adhered to the surface of the slide. There was some removal of the aluminium metal at the periphery of the bubble (probably by a microstreaming mechanism) giving a ‘ghost’ outline. The majority of aluminium removal was caused by numerous microbubbles of non-resonant sizes (typically 1 to 2 μm diameter) formed by surface wave induced fragmentation of the parent bubble.The damaging and erosive effects of transient cavitational activity appear to be the result of sub-resonant sized microbubble formation from larger parent bubbles.     

石英毛细管椭球微气泡模式特性及传感技术

利用有限元数值分析方法研究了椭球状石英毛细管微气泡回音壁模式特性及其折射率传感性能.计算分析了不同半径与内壁厚度情况下空芯和液芯椭球形微气泡模式特征,包括品质因数、有效折射率和能量比等,并探讨了微气泡在高灵敏度和高分辨率折射率传感方面的应用潜能.研究结果表明微气泡膨胀至350μm,且内壁厚度为1μm时分辨率和灵敏度最佳;在该厚度范围附近,微气泡分辨率不会因为半径尺寸的改变而发生太大变化;二阶径向模具有较高品质因数,其灵敏度略高于一阶基模,且使用二阶径向模可降低在制造时对结构壁厚控制精度的要求,可用于实际传感应用中.研究结果对微气泡的进一步实验研制具有理论参考价值.     

Phospholipid-stabilized microbubbles: Influence of shell chemistry on cavitation threshold and binding to giant uni-lamellar vesicles

We demonstrate the feasibility of covalently linking a single microbubble to a single, giant uni-lamellar vesicle (GUV). Such a combination of GUV plus microbubble might prove useful as a new drug delivery vehicle involving microbubble cavitation-induced sonoporation of the vesicle bilayer as a release mechanism. We therefore applied the well known methodology of passive cavitation detection to measure the influence of lipid shell chemistry on inertial cavitation thresholds for externally added microbubbles. We find that cavitation threshold changes significantly with changes in either molecular weight or mole fraction of poly(ethylene glycol), historically used to impede gas dissolution and microbubble coalescence. We attribute changes in cavitation threshold to changes in microbubble resonance frequency resulting from changes in microbubble shell bending elasticity. To further demonstrate the influence of shell chemistry on microbubble behavior, we describe how several common bubble phenomena - and some new - respond to changes in lipid chain length.     

Microstreaming velocity field and shear stress created by an oscillating encapsulated microbubble near a cell membrane

Sonoporation mediated by microbubbles is being extensively studied as a promising technology to facilitate gene/drug delivery to cells. However, the theoretical study regarding the mechanisms involved in sonoporation is still in its infancy. Microstreaming generated by pulsating microbubble near the cell membrane is regarded as one of the most important mechanisms in the sonoporation process. Here, based on an encapsulated microbubble dynamic model with considering nonlinear rheological effects of both shell elasticity and viscosity, the microstreaming velocity field and shear stress generated by an oscillating microbubble near the cell membrane are theoretically simulated. Some factors that might affect the behaviors of microstreaming are thoroughly investigated, including the distance between the bubble center and cell membrane (d), shell elasticity (χ), and shell viscosity (κ). The results show that (i) the presence of cell membrane can result in asymmetric microstreaming velocity field, while the constrained effect of the membrane wall decays with increasing the bubble-cell distance; (ii) the bubble resonance frequency increases with the increase in d and χ, and the decrease in κ, although it is more dominated by the variation of shell elasticity; and (iii) the maximal microstreaming shear stress on the cell membrane increases rapidly with reducing the d, χ, and κ. The results suggest that microbubbles with softer and less viscous shell materials might be preferred to achieve more efficient sonoporation outcomes, and it is better to have bubbles located in the immediate vicinity of the cell membrane.     

Shock wave-inertial microbubble interaction: a theoretical study based on the Gilmore formulation for bubble dynamics

The Gilmore formulation for bubble dynamics coupled with zeroth-order gas diffusion were used to investigate theoretically the cavitation activity produced by a modified XL-1 lithotripter [J. Acoust. Soc. Am. 105, 1997-2009 (1999)]. The model calculation confirms many of the basic features in bubble dynamics observed experimentally, in particular the strong secondary shock wave emission generated by in situ lithotripter shock wave-inertial microbubble interaction. In addition, shock wave-inertial microbubble interaction produced by a Dornier HM-3, the most commonly used clinical lithotripter, was evaluated. It was shown that the forced collapse of inertial microbubbles with strong secondary shock wave emission could be produced consistently, provided that an appropriate preceding shock wave and interpulse delay were used. Further, it was demonstrated that truncation of the tensile stress of the lithotripter shock wave could significantly reduce the large expansion of the bubble following shock wave-inertial microbubble interaction, which may alleviate the risk for vascular injury during shock wave exposure.     

Bubble motions confined in a microspace observed with stroboscopic technique

Dynamic motions of gas bubble confined in a microspace, i.e., in a channel of a microreactor, were observed with a video microscope and stroboscopic technique using a light emitting diode operated in a pulsed mode. There are many important phenomena related to the bubble dynamics synchronized with ultrasonic wave and continued for more than a few minutes. With the stroboscopic technique, the time-expanded bubble motions synchronized with ultrasound wave and the real time background images can be simultaneously observed. A number of interesting phenomena resulting from the dynamic motions of a microbubble in a microspace were observed; nonspherical bubble oscillation, rectified diffusion, emergence of cavitation, and microstreaming of different patterns depending on the input power of ultrasound. The observation technique described in this investigation could be a convenient tool for taming the bubble under a microscope to investigate the bubble dynamics in detail.     

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.     

枝晶生长和气泡形成的数值模拟

本文建立了二维的格子玻尔兹曼方法-元胞自动机(lattice Boltzmann method-cellular automaton, LBM-CA)耦合模型, 对凝固过程中枝晶生长和气泡形成进行模拟研究. 本模型采用CA方法模拟枝晶的生长, 根据界面溶质平衡法计算枝晶生长的驱动力. 采用基于Shan-Chen多相流的LBM模拟气泡在液相中的生长和运动. 在LBM-CA的耦合模型中包含了固-液-气三相之间的相互作用. 应用Laplace定理和模拟气-液-固三相之间的润湿现象对模型进行了验证. 应用所建立的LBM-CA耦合模型模拟研究了气-液相互作用系数对单气泡生长的影响. 发现单气泡的生长速度和平衡半径随气-液相互作用系数的增大而增大. 定向凝固过程中枝晶和气泡生长的模拟结果再现了枝晶的择优生长、 气泡的优先形核位置、气泡的长大、合并、在枝晶间受挤变形以及在液相通道中的运动等物理现象, 与实验结果符合良好. 此外, 初始气体含量越高, 凝固结束时气泡的体积分数也相对较高. 本模型的模拟结果可以揭示在凝固过程中气泡形核、 生长和运动演化以及与枝晶生长相互作用的物理机理.     

Interaction of microbubbles with high intensity pulsed ultrasound

High intensity pulsed ultrasound, interacting with microbubble contrast agents, is potentially useful for drug delivery, cancer treatment, and tissue ablation, among other applications. To establish the fundamental understanding on the interaction of a microbubble (in an infinite volume of water) with an ultrasound pressure field, a numerical study is performed using the boundary element method. The response of the bubble, in terms of its shape at different times, the maximum bubble radius obtained, the oscillation time, the jet velocity, and its translational movement, is studied. The effect of ultrasound intensity and initial bubble size is examined as well. One important outcome is the determination of the conditions under which a clear jet will be formed in a microbubble in its interaction with a specific sound wave. The high speed jet is crucial for the aforementioned intended applications.