考虑水蒸气蒸发和冷凝的球状泡群中泡的动力学特性

为了深入探究空化泡群中气泡的动力学特性,建立了超声驱动下考虑水蒸气的蒸发和冷凝的泡群中泡的动力方程.基于该方程,研究了泡群中泡的位置、泡的数量、泡的初始半径对其动力学特性的影响,探究了超声作用下球状泡群中气泡半径、能量、温度、压力和气泡内水蒸气分子数的变化规律.结果表明:泡群中泡的运动受到周围气泡的抑制作用;泡群中泡的初始半径大小对泡群中泡的半径、能量、温度、压力和气泡内水蒸气分子数有显著影响;泡群中泡的位置距离泡群中心越远,泡的膨胀半径越大;随着泡群中泡的数目增加,泡的振幅减小;超声频率增加,泡群中泡的空化效应减弱;超声声压增加,泡群中泡的空化效应增加.研究结果为超声空化泡群的研究提供了理论参考.     

低频超声空化场中柱状泡群内气泡的声响应

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,得到了均匀柱状泡群内振动气泡的动力学方程,以此为基础分析了低频超声空化场中柱形气泡聚集区内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,降低了气泡的自然频率,增强了气泡的非线性声响应.随着气泡数密度的增加,气泡的自然共振频率降低,受迫振动气泡受到的抑制增强.数值分析结果表明:1)驱动声波频率越低,气泡的初始半径越小,气泡数密度变化对气泡最大半径变化幅度的影响越大;2)气泡振动幅值响应存在不稳定区,不稳定区域分布与气泡初始半径、驱动声波压力幅值、驱动声波频率等因素有关.在低频超声波作用下,对初始半径处在1—10μm之间的空化气泡而言,气泡初始半径越小,气泡最大半径不稳定区分布范围越大,表明小气泡具有更强的非线性特征.因此,气泡初始半径越小,声环境变化对空化泡声响应稳定性影响越显著.     

超声场中单气泡的平移和非球形振动

基于摄动理论和广义伯努利方程,推导出单气泡在超声场中径向振动方程、平移方程和气泡形变方程.数值计算这3个方程,可以得到气泡半径、气泡中心的位移和气泡形变随时间的演化图.计算结果表明:当气泡初始半径和驱动声压不变时,气泡中心初始平移速度增大,气泡径向振动几乎不变,但气泡中心位移和形变量增大,气泡非球形振动愈加明显.当初始平移速度比较小时,气泡的R_0-p_a相图中,不稳定区域仅集中在高驱动声压区域.随着气泡中心初始平移速度不断增大,半径和驱动声压均较小的区域开始呈现不稳定性,且整体不稳定空间范围逐渐增大.另外,气泡在声驻波场中不同位置呈现出不同的振动特征.离波腹点越近的气泡,其径向振动幅度越大,但气泡的平移和形变量变化很小,R_0-p_a相图中不稳定性区域平面分数之间的误差小于4%.     

微泡对高强度聚焦超声声压场影响的仿真研究*

微泡对高强度聚焦超声(HIFU)治疗焦域具有增效作用,而HIFU治疗中不同声学条件下微泡对HIFU形成声压场的影响尚不清楚。本文基于气液混合声波传播方程、Keller气泡运动方程、时域有限差分(FDTD)法和龙格-库塔(RK)法数值仿真研究输入声压、激励频率、气泡初始空隙率和气泡初始半径对HIFU形成声压场的影响。研究结果表明,随着输入声压的增大,焦点处声压升高但焦点处最大声压与输入声压的比值减小,焦点位置几乎不变;随着激励频率和气泡初始半径的增大,焦点处声压升高且焦点位置向远离换能器方向移动;随着气泡初始空隙率的增大,焦点处声压降低且焦点位置向换能器方向移动。     

超声波作用下泡群的共振声响应

从球状泡群气泡动力学方程出发, 考虑泡群间次级声辐射的影响, 得到了声场中两泡群共同存在时气泡振动的动力学方程, 并以此为基础探讨声波驱动下双泡群振动系统的共振响应特征. 由于泡群间气泡间的相互作用, 系统存在低频共振和高频共振现象, 两不同共振频率的数值与泡群内气泡的本征频率相关. 泡群内气泡的本征频率又受到初始半径、泡群大小和泡群内气泡数量的影响. 气泡自由振动和驱动声波的耦合激起泡群内气泡的受迫振动, 气泡初始半径、气泡数密度和驱动声波频率等都会影响泡群内气泡的振动幅值和初相位. 关键词： 气泡群 共振 声响应 超声空化     

超声波声孔效应中气泡动力学的研究

在超声快速制取组织细胞病理切片的过程中，发现激励信号对切片制取效果有明显的影响.为了掌握超声激励信号对组织细胞的影响规律，达到快速制取病理切片的最佳状态，从气泡空化模型入手，通过改变激励信号频率、声压、气泡初始半径和液体黏滞系数等参量，研究了声孔效应中气泡动力学激励机制.数值计算表明：空化泡振动随激励声压增强而升高，随液体黏滞系数增强而减弱；一定频率范围内空化泡振动能保持在膨胀、收缩和振荡的稳定空化状态，存在空化泡稳态振动的最佳激励频率；一定初始半径能保证空化泡产生稳定的振动，存在空化泡稳态振动幅度最大的初始半径.实际操作中，在频率、声压、初始半径和黏滞系数综合作用的若干空化阈内，声孔效应使超声快速法制取细胞组织切片获得最佳效果. 关键词： 声孔效应 超声空化 气泡振动 稳态空化域     

超声场下刚性界面附近溃灭空化气泡的速度分析

为了揭示刚性界面附近气泡空化参数与微射流的相互关系, 从两气泡控制方程出发, 利用镜像原理, 建立了考虑刚性壁面作用的空化泡动力学模型. 数值对比了刚性界面与自由界面下气泡的运动特性, 并分析了气泡初始半径、气泡到固壁面的距离、声压幅值和超声频率对气泡溃灭的影响. 在此基础上, 建立了气泡溃灭速度和微射流的相互关系. 结果表明: 刚性界面对气泡振动主要起到抑制作用; 气泡溃灭的剧烈程度随气泡初始半径和超声频率的增加而降低, 随着气泡到固壁面距离的增加而增加; 声压幅值存在最优值, 固壁面附近的气泡在该最优值下气泡溃灭最为剧烈; 通过研究气泡溃灭速度和微射流的关系发现, 调节气泡溃灭速度可以达到间接控制微射流的目的.     

声场作用下两空化泡相互作用的研究

建立了声场作用下两空化泡泡壁的运动方程,得出了双空化泡的共振频率,振动半径及空化噪声声压．由频率方程,振动半径和声压方程可以看出两气泡的运动情况与单气泡的运动情况有着明显的不同．共振频率,共振振幅及声压与两气泡之间的间距有关．在一定的简化条件下,运用MATLAB语言对共振频率,共振振幅及空化噪声声压进行了数值求解,发现共振频率和共振振幅随空泡间距的增大而增大,空化噪声声压随距离增大先增大后减小． 关键词： 超声 空化 频率 声压     

声场中双空化泡的运动特性

空化泡的运动特性是声场作用下的动力学行为,受空化泡初始半径,声压幅值,驱动声压频率,液体特性等众多因素的影响,是个复杂工程。本文从双空化泡运动方程出发,考虑到液体粘滞系数、空化泡辐射阻尼项的影响,研究了不同初始半径、驱动声压频率、驱动声压幅值、液体粘滞系数下空化泡泡壁的运动情况,研究结果表明不同初始半径、外界驱动声压频率、驱动声压幅值、液体粘滞系数均会对空化泡的膨胀比和空化泡的溃灭时间有一定影响。     

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。     

Effect of surfactant addition on removal of microbubbles using ultrasound

It is difficult to control the bubble in a liquid by the external operation, because the behavior of the bubble is controlled in buoyancy and flow of liquid. On the other hand, microbubbles, whose diameter is several decades μm, stably disperse in static liquid because of their small buoyancy and electrical repulsion. When an ultrasound, whose frequency was 2.4 MHz, was irradiated, the milky white microbubbles suspended solution became rapidly clear. In this study, the effects of surfactant addition on the removal of microbubbles from a liquid in an ultrasonic field were investigated. The efficiency of removal of microbubbles decreased with surfactant addition. Surfactant type influenced the size of agglomerated microbubbles, and the efficiency of removal of microbubbles changed. The surface of microbubble was modified by surfactant adsorption, and the steric inhibition influenced the removal of microbubbles.     

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.     

Modeling subharmonic response from contrast microbubbles as a function of ambient static pressure

Variation of subharmonic response from contrast microbubbles with ambient pressure is numerically investigated for non-invasive monitoring of organ-level blood pressure. Previously, several contrast microbubbles both in vitro and in vivo registered approximately linear (5-15 dB) subharmonic response reduction with 188 mm Hg change in ambient pressure. In contrast, simulated subharmonic response from a single microbubble is seen here to either increase or decrease with ambient pressure. This is shown using the code BUBBLESIM for encapsulated microbubbles, and then the underlying dynamics is investigated using a free bubble model. The ratio of the excitation frequency to the natural frequency of the bubble is the determining parameter--increasing ambient pressure increases natural frequency thereby changing this ratio. For frequency ratio below a lower critical value, increasing ambient pressure monotonically decreases subharmonic response. Above an upper critical value of the same ratio, increasing ambient pressure increases subharmonic response; in between, the subharmonic variation is non-monotonic. The precise values of frequency ratio for these three different trends depend on bubble radius and excitation amplitude. The modeled increase or decrease of subharmonic with ambient pressure, when one happens, is approximately linear only for certain range of excitation levels. Possible reasons for discrepancies between model and previous experiments are discussed.     

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.     

微泡对高强度聚焦超声焦域影响的研究

微泡对高强度聚焦超声(HIFU)治疗具有增效作用,而HIFU治疗中不同声学条件下微泡对HIFU治疗焦域的影响尚不清楚。本文基于声传播方程、Yang-Church气泡运动方程、生物热传导方程、时域有限差分法(FDTD)、龙格-库塔(RK)法数值仿真研究输入功率、激励频率和气泡初始半径对HIFU在含气泡体模中形成焦域的影响,并利用含Sono Vue造影剂的仿组织体模研究进行实验验证。结果表明,增大输入功率、气泡初始半径和升高激励频率均可增大焦域,随着输入功率的增大,焦域形状可能发生变化,而随着激励频率升高和气泡初始半径的增大,焦域会向远离换能器的方向移动。     

Forced vibrations of a bubble in a liquid-filled elastic vessel

There is increasing demand for accurate characterization of the in vivo behavior of microbubble agents used for ultrasound imaging and therapy. This study examines bubble-vessel interaction, in particular the propagation of disturbances along the vessel wall. Finite element simulations of a 3 μm radius microbubble suspended in a viscous liquid and enclosed in a 4 μm radius elastic vessel were performed, and the results compared with existing analytical results for wave propagation in elastic liquid-filled tubes. The vessel wall was shown to have a significant effect upon the amplitude of bubble oscillation and hence acoustic radiation from it, as well as distension of the vessel wall. It was found that the most important factor was the ratio of the excitation frequency to the natural "ring" frequency of the vessel which in turn depends upon its dimensions and mechanical properties. As this ratio increases, the motion of the vessel wall becomes increasingly localized to the site of the bubble. It was also shown that the validity of the results obtained using the applied model of vessel elasticity is limited to frequencies below the ring frequency, and this should be taken into account in the development of protocols for ultrasound safety and/or therapeutic procedures.     

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.     

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.     

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.     

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.