Subharmonic behavior of phospholipid-coated ultrasound contrast agent microbubbles

Coated microbubbles, unlike tissue are able to scatter sound subharmonically. Therefore, the subharmonic behavior of coated microbubbles can be used to enhance the contrast in ultrasound contrast imaging. Theoretically, a threshold amplitude of the driving pressure can be calculated above which subharmonic oscillations of microbubbles are initiated. Interestingly, earlier experimental studies on coated microbubbles demonstrated that the threshold for these bubbles is much lower than predicted by the traditional linear viscoelastic shell models. This paper presents an experimental study on the subharmonic behavior of differently sized individual phospholipid coated microbubbles. The radial subharmonic response of the microbubbles was recorded with the Brandaris ultra high-speed camera as a function of both the amplitude and the frequency of the driving pulse. Threshold pressures for subharmonic generation as low as 5 kPa were found near a driving frequency equal to twice the resonance frequency of the bubble. An explanation for this low threshold pressure is provided by the shell buckling model proposed by Marmottant et al. [J. Acoust. Soc. Am. 118, 3499-3505 (2005)]. It is shown that the change in the elasticity of the bubble shell as a function of bubble radius as proposed in this model, enhances the subharmonic behavior of the microbubbles.     

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.     

Excitation threshold for subharmonic generation from contrast microbubbles

Six models of contrast microbubbles are investigated to determine the excitation threshold for subharmonic generation. The models are applied to a commercial contrast agent; its characteristic parameters according to each model are determined using experimentally measured ultrasound attenuation. In contrast to the classical perturbative result, the minimum threshold for subharmonic generation is not always predicted at excitation with twice the resonance frequency; instead it occurs over a range of frequencies from resonance to twice the resonance frequency. The quantitative variation of the threshold with frequency depends on the model and the bubble radius. All models are transformed into a common interfacial rheological form, where the encapsulation is represented by two radius dependent surface properties-effective surface tension and surface dilatational viscosity. Variation of the effective surface tension with radius, specifically having an upper limit (resulting from strain softening or rupture of the encapsulation during expansion), plays a critical role. Without the upper limit, the predicted threshold is extremely large, especially near the resonance frequency. Having a lower limit on surface tension (e.g., zero surface tension in the buckled state) increases the threshold value at twice the resonance frequency, in some cases shifting the minimum threshold toward resonance.     

调频激励增强微气泡的次谐波理论和实验研究

超声造影剂的次谐波成像可以提高造影组织比，提供更好的图像质量. 提出一种利用调频脉冲激励以增强造影剂微气泡产生的次谐波新方法. 基于修正的Church方程，从理论上讨论了次谐波的产生与调频激励声压的关系及产生阈值，并且实验证实了优化调频信号的带宽及调频时间可以提高次谐波信号幅度及改善主瓣和旁瓣特性. 理论与实验表明，与传统脉冲信号激励相比，调频信号激励产生的次谐波幅度可提高约22dB. 关键词： 调频激励 超声造影剂 微气泡 次谐波     

Frequency relationships for ultrasonic activation of free microbubbles, encapsulated microbubbles, and gas-filled micropores.

The ultrasonic activation of free microbubbles, encapsulated microbubbles, and gas-filled micropores was explored using available linear theory. Encapsulated microbubbles, used in contrast agents for diagnostic ultrasound, have relatively high resonance frequencies and damping. At 2 MHz the resonance radii are 1.75 microns for free microbubbles, 4.0 microns for encapsulated microbubbles, and 1.84 microns for gas-filled micropores. Higher-pressure amplitudes are needed to elicit equivalent subharmonic, fundamental, or second-harmonic responses from the encapsulated microbubbles, and this behavior increases for higher frequencies. If an encapsulated microbubble becomes destabilized during exposure,the resulting liberated microbubble would be about twice the linear resonance size, which would be likely to produce subharmonic signals. Scattered signals used for medical imaging purposes may be indicative of bioeffects potential: The second harmonic signal is proportional to local shear stress for a microbubble on a boundary, and a strong subharmonic signal may imply destabilization and nucleation of free-microbubble cavitation activity. The potential for bioeffects from contrast agent gas bodies decreases rapidly with increasing frequency. This information should be valuable for understanding of the etiology of bioeffects related to contrast agents and for developing exposure indices and risk management strategies for their use in diagnostic ultrasound.     

Resonance frequencies of lipid-shelled microbubbles in the regime of nonlinear oscillations

Knowledge of resonant frequencies of contrast microbubbles is important for the optimization of ultrasound contrast imaging and therapeutic techniques. To date, however, there are estimates of resonance frequencies of contrast microbubbles only for the regime of linear oscillation. The present paper proposes an approach for evaluating resonance frequencies of contrast agent microbubbles in the regime of nonlinear oscillation. The approach is based on the calculation of the time-averaged oscillation power of the radial bubble oscillation. The proposed procedure was verified for free bubbles in the frequency range 1-4 MHz and then applied to lipid-shelled microbubbles insonified with a single 20-cycle acoustic pulse at two values of the acoustic pressure amplitude, 100 kPa and 200 kPa, and at four frequencies: 1.5, 2.0, 2.5, and 3.0 MHz. It is shown that, as the acoustic pressure amplitude is increased, the resonance frequency of a lipid-shelled microbubble tends to decrease in comparison with its linear resonance frequency. Analysis of existing shell models reveals that models that treat the lipid shell as a linear viscoelastic solid appear may be challenged to provide the observed tendency in the behavior of the resonance frequency at increasing acoustic pressure. The conclusion is drawn that the further development of shell models could be improved by the consideration of nonlinear rheological laws.     

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。     

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.     

A preliminary in vitro assessment of polymer-shelled microbubbles in contrast-enhanced ultrasound imaging

This paper focuses on the use of poly (vinyl alcohol)-shelled microbubbles as a contrast agent in ultrasound medical imaging. The objective was an in vitro assessment of the different working conditions and signal processing methods for the visual detection (especially in small vessels) of such microbubbles, while avoiding their destruction. Polymer-shelled microbubbles have recently been proposed as ultrasound contrast agents with some important advantages. The major drawback is a shell that is less elastic than that of the traditional lipidic microbubbles. Weaker echoes are expected, and their detection at low concentrations may be critical. In vitro experiments were performed with a commercial ultrasound scanner equipped with a dedicated acquisition board. A concentration of 100 bubbles/mm³, excitation pressure amplitudes from 120 kPa to 320 kPa, and a central frequency of 3 MHz or 4.5 MHz were used. Three multi-pulse techniques (i.e., pulse inversion, contrast pulse sequence based on three transmitted signals, and contrast pulse sequence in combination with the chirp pulse) were compared. The results confirmed that these microbubbles produce a weaker ultrasound response than lipidic bubbles with a reduced second-order nonlinear component. Nevertheless, these microbubbles can be detected by the contrast pulse sequence technique, especially when the chirp pulse is adopted. The best value of the contrast-to-tissue ratio was obtained at an excitation pressure amplitude of 230 kPa: although this pressure amplitude is higher than what is typically used for lipidic microbubbles, it does not cause the rupture of the polymeric contrast agent.     

Ambient pressure dependence of the ultra-harmonic response from contrast microbubbles

Sub-harmonic response from ultrasound contrast agent microbubbles has been demonstrated to be an effective modality for noninvasive pressure measurement. In the present study, the dependence of ultra-harmonic response on the ambient overpressure was investigated by both experimental measurements and simulations. In the measurements, the microbubbles were exposed to Gaussian pulses with varied driving frequencies and pulse lengths, at an acoustic pressure of 0.3 MPa. The amplitudes of sub- and ultra-harmonic components were measured when the ambient overpressures varied from 0-25 kPa. At the driving frequency of 1.33 MHz, the ultra-harmonic energy decreased but the sub-harmonic energy increased with the increasing overpressure; while at the driving frequency of 4 MHz, both the sub- and ultra-harmonic components showed the same tendency that the corresponding energy decreased as the overpressure was increased. A 4-MHz Gaussian pulse with 64 cycles could provide an ultra-harmonic response with both good ambient pressure sensitivity and high linearity. Furthermore, the effects of shell parameters of a microbubble on the generation of ultra- and sub-harmonic responses were discussed based on simulations using Marmottant's model. This study suggests that the ultra-harmonic response from contrast microbubbles might be applicable for noninvasive pressure measurement.     

调频超声脉冲驱动微气泡运动偏移的研究

提出调频超声辐射力技术驱动微泡群,以加强微泡的吸附效率.基于改进的RP方程及粒子轨迹方程研究了微泡群整体的运动位移与调频信号的中心频率、调频范围、信号声压,以及微泡半径分布关系.研究结果表明调频信号在驱动半径具有宽泛分布的气泡群,以及半径分布远离谐振半径的气泡群时,作用效果好于传统正弦波信号.例如中心频率1 MHz、调频范围0.75 MHz的调频脉冲作用高斯分布（平均半径3.5 μm、均方差为1）的微泡群200 μs,可比同等声压的正弦波多约12%的微气泡产生位移30 μm. 关键词： 超声辐射力 调频波 高斯分布     

"Compression-only" behavior: a second-order nonlinear response of ultrasound contrast agent microbubbles

Oscillating phospholipid-coated ultrasound contrast agent microbubbles display a so-called "compression-only" behavior, where it is observed that the bubbles compress efficiently while their expansion is suppressed. Here, a theoretical understanding of the source of this nonlinear behavior is provided through a weakly nonlinear analysis of the shell buckling model proposed by Marmottant et al. [J. Acoust. Soc. Am. 118, 3499-3505 (2005)]. It is shown that the radial dynamics of the bubble can be considered as a superposition of a linear response at the fundamental driving frequency and a second-order nonlinear low-frequency response that describes the negative offset of the mean bubble radius. The analytical solution deduced from the weakly nonlinear analysis shows that the compression-only behavior results from a rapid change of the shell elasticity with bubble radius. In addition, the radial dynamics of single phospholipid-coated microbubbles was recorded as a function of both the amplitude and the frequency of the driving pressure pulse. The comparison between the experimental data and the theory shows that the magnitude of compression-only behavior is mainly determined by the initial phospholipids concentration on the bubble surface, which slightly varies from bubble to bubble.     

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.     

Experimental evaluation of a non-linear coded excitation method for contrast imaging

Previously, we have shown that for a single bubble, using chirps as the excitation signal improves both the linear and the non-linear response. Computer simulations of randomly distributed contrast agent bubbles show an increase of 10-13 dB in response when comparing pulse excitations with chirp excitations that have equal bandwidths and peak amplitudes. Second harmonic compression of simulated bubble echoes with chirp excitation shows low side-lobe levels and limited loss of axial resolution when compared to pulse excitation. Experimental results from water tank measurements with SonoVue contrast agent are in agreement with computer simulations showing increased signal-to-noise ratio and an increase of approximately 12 dB at the second harmonic when comparing pulse and chirp excitation.     

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。     

Subharmonic imaging of contrast agents

Ultrasound contrast agents promise to improve the sensitivity and specificity of diagnostic ultrasound imaging. It is of great importance to adapt ultrasound equipment for optimal use with contrast agents e.g., by exploiting the nonlinear properties of the contrast microbubbles. Harmonic imaging is one technique that has been extensively studied and is commercially available. However, harmonic imaging is associated with problems, due to second harmonic generation and accumulation within the tissue itself. Given the lack of subharmonic generation in tissue, one alternative is the creation of subharmonic images by transmitting at the fundamental frequency (fo) and receiving at the subharmonic (fo/2). Subharmonic imaging should have a much better lateral resolution and may be suitable for scanning deep-lying structures owing to the higher transmit frequency and the much smaller attenuation of scattered subharmonic signals. In this paper, we will review different aspects of subharmonic imaging including implementation, in-vitro gray-scale imaging and subharmonic aided pressure estimation.     

Impact of acoustic pressure on ambient pressure estimation using ultrasound contrast agent

Local blood pressure measurements provide important information on the state of health of organs in the body and can be used to diagnose diseases in the heart, lungs, and kidneys. This paper presents an approach for investigating the ambient pressure sensitivity of a contrast agent using diagnostic ultrasound. The experimental setup resembles a realistic clinical setup utilizing a single array transducer for transmit and receive. The ambient pressure sensitivity of SonoVue (Bracco, Milano, Italy) was measured twice using two different acoustic driving pressures, which were selected based on a preliminary experiment. To compensate for variations in bubble response and to make the estimates more robust, the relation between the energy of the subharmonic and the fundamental component was chosen as a measure over the subharmonic peak amplitude. The preliminary study revealed the growth stage of the subharmonic component to occur at acoustic driving pressures between 300 and 500 kPa. Based on this, the pressure sensitivity was investigated using a driving pressure of 485 and 500 kPa. At 485 kPa, a linear pressure sensitivity of 0.42 dB/kPa was found having a linear correlation coefficient of 0.94. The second measurement series at 485 kPa showed a sensitivity of 0.41 dB/kPa with a correlation coefficient of 0.89. Based on the measurements at 500 kPa, this acoustic driving pressure was concluded to be too high causing the bubbles to be destroyed. The pressure sensitivity for these two measurement series were 0.42 and 0.25 dB/kPa with linear correlation coefficients of 0.98 and 0.93, respectively.     

Experimental investigation of the effect of ambient pressure on laser-induced bubble dynamics

The effect of ambient pressure on the dynamics of laser-induced bubbles was investigated by a fiber-optic diagnostic technique based on probe beam deflection (PBD). The experimental criterion for judging the maximum bubble radius is modified to the average value of the detecting distances at which the characteristic waveform signals appear. The ambient pressure affects the maximum radius and collapse of bubble strongly. The experimental results indicate that the maximum bubble radius and the collapse time both decrease nonlinearly while the ambient pressure increases linearly, and the decreasing velocities of them are smaller at a larger ambient pressure. The predicted value of collapse time has a good agreement with experiment at larger ambient pressure.     

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.     

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.