Translational instability of a spherical bubble in a standing ultrasound wave

Translational bubble dynamics is much less studied than the dynamics of radial bubble oscillation, while in many scientific and engineering applications the control of space location of cavitation bubbles is of great practical importance. This paper aims at the theoretical study of various aspects of the translational motion of a spherical gas bubble in a high-frequency standing wave. In particular, it is shown that the translational instability that gives rise to the reciprocal translation of a spherical bubble between the pressure antinode and the pressure node is caused by the hysteresis in the main resonance of the bubble. Different types of translational trajectories that can occur in a standing wave are illustrated by numerical simulations. A general classification of the observed translational trajectories is proposed.     

A numerical investigation of the resonance of gas-filled microbubbles: resonance dependence on acoustic pressure amplitude

The general Keller-Herring equation for free gas bubbles is augmented by specific terms to describe the elasticity, viscosity and thickness of the encapsulating shell in ultrasound contrast agent microbubbles. A numerical investigation that analyses the acoustic backscatter from bubbles is employed to identify resonance frequencies that can be compared, for increasing driving pressure amplitude, with linear approximations obtained via analytical considerations. Calculations for bubbles of the size employed in diagnostic ultrasound, between 2 and 6 mum diameter, that are immersed in water and blood and exposed to monochromatic insonation, causing the bubbles to undergo stable cavitation, reveal that the resonance frequency diverges from the linear approximation as the pressure amplitude is increased. The shift in resonance, to lower frequency values, is found to be more pronounced for larger bubbles with the calculated value differing by up to 40% from the linear approximation. The results of this simulation might be potentially useful in preparation of formulations of ultrasound contrast agents with the specifically desired features, such as for instance resonance frequency.     

Real-Time Measurements and Modelling on Dynamic Behaviour of SonoVue Bubbles Based on Light Scattering Technology

The dynamic behaviour of SonoVue microbubbles, a new generation ultrasound contrast agent, is investigated in real time with light scattering method. Highly diluted SonoVue microbubbles are injected into a diluted gel made of xanthan gum and water. The responses of individual SonoVue bubbles to driven ultrasound pulses are measured. Both linear and nonlinear bubble oscillations are observed and the results suggest that SonoVue microbubbles can generate strong nonlinear responses. By fitting the experimental data of individual bubble responses with Sarkar＇s model, the shell coating parameter of the bubbles and dilatational viscosity is estimated to be 7.0 nm-s-Pa.     

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.     

Use of ultrasonics in shear layer cavitation control

In this paper we report results from some investigations on the use of ultrasonics in controlling hydrodynamic cavitation in the shear layer downstream of a sudden expansion. Control of this type of cavitation has been achieved by modulating the local pressure that was experienced by a nucleus present in the shear layer. This modulation was made possible by using a piezoelectric device, termed as Ultrasonic Pressure Modulator (UPM). The performance of UPM has been studied at different dissolved gas concentrations with electrolysis bubbles as nuclei. Control of cavitation due to natural nuclei has also been attempted. Efficiency of UPM, in reducing cavitation, was seen to be dependent on the driving frequency employed. Experimental and numerical studies have been conducted to bring out the physics behind this approach of cavitation control. Different measures of cavitation control have been identified and some possible applications of this method have also been outlined.     

Ultrasonic scattering cross sections of shell-encapsulated gas bubbles immersed in a viscoelastic liquid: first and second harmonics

The oscillations of gas bubbles, without shell, immersed in viscoelastic liquids and driven by an acoustic wave have been the subject of several investigations. They demonstrate that the viscosity coefficient and the spring constant of the liquid have significant influence on the scattering cross section of the gas bubble. For shell-encapsulated gas bubbles, the investigations have been concentrated to bubbles immersed in a pure viscous liquid. This present work computes the ultrasonic scattering cross section, first and second harmonics, of shell-encapsulated gas bubbles immersed in a viscoelastic liquid. The theoretical model of the bubble oscillation is based on the generalized Rayleigh-Plesset equation of motion of a spherical cavity immersed in a viscoelastic liquid represented by a three-parameter linear Oldroyd model. The scattering cross section is computed for Albunex type of bubble (shell thickness=15 nm, shell shear viscosity=1.77 Pas, shell modulus of rigidity=88.8 MPa) irradiated by a 3.5 MHz ultrasonic pressure wave with an amplitude of 30 kPa. The results demonstrate that encapsulated bubbles respond independently of the surrounding liquid being pure viscous or viscoelastic as long as the surrounding liquid shear viscosity is as low as 10(-3) Pas. Nevertheless, for higher shear viscosities, the bubble responds differently if the surrounding liquid is pure viscous or viscoelastic. In general, the scattering cross sections of first and second harmonics are larger for the viscoelastic liquid.     

The Rayleigh-Plesset equation in terms of volume with explicit shear losses

The most common nonlinear equation of motion for the damped pulsation of a spherical gas bubble in an infinite body of liquid is the Rayleigh-Plesset equation, expressed in terms of the dependency of the bubble radius on the conditions pertaining in the gas and liquid (the so-called ‘radius frame’). However over the past few decades several important analyses have been based on a heuristically derived small-amplitude expansion of the Rayleigh-Plesset equation which considers the bubble volume, instead of the radius, as the parameter of interest, and for which the dissipation term is not derived from first principles. So common is the use of this equation in some fields that the inherent differences between it and the ‘radius frame’ Rayleigh-Plesset equation are not emphasised, and it is important in comparing the results of the two equations to understand that they differ both in terms of damping, and in the extent to which they neglect higher order terms. This paper highlights these differences. Furthermore, it derives a ‘volume frame’ version of the Rayleigh-Plesset equation which contains exactly the same basic physics for dissipation, and retains terms to the same high order, as does the ‘radius frame’ Rayleigh-Plesset equation. Use of this equation will allow like-with-like comparisons between predictions in the two frames.     

Modeling of the acoustic response from contrast agent microbubbles near a rigid wall

In ultrasonic targeted imaging, specially designed encapsulated microbubbles are used, which are capable of selectively adhering to the target site in the body. A challenging problem is to distinguish the echoes from such adherent agents from echoes produced by freely circulating agents. In the present paper, an equation of radial oscillation for an encapsulated bubble near a plane rigid wall is derived. The equation is then used to simulate the echo from a layer of contrast agents localized on a wall. The echo spectrum of adherent microbubbles is compared to that of free, randomly distributed microbubbles inside a vessel, in order to examine differences between the acoustic responses of free and adherent agents. It is shown that the fundamental spectral component of adherent bubbles is perceptibly stronger than that of free bubbles. This increase is accounted for by a more coherent summation of echoes from adherent agents and the acoustic interaction between the agents and the wall. For cases tested, the increase of the fundamental component caused by the above two effects is on the order of 8-9 dB. Bubble aggregates, which are observed experimentally to form near a wall due to secondary Bjerknes forces, increase the intensity of the fundamental component only if they are formed by bubbles whose radii are well below the resonant radius. If the formation of aggregates contributes to the growth of the fundamental component, the increase can exceed 17 dB. Statistical analysis for the comparison between adhering and free bubbles, performed over random space bubble distributions, gives p-values much smaller than 0.05.     

Modeling of nonlinear viscous stress in encapsulating shells of lipid-coated contrast agent microbubbles

A general theoretical approach to the development of zero-thickness encapsulation models for contrast microbubbles is proposed. The approach describes a procedure that allows one to recast available rheological laws from the bulk form to a surface form which is used in a modified Rayleigh-Plesset equation governing the radial dynamics of a contrast microbubble. By the use of the proposed procedure, the testing of different rheological laws for encapsulation can be carried out. Challenges of existing shell models for lipid-encapsulated microbubbles, such as the dependence of shell parameters on the initial bubble radius and the “compression-only” behavior, are discussed. Analysis of the rheological behavior of lipid encapsulation is made by using experimental radius-time curves for lipid-coated microbubbles with radii in the range 1.2-2.5 μm. The curves were acquired for a research phospholipid-coated contrast agent insonified with a 20 cycle, 3.0 MHz, 100 kPa acoustic pulse. The fitting of the experimental data by a model which treats the shell as a viscoelastic solid gives the values of the shell surface viscosity increasing from 0.30 × 10⁻⁸ kg/s to 2.63 × 10⁻⁸ kg/s for the range of bubble radii, indicated above. The shell surface elastic modulus increases from 0.054 N/m to 0.37 N/m. It is proposed that this increase may be a result of the lipid coating possessing the properties of both a shear-thinning and a strain-softening material. We hypothesize that these complicated rheological properties do not allow the existing shell models to satisfactorily describe the dynamics of lipid encapsulation. In the existing shell models, the viscous and the elastic shell terms have the linear form which assumes that the viscous and the elastic stresses acting inside the lipid shell are proportional to the shell shear rate and the shell strain, respectively, with constant coefficients of proportionality. The analysis performed in the present paper suggests that a more general, nonlinear theory may be more appropriate. It is shown that the use of the nonlinear theory for shell viscosity allows one to model the “compression-only” behavior. As an example, the results of the simulation for a 2.03 μm radius bubble insonified with a 6 cycle, 1.8 MHz, 100 kPa acoustic pulse are given. These parameters correspond to the acoustic conditions under which the “compression-only” behavior was observed by de Jong et al. [Ultrasound Med. Biol. 33 (2007) 653-656]. It is also shown that the use of the Cross law for the modeling of the shear-thinning behavior of shell viscosity reduces the variance of experimentally estimated values of the shell viscosity and its dependence on the initial bubble radius.     

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.     

Non-Axisymmetric Oscillation of Acoustically Levitated Water Drops at Specific Frequencies

A category of non-axisymmetric oscillations of acoustically levitated water drops was observed. These oscillations can be qualitatively described by superposing a sectorial oscillating term upon the initial oblate shape resulting from the effect of acoustic radiation pressure. The oscillation frequencies are around 25 Hz for the 2-lobed mode and exactly 50 Hz for the 3- and 4-1obed modes. These oscillations were excited by the disturbance from the power supply. For the same water drop, higher mode oscillations were observed with more oblate initial shape, indicating that the eigenfrequencies of these non-axisymmetric oscillations decrease with increasing initial distortion. The maximum velocity and acceleration within the oscillating drop can attain 0.3 m·s^-1 and 98.7 m·s^-2 respectively, resulting in strong fluid convection and enhanced heat and mass transfer.     

Dispersion and frequency dependent nonlinearity parameters in a graphite-epoxy composite

Longitudinal phase velocity and nonlinearity parameter have been measured as a function of frequency in the low megaHertz range in a laminate graphite-fiber-epoxy-resin composite. Amplitudes of both the fundamental and generated second harmonics were measured absolutely with a capacitive receiver. Phase velocity and nonlinearity parameter vary with frequency. The extent of the variance depends on the orientation of the fiber layers. Comparison is made between the nonlinear differential equation appropriate for crystals and a new equation that accounts for frequency dependence of phase velocity and nonlinearity parameter. The newer equation describes the data more accurately than the crystalline model does, but appears to require additional terms.     

Oscillation characteristics of a laser-induced cavitation bubble in water at different temperatures

Comprehensive numerical and experimental analyses of the effect of temperature on cavitation oscillations are performed. In the experimental study, the oscillation of a laser-generated single cavitation bubble near a rigid boundary is obtained using a fiber-optic diagnostic technique based on optical beam detection (OBD). The maximum and minimum bubble radii as well as the oscillation times for each oscillation cycle are determined according to the characteristic signals. And cavitation bubble tests are performed using water at different temperatures, and its temperature ranges from freezing point (0 °C) to near boiling. Furthermore, a modified Rayleigh-Plesset equation is derived for calculating the temporal development of the bubble radius at different temperatures. Both the experimental and the numerical results show that the maximum bubble radius and bubble lifetime both increase as temperature increases. The mechanism behind it has also been discussed.     

Nonlinear change of on-axis pressure and intensity maxima positions and its relation with the linear focal shift effect

A comprehensive experimental, analytical and numerical study of the true focal region drift relative to the geometrical focus (focal shift effect) in acoustic focused beams and its nonlinear evolution is presented. For this aim, the concept of Fresnel number, proportional to the linear gain, is introduced as a convenient parameter for characterizing focused sources. It is shown that the magnitude of the shift is strongly dependent on the Fresnel number of the source, being larger for weakly focused systems where a large initial shift occurs. Analytical expressions for axial pressure distributions in linear regime are presented for the general case of truncated Gaussian beams. The main new contribution of this work is the examination of the connection between the linear and nonlinear stages of the focal shift effect, and its use for the estimation of the more complicated nonlinear stage. Experiments were carried out using a continuous-wave ultrasonic beam in water, radiated by a focused source with nominal frequency f = 1 MHz, aperture radius a = 1.5 cm and geometrical focal distance R = 11.7 cm, corresponding to a Fresnel number N_F = 1.28. The maximum measured shifts for peak pressure and intensity were 4.4 and 1.1 cm, respectively. The evolution of the different maxima with the source amplitude, and the disparity in their axial positions, is interpreted in terms of the dynamics of the nonlinear distortion process. Analytical results for the particular case of a sound beam with initial Gaussian distribution are also presented, demonstrating that the motion of peak pressure and peak intensity may occur in opposite directions.     

Evanescent modes and anomalous streaming in a thermoacoustic device

An oil-heated thermoacoustic refrigerator was constructed in order to investigate the use of waste-heat sources to operate a refrigerator. Fluid flows within the resonator in the vicinity of the stack/heat exchanger assemblies were measured through optical means. During the course of the experiment, anomalous centerline steady flows were observed at magnitudes of up to three times the acoustic amplitudes within the resonator of the thermoacoustic device. An evanescent component of the acoustic field was also measured at the same location. An order of magnitude calculation indicates that the body force induced by the evanescent mode is of sufficient magnitude and structure to be the source of the streaming.     

The transmission of finite amplitude sound beam in multi-layered biological media

Based on the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation, a model in the frequency domain is given to describe the transmission of finite amplitude sound beam in multi-layered biological media. Favorable agreement between the theoretical analyses and the measured results shows this approach could effectively describe the transmission of finite amplitude sound wave in multi-layered biological media.     

Evolution of acoustic waves in microinhomogeneous media with quadratic elastic nonlinearity and relaxation

A nonlinear wave equation for the velocity “relaxator” is derived in the framework of the rheological model and the corresponding equation of state of a microinhomogeneous medium containing viscoelastic defects with quadratic nonlinear elasticity. The equation is qualitatively analyzed, and numerical solutions to it are presented for a stationary symmetric shock wave and the evolution of initially harmonic waves.     

Dynamics of laser-induced channel formation in water and influence of pulse duration on the ablation of biotissue under water with pulsed erbium-laser radiation

The ability to use fiber-delivered erbium-laser radiation for non-contact arthroscopic meniscectomy in a liquid environment was studied. The laser radiation is transmitted through a water-vapor channel created by the leading part of the laser pulse. The dynamics of the channel formation around a submerged fiber tip was investigated with time-resolved flash photography. Strong pressure transients with amplitudes up to a few hundreds of bars measured with a needle hydrophone were found to accompany the channel formation process. Additional pressure transients in the range of kbars were observed after the laser pulse associated with the collapse of the vapor channel. Transmission measurements revealed that the duration the laser-induced channel stays open, and therefore the energy transmittable through it, is substantially determined by the laser pulse duration. The optimum pulse duration was found to be in the range between 250 and 350 µS. This was confirmed by histological evaluations of the laser incisions in meniscus: Increasing the pulse duration from 300 to 800 µs leads to a decrease in the crater depth from 1600 to 300 µm. A comparison of the histological examination after laser treatment through air and through water gave information on the influence of the vapor channel on the ablation efficiency, the cutting quality and the induced thermal damage in the adjacent tissue. The study shows that the erbium laser combined with an adequate fiber delivery system represents an effective surgical instrument liable to become increasingly accepted in orthopedic surgery.     

Resonance Shift of Single-Axis Acoustic Levitation

The resonance shift due to the presence and movement of a rigid spherical sample in a single-axis acoustic levitator is studied with the boundary element method on the basis of a two-cylinder model of the levitator. The introduction of a sample into the sound pressure nodes, where it is usually levitated, reduces the resonant interval H~ （n is the mode number） between the reflector and emitter. The larger the sample radius, the greater the resonance shift. When the sample moves along the symmetric axis, the resonance interval Hn varies in an approximately periodical manner, which reaches the minima near the pressure nodes and the maxima near the pressure antinodes. This suggests a resonance interval oscillation around its minimum if the stably levitated sample is slightly perturbed. The dependence of the resonance shift on the sample radius 17 and position h for the single-axis acoustic levitator is compared with Leung＇s theory for a closed rectangular chamber, which shows a good agreement.     

The effect of ultrasonic irradiation on doxorubicin-induced cytotoxicity in three human bladder cancer cell lines

Although ultrasonic irradiation has been proven to increase membrane permeability and enhance chemotherapeutic cytotoxicity in a number of cell lines, this effect has never been demonstrated in bladder cancer cells. Bladder cancer may offer a unique setting for ultrasound enhancement of chemotherapy, since intravesicular rather than intravenous administration of chemotherapy is used in superficial cases. The aim of this study was to investigate whether a non-toxic dose of ultrasound could increase membrane permeability, and potentiate the cytotoxicity of doxorubicin to three human bladder carcinoma cell lines (TCC-SUP, T24, and RT4) in vitro. An EuTDA-Efflux assay, which measures the amount of a chemical that is allowed to seep out of labeled cells, was used to analyze membrane permeability, and an MTS assay, which directly measures cell viability, was used to determine the effect of chemotherapy on cells after they were treated with a variety of doxorubicin concentrations and ultrasonic exposures. Ultrasound treatment for 5 min and 10 min at an intensity of approximately 0.3 W/cm² resulted in a significant increase in EuTDA efflux in all three cell lines. However, no ultrasonic enhancement of doxorubicin growth inhibition in these human bladder carcinoma cells was observed. This suggests that either ultrasound does not increase doxorubicin uptake by the cell or that doxorubicin uptake is increased but in insufficient amounts to affect growth inhibition. Further investigation should focus on explaining these results.