The natural frequencies of microbubble oscillation in elastic vessels

Interaction of ultrasonically driven bubble with a soft tissue-like boundary

This study investigates the size-dependent dynamics of bubbles and their interaction with soft boundaries under various ultrasound (US) conditions. We found that bubble behavior is influenced by size, with smaller bubbles displaying reduced inertial motion in similar ultrasound environments. Detailed analyses of three bubble sizes (1.5 µm, 15 µm, and 150 µm) next to a soft 1 kPa boundary revealed distinct patterns in radial oscillation, bubble center displacement, and boundary deflection for different ultrasound frequencies (5 kHz - 4 MHz). The smallest bubble maintained a spherical shape, while the largest experienced significant shape changes, indicative of impending jet formation. Investigating interactions at various frequencies highlighted the collapse tendency of the larger bubbles, showcasing maximum radial amplitude, displacement, and bubble wall velocity around its natural frequency. The presence of a soft boundary minimally affected radial amplitude and velocity, while the bubble displacement was contingent on the soft boundary modulus. Furthermore, boundary responses demonstrated that softer boundaries experienced less stress during bubble oscillations, exhibiting sharper peaks at resonance frequencies for larger bubbles. These findings provide valuable insights into optimizing ultrasound conditions for a variety of applications, highlighting the influence of bubble size and boundary properties on outcomes.

Numerical investigation of the effect of bubble properties on the linear resonance frequency shift due to inter-bubble interactions in ultrasonically excited lipid coated microbubbles

Ultrasonically excited microbubbles (MBs) have numerous applications in various fields, such as drug delivery, and imaging. Ultrasonically excited MBs are known to be nonlinear oscillators that generate secondary acoustic emissions in the media when excited by a primary ultrasound wave. The propagation of acoustic waves in the liquid is limited to the speed of sound, resulting in each MB receiving the primary and secondary waves at different times depending on their distance from the ultrasound source and the distance between MBs. These delays are referred to as primary and secondary delays, respectively. A previous study demonstrated that the inclusion of secondary delays in a model describing the interactions between MBs exposed to ultrasound results in an increase in the linear resonance frequency of MBs as they approach each other. This work investigates the impact of various MB properties on the change in linear resonance frequency resulting from changes in inter-bubble distances. The effects of shell properties, including the initial surface tension, surface dilatational viscosity of the shell monolayer, elastic compression modulus of the shell, and the initial radius of the MBs, are examined. MB size is a significant factor influencing the rate of linear resonance frequency increase with increasing concentration. Moreover, it is found that the shell properties of MBs play a negligible role in the rate of change in linear resonance frequency of MBs as the inter-bubble distances change.The findings of this study have implications for various applications of MBs in the biomedical field. By understanding the impact of inter-bubble distances and shell properties on the linear resonance frequency of MBs, the utilization of MBs in applications reliant on their resonant behavior can be optimized.

Laser induced spherical bubble dynamics in partially confined geometry with acoustic feedback from container walls

We investigated laser-induced cavitation dynamics in a small container with elastic thin walls and free or partially confined surface both experimentally and by numerical investigations. The cuvette was only 8-25 times larger than the bubble in its center. The liquid surface was either free, or two thirds were confined by a piston-shaped pressure transducer. Different degrees of confinement were realized by filling the liquid up to the transducer surface or to the top of the cuvette. For reference, some experiments were performed in free liquid. We recorded the bubble dynamics simultaneously by high-speed photography, acoustic measurements, and detection of probe beam scattering. Simultaneous single-shot recording of radius-time curves and oscillation times enabled to perform detailed investigations of the bubble dynamics as a function of bubble size, acoustic feedback from the elastic walls, and degree of surface confinement. The bubble dynamics was numerically simulated using a Rayleigh-Plesset model extended by terms describing the acoustically mediated feedback from the bubble's environment. Bubble oscillations were approximately spherical as long as no secondary cavitation by tensile stress occurred. Bubble expansion was always similar to the dynamics in free liquid, and the environment influenced mainly the collapse phase and subsequent oscillations. For large bubbles, strong confinement led to a slight reduction of maximum bubble size and to a pronounced reduction of the oscillation time, and both effects increased with bubble size. The joint action of breakdown-induced shock wave and bubble expansion excites cuvette wall vibrations, which produce alternating pressure waves that are focused onto the bubble. This results in a prolongation of the collapse phase and an enlargement of the second oscillation, or in time-delayed re-oscillations. The details of the bubble dynamics depend in a complex manner on the degree of surface confinement and on bubble size. Numerical simulations of the first bubble oscillation agreed well with experimental data. They suggest that the alternating rarefaction/compression waves from breakdown-induced wall vibrations cause a prolongation of the first oscillation. By contrast, liquid mass movement in the cuvette corners result in wall vibrations causing late re-oscillations. The strong and rich interaction between the bubble and its surroundings may be relevant for a variety of applications such as intraluminal laser surgery and laser-induced cavitation in microfluidics.

Prediction of vascular injury by cavitation microbubbles in a focused ultrasound field

Many studies have shown that microbubble cavitation is one mechanism for vascular injury under ultrasonic excitation. Previous work has attributed vascular damage to vessel expansions and invaginations due to the expansion and contraction of microbubbles. However, the mechanisms of vascular damage are not fully understood. In this paper, we investigate, theoretically and experimentally, the vessel injury due to stress induced by ultrasound-induced cavitation (UIC). A bubble-fluid-vessel coupling model is constructed to investigate the interactions of the coupling system. The dynamics process of vessel damage due to UIC is theoretically simulated with a finite element method, and a focused ultrasound (FU) setup is carried out and used to assess the vessel damage. The results show that shear stress contributes to vessel injury by cell detachment while normal stress mainly causes distention injury. Similar changes in cell detachment in a vessel over time can be observed with the experimental setup. The severity of vascular injury is correlated to acoustic parameters, bubble-wall distance, and microbubble sizes, and the duration of insonation..

The role of primary and secondary delays in the effective resonance frequency of acoustically interacting microbubbles

Acoustically excited microbubbles (MBs) are known to be nonlinear oscillators with complex dynamics. This has enabled their use in a wide range of applications from medicine to industry and underwater acoustics. To better utilize their potential in applications and possibly invent new ones a comprehensive understanding of their dynamics is required. In this work, we explore the effect of bubble-bubble interactions on the resonance frequency of MB suspensions. MBs oscillate in response to an external acoustic wave and since bubbles in a cluster are at different locations compared to the excitation source, they are excited at different times. In this work we refer to these delays as primary delays. Interactions between the scattered pressure fields from adjacent bubbles have also been shown to alter the dynamics of MBs that exist within clusters. These secondary waves generated by MBs reach MBs in their proximity at different times that depend on their spatial location in the cluster. Here we refer to these delays as secondary delays. Inclusion of the secondary delays modifies the class of the differential equations governing the oscillations of interacting MBs in a cluster from ordinary differential equations to neutral delay differential equations. Previous work has not considered the all the delays associated with the bubble distances when modeling the interactions between bubbles. In this work we investigate the effect of both the primary and secondary delays on the effective resonance frequency of MB clusters. It is shown that primary delays cause spreading the resonance frequency of identical MBs within a range where the closest MB to the acoustic source exhibits the lowest resonance frequency and the furthest MB resonates at the highest frequency. This range has been shown to be up to 0.12 MHz for the examples investigated in this work. The effect of secondary delays is shown to be very significant. In the absence of secondary delays, the ordinary differential equation model predicts a decrease of up to 26% in the resonance frequency of 4 identical interacting MBs as the inter-bubble distances are decreased. However, we show that inclusion of the secondary delays result in the increase of the resonance frequency of MBs if they are situated close to each other. This increase is shown to be significant and for the case of 4 identical interacting MBs we show an increase of 58% in the resonance frequency.

A 3D finite element model to study the cavitation induced stresses on blood-vessel wall during the ultrasound-only phase of photo-mediated ultrasound therapy

Photo-mediated ultrasound therapy (PUT) is a novel technique utilizing synchronized ultrasound and laser to generate enhanced cavitation inside blood vessels. The enhanced cavitation inside blood vessels induces bio-effects, which can result in the removal of micro-vessels and the reduction in local blood perfusion. These bio-effects have the potential to treat neovascularization diseases in the eye, such as age-related macular degeneration and diabetic retinopathy. Currently, PUT is in the preclinical stage, and various PUT studies on in vivo rabbit eye models have shown successful removal of micro-vessels. PUT is completely non-invasive and particle-free as opposed to current clinical treatments such as anti-vascular endothelial growth factor therapy and photodynamic therapy, and it precisely removes micro-vessels without damaging the surrounding tissue, unlike laser photocoagulation therapy. The stresses produced by oscillating bubbles during PUT are responsible for the induced bio-effects in blood vessels. In our previous work, stresses induced during the first phase of PUT due to combined ultrasound and laser irradiation were studied using a 2D model. In this work, stresses induced during the third or last phase of PUT due to ultrasound alone were studied using a 3D finite element method-based numerical model. The results showed that the circumferential and shear stress increased as the bubble moves from the center of the vessel toward the vessel wall with more than a 16 times increase in shear stress from 1.848 to 31.060 kPa as compared to only a 4 times increase in circumferential stress from 211 to 906 kPa for a 2 µm bubble placed inside a 10 µm vessel on the application of 1 MHz ultrasound frequency and 130 kPa amplitude. In addition, the stresses decreased as the bubble was placed in smaller sized vessels with a larger decrease in circumferential stress. The changes in shear stress were found to be more dependent on the bubble-vessel wall distance, and the changes in circumferential stress were more dependent on the bubble oscillation amplitude. Moreover, the bubble shape changed to an ellipsoidal with a higher oscillation amplitude in the vessel's axial direction as it was moved closer to the vessel wall, and the bubble oscillation amplitude decreased drastically as it was placed in vessels of a smaller size.

Radial oscillation and translational motion of a gas bubble in a micro-cavity

According to classical nucleation theory, a gas nucleus can grow into a cavitation bubble when the ambient pressure is negative. Here, the growth process of a gas nucleus in a micro-cavity was simplified to two "events", and the full confinement effect of the surrounding medium of the cavity was considered by including the bulk modulus in the equation of state. The Rayleigh-Plesset-like equation of the cavitation bubble in the cavity was derived to model the radial oscillation and translational motion of the cavitation bubble in the local acoustic field. The numerical results show that the nucleation time of the cavitation bubble is sensitive to the initial position of the gas nucleus. The cavity size affects the duration of the radial oscillation of the cavitation bubble, where the duration is shorter for smaller cavities. The equilibrium radius of a cavitation bubble grown from a gas nucleus increases with increasing size of the cavity. There are two possible types of translational motion: reciprocal motion around the center of the cavity and motion toward the cavity wall. The growth process of gas nuclei into cavitation bubbles is also dependent on the compressibility of the surrounding medium and the magnitude of the negative pressure. Therefore, gas nuclei in a liquid cavity can be excited by acoustic waves to form cavitation bubbles, and the translational motion of the cavitation bubbles can be easily observed owing to the confining influence of the medium outside the cavity.

Pulsating Microbubble in a Micro-vessel and Mechanical Effect on Vessel Wall: A Simulation Study

Background:

Microbubbles are widely used in diagnostic ultrasound applications as contrast agents. Recently, many studies have shown that microbubbles have good potential for the use in therapeutic applications such as drug and gene delivery and opening of blood- brain barrier locally and transiently. When microbubbles are located inside an elastic microvessel and activated by ultrasound, they oscillate and induce mechanical stresses on the vessel wall. However, the mechanical stresses have beneficial therapeutic effects, they may induce vessel damage if they are too high. Microstreaming-induced shear stress is one of the most important wall stresses.

Objective:

The overall aim of this study is to simulate the interaction between confined bubble inside an elastic microvessel and ultrasound field and investigate the effective parameters on microstreaming-induced shear stress.

Material and Methods:

In this Simulation study, we conducted a 2D finite element simulation to study confined microbubble dynamics, also we investigated both acoustical and bubble material parameters on microbubble oscillation and wall stress.

Results:

Based on our results, for acoustic parameters in the range of therapeutic applications, the maximum shear stress was lower than 4 kPa. Shear stress was approximately independent from shell viscosity whereas it decreased by increasing the shell stiffness. Moreover, shear stress showed an increasing trend with acoustic pressure.

Conclusion:

Beside the acoustical parameters, bubble properties have important effects on bubble behavior so that the softer and larger bubbles are more appropriate for therapeutic application as they can decrease the required frequency and acoustic pressure while inducing the same biological effects.

Microstreaming inside Model Cells Induced by Ultrasound and Microbubbles

Studies on the bioeffects produced by ultrasound and microbubbles have focused primarily on transport in bulk tissue, drug uptake by individual cells, and disruption of biological membranes. Relatively little is known about the physical perturbations and fluid dynamics of the intracellular environment during ultrasound exposure. To investigate this, a custom acoustofluidic chamber was designed to expose model cells, in the form of giant unilamellar vesicles, to ultrasound and microbubbles. The motion of fluorescent tracer beads within the lumen of the vesicles was tracked during exposure to laminar flow (∼1 mm s^-1), ultrasound (1 MHz, ∼150 kPa, 60 s), and phospholipid-coated microbubbles, alone and in combination. To decouple the effects of fluid flow and ultrasound exposure, the system was also modeled numerically by using boundary-driven streaming field equations. Both the experimental and numerical results indicate that all conditions produced internal streaming within the vesicles. Ultrasound alone produced an average bead velocity of 6.5 ± 1.3 μm/s, which increased to 8.5 ± 3.8 μm/s in the presence of microbubbles compared to 12 ± 0.12 μm/s under laminar flow. Further research on intracellular forces in mammalian cells and the associated biological effects in vitro and in vivo are required to fully determine the implications for safety and/or therapy.

Temporal stability of lipid-shelled microbubbles during acoustically-mediated blood-brain barrier opening

Non-invasive blood-brain barrier (BBB) opening using focused ultrasound (FUS) is being tested as a means to locally deliver drugs into the brain. Such FUS therapies require injection of preformed microbubbles, currently used as contrast agents in ultrasound imaging. Although their behavior during exposure to imaging sequences has been well described, our understanding of microbubble stability within a therapeutic field is still not complete. Here, we study the temporal stability of lipid-shelled microbubbles during therapeutic FUS exposure in two timescales: the short time scale (i.e., μs of low-frequency ultrasound exposure) and the long time scale (i.e., days post-activation). We first simulated the microbubble response to low-frequency sonication, and found a strong correlation between viscosity and fragmentation pressure. Activated microbubbles had a concentration decay constant of 0.02 d^-1 but maintained a quasi-stable size distribution for up to 3 weeks (< 10% variation). Microbubbles flowing through a 4-mm vessel within a tissue-mimicking phantom (5% gelatin) were exposed to therapeutic pulses (f_c: 0.5 MHz, peak-negative pressure: 300 kPa, pulse length: 1 ms, pulse repetition frequency: 1 Hz, n=10). We recorded and analyzed their acoustic emissions, focusing on emitted energy and its temporal evolution, alongside the frequency content. Measurements were repeated with concentration-matched samples (10⁷ microbubbles/ml) on day 0, 7, 14, and 21 after activation. Temporal stability decreased while inertial cavitation response increased with storage time both in vitro and in vivo, possibly due to changes in the shell lipid content. Using the same parameters and timepoints, we performed BBB opening in a mouse model (n=3). BBB opening volume measured through T1-weighted contrast-enhanced MRI was equal to 19.1 ± 7.1 mm³, 21.8 ± 14 mm³, 29.3 ± 2.5 mm³, and 38 ± 20.1 mm³ on day 0, 7, 14, and 21, respectively, showing no significant difference over time (p-value: 0.49). Contrast enhancement was 24.9 ± 1.7 %, 23.7 ± 11.7 %, 28.9 ± 5.3 %, and 35 ± 13.4 %, respectively (p-value: 0.63). In conclusion, the in-house made microbubbles studied here maintain their capacity to produce similar therapeutic effects over a period of 3 weeks after activation, as long as the natural concentration decay is accounted for. Future work should focus on stability of commercially available microbubbles and tailoring microbubble shell properties towards therapeutic applications.

Characterization of different bubble formulations for blood-brain barrier opening using a focused ultrasound system with acoustic feedback control

Focused ultrasound combined with bubble-based agents serves as a non-invasive way to open the blood-brain barrier (BBB). Passive acoustic detection was well studied recently to monitor the acoustic emissions induced by the bubbles under ultrasound energy, but the ability to perform reliable BBB opening with a real-time feedback control algorithm has not been fully evaluated. This study focuses on characterizing the acoustic emissions of different types of bubbles: Optison, Definity, and a custom-made nanobubble. Their performance on reliable BBB opening under real-time feedback control based on acoustic detection was evaluated both in-vitro and in-vivo. The experiments were conducted using a 0.5 MHz focused ultrasound transducer with in-vivo focal pressure ranges from 0.1-0.7 MPa. Successful feedback control was achieved with all three agents when combining with infusion injection. Localized opening was confirmed with Evans blue dye leakage. Microscopic images were acquired to review the opening effects. Under similar total gas volume, nanobubble showed a more reliable opening effect compared to Optison and Definity (p < 0.05). The conclusions obtained from this study confirm the possibilities of performing stable opening using a feedback control algorithm combined with infusion injection. It also opens another potential research area of BBB opening using sub-micron bubbles.

Rapid short-pulse sequences enhance the spatiotemporal uniformity of acoustically driven microbubble activity during flow conditions

Despite the promise of microbubble-mediated focused ultrasound therapies, in vivo findings have revealed over-treated and under-treated regions distributed throughout the focal volume. This poor distribution cannot be improved by conventional pulse shapes and sequences, due to their limited ability to control acoustic cavitation dynamics within the ultrasonic focus. This paper describes the design of a rapid short-pulse (RaSP) sequence which is comprised of short pulses separated by μs off-time intervals. Improved acoustic cavitation distribution was based on the hypothesis that microbubbles can freely move during the pulse off-times. Flowing SonoVue^® microbubbles (flow velocity: 10 mm/s) were sonicated with a 0.5 MHz focused ultrasound transducer using RaSP sequences (peak-rarefactional pressures: 146-900 kPa, pulse repetition frequency: 1.25 kHz, and pulse lengths: 5-50 cycles). The distribution of cavitation activity was evaluated using passive acoustic mapping. RaSP sequences generated uniform distributions within the focus in contrast to long pulses (50 000 cycles) that produced non-uniform distributions. Fast microbubble destruction occurred for long pulses, whereas microbubble activity was sustained for longer durations for shorter pulses. High-speed microscopy revealed increased mobility in the direction of flow during RaSP sonication. In conclusion, RaSP sequences produced spatiotemporally uniform cavitation distributions and could result in efficient therapies by spreading cavitation throughout the treatment area.

An overview of the influence of therapeutic ultrasound exposures on the vasculature: high intensity ultrasound and microbubble-mediated bioeffects

It is well established that the interaction of ultrasound with soft tissues can induce a wide range of bioeffects. One of the most important and complex of these interactions in the context of therapeutic ultrasound is with the vasculature. Potential vascular effects range from enhancing microvascular permeability to inducing vascular damage and vessel occlusion. While aspects of these effects are broadly understood, the development of improved approaches to exploit these effects and gain a more detailed mechanistic understanding is ongoing and largely anchored in preclinical research. Here a general overview of this established yet rapidly evolving topic is provided, with a particular emphasis on effects arising from high-intensity focused ultrasound and microbubble-mediated exposures.

Acoustic characterization of contrast-to-tissue ratio and axial resolution for dual-frequency contrast-specific acoustic angiography imaging

Recently, dual-frequency transducers have enabled high-spatial-resolution and high-contrast imaging of vasculature with minimal tissue artifacts by transmitting at a low frequency and receiving broadband superharmonic echoes scattered by microbubble contrast agents. In this work, we examine the imaging parameters for optimizing contrast-to-tissue ratio (CTR) for dual-frequency imaging and the relationship with spatial resolution. Confocal piston transducers are used in a water bath setup to measure the SNR, CTR, and axial resolution for ultrasound imaging of nonlinear scattering of microbubble contrast agents when transmitting at a lower frequency (1.5 to 8 MHz) and receiving at a higher frequency (7.5 to 25 MHz). Parameters varied include the frequency and peak negative pressure of transmitted waves, center frequency of the receiving transducer, microbubble concentration, and microbubble size. CTR is maximized at the lowest transmission frequencies but would be acceptable for imaging in the 1.5 to 3.5 MHz range. At these frequencies, CTR is optimized when a receiving transducer with a center frequency of 10 MHz is used, with the maximum CTR of 25.5 dB occurring when transmitting at 1.5 MHz with a peak negative pressure of 1600 kPa and receiving with a center frequency of 10 MHz. Axial resolution is influenced more heavily by the receiving center frequency, with a weak decrease in measured pulse lengths associated with increasing transmit frequency. A microbubble population containing predominately 4-μm-diameter bubbles yielded the greatest CTR, followed by 1- and then 2-μm bubbles. Varying concentration showed little effect over the tested parameters. CTR dependence on transmit frequency and peak pressure were confirmed through in vivo imaging in two rodents. These findings may lead to improved imaging of vascular remodeling in superficial or luminal cancers such as those of the breast, prostate, and colon.

Radial modulation contrast imaging using a 20-MHz single-element intravascular ultrasound catheter

Contrast-enhanced intravascular ultrasound imaging is a promising tool for the characterization of coronary vasa vasorum proliferation, which has been identified as a marker of, and possible etiologic factor in, the development of high-risk atherosclerotic plaques. Resonance-based nonlinear detection methods have required the development of prototype catheters which are not commercially available, thus limiting clinical translation. In this study, we investigated the performances of a radial modulation imaging approach (25/3 MHz combination) using simulations, implemented it on a clinical 20-MHz rotating catheter, and tested it in a wall-less tissue-mimicking flow phantom perfused with lipid-encapsulated microbubbles (MBs). The effects of the phase lag, low-frequency pressure, and MB concentration on the envelope subtracted radial modulation signals were investigated as a function of depth. Our dual-pulse dual-frequency approach produced contrast- specific images with contrast-to-tissue improvements over B-mode of 15.1 ± 2.1 dB at 2 mm and 6.8 ± 0.1 dB at 4 mm depths. Using this imaging strategy, 200-μm-diameter cellulose tubing perfused with MBs could be resolved while surrounding tissue scattering was suppressed. These results raise promise for the detection of coronary vasa vasorum and may ultimately facilitate the detection of plaque at risk for rupture.

The fast dynamics of cavitation bubbles within water confined in elastic solids

Many applications such as ultrasonic cleaning or sonochemistry use the ability of bubbles to oscillate and drive liquid flow. But bubbles have also received attention in porous media, where drying may cause cavitation, a phenomenon occurring in plant tissues. Here we explore the dynamics of cavitation bubbles when the liquid is fully entrapped in an elastic solid, using light scattering, laser strobe photography and high speed camera recordings. Our experiments show unexpectedly fast bubble oscillations in volume. They depend on the confinement size and elasticity, which we explain with a simple model where liquid compressibility is a key parameter. We also observe rich non-spherical dynamics, with ejection away from the walls and bubble fragmentation, which reveal extreme fluid motion at short timescales.

Single bubble acoustic characterization and stability measurement of adherent microbubbles

This article examines how the acoustic and stability characteristics of single lipid-shelled microbubbles (MBs) change as a result of adherence to a target surface. For individual adherent and non-adherent MBs, the backscattered echo from a narrowband 2-MHz, 90-kPa peak negative pressure interrogation pulse was obtained. These measurements were made in conjunction with an increasing amplitude broadband disruption pulse. It was found that, for the given driving frequency, adherence had little effect on the fundamental response of an MB. Examination of the second harmonic response indicated an increase of the resonance frequency for an adherent MB: resonance radius increasing of 0.3 ± 0.1 μm for an adherent MB. MB stability was seen to be closely related to MB resonance and gave further evidence of a change in the resonance frequency due to adherence.

Effect of an elastic wall on the dynamics of an encapsulated microbubble: A simulation study

The purpose of the present simulation study is to reveal how confining surfaces with different mechanical properties affect the acoustic response of a contrast agent microbubble. To this end, numerical simulations are carried out for three types of walls: a plastic (OptiCell) wall, an aluminium wall, and a biological tissue. For each wall, the behaviour of contrast microbubbles of three sizes is investigated. The spectral characteristics of the scattered pressure produced by the microbubbles are compared for two cases: the bubble oscillates far away from the wall and the same bubble oscillates in the immediate vicinity of the wall. The results of the simulations allow one to make the following main conclusions. The effect of the OptiCell wall on the acoustic bubble response is stronger than that of the aluminium and tissue walls. Changes in the bubble response near the wall are stronger when bubbles are excited above their resonance frequency. Considering changes in the fundamental and the 2nd harmonic with respect to the peak values of these components at different bubble radii, it is found that the changes are stronger for smaller bubbles and that the changes in the 2nd harmonic are stronger than those in the fundamental. These results allow one to gain an insight into conditions under which the effect of an elastic wall on the acoustic response of a contrast agent microbubble is easier to be detected.

Microbubble oscillations in capillary tubes

In diagnostic medicine, microbubbles are used as contrast agents to image blood flow and perfusion in large and small vessels. The small vessels (the capillaries) have diameters from a few hundred micrometers down to less than 10 μ m. The effect of such microvessels surrounding the oscillating microbubbles is currently unknown, and is important for increased sensitivity in contrast diagnostics and manipulation of microbubbles for localized drug release. Here, oscillations of microbubbles in tubes with inner diameters of 25 μm and 160 ¿m are investigated using an ultra-high-speed camera at frame rates of ~12 million frames/s. A reduction of up to 50% in the amplitude of oscillation was observed for microbubbles in the smaller 25-μm tube, compared with those in a 160-μm tube. In the 25-μm tube, at 50 kPa, a 48% increase of microbubbles that did not oscillate above the noise level of the system was observed, indicating increased oscillation damping. No difference was observed between the resonance frequency curves calculated for microbubbles in 25-μm and 160-μm tubes. Although previous investigators have shown the effect of microvessels on microbubble oscillation at high ultrasound pressures, the present study provides the first optical images of low-amplitude microbubble oscillations in small tubes.

Model for bubble pulsation in liquid between parallel viscoelastic layers

A model is presented for a pulsating spherical bubble positioned at a fixed location in a viscous, compressible liquid between parallel viscoelastic layers of finite thickness. The Green's function for particle displacement is found and utilized to derive an expression for the radiation load imposed on the bubble by the layers. Although the radiation load is derived for linear harmonic motion it may be incorporated into an equation for the nonlinear radial dynamics of the bubble. This expression is valid if the strain magnitudes in the viscoelastic layer remain small. Dependence of bubble pulsation on the viscoelastic and geometric parameters of the layers is demonstrated through numerical simulations.

Theoretical and experimental characterisation of magnetic microbubbles

In addition to improving image contrast, microbubbles have shown great potential in molecular imaging and drug/gene delivery. Previous work by the authors showed that considerable improvements in gene transfection efficiency were obtained using microbubbles loaded with magnetic nanoparticles under simultaneous exposure to ultrasound and magnetic fields. The aim of this study was to characterise the effect of nanoparticles on the dynamic and acoustic response of the microbubbles. High-speed video microscopy indicated that the amplitude of oscillation was very similar for magnetic and nonmagnetic microbubbles of the same size for the same ultrasound exposure (0.5 MHz, 100 kPa, 12-cycle pulse) and that this was minimally affected by an imposed magnetic field. The linear scattering to attenuation ratio (STAR) was also similar for suspensions of both bubble types although the nonlinear STAR was ~50% lower for the magnetic microbubbles. Both the video and acoustic data were supported by the results from theoretical modelling.

Demonstration comparing sound wave attenuation inside pipes containing bubbly water and water droplet fog

This paper describes a demonstration and explanation of sound absorption in water due to bubbles, and in air due to a fog of water droplets. It is suitable for 10-12 year olds, but the paper indicates where further exploration of the simplifications in the explanations provided for that age range would allow the demonstration to be used for undergraduate and Masters-level teaching. Applications to submarines, the space shuttle, and neutron generators are described. The demonstration is designed for transportation in a family-sized car.

A three-dimensional model of an ultrasound contrast agent gas bubble and its mechanical effects on microvessels

Ultrasound contrast agents inside a microvessel, when driven by ultrasound, oscillate and induce mechanical stresses on the vessel wall. These mechanical stresses can produce beneficial therapeutic effects but also induce vessel rupture if the stresses are too high. Therefore, it is important to use sufficiently low pressure amplitudes to avoid rupturing the vessels while still inducing the desired therapeutic effects. In this work, we developed a comprehensive three-dimensional model of a confined microbubble inside a vessel while considering the bubble shell properties, blood viscosity, vessel wall curvature and the mechanical properties of the vessel wall. Two bubble models with the assumption of a spherical symmetric bubble and a simple asymmetrical bubble were simulated. This work was validated with previous experimental results and enabled us to evaluate the microbubbles' behaviour and the resulting mechanical stresses induced on the vessel walls. In this study, the fluid shear and circumferential stresses were evaluated as indicators of the mechanical stresses. The effects of acoustical parameters, vessel viscoelasticity and rigidity, vessel/bubble size and off-centre bubbles on bubble behaviour and stresses on the vessel were investigated. The fluid shear and circumferential stresses acting on the vessel varied with time and location. As the frequency changed, the microbubble oscillated with the highest amplitude at its resonance frequency which was different from the resonance frequency of an unbound bubble. The bubble resonance frequency increased as the rigidity of a flexible vessel increased. The fluid shear and circumferential stresses peaked at frequencies above the bubble's resonance frequency. The more rigid the vessels were, the more damped the bubble oscillations. The synergistic effect of acoustic frequency and vessel elasticity had also been investigated since the circumferential stress showed either an increasing trend or a decreasing one versus the vessel rigidity at different acoustic frequencies. When the acoustic pressure was increased from 52 to 680 kPa, the maximum bubble radius increase by 2.5 fold, and the maximum shear and circumferential stress increased by 15.7 and 18.3 fold, respectively. The shear stress was largest when the acoustic frequency was higher (3.25 MHz) and the ratio of the vessel radius to the bubble radius was lower. The circumferential stress was largest when the bubble wall was closer to the vessel wall. An oscillating off-centre bubble forms a mushroom shape with the most damping on the points closest to the vessel wall.

Natural frequencies of two bubbles in a compliant tube: analytical, simulation, and experimental results

Motivated by various clinical applications of ultrasound contrast agents within blood vessels, the natural frequencies of two bubbles in a compliant tube are studied analytically, numerically, and experimentally. A lumped parameter model for a five degree of freedom system was developed, accounting for the compliance of the tube and coupled response of the two bubbles. The results were compared to those produced by two different simulation methods: (1) an axisymmetric coupled boundary element and finite element code previously used to investigate the response of a single bubble in a compliant tube and (2) finite element models developed in comsol Multiphysics. For the simplified case of two bubbles in a rigid tube, the lumped parameter model predicts two frequencies for in- and out-of-phase oscillations, in good agreement with both numerical simulation and experimental results. For two bubbles in a compliant tube, the lumped parameter model predicts four nonzero frequencies, each asymptotically converging to expected values in the rigid and compliant limits of the tube material.

The inertial terms in equations of motion for bubbles in tubular vessels or between plates

Equations resembling the Rayleigh-Plesset and Keller-Miksis equations are frequently used to model bubble dynamics in confined spaces, using the standard inertial term RR+3R([middle dot]) (2)/2, where R is the bubble radius. This practice has been widely assumed to be defensible if the bubble is much smaller than the radius of the confining vessel. This paper questions this assumption, and provides a simple rigid wall model for worst-case quantification of the effect on the inertial term of the specific confinement geometry. The relevance to a range of scenarios (including bubbles confined in microfluidic devices; or contained in test chambers for insonification or imaging; or in blood vessels) is discussed.

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.

Blood-brain barrier disruption and vascular damage induced by ultrasound bursts combined with microbubbles can be influenced by choice of anesthesia protocol

Numerous animal studies have demonstrated that ultrasound bursts combined with a microbubble-based ultrasound contrast agent can temporarily disrupt the blood-brain barrier (BBB) with little or no other apparent effects to the brain. As the BBB is a primary limitation to the use of most drugs in the brain, this method could enable a noninvasive means for targeted drug delivery in the brain. This work investigated whether BBB disruption and vessel damage when overexposure occurs can be influenced by choice of anesthesia protocol, which have different vasoactive effects. Four locations were sonicated transcranially in each brain of 16 rats using an unfocused 532 kHz piston transducer. Burst sonications (10 ms bursts applied at 1 Hz for 60 s) were combined with intravenous Definity (10 μl/kg) injections. BBB disruption was evaluated using contrast-enhanced MRI. Half of the animals were anesthetized with i.p. ketamine and xylazine, and the other half with inhaled isoflurane and oxygen. Over the range of exposure levels tested, MRI contrast enhancement was significantly higher (p < 0.05) for animals anesthetized with ketamine/xylazine. Furthermore, the threshold for extensive erythrocyte extravasation was lower with ketamine/xylazine. These results suggest that BBB disruption and/or vascular damage can be affected by vascular or other factors that are influenced by different anesthesia protocol. These experiments may also have been influenced by the recently reported findings that the circulation time for perfluorocarbon microbubbles is substantially reduced when oxygen is used as the carrier gas.

In vivo transcranial cavitation threshold detection during ultrasound-induced blood-brain barrier opening in mice

The in vivo cavitation response associated with blood-brain barrier (BBB) opening as induced by transcranial focused ultrasound (FUS) in conjunction with microbubbles was studied in order to better identify the underlying mechanism in its noninvasive application. A cylindrically focused hydrophone, confocal with the FUS transducer, was used as a passive cavitation detector (PCD) to identify the threshold of inertial cavitation (IC) in the presence of Definity® microbubbles (mean diameter range: 1.1-3.3 µm, Lantheus Medical Imaging, MA, USA). A vessel phantom was first used to determine the reliability of the PCD prior to in vivo use. A cerebral blood vessel was simulated by generating a cylindrical channel of 610 µm in diameter inside a polyacrylamide gel and by saturating its volume with microbubbles. The microbubbles were sonicated through an excised mouse skull. Second, the same PCD setup was employed for in vivo noninvasive (i.e. transdermal and transcranial) cavitation detection during BBB opening. After the intravenous administration of Definity® microbubbles, pulsed FUS was applied (frequency: 1.525 or 1.5 MHz, peak-rarefactional pressure: 0.15-0.60 MPa, duty cycle: 20%, PRF: 10 Hz, duration: 1 min with a 30 s interval) to the right hippocampus of twenty-six (n = 26) mice in vivo through intact scalp and skull. T1 and T2-weighted MR images were used to verify the BBB opening. A spectrogram was generated at each pressure in order to detect the IC onset and duration. The threshold of BBB opening was found to be at a 0.30 MPa peak-rarefactional pressure in vivo. Both the phantom and in vivo studies indicated that the IC pressure threshold had a peak-rarefactional amplitude of 0.45 MPa. This indicated that BBB opening may not require IC at or near the threshold. Histological analysis showed that BBB opening could be induced without any cellular damage at 0.30 and 0.45 MPa. In conclusion, the cavitation response could be detected without craniotomy in mice and IC may not be required for BBB opening at relatively low pressures.

A study of bubble activity generated in ex vivo tissue by high intensity focused ultrasound

Cancer treatment by extracorporeal high-intensity focused ultrasound (HIFU) is constrained by the time required to ablate clinically relevant tumour volumes. Although cavitation may be used to optimize HIFU treatments, its role during lesion formation is ambiguous. Clear differentiation is required between acoustic cavitation (noninertial and inertial) effects and bubble formation arising from two thermally-driven effects (the vapourization of liquid into vapour, and the exsolution of formerly dissolved permanent gas out of the liquid and into gas spaces). This study uses clinically relevant HIFU exposures in degassed water and ex vivo bovine liver to test a suite of cavitation detection techniques that exploit passive and active acoustics, audible emissions and the electrical drive power fluctuations. Exposure regimes for different cavitation activities (none, acoustic cavitation and, for ex vivo tissue only, acoustic cavitation plus thermally-driven gas space formation) were identified both in degassed water and in ex vivo liver using the detectable characteristic acoustic emissions. The detection system proved effective in both degassed water and tissue, but requires optimization for future clinical application.