Acoustic scattering from a contrast agent microbubble near an elastic wall of finite thickness

Dependence of sonoporation efficiency on microbubble size: An in vitro monodisperse microbubble study

Sonoporation is the process where intracellular drug delivery is facilitated by ultrasound-driven microbubble oscillations. Several mechanisms have been proposed to relate microbubble dynamics to sonoporation including shear and normal stress. The present work aims to gain insight into the role of microbubble size on sonoporation and thereby into the relevant mechanism(s) of sonoporation. To this end, we measured the sonoporation efficiency while varying microbubble size using monodisperse microbubble suspensions. Sonoporation experiments were performed in vitro on cell monolayers using a single ultrasound pulse with a fixed frequency of 1 MHz while the acoustic pressure amplitude and pulse length were varied at 250, 500, and 750 kPa, and 10, 100, and 1000 cycles, respectively. Sonoporation efficiency was quantified using flow cytometry by measuring the FITC-dextran (4 kDa and 2 MDa) fluorescence intensity in 10,000 cells per experiment to average out inherent variations in the bioresponse. Using ultra-high-speed imaging at 10 million frames per second, we demonstrate that the bubble oscillation amplitude is nearly independent of the equilibrium bubble radius at acoustic pressure amplitudes that induce sonoporation (≥ 500 kPa). However, we show that sonoporation efficiency is strongly dependent on the equilibrium bubble size and that under all explored driving conditions most efficiently induced by bubbles with a radius of 4.7 μm. Polydisperse microbubbles with a typical ultrasound contrast agent size distribution perform almost an order of magnitude lower in terms of sonoporation efficiency than the 4.7-μm bubbles. We elucidate that for our system shear stress is highly unlikely the mechanism of action. By contrast, we show that sonoporation efficiency correlates well with an estimate of the bubble-induced normal stress.

Ultrasonic Characterization of Ibidi μ-Slide I Luer Channel Slides for Studies With Ultrasound Contrast Agents

Understanding and controlling the ultrasound contrast agent (UCA)'s response to an applied ultrasound pressure field are crucial when investigating ultrasound imaging sequences and therapeutic applications. The magnitude and frequency of the applied ultrasonic pressure waves affect the oscillatory response of the UCA. Therefore, it is important to have an ultrasound compatible and optically transparent chamber in which the acoustic response of the UCA can be studied. The aim of our study was to determine the in situ ultrasound pressure amplitude in the ibidi μ -slide I Luer channel, an optically transparent chamber suitable for cell culture, including culture under flow, for all microchannel heights (200, 400, 600, and [Formula: see text]). First, the in situ pressure field in the 800- [Formula: see text] high channel was experimentally characterized using Brandaris 128 ultrahigh-speed camera recordings of microbubbles (MBs) and a subsequent iterative processing method, upon insonification at 2 MHz, 45° incident angle, and 50-kPa peak negative pressure (PNP). Control studies in another cell culture chamber, the CLINIcell, were compared with the obtained results. The pressure amplitude was -3.7 dB with respect to the pressure field without the ibidi μ -slide. Second, using finite-element analysis, we determined the in situ pressure amplitude in the ibidi with the 800- [Formula: see text] channel (33.1 kPa), which was comparable to the experimental value (34 kPa). The simulations were extended to the other ibidi channel heights (200, 400, and [Formula: see text]) with either 35° or 45° incident angle, and at 1 and 2 MHz. The predicted in situ ultrasound pressure fields were between -8.7 and -1.1 dB of the incident pressure field depending on the listed configurations of ibidi slides with different channel heights, applied ultrasound frequencies, and incident angles. In conclusion, the determined ultrasound in situ pressures demonstrate the acoustic compatibility of the ibidi μ -slide I Luer for different channel heights, thereby showing its potential for studying the acoustic behavior of UCAs for imaging and therapy.

A numerical investigation of passive acoustic mapping for monitoring bubble-mediated focused ultrasound treatment of the spinal cord

Focused ultrasound (FUS) combined with intravenous microbubbles (MBs) has been shown to increase drug delivery to the spinal cord in animal models. Eventual clinical translation of such a technique in the sensitive spinal cord requires robust treatment monitoring to ensure efficacy, localization, safety, and provide key intraprocedural feedback. Here, the use of passive acoustic mapping (PAM) of MB emissions with a spine-specific detector array in the context of transvertebral FUS sonications is investigated in silico. Using computed tomography-derived human vertebral geometry, transvertebral detection of MBs is evaluated over varying source locations with and without phase and amplitude corrections (PACs). The impact of prefocal cavitation is studied by simulating concurrent cavitation events in the canal and pre-laminar region. Spatially sensitive application of phase and amplitude is used to balance signal strengths emanating from different axial depths in combination with multiple dynamic ranges to elicit multisource viewing. Collectively, the results of this study encourage the use of PAM in transvertebral FUS applications with PACs to not only localize sources originating in the spinal canal but also multiple sources of innate amplitude mismatches when corrective methods are applied.

Biomechanical Sensing Using Gas Bubbles Oscillations in Liquids and Adjacent Technologies: Theory and Practical Applications

Gas bubbles present in liquids underpin many natural phenomena and human-developed technologies that improve the quality of life. Since all living organisms are predominantly made of water, they may also contain bubbles—introduced both naturally and artificially—that can serve as biomechanical sensors operating in hard-to-reach places inside a living body and emitting signals that can be detected by common equipment used in ultrasound and photoacoustic imaging procedures. This kind of biosensor is the focus of the present article, where we critically review the emergent sensing technologies based on acoustically driven oscillations of bubbles in liquids and bodily fluids. This review is intended for a broad biosensing community and transdisciplinary researchers translating novel ideas from theory to experiment and then to practice. To this end, all discussions in this review are written in a language that is accessible to non-experts in specific fields of acoustics, fluid dynamics and acousto-optics.

Radiation force on a bubble located near an interface

The presence of a boundary produces marked changes in the oscillation amplitudes and types of bubble distortion modes excited by an external acoustic field. In the majority of cases, the radiation force can be determined based on the linearized equations of motion. Bispherical coordinates are used to obtain an analytical description of linearized bubble dynamics at distances from the interface comparable to those of the bubble size. In the limit of weak dissipation, explicit formulas have been derived that describe the dependence of the radiation force on the separation distance between the bubble and the interface, the material parameters of the contacting media, and the angle of incidence of the incoming wave. The component of the radiation force directed to the interface has been shown to exhibit qualitative changes when the direction of the incoming field passes through the angle of the total internal reflection.

Acoustic frequency combs using gas bubble cluster oscillations in liquids: a proof of concept

We propose a new approach to the generation of acoustic frequency combs (AFC)-signals with spectra containing equidistant coherent peaks. AFCs are essential for a number of sensing and measurement applications, where the established technology of optical frequency combs suffers from fundamental physical limitations. Our proof-of-principle experiments demonstrate that nonlinear oscillations of a gas bubble cluster in water insonated by a low-pressure single-frequency ultrasound wave produce signals with spectra consisting of equally spaced peaks originating from the interaction of the driving ultrasound wave with the response of the bubble cluster at its natural frequency. The so-generated AFC posses essential characteristics of optical frequency combs and thus, similar to their optical counterparts, can be used to measure various physical, chemical and biological quantities.

Angular dependence of the acoustic signal of a microbubble cloud

Microbubble-mediated ultrasound therapies have a common need for methods that can noninvasively monitor the treatment. One approach is to use the bubbles' acoustic emissions as feedback to the operator or a control unit. Current methods interpret the emissions' frequency content to infer the microbubble activities and predict therapeutic outcomes. However, different studies placed their sensors at different angles relative to the emitter and bubble cloud. Here, it is evaluated whether such angles influence the captured emissions such as the frequency content. In computer simulations, 128 coupled bubbles were sonicated with a 0.5-MHz, 0.35-MPa pulse, and the acoustic emissions generated by the bubbles were captured with two sensors placed at different angles. The simulation was replicated in experiments using a microbubble-filled gel channel (0.5-MHz, 0.19-0.75-MPa pulses). A hydrophone captured the emissions at two different angles. In both the simulation and the experiments, one angle captured periodic time-domain signals, which had high contributions from the first three harmonics. In contrast, the other angle captured visually aperiodic time-domain features, which had much higher harmonic and broadband content. Thus, by placing acoustic sensors at different positions, substantially different acoustic emissions were captured, potentially leading to very different conclusions about the treatment outcome.

Ultrasound Contrast Agent Modeling: A Review

Ultrasound is extensively used in medical imaging, being safe and inexpensive and operating in real time. Its scope of applications has been widely broadened by the use of ultrasound contrast agents (UCAs) in the form of microscopic bubbles coated by a biocompatible shell. Their increased use has motivated a large amount of research to understand and characterize their physical properties as well as their interaction with the ultrasound field and their surrounding environment. Here we review the theoretical models that have been proposed to study and predict the behavior of UCAs. We begin with a brief introduction on the development of UCAs. We then present the basics of free-gas-bubble dynamics upon which UCA modeling is based. We review extensively the linear and non-linear models for shell elasticity and viscosity and present models for non-spherical and asymmetric bubble oscillations, especially in the presence of surrounding walls or tissue. Then, higher-order effects such as microstreaming, shedding and acoustic radiation forces are considered. We conclude this review with promising directions for the modeling and development of novel agents.

Effect of scattered pressures from oscillating microbubbles on neuronal activity in mouse brain under transcranial focused ultrasound stimulation

Previous studies have indicated that the presence of microbubbles (MBs) during sonication has an impact on neuronal activity, while the underlying mechanisms remain to be revealed. In this study, a model for the scattered pressures produced by the pulsating lipid-encapsulated MBs in mouse brain was developed to numerically investigate the effect of MBs on neuronal activity during transcranial focused ultrasound stimulation. The additional summed scattered pressure (P_{summed_scat}) from the oscillating MBs was calculated from the model. The level of neuronal activity was experimentally verified using an immunofluorescence assay with antibodies against c-fos. The pressure difference (ΔP) between acoustic pressures at which the same level of neuronal activity is excited by ultrasound stimulation with and without MBs was obtained from the experiments. The results showed that P_{summed_scat} accounts for about half of the ΔP when the MBs experience a "compression-only" response. The P_{summed_scat} suddenly increased at a critical acoustic pressure, around which a rapid enhancement of ΔP obtained from experiment also occurred. This work suggested that the additional scattered pressures from pulsating MBs are probably a mechanism that affects neuronal activity under transcranial focused ultrasound stimulation.

Enhanced neuronal activity in mouse motor cortex with microbubbles' oscillations by transcranial focused ultrasound stimulation

Microbubbles (MBs) are known to serve as an amplifier of the mechanical effects of ultrasound, which combined with ultrasound are widely used in brain. The goal of this study is to investigate the effect of oscillating MBs on the neuronal activity in the central nervous system (CNS) of mammals. The motor cortex of mice brain was subjected to ultrasound stimulation with and without MBs, and evoked electromyogram signals were recorded. A c-fos immunofluorescence assay was performed to evaluate the neuronal activation in the region of ultrasound stimulation. BBB integrity during ultrasound stimulation with MBs was assessed in this study. Moreover, the safety of ultrasound stimulation with MBs was examined. Using ultrasound at 620 kHz, the injection of MBs significantly increased the success rate of motor response from 0.065 ± 0.06 to 0.28 ± 0.10 when stimulation was applied at 0.12 MPa and from 0.38 ± 0.09 to 0.77 ± 0.18 at 0.25 MPa (p < 0.001). The results of the c-fos immunofluorescence assay showed that the mean densities of c-fos⁺ cells were significantly increased from 15.67 ± 3.51 to 53.01 ± 9.54 at 0.12 MPa acoustic pressure. At 0.25 MPa, the mean density of c-fos + cells was 81 ± 10.97 without MBs and it significantly increased to 124.12 ± 25.71 with MBs (p < 0.05). Enhanced neuronal activities were observed with 0.12 MPa ultrasound stimulation with MBs, while the integrity of BBB was not compromised, but 0.25 MPa ultrasound stimulation with MBs resulted in BBB disruption. These findings reveal that the oscillations of MBs can enhance neuronal activity in the CNS of mammals, and may provide an insight into the application of MBs combined with ultrasound in brain.

A Review of Phospholipid Encapsulated Ultrasound Contrast Agent Microbubble Physics

Ultrasound contrast agent microbubbles have expanded the utility of biomedical ultrasound from anatomic imaging to the assessment of microvascular blood flow characteristics and ultrasound-assisted therapeutic applications. Central to their effectiveness in these applications is their resonant and non-linear oscillation behaviour. This article reviews the salient physics of an oscillating microbubble in an ultrasound field, with particular emphasis on phospholipid-coated agents. Both the theoretical underpinnings of bubble vibration and the experimental evidence of non-linear encapsulated bubble dynamics and scattering are discussed and placed within the context of current and emerging applications.

Direct simulation of acoustic scattering problems involving fluid-structure interaction using an efficient immersed boundary-lattice Boltzmann method

An efficient immersed boundary-lattice Boltzmann method (IB-LBM) is applied to carry out the direct simulation of acoustic scattering problems involving fluid-structure interaction. In the simulation, the lattice Boltzmann method is adopted for the fluid domain, the immersed boundary method is used to handle the fluid-structure interaction and the instantaneous fluid pressure perturbation is computed to obtain the acoustic field. Compared with the conventional IB-LBMs, a force correction technique is introduced in this method to enforce the non-slip boundary conditions at the immersed boundaries and the acoustic scattering field thus can be obtained more accurately. The study of the numerical result comparison with the conventional IB-LBMs or analytical solutions is conducted on four acoustic problems, such as acoustic radiation from a pulsing cylinder, acoustic scattering from a static cylinder with pulse, or harmonic Gaussian sources and a moving two-dimensional sedimentating particle. The better efficiency of the present method is validated.

Hidden Attractors in a Model of a Bubble Contrast Agent Oscillating Near an Elastic Wall

A model describing the dynamics of a spherical gas bubble in a compressible viscous liquid is studied. The bubble is oscillating close to an elastic wall of finite thickness under the influence of an external pressure field which simulates a contrast agent oscillating close to a blood vessel wall. Here we investigate numerically the coexistence of chaotic and periodic attractors in this model. One of the tools applied for seeking coexisting attractors is the perpetual points method. This method can be helpful for localizing coexisting attractors, occurring in various physically realistic ranges of variation of the control parameters. We provide some examples of coexisting attractors to demonstrate the importance of the multistability problem for the applications.

General Solution of the Rayleigh Equation for the Description of Bubble Oscillations Near a Wall

We consider a generalization of the Rayleigh equation for the description of the dynamics of a spherical gas bubble oscillating near an elastic or rigid wall. We show that in the non–dissipative case, i.e. neglecting the liquid viscosity and compressibility, it is possible to construct the general analytical solution of this equation. The corresponding general solution is expressed via the Weierstrass elliptic function. We analyze the dependence of this solution properties on the physical parameters.

Surface waves on a soft viscoelastic layer produced by an oscillating microbubble

Ultrasound-driven bubbles can cause significant deformation of soft viscoelastic layers, for instance in surface cleaning and biomedical applications. The effect of the viscoelastic properties of a boundary on the bubble-boundary interaction has been explored only qualitatively, and remains poorly understood. We investigate the dynamic deformation of a viscoelastic layer induced by the volumetric oscillations of an ultrasound-driven microbubble. High-speed video microscopy is used to observe the deformation produced by a bubble oscillating at 17-20 kHz in contact with the surface of a hydrogel. The localised oscillating pressure applied by the bubble generates surface elastic (Rayleigh) waves on the gel, characterised by elliptical particle trajectories. The tilt angle of the elliptical trajectories varies with increasing distance from the bubble. Unexpectedly, the direction of rotation of the surface elements on the elliptical trajectories shifts from prograde to retrograde at a distance from the bubble that depends on the viscoelastic properties of the gel. To explain these behaviours, we develop a simple three-dimensional model for the deformation of a viscoelastic solid by a localised oscillating force. By using as input for the model the values of the shear modulus obtained from the propagation velocity of the Rayleigh waves, we find good qualitative agreement with the experimental observations.

Reparable Cell Sonoporation in Suspension: Theranostic Potential of Microbubble

The conjunction of low intensity ultrasound and encapsulated microbubbles can alter the permeability of cell membrane, offering a promising theranostic technique for non-invasive gene/drug delivery. Despite its great potential, the biophysical mechanisms of the delivery at the cellular level remains poorly understood. Here, the first direct high-speed micro-photographic images of human lymphoma cell and microbubble interaction dynamics are provided in a completely free suspension environment without any boundary parameter defect. Our real-time images and theoretical analyses prove that the negative divergence side of the microbubble's dipole microstreaming locally pulls the cell membrane, causing transient local protrusion of 2.5 µm in the cell membrane. The linear oscillation of microbubble caused microstreaming well below the inertial cavitation threshold, and imposed 35.3 Pa shear stress on the membrane, promoting an area strain of 0.12%, less than the membrane critical areal strain to cause cell rupture. Positive transfected cells with pEGFP-N1 confirm that the interaction causes membrane poration without cell disruption. The results show that the overstretched cell membrane causes reparable submicron pore formation, providing primary evidence of low amplitude (0.12 MPa at 0.834 MHz) ultrasound sonoporation mechanism.

Individual lipid encapsulated microbubble radial oscillations: Effects of fluid viscosity

Ultrasound-stimulated microbubble dynamics have been shown to be dependent on intrinsic bubble properties, including size and shell characteristics. The effect of the surrounding environment on microbubble response, however, has been less investigated. In particular, microbubble optimization studies are generally conducted in water/saline, characterized by a 1 cP viscosity, for application in the vasculature (i.e., 4 cP). In this study, ultra-high speed microscopy was employed to investigate fluid viscosity effects on phospholipid encapsulated microbubble oscillations at 1 MHz, using a single, eight-cycle pulse at peak negative pressures of 100 and 250 kPa. Microbubble oscillations were shown to be affected by fluid viscosity in a size- and pressure-dependent manner. In general, the oscillation amplitudes exhibited by microbubbles between 3 and 6 μm in 1 cP fluid were larger than in 4 cP fluid, reaching a maximum of 1.7-fold at 100 kPa for microbubbles 3.8 μm in diameter and 1.35-fold at 250 kPa for microbubbles 4.8 μm in diameter. Simulation results were in broad agreement at 250 kPa, however generally underestimated the effect of fluid viscosity at 100 kPa. This is the first experimental demonstration documenting the effects of surrounding fluid viscosity on microbubble oscillations, resulting in behavior not entirely predicted by current microbubble models.

Molecular Imaging-Guided Interventional Hyperthermia in Treatment of Breast Cancer

Breast cancer is the most frequent malignancy in women worldwide. Although it is commonly treated via chemotherapy, responses vary among its subtypes, some of which are relatively insensitive to chemotherapeutic drugs. Recent studies have shown that hyperthermia can enhance the effects of chemotherapy in patients with refractory breast cancer or without surgical indications. Recent advances in molecular imaging may not only improve early diagnosis but may also facilitate the development and response assessment of targeted therapies. Combining advanced techniques such as molecular imaging and hyperthermia-integrated chemotherapy should open new avenues for effective management of breast cancer.

Sounds of marine seeps: a study of bubble activity near a rigid boundary

A passive acoustic method for detecting environmentally dangerous gas leaks from pipelines and methane naturally leaking from the seabed has been investigated. Gas escape involves the formation and release of bubbles of different sizes. Each bubble emits a sound at a specific frequency. Determination of the bubble radius from the frequency of its signature passive acoustic emission by use of so-called Minnaert formula has a restricted area of applicability near the seabed. The point is that the inertial mass and the damping constant of the birthing bubble are markedly different from those of a free bubble. The theoretical model for the bubble volume oscillations near the seabed has been proposed and an analytical solution has been derived. It was shown that the bispherical coordinates provide separation of variables and are more suitable for analysis of the volume oscillations of these constrained bubbles. Explicit formulas have been derived, which describe the dependence of the bubble emission near a rigid wall on its size and the separation distance between the bubble and the boundary.

The influence of compliant boundary proximity on the fundamental and subharmonic emissions from individual microbubbles

The proximity of a solid-liquid boundary has been theoretically predicted to affect nonlinear microbubble emissions, but to date there has been no experimental validation of this effect. In this study, individual microbubbles (n = 15) were insonicated at f = 11 MHz as a function of offset distance from a compliant (agarose) planar boundary by employing an optical trapping apparatus. It was found that fundamental scattering increases while subharmonic scattering decreases as the microbubble approaches the boundary. Although a microbubble-boundary model can predict the qualitative trends observed for a subset of encapsulation properties, further modeling efforts are required to completely model compliant boundary-microbubble interactions.

Study of non-spherical bubble oscillations near a surface in a weak acoustic standing wave field

The interaction of acoustically driven bubbles with a wall is important in many applications of ultrasound and cavitation, as the close boundary can severely alter the bubble dynamics. In this paper, the non-spherical surface oscillations of bubbles near a surface in a weak acoustic standing wave field are investigated experimentally and numerically. The translation, the volume, and surface mode oscillations of bubbles near a flat glass surface were observed by a high speed camera in a standing wave cell at 46.8 kHz. The model approach is based on a modified Keller-Miksis equation coupled to surface mode amplitude equations in the first order, and to the translation equations. Modifications are introduced due to the adjacent wall. It was found that a bubble's oscillation mode can change in the presence of the wall, as compared to the bubble in the bulk liquid. In particular, the wall shifts the instability pressure thresholds to smaller driving frequencies for fixed bubble equilibrium radii, or to smaller equilibrium radii for fixed excitation frequency. This can destabilize otherwise spherical bubbles, or stabilize bubbles undergoing surface oscillations in the bulk. The bubble dynamics observed in experiment demonstrated the same trend as the theoretical results.

Encapsulated microbubbles and echogenic liposomes for contrast ultrasound imaging and targeted drug delivery

Micron- to nanometer-sized ultrasound agents, like encapsulated microbubbles and echogenic liposomes, are being developed for diagnostic imaging and ultrasound mediated drug/gene delivery. This review provides an overview of the current state of the art of the mathematical models of the acoustic behavior of ultrasound contrast microbubbles. We also present a review of the in vitro experimental characterization of the acoustic properties of microbubble based contrast agents undertaken in our laboratory. The hierarchical two-pronged approach of modeling contrast agents we developed is demonstrated for a lipid coated (Sonazoid™) and a polymer shelled (poly D-L-lactic acid) contrast microbubbles. The acoustic and drug release properties of the newly developed echogenic liposomes are discussed for their use as simultaneous imaging and drug/gene delivery agents. Although echogenicity is conclusively demonstrated in experiments, its physical mechanisms remain uncertain. Addressing questions raised here will accelerate further development and eventual clinical approval of these novel technologies.

Mesoporous silica nanoparticles as a breast-cancer targeting ultrasound contrast agent

Ultrasound (US) is used widely in the context of breast cancer. While it is advantageous for a number of reasons, it has low specificity and requires the use of a contrast agent. Its use as a standalone diagnostic and real-time imaging modality could be achieved by development of a tumor-targeted ultrasound contrast agent (UCA); functionalizing the UCA with a tumor-targeting agent would also allow the targeted administration of anti-cancer drugs at the tumor site. In this article, clinical US techniques are used to show that mesoporous silica nanoparticles (MSNs), functionalized with the monoclonal antibody Herceptin(®), can be used as an effective UCA by increasing US image contrast. Furthermore, in vitro assays show the successful localization and binding of the MSN-Herceptin conjugate to HER2+ cancer cells, resulting in tumor-specific cytotoxicity. These results demonstrate the potential of MSNs as a stable, biocompatible, and effective therapeutic and diagnostic ("theranostic") agent for US-based breast cancer imaging, diagnosis, and treatment.

Model for the dynamics of a spherical bubble undergoing small shape oscillations between parallel soft elastic layers

A model is developed for a pulsating and translating gas bubble immersed in liquid in a channel formed by two soft, thin elastic parallel layers having densities equal to that of the surrounding liquid and small, but finite, shear moduli. The bubble is nominally spherical but free to undergo small shape deformations. Shear strain in the elastic layers is estimated in a way which is valid for short, transient excitations of the system. Coupled nonlinear second-order differential equations are obtained for the shape and position of the bubble, and numerical integration of an expression for the liquid velocity at the layer interfaces yields an estimate of the elastic layer displacement. Numerical integration of the dynamical equations reveals behavior consistent with laboratory observations of acoustically excited bubbles in ex vivo vessels reported by Chen et al. [Phys. Rev. Lett. 106, 034301 (2011) and Ultrasound Med. Biol. 37, 2139-2148 (2011)].

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.

Effect of ultrasound on adherent microbubble contrast agents

An investigation into the effect of clinical ultrasound exposure on adherent microbubbles is described. A flow phantom was constructed in which targeted microbubbles were attached using biotin-streptavidin linkages. Microbubbles were insonated by broadband imaging pulses (centred at 2.25 MHz) over a range of pressures (peak negative pressure (PNP) = 60-375 kPa). Individual adherent bubbles were observed optically and classified as either being isolated or with a single neighbouring bubble. It is found that bubble detachment and deflation are two significant effects, even during low amplitude ultrasound exposure. Specifically, while at very low acoustic pressure (PNP < 75 kPa) 95% of the bubbles were not affected, at medium pressure (151 kPa < P < 225 kPa) 53% of the bubbles detached and at higher pressures (301 kPa < P < 375 kPa) 96% of the bubbles detached. In addition, more than 50% of the bubbles underwent deflation at pressures between 301 and 375 kPa. At pressures between 226 and 300 kPa, more adherent bubbles detached when there was a neighbouring bubble, suggesting the role of multiple scattering and secondary Bjerknes force on bubble detachment. The flow shear, primary and secondary Bjerknes forces exerted on each bubble were calculated and compared to the estimated forces acting on the bubble due to oscillations. The oscillation force is shown to be much higher than other forces. The mechanisms of bubble detachment are discussed.

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.

Nonlinear dynamic behavior of microscopic bubbles near a rigid wall

The nonlinear dynamic behavior of microscopic bubbles near a rigid wall is investigated. Oscillations are driven by the ultrasonic pressure field that arises in various biomedical applications such as ultrasound imaging or targeted drug delivery. It is known that, when bubbles approach a blood-vessel wall, their linear dynamic response is modified. This modification may be very useful for real-time detection of bubbles that have found targets; in future therapeutic technologies, it may be useful for controlled release of medical agents encapsulating microbubbles. In this paper, the nonlinear response of microbubbles near a wall is studied. The Keller-Miksis-Parlitz equation is adopted, but modified to account for the presence of a rigid wall. This base model describes the time evolution of the bubble surface, which is assumed to remain spherical, and accounts for the effect of acoustic radiation losses owing to liquid compressibility in the momentum conservation. Two situations are considered: the base case of an isolated bubble in an unbounded medium, and a bubble near a rigid wall. In the latter case, the wall influence is modeled by including a symmetrically oscillating image bubble. The bubble dynamics is traced using a numerical solution of the model equation. Subsequently, Floquet theory is used to accurately detect the bifurcation point where bubble oscillations stop following the driving ultrasound frequency and undergo period-changing bifurcations. Of particular interest is the detection of the subcritical period-tripling and -quadrupling transition. The parametric bifurcation maps are obtained as functions of nondimensional parameters representing the bubble radius, the frequency and pressure amplitude of the driving ultrasound field, and the distance from the wall. It is shown that the presence of the wall generally stabilises the bubble dynamics, so that much larger values of the pressure amplitude are needed to generate nonlinear responses. Thus, a clinical protocol in which selected nonlinear harmonics are examined under varying insonation amplitudes may be useful in detecting microbubble proximity to walls.

Dynamics of a contrast agent microbubble attached to an elastic wall

A modified Rayleigh-Plesset equation is derived to model the oscillation of a contrast agent microbubble attached to an elastic wall. The obtained equation shows that contact with the wall affects the bubble oscillation as if the bubble oscillated in a liquid with a changed (effective) density. Depending on the wall properties, the effective density can be either higher or lower than the real liquid density and hence the natural frequency of the attached bubble can be either lower or higher than the natural frequency of the same bubble in an unbounded liquid. Numerical simulations are made for a contrast bubble with shell properties similar to those used in the Marmottant shell model. The cases of a rigid wall and a plastic wall are compared. The properties of the plastic wall are set to correspond to walls of OptiCell chambers commonly used in experiments. It is shown that contact with the rigid wall decreases the natural frequency of the bubble as compared to its natural frequency in an unbounded liquid, whereas contact with the OptiCell wall increases the natural frequency of the bubble. Bubble resonance curves for three cases are compared: the bubble in an unbounded liquid; the bubble at a distance from an OptiCell wall; the bubble in contact with an OptiCell wall. Results obtained for a 2- μm -radius bubble insonified with a 10-cycle, 40 kPa, 2.1 MHz Gaussian pulse show that contact with the OptiCell wall leads to the following effects. The amplitude of the radial oscillation of the attached bubble is decreased by about 70% as compared to that of the same bubble in an unbounded liquid. The fundamental component in the spectrum of the scattered pressure of the attached bubble is decreased by 12 dB. A strong second harmonic appears in the spectrum of the scattered pressure of the attached bubble; its magnitude is about 11.5 dB higher than the level corresponding to the case of an unbounded liquid.