Resonance Frequency Of Microbubbles Research Articles

Monodisperse microbubble-mediated drug delivery: Influence of microbubbles size on drug delivery outcome

As the microbubble's resonance frequency is size-dependent, polydisperse microbubbles induce varying drug delivery outcomes at one ultrasound frequency. This study aimed to investigate drug delivery outcome of monodisperse MBs (mMBs) with radii ranging from 1.5–2.9 μm insonified at 2 MHz. Phospholipid-coated mMBs were generated using the Horizon microfluidic flow-focusing device. In vitro experiments were conducted on single microbubble-endothelial cells (n = 68) using confocal microscopy and 10 Mfps ultra-high-speed imaging. At 220 kPa PNP for 10 cycles, the 1.5 μm mMBs exhibited the highest PI uptake in 81.3% of cases, followed by 77.3% for 2.2 μm, 36.8% for 2.7 μm and 13.3% for 2.9 μm mMBs. Conversely, the 1.5 μm mMBs had the second lowest excursion amplitude (R;max-R;0) of 0.8 ± 0.3 μm as this was 1.2 ± 0.3 μm for 2.2 μm mMBs, 1.0 ± 0.3 μm for 2.7 μm mMBs, and 0.7 ± 0.2 μm for 2.9 μm mMBs. Additionally, for the 1.5, 2.2, and 2.7 μm mMBs, PI uptake and tunnel formation occurred more often (1.6, 1.8, and 1.3 times, respectively) than PI uptake and a resealing membrane pore. During insonification, mMB pinch-off occurred more frequently in tunnel formation (70.8%) than resealing pore formation (53.3%). This research revealed the impact of mMBs size on drug delivery outcome.

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.

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.

Enhancement of the ionoacoustic effect through ultrasound and photoacoustic contrast agents

The characteristic depth dose deposition of ion beams, with a maximum at the end of their range (Bragg peak) allows for local treatment delivery, resulting in better sparing of the adjacent healthy tissues compared to other forms of external beam radiotherapy treatments. However, the optimal clinical exploitation of the favorable ion beam ballistic is hampered by uncertainties in the in vivo Bragg peak position. Ionoacoustics is based on the detection of thermoacoustic pressure waves induced by a properly pulsed ion beam (e.g., produced by modern compact accelerators) to image the irradiated volume. Co-registration between ionoacoustics and ultrasound imaging offers a promising opportunity to monitor the ion beam and patient anatomy during the treatment. Nevertheless, the detection of the ionoacoustic waves is challenging due to very low pressure amplitudes and frequencies (mPa/kHz) observed in clinical applications. We investigate contrast agents to enhance the acoustic emission. Ultrasound microbubbles are used to increase the ionoacoustic frequency around the microbubble resonance frequency. Moreover, India ink is investigated as a possible mean to enhance the signal amplitude by taking advantage of additional optical photon absorption along the ion beam and subsequent photoacoustic effect. We report amplitude increase of up to 200% of the ionoacoustic signal emission in the MHz frequency range by combining microbubbles and India ink contrast agents.

Nonlinear acoustic characteristics of multilayer magnetic microbubbles

The combination of superparamagnetic iron oxide nanoparticles (SPIOs) with ultrasonic contrast agent (UCA) microbubble is called magnetic microbubble (MMB) and has been used to produce multimodal contrast agents to enhance medical ultrasound and magnetic resonance imaging. The nanoparticles are either covalently linked to the shell or physically entrapped into the shell. Considering the effect of the volume fraction of SPIOs on the shell density and viscosity, a nonlinear dynamic equation of magnetic microbubbles (MMBs) with multilayer membrane structure is constructed based on the basic theory of bubble dynamics. The influences of the driving sound pressure and frequency, particle volume fraction, shell thickness and surface tension on the acoustic-dynamics behavior of microbubbles are numerically analyzed. The results show that when the volume fraction of magnetic particles is small and <i>α</i> ≤ 0.1, the acoustic properties of magnetic microbubbles are similar to those of ordinary UCA microbubbles. The acoustic response of the microbubble depends on its initial size and driving pressure. The critical sound pressure of microbubble vibration instability is lowest when the driving sound field frequency is twice the magnetic microbubble resonance frequency <i>f</i><sub>0</sub> (<i>f</i> = 2<i>f</i><sub>0</sub>). The presence of magnetic particles inhibits the bubbles from expanding and contracting, but the inhibition effect is very limited. The surface tension parameter <i>K</i> of the outer film material and thickness of the shell also affect the vibration of the microbubble. When <i>K</i> and film thickness are 0.2–0.4 N/m and 50–150 nm respectively, it is observed that the bubble has an unstable vibration response region.

Changes in microbubble dynamics upon adhesion to a solid surface.

The interaction between an acoustically driven microbubble and a surface is of interest for a variety of applications, such as ultrasound imaging and therapy. Prior investigations have mainly focused on acoustic effects of a rigid boundary, where it was generally observed that the wall increases inertia and reduces the microbubble resonance frequency. Here we investigate the response of a lipid-coated microbubble adherent to a rigid wall. Firm adhesion between the microbubble and a glass surface was achieved through either specific (biotin/avidin) or nonspecific (lipid/glass) interactions. Total internal reflection fluorescence microscopy was used to verify conditions leading to either adhesion or non-adhesion of the bubble to a glass or rigid polymer surface. Individual microbubbles were driven acoustically to sub-nanometer-scale radial oscillations using a photoacoustic technique. Remarkably, adherent microbubbles were shown to have a higher resonance frequency than non-adherent microbubbles resting against the wall. Analysis of the resonance curves indicates that adhesion stiffens the bubble by an apparent increase in the shell elasticity term and decrease in the shell viscosity. Based on these results, we conclude that surface adhesion is dominant over acoustic effects for low-amplitude microbubble oscillations.

Quantitative analysis of the angiogenic microvasculature in tumor using multiple scattering and dual-frequency transducers

The objective is to characterize angiogenic networks using contrast-enhanced multiple scattering. The methods relies on the measurement of the diffusion constant from the time evolution of the incoherent backscattered intensity. Dual-frequency arrays allow to emit a pulse at a frequency close to resonance frequency of microbubbles, and to receive the backscattered echoes at higher harmonics, resulting in better contrast-to-tissue ratio compared to single frequency transducers. At 8 MHz, we demonstrated that the diffusion constant enables the quantification of the vascular density and anisotropy in tumor-related vasculature in rat models in vivo. We show here that the results could be further improved using a dual-frequency approach, using two linear arrays with different central frequencies (7 MHz/18 MHz) and using a custom made dual frequency transducer (3 MHz/15 MHz). The minimum detectable distance between two vessel-mimicking cellulose tubes filled with contrast agents was measured via the diffusion constant. The dual-frequency approach drastically reduced the smallest detectable distance between tubes, which was found to be 25µm using a single frequency, 20µm using two linear arrays and 10µm using the custom dual-frequency array, respectively. These results show that measuring the diffusion constant with a dual frequency array can enable the quantification of vessel density with high accuracy

Microbubble oscillating in a microvessel filled with viscous fluid: A finite element modeling study

Understanding the dynamics of coated-microbubble oscillating in an elastic microvessel is important for effective and safe applications of ultrasound contrast agents (UCAs) in imaging and therapy. Numerical simulations are performed based on a two-dimensional (2D) asymmetric finite element model to investigate the influences of both acoustic driving parameters (e.g., pressure and frequency) and material properties (vessel size, microbubble shell visco-elastic parameters and fluid viscosity) on the dynamic interactions in the bubble–blood–vessel system. The results show that, the constrained effect of the blood vessel along the radial direction will induce the asymmetric bubble oscillation and vessel deformation, as well as shifting the bubble resonance frequency toward the higher frequency range. For a bubble (1.5-μm radius) activated by 1-MHz ultrasound pulses in a microvessel with a radius varying between 2 and 6.5μm, up to 26.95kPa shear stress could be generated on the vessel wall at a driving pressure of 0.2MPa, which should be high enough to damage the vascular endothelial cells. The asymmetrical oscillation ratio of the bubble can be aggravated from 0.12% to 79.94% with the increasing acoustic driving pressure and blood viscosity, or the decreasing vessel size and microbubble shell visco-elastic properties. The maximum compression velocity on the bubble shell will be enhanced from 0.19 to 22.79m/s by the increasing vessel size and acoustic pressure, or the decreasing microbubble shell visco-elasticity and blood viscosity. As the results, the peak values of microstreaming-induced shear stress on the vessel wall increases from 0.003 to 26.95kPa and the deformation degree of vessel is raised from 1.01 to 1.49, due to the enhanced acoustic amplitude, or the decreasing vessel size, blood viscosity and microbubble shell visco-elasticity. Moreover, it also suggests that, among above impact parameters, microbubble resonance frequency and UCA shell elasticity might play more dominant roles in dynamic interactions of the bubble–blood–vessel system.

Dynamic acousto-elastic testing applied to a highly dispersive medium and evidence of shell buckling of lipid-coated gas microbubbles.

Dynamic acousto-elastic testing is applied to a mixture of lipid-coated microbubbles in water. A dynamic change of ambient pressure is produced by a 16 kHz pressure wave having a peak pressure amplitude of 28 kPa. The induced changes of phase velocity and attenuation are captured by a sequence of short ultrasound pulses with a center frequency of 4 MHz. As a consequence of the dispersion brought about by the resonance of microbubbles at a frequency close to 2 MHz, time-domain approaches like the cross-correlation method are shown to be unsuited to determine the variation in ultrasound wavespeed. A frequency-domain analysis shows that the acousto-elastic effect (first order pressure derivative of ultrasound phase velocity) depends on the ultrasound frequency. The acousto-elastic effect tends to that measured in water for an ultrasound frequency above the resonance frequency of microbubbles, while it is two orders of magnitude larger for an ultrasound frequency close to or below the resonance frequency of microbubbles. Besides the large magnitude of the acousto-elastic effect observed for an ultrasound frequency below the resonance frequency of microbubbles, the first order pressure derivative of ultrasound phase velocity is negative. This supports the occurrence of shell buckling of lipid-coated microbubbles induced by the 16 kHz pressure wave.

Acoustic Estimation of Resonance Frequency and Sonodestruction of SonoVue Microbubbles

AbstractAcoustic properties of ultrasound (US) contrast agent microbubbles (MB) highly influence sonoporation efficiency and intracellular drug and gene delivery. In this study we propose an acoustic method to monitor passive and excited MBs in a real time. MB monitoring system consisted of two separate transducers. The first transducer delivered over an interval of 1 s US pulses (1 MHz, 1% duty cycle, 100 Hz repetition frequency) with stepwise increased peak negative pressure (PNP), while the second one continuously monitored acoustic response of SonoVue MBs. Pulse echo signals were processed according to the substitution method to calculate attenuation coefficient spectra and loss of amplitude. During US exposure at 50–100 kPa PNP we observed a temporal increase in loss of amplitude which coincided with the US delivery. Transient increase in loss of amplitude vanished at higher PNP values. At higher PNP values loss of amplitude decreased during the US exposure indicating MB sonodestruction. Analysis of transient attenuation spectra revealed that attenuation coefficient was maximal at 1.5 MHz frequency which is consistent with resonance frequency of SonoVue MB. The method allows evaluation of the of resonance frequency of MB, onset and kinetics of MB sonodestruction.

Influence of Shell Composition on the Resonance Frequency of Microbubble Contrast Agents

The effect of variations in microbubble shell composition on microbubble resonance frequency is revealed through experiment. These variations are achieved by altering the mole fraction and molecular weight of functionalized polyethylene glycol (PEG) in the microbubble phospholipid monolayer shell and measuring the microbubble resonance frequency. The resonance frequency is measured via a chirp pulse and identified as the frequency at which the pressure amplitude loss of the ultrasound wave is the greatest as a result of passing through a population of microbubbles. For the shell compositions used herein, we find that PEG molecular weight has little to no influence on resonance frequency at an overall PEG mole fraction (0.01) corresponding to a mushroom regime and influences the resonance frequency markedly at overall PEG mole fractions (0.050–0.100) corresponding to a brush regime. Specifically, the measured resonance frequency was found to be 8.4, 4.9, 3.3 and 1.4 MHz at PEG molecular weights of 1000, 2000, 3000 and 5000 g/mol, respectively, at an overall PEG mole fraction of 0.075. At an overall PEG mole fraction of just 0.01, on the other hand, resonance frequency exhibited no systematic variation, with values ranging from 5.7 to 4.9 MHz. Experimental results were analyzed using the Sarkar bubble dynamics model. With the dilatational viscosity held constant (10–8 N·s/m) and the elastic modulus used as a fitting parameter, model fits to the pressure amplitude loss data resulted in elastic modulus values of 2.2, 2.4, 1.6 and 1.8 N/m for PEG molecular weights of 1000, 2000, 3000 and 5000 g/mol, respectively, at an overall PEG mole fraction of 0.010 and 4.2, 1.4, 0.5 and 0.0 N/m, respectively, at an overall PEG mole fraction of 0.075. These results are consistent with theory, which predicts that the elastic modulus is constant in the mushroom regime and decreases with PEG molecular weight to the inverse 3/5 power in the brush regime. Additionally, these results are consistent with inertial cavitation studies, which revealed that increasing PEG molecular weight has little to no effect on inethe rtial cavitation threshold in the mushroom regime, but that increasing PEG molecular weight decreases inertial cavitation markedly in the brush regime. We conclude that the design and synthesis of microbubbles with a prescribed resonance frequency is attainable by tuning PEG composition and molecular weight.

Phospholipid-stabilized microbubbles: Influence of shell chemistry on cavitation threshold and binding to giant uni-lamellar vesicles

We demonstrate the feasibility of covalently linking a single microbubble to a single, giant uni-lamellar vesicle (GUV). Such a combination of GUV plus microbubble might prove useful as a new drug delivery vehicle involving microbubble cavitation-induced sonoporation of the vesicle bilayer as a release mechanism. We therefore applied the well known methodology of passive cavitation detection to measure the influence of lipid shell chemistry on inertial cavitation thresholds for externally added microbubbles. We find that cavitation threshold changes significantly with changes in either molecular weight or mole fraction of poly(ethylene glycol), historically used to impede gas dissolution and microbubble coalescence. We attribute changes in cavitation threshold to changes in microbubble resonance frequency resulting from changes in microbubble shell bending elasticity. To further demonstrate the influence of shell chemistry on microbubble behavior, we describe how several common bubble phenomena – and some new – respond to changes in lipid chain length.

Dual high-frequency difference excitation for contrast detection

Stimulating high-frequency nonlinear oscillations of ultrasound contrast agents is helpful to distinguish microbubbles from background tissues. Nevertheless, inefficiency of such oscillations from most commercially available contrast agents and intense attenuation of the resultant high-frequency harmonics limit microbubble detection with high-frequency ultrasound. To avoid this high-frequency nature, we devised and explored a dual-frequency difference excitation technique to induce efficiently low-frequency, rather than high-frequency, nonlinear scattering from microbubbles by using high-frequency ultrasound. The proposed excitation pulse is comprised of 2 high-frequency sinusoids with frequency difference subject to the microbubble resonance frequency. Its envelope, with frequency being the difference between the 2 frequencies, is used to stimulate nonlinear oscillation of microbubbles for the consonant low-frequency harmonic generation, whereas high-imaging resolution is retained because of narrow high-frequency transmit beams. Hydrophone measurements and phantom experiments of speckle-generating flow phantoms were performed to demonstrate the efficacy of the proposed technique. The results show that, especially when the envelope frequency is near the microbubbleiquests resonance frequency, the envelope of the proposed excitation pulse can induce significant nonlinear scattering from microbubbles, the induced nonlinear responses tend to increase with the pulse pressures, and up to 26 dB and 36 dB contrast-to-tissue ratios with second- and fourth-order nonlinear responses, respectively, can be obtained. Potential applications of this method include microbubble fragmentation and cavitation with high-frequency ultrasound.

Nonlinear propagation of ultrasound through microbubble contrast agents and implications for imaging

Microbubble contrast agents produce nonlinear echoes under ultrasound insonation, and current imaging techniques detect these nonlinear echoes to generate contrast agent images accordingly. For these techniques, there is a potential problem in that bubbles along the ultrasound transmission path between transducer and target can alter the ultrasound transmission nonlinearly and contribute to the nonlinear echoes. This can lead to imaging artefacts, especially in regions at depth. In this paper we provide insight, through both simulation and experimental measurement, into the nonlinear propagation caused by microbubbles and the implications for current imaging techniques. A series of investigations at frequencies below, at, and above the resonance frequency of microbubbles were performed. Three specific effects on the pulse propagation (i.e., amplitude attenuation, phase changes, and harmonic generation) were studied. It was found that all these effects are dependent on the initial pulse amplitude, and their dependence on the initial phase of the pulse is shown to be insignificant. Two types of imaging errors are shown to result from this nonlinear propagation: first, that tissue can be misclassified as microbubbles; second, the concentration of microbubbles in the image can be misrepresented. It is found that these imaging errors are significant for all three pulse frequencies when the pulses transmit through a microbubble suspension of 6 cm in path length. It also is found that the first type of error is larger at the bubble resonance frequency.

Resonance frequency of microbubbles in small blood vessels: a numerical study

Microbubbles are currently used as ultrasound contrast agents. Their potential therapeutic applications are also under investigation. This work is designed to provide some insight into the mechanisms of energy absorption and deposition by a preformed gas bubble in the microvasculature to optimize its efficacy. In the linear regime, the most favourable condition for the transfer of energy from an ultrasonic field to a gas bubble occurs when the centre frequency of the ultrasonic field equals the resonance frequency of the bubble. The resonance frequency of gas microbubbles has been investigated up to now mainly in unbounded liquids; however when bubbles are confined in small regions, their resonance frequency is strongly affected by the surrounding boundaries. A parametric study on how the resonance frequency of microbubbles in blood vessels is affected by the bubble radius, vessel radius and the bubble position in the vessel is presented. The resonance frequency decreases below its free value with decreasing vessel radius for vessels smaller than 200–300 µm depending on the bubble size. This model suggests the possibility of using ultrasound in a range of frequencies that are, in general, lower than the ones used now for therapeutic and diagnostic applications of ultrasound (a few MHz). When microbubbles oscillate at their resonance frequency they absorb and therefore emit more energy. This energy may allow specific blood vessels to be targeted for both diagnostic and therapeutic applications of ultrasound.

Resonance frequency of microbubbles: effect of viscosity.

The transmitted frequency at which a gas bubble of millimeter or submillimeter size oscillates resonantly in a low-viscosity liquid is approximately equal to the undamped natural frequency (referred to as the Minnaert frequency if surface tension effects are disregarded). Based on a theoretical analysis of bubble oscillation, this paper shows that such an approximation cannot be validated for microbubbles used in contrast-enhanced ultrasound imaging. The contrast-agent microbubbles represent either encapsulated bubbles of size less than 10 microm or free (nonencapsulated) bubbles of submicron size. The resonance frequency of the microbubbles deviates significantly from the undamped natural frequency over the whole range of microbubble sizes due to the increased viscous damping coefficient. The difference between these two frequencies is shown to have a tremendous impact on the resonant backscatter by the microbubbles. In particular, the first and second harmonics of the backscattered signal from the microbubbles are characterized by their own resonance frequencies, equal to neither the microbubble resonance frequency nor the undamped natural frequency.