Microbubble Radius Research Articles

Modelling the dynamics of microbubble undergoing stable and inertial cavitation: Delineating the effects of ultrasound and microbubble parameters on sonothrombolysis

Sonothrombolysis induces clot breakdown using ultrasound waves to excite microbubbles. Despite the great potential, selecting optimal ultrasound (frequency and pressure) and microbubble (radius) parameters remains a challenge. To address this, a computational model was developed to investigate the bubble behaviour during sonothrombolysis. The blood and clot were assumed to be non-Newtonian and porous, respectively. The effects of ultrasound and microbubble parameters on flow-induced shear stress on the clot surface during stable and inertial cavitation were investigated. It was found that microbubble translation towards the clot and the shear stress on the clot surface during stable cavitation were significant when the bubble was about to undergo inertial cavitation. While insonation of large microbubble (radius of 1.65μm) at low frequency (0.50 MHz) produced the highest shear stress during stable cavitation, selection of these parameters is not as intuitive for inertial cavitation due to the strong competing effect between jet velocity and translational distance. An increase in jet velocity is always accompanied by a decrease in the translational distance and vice versa. Therefore, a right balance between the jet velocity and the translational distance is critical to maximise the shear stress on the clot surface. A jet velocity of 303 m/s and a distance travelled of 5.12μm at an initial bubble-clot separation of 10μm produced the greatest clot surface shear stress. This is achievable by insonating a 0.55μm microbubble using 0.50 MHz and 600 kPa ultrasound.

Acoustic emissions based estimation of the temporal changes in microbubble radius during ultrasonic excitation

Our ability to study microbubble dynamics in vivo and link them to distinct mechano-biological effects hinges on our ability to accurately estimate the temporal changes in MB radius during ultrasonic excitation. Here, we hypothesize that real-time passive cavitation detection (PCD) monitoring combined with linear acoustic wave propagation theory can accurately estimate stable MB radius dynamics under in vivo conditions. To test our hypothesis, we employed numerical simulations, based on Rayleigh–Plesset modeling, followed by experimental validation, using calibrated PCDs with concurrent optical imaging of MB dynamics using high frame rate microscopy. Our method termed linear acoustic wave propagation and superposition (LAWPS) algorithm, combines Fourier series expansion with Euler’s relationship to estimate the acoustic emission (AE) from single MB, which is considered as a monopole source (i.e., R0 + ΔR < λ). LAWPS algorithm, which is independent of MB properties and, thus, can be linearly reversed to calculate MB oscillation radius from AE, was able to accurately capture the radiated pressure generated from a Rayleigh–Plesset MB modeling. Crucially, inverse LAWPS algorithm onto AE generated by Vokurka et al. resulted in the original MB model. Experimental observation using monodisperse MBs was able to accurately estimate the temporal changes in MB radius during 0.5 MHz ultrasonic excitation

On the theory of multiple encapsulated microbubbles interaction: Effect of lipid shell thickness

Encapsulated microbubbles are empty, micrometer-sized, spherical bubbles, typically micron which are used in many applications as lipid-shells in soft tissues. Here, this paper proposes the theoretical and mathematical modelling of the interaction of lipid-encapsulated microbubbles in soft tissues, as well as an examination of the effect of the thickness of the lipid-encapsulated microbubbles envelope located between the inner and outer radius of the microbubble. The mathematical models are formulated for a single encapsulated microbubble and interacting microbubbles in lipid shells. The first models are placed while considering the effect of shell-thickness on microbubbles in soft tissues. The second one has weak shell-thickness layers on it. In encapsulated single microbubbles and interacting microbubbles, the modified Church equations of shell-thickness microbubbles are formulated and solved analytically. Under the effect of layer thickness, the radii of outer microbubble dynamics are larger than those of inner radii of encapsulated microbubble dynamics, and the radii of bubbles with weak shell thickness in soft tissue are smaller. The clusterization of microbubbles reduces the process of microbubble growth, and interparticle interaction enhances it. In addition, the approximate value of the inner and outer microbubble radius was calculated at the different time intervals when the thickness of the shell, δ=0,15,150,250,350nm. Moreover, the growth process has been studied in different materials such as polymers, albumin, lipids, and liquids, and it turns out the results are consistent with previous works.

Transient formation theory of air-microbubble oil and testing its oil-spraying mechanism

In oil–air lubrication systems, large numbers of air microbubbles are often included in the oil phase. However, the principles of microbubble formation in oil–air annular flow and their influencing factors remain uncertain, and previous conclusions regarding the effects of microbubbles on the viscosity properties of the lubricant oil are inconsistent. Thus, there is an urgent need for experimental verification. In this paper, a transient force balance model is established and used to ascertain the formation of air microbubbles in oil (AB-oil) for an oil–air annular flow. The stability of these microbubbles is analyzed using the Rayleigh–Plesset equation. Theoretical analysis shows that the microbubble radius is the key factor affecting the force balance and stability of microbubbles in oil. Experiments are conducted based on this theoretical analysis, and the void fraction of AB-oil is determined through image analysis to verify the principles and influencing factors of AB-oil formation in oil–air lubrication systems. The viscosity properties of AB-oil are then tested using a rheometer. The experimental results indicate that the formation of AB-oil is affected by oil viscosity, pipe range, oil feeding rate, and air pressure. AB-oil exhibit different viscosity properties at different shear rates and void fractions. Finally, the relationship between the void fraction and viscosity at different shear rates is determined from the experimental data. The outcomes of this research provide insights into the characteristics of oil–air lubrication systems for high-speed machine tool spindles.

Acoustic scattering properties of multilayer membrane structured magnetic microbubbles

Normal ultrasound contrast agents (UCAs) loaded with magnetic nanoparticles are called magnetic microbubbles (MMBs), which can be used in multimodal imaging, thrombolytic therapy, and targeted drug delivery. The MMBs are often studied by <i>in situ</i> measurement techniques, however scattering model is the basis of inversion techniques. Therefore, we develop a scattering model of multilayer structured MMBs with magnetic fluid inner layer and phospholipid outer layer, in which outer layer’s viscoelasticity and the effect of nanoparticles on inner layer’s density are considered, while scattered sound fields in each region are obtained by solving normal series. The MMB model is compared with other bubbles, and its acoustic scattering characteristics are analyzed numarically, including the effects of radius, magnetic nanoparticle volume fraction, inner layer thickness and outer layer characteristics parameters. The results show that when the volume fraction <i>α</i> of magnetic nanoparticles in the inner layer does not exceed 0.1, magnetic nanoparticles have a two-sided effect on resonant scattering of MMBs, depending mainly on its radius, and the bubble has a critical radius value. If the radius of MMBs exceeds this critical value, the particles will enhance scattering, on the contrary, if the radius of MMBs is smaller than this critical value, the particles will reduce scattering; for a given microbubble radius, when <i>α</i> is not more than 0.1, the larger the <i>α</i> value<i>,</i> the stronger the resonant scattering of MMBs will be; the smaller the thickness of the inner film layer and outer film layer or the Larmé constant, the stronger the scattering will be. This study provides a theoretical guidance for the optimal structural design of MMBs and its <i>in situ</i> monitoring and therapeutic applications.

Numerical analysis of the biomechanical effects on micro-vessels by ultrasound-driven cavitation

The goal of this study was to evaluate the biomechanical effects such as sonoporation or permeability, produced by ultrasound- driven microbubbles (UDM) within microvessels with various parameters. In this study, a bubble-fluid-solid coupling system was established through combination of finite element method. The stress, strain and permeability of the vessel wall were theoretically simulated for different ultrasound frequencies, vessel radius and vessel thickness. the bubble oscillation induces the vessel wall dilation and invagination under a pressure of 0.1 MPa. The stress distribution over the microvessel wall was heterogeneous and the maximum value of the midpoint on the inner vessel wall could reach 0.7 MPa as a frequency ranges from 1 to 3 MHz, and a vessel radius and an initial microbubble radius fall within the range of 3.5-13 μm and 1-4 μm, respectively. With the same conditions, the maximum shear stress was equal to 1.2 kPa and occurred at a distance of ±5 μm from the midpoint of 10 μm and the maximum value of permeability was 3.033 × 10^-13. Results of the study revealed a strong dependence of biomechanical effects on the excitation frequency, initial bubble radius, and vessel radius. Numerical simulations could provide insight into understanding the mechanism behind bubble-vessel interactions by UDM, which may explore the potential for further improvements to medical applications.

Frequency response curves for a Mooney-Rivlin hyperelastic microbubble oscillating as a contrast agent in an acoustic pressure field

In this work, we have developed numerical simulations and weakly nonlinear analysis based on the multiple-scales perturbation technique for a coated microbubble that performs radial pulsations subject to an acoustic pressure disturbance in the far-field and whose encapsulated hyperelastic material obeys the Mooney-Rivlin equation. Departing from an elastic coating as a hyperelastic shell of finite thickness, we assume eventually that the shell is of very small thickness in comparison with the microbubble radius. Under this condition, we then perform weakly nonlinear analysis, to identify resonance conditions for small pressure disturbances of the acoustic field. In parallel and also for the limit of small thickness, we have carried out numerical simulations of the radial motion of the microbubble, identifying the onset of limit cycles via the construction of Poincare maps. Under both schemes, we have recognized the importance of two dimensionless hyperelastic parameters that dictate the main behavior of the oscillations: α∗ and β∗. Decreasing the values of these parameters, the resonance conditions are drastically amplified, which is an expected result because of the weak rigidity of the hyperelastic solid, prevails. In this manner, we suggest that moderate values for these previous parameters can be widely advisable when, in medical diagnostic applications, we are applying microbubbles as contrast agents. Therefore, we recommend widely the use of shell softens, because in this case the amplitude of radial pulsation is always amplified.

Blood Brain Barrier Disruption by Focused Ultrasound and Microbubbles: A Numerical Study on Mechanical Effects

Introduction: Microbubbles are widely used as contrast agent in diagnostic ultrasound. Recently they have shown good potential for applications in the therapeutic field such as drug delivery to the brain. Recent studies have shown focused ultrasound in conjunction with injected micro-bubbles could temporarily disrupt blood-brain barrier and let therapeutic agents transport into the brain tissue. The main aim of current study was to investigate, the interactions between ultrasonic acoustic field and microbubbles and the resultant mechanical effects on microvessels. Materials and Methods: In this study, we have used numerical approach to simulate microbubble confined in a microvessel filled with viscose fluid as blood. In the main stream of our study two crucial equations have been solved: equation of bubble oscillation on the bubble surface in an ultrasonic acoustic field (R-P equation), and equations of mass conservation and continuity (Navier Stokes) in fluid domain. Microbubble radius change, subjected to ultrasonic wave, and the force-fluid coupling which cause high velocity gradient and subsequent exertion of shear stress on interior vessel wall have been calculated. In this study microvessel considered as a viscoelastic solid. Acoustic pressure amplitude has been varied between 1.5P0 and 5P0 (P0 is hydrostatic pressure in fluid, P0~ 104.6kPa) with a constant frequency (f=1MHz). Then at a constant pressure of 2.5P0 acoustic frequency has been changed between 1 and 6MHz. Shear stress and transmural pressure, two important metrics for mechanical effects and vessel damage, have been calculated for each case. Results: The results obtained from the preliminary analysis of simulation study demonstrate that by increasing acoustic pressure both shear stress and transmural pressure increase linearly between 4-20 and 300-650kPa respectively. When the acoustic pressure reached the value 5P0 vessel ruptured and at this point, our simulation was stopped. This study has shown that by increasing acoustic frequency, relative difference of bubble radius, increase to%66 and then decrease to %12. In this case, shear stress and transmural pressure reached almost to a maximum of 10 and 450kPa respectively. Conclusion: The present study has gone some way towards enhancing our understanding of interaction between the acoustic field and micro bubbles. Mechanical effects on vessel wall are pressure and frequency dependant and it’s important to find a threshold for acoustic pressure that below it vessel damages won’t occur. This study has identified threshold for acoustic pressure is about 0.45P0. Also, it is very important to consider microbubbles resonance frequency at which maximum amplitude of oscillation and mechanical effects occur.

Boiling water jet outflow from a thin nozzle: spatial modeling

This study presents dual-temperature two-phase model for liquid-vapor mixture with account for evaporation and inter-phase heat transfer (taken in single-velocity single-pressure approximation). Simulation was performed using the shock-capturing method and moving Lagrangian grids. Analysis was performed for simulated and experimental values of nucleation frequency (for refining the initial number and radius of microbubbles) which affect the evaporation rate. Validity of 2D and 1D simulation was examined through comparison with experimental data. The peculiarities of the water-steam formation at the initial stage of outflow through a thin nozzle were studied for different initial equilibrium states of water for the conditions close to chosen experimental conditions.

Analysis of the Uncertainty in Microbubble Characterization

There is increasing interest in the use of microbubble contrast agents for quantitative imaging applications such as perfusion and blood pressure measurement. The response of a microbubble to ultrasound excitation is, however, extremely sensitive to its size, the properties of its coating and the characteristics of the sound field and surrounding environment. Hence the results of microbubble characterization experiments can be significantly affected by experimental uncertainties, and this can limit their utility in predictive modelling. The aim of this study was to attempt to quantify these uncertainties and their influence upon measured microbubble characteristics. Estimates for the parameters characterizing the microbubble coating were obtained by fitting model data to numerical simulations of microbubble dynamics. The effect of uncertainty in different experimental parameters was gauged by modifying the relevant input values to the fitting process. The results indicate that even the minimum expected uncertainty in, for example, measurements of microbubble radius using conventional optical microscopy, leads to variations in the estimated coating parameters of ∼20%. This should be taken into account in designing microbubble characterization experiments and in the use of data obtained from them.

Motion Characteristics of Microbubble in Water

The motion characteristics of microbubble in the water or solution have important influence to crystallization process. In the paper, the movement equation of single bubble was modeled based on force equilibrium, the mechanics factors influence on the single bubble motion were discussed, and the velocity of microbubble was analysed with the different bubble sizes. The results show that the velocity of microbubble in static water is increasing with time increasing, the influence of virtual mass force and Basset force caused by the acceleration on the velocity of microbubble must be considered in the initial stage of microbubble motion. In the processes of microbubble motion, compared with constant microbubble radius the variation laws of velocity fluctuations mean with microbubble radius changing are uniform.

Measuring Absolute Blood Pressure Using Microbubbles

Gas microbubbles are highly compressible, which makes them very efficient sound scatterers. As another consequence of their high compressibility, the radii of the microbubbles are affected by the pressure of the fluid around them, which changes their resonance frequency. Although the pressures present within the human body cause only minor variations in the radii of uncoated microbubbles (∼0.2% per 10 mmHg) and, therefore, very small variations in the resonance frequency (∼1 kHz per 10 mmHg), it was found in the work described here, through both simulations and in vitro measurements, that large changes in resonance frequency can occur in phospholipid-coated microbubbles for small blood pressure variations because of the exotic buckling dynamics of phospholipid monolayers (up to 240 kHz per 10 mmHg). This method should allow non-invasive measurement of the gauge blood pressure in deep blood vessels as long as the microbubble physical properties are well controlled.

Observation of Encapsulated Bubble Oscillations Driven by Ultrasound

Using a long-distance microscope imaging system and a technique using a movable lock-in pulse laser, optical measurement demonstrated the behavior of a SonoVue® contrast agent microbubble exposed to a low-amplitude, 478 kHz ultrasound field. The microbubble consisted of the gas SF6 encapsulated by a polymer shell. Eighty-four frames of a microbubble oscillating in response to an ultrasound field were captured in one acoustic cycle. The experimental data on microbubble radius were fitted by the numerical calculations of the Hoff, Yasui, and Keller–Miksis models. The results showed good agreement between the data and the theoretical calculation of the Hoff model using our experimental parameters. In addition, the spectral analysis of the time-radius data indicated that the relative intensity of the second harmonic increased with the increase in acoustic pressure amplitude.

Dynamics of micro-bubble sonication inside a phantom vessel

A model for sonicated micro-bubble oscillations inside a phantom vessel is proposed. The model is not a variant of conventional Rayleigh-Plesset equation and is obtained from reduced Navier-Stokes equations. The model relates the micro-bubble oscillation dynamics with geometric and acoustic parameters in a consistent manner. It predicts micro-bubble oscillation dynamics as well as micro-bubble fragmentation when compared to the experimental data. For large micro-bubble radius to vessel diameter ratios, predictions are damped, suggesting breakdown of inherent modeling assumptions for these cases. Micro-bubble response with acoustic parameters is consistent with experiments and provides physical insight to the micro-bubble oscillation dynamics.

Amplitude-Modulation Chirp Imaging for Contrast Detection

We propose an amplitude-modulation chirp imaging method for contrast detection with high-frequency ultrasound. Our proposed method detects microbubbles by extracting and then selectively compressing the component of the backscattered chirp signal modulated by changes in the radii of microbubbles at their resonance frequency. Microbubbles are sonicated simultaneously with a narrowband, low-frequency pumping signal at their resonance frequency and a wideband, high-frequency imaging chirp signal. Changes in the radii of the resonant microbubbles result in periodic changes in their acoustic cross section that modulate the amplitude of the backscattered imaging chirp signal, forming pumping and imaging frequency sum-and-difference chirp terms. The frequency-sum or -difference chirp component is then extracted by a bandpass filter (BPF). Because a long imaging pulse duration is required to obtain a sufficient modulation depth on the chirp for contrast detection and to facilitate frequency-sum-and-difference signal extraction with the BPF, a chirp with a longer-than-usual waveform is used so pulse compression of the extracted chirp signal can then be performed to maintain the axial resolution, and even further improve the signal-to-noise ratio and contrast-to-tissue ratio. Experiments performed on flow phantoms with and without a speckle-generating background were performed to demonstrate the efficacy of the proposed technique. These results indicate that our proposed method can potentially provide high-resolution contrast detection in the microvasculature. (E-mail: ckyeh@mx.nthu.edu.tw)

Optimization of ultrasound contrast agents with computational models to improve selection of ligands and binding strength

Diagnosis of cardiovascular disease is currently limited by the testing modality. Serum tests for biomarkers can provide quantification of severity but lack the ability to localize the source of the cardiovascular disease, while imaging technology such as angiography and ultrasound can only determine areas of reduced flow but not the severity of tissue ischemia. Targeted imaging with ultrasound contrast agents offers the ability to locally image as well as determine the degree of ischemia by utilizing agents that will cause the contrast agent to home to the affected tissue. Ultrasound molecular imaging via targeted microbubbles (MB) is currently limited by its sensitivity to molecular markers of disease relative to other techniques (e.g., radiolabeling). We hypothesize that computational modeling may provide a useful first approach to maximize microbubble binding by defining key parameters governing adhesion. Adhesive dynamics (AD) was used to simulate the fluid dynamic and stochastic molecular binding of microbubbles to inflamed endothelial cells. Sialyl Lewis(X) (sLe(x)), P-selectin aptamer (PSA), and ICAM-1 antibody (abICAM) were modeled as the targeting receptors on the microbubble surface in both single- and dual-targeted arrangements. Microbubble properties (radius [R(c)], kinetics [k(f), k(r)], and densities of targeting receptors) and the physical environment (shear rate and target ligand densities) were modeled. The kinetics for sLe(x) and PSA were measured with surface plasmon resonance. R(c), shear rate, and densities of sLe(x), PSA, or abICAM were varied independently to assess model sensitivity. Firm adhesion was defined as MB velocity <2% of the free stream velocity. AD simulations revealed an optimal microbubble radius of 1-2 µm and thresholds for kf(in) ( >10(2) s(-1)) and kr(o) (<10(-3) s(-1)) for firm adhesion in a multi-targeted system. State diagrams for multi-targeted microbubbles suggest sLe(x) and abICAM microbubbles may require 10-fold more ligand to achieve firm adhesion at higher shear rates than sLe(x) and PSA microbubbles. The AD model gives useful insight into the key parameters for stable microbubble binding, and may allow flexible, prospective design, and optimization of microbubbles to enhance clinical translation of ultrasound molecular imaging.

Acoustic responses of monodisperse lipid encapsulated microbubble contrast agents produced by flow focusing

Lipid-encapsulated microbubbles are used as contrast agents in ultrasound imaging. Currently available commercially made contrast agents have a polydisperse size distribution. It has been hypothesised that improved imaging sensitivity could be achieved with a uniform microbubble radius. We have recently developed microfluidics technology to produce contrast agents with a nearly monodisperse distribution. In this manuscript, we analyze echo responses from individual microbubbles from monodisperse populations in order to establish the relationship between scattered echo, microbubble radius, and excitation frequency. Simulations of bubble response from a modified Rayleigh-Plesset type model corroborate experimental data. Results indicate that microbubble echo response can be greatly increased by optimal combinations of microbubble radius and acoustic excitation frequency. These results may have a significant impact in the formulation of contrast agents to improve ultrasonic sensitivity.

Chaotic dynamics of microbubbles in ultrasonic fields

Chaos is present in non-linear systems that describe temporal phenomena in the physical and life sciences. Well-known instances of chaos include the logistic map, the Lorenz equations, and forced non-linear oscillators. The regular and chaotic dynamics of free gas bubbles and gas-encapsulated microbubbles (contrast agents) are of immense importance in the efficient implementation of ultrasonic contrast imaging. A modification of the Keller-Herring model, which takes into account the elastic properties of the encapsulating shell, is investigated with respect to the bifurcation structure of the time-dependent microbubble radius. Numerical simulations show that the radial oscillations can be periodic as well as chaotic in appropriate parameter domains. Several investigations on chaotic aspects of dynamics presented here are new and highlighted appropriately. The influence of the acoustic field and shell parameters are investigated to identify values where the oscillations undergo bifurcations and the bubble response becomes chaotic. An analysis of chaotic behaviour in multiple-bubble systems completes the investigation and reveals the significant influence the free gas bubbles have on the acoustic response of their encapsulated counterparts.

Characterization of individual submicron perfluorocarbon gas bubbles by ultrasonic backscatter

Measurements were undertaken to determine the unknown microbubble-size distribution of a dodecafluoropentane (DDFP) emulsion consisting of 1012 droplets/ml in surfactant-stabilized water. The acoustic backscatter of 2-microsecond-duration tonebursts of 30-MHz focused ultrasound was measured from the emulsion as it moved in a coaxial flow. Calibration for the system was accomplished using 3-μm-radius polystyrene spheres, using a linear scattering model and literature values for polystyrene. Applying viscous linear scattering theory to the backscatter data from individual DDFP bubbles allowed inversion of the radius–backscatter relation. A mean microbubble radius of 130 nm was inferred for the DDFP population.

Observations of contrast agents during insonation with a high-speed imaging system

With the use of a high-speed imaging system, fluctuations in microbubble radius and asymmetries leading to destruction at clinical ultrasonic frequencies can be evaluated. The extraordinary temporal resolution necessary to obtain these observations was achieved using a 10-W copper-vapor laser in conjunction with a high-speed digital camera. This combination produces an effective shutter speed of 50 MHz, which allows for imaging of the fluctuations in radius over the acoustic pressure cycle. Using this imaging technique in combination with image-analysis software, radius versus time curves of bubble expansion and contraction during the acoustic pressure cycle can be produced. It is observed that contrast agent microbubbles can expand and contract by a large fraction of their resting diameter (130%) during insonation while remaining intact at low acoustic pressures (180 kPa). At higher acoustic pressures (2.3 MPa), bubbles can expand up to 500% during the rarefactional half-cycle, after which they usually fragment into smaller bubbles. Since the echo from a bubble is determined by the radial fluctuation and resulting wall velocity, mapping such changes over time is essential if the radiated pressure waveform is to be predicted. For Biomedical Ultrasound/Bioresponse to Vibration Best Student Paper Award.