Forced linear oscillations of microbubbles in blood capillaries

Microbubble-enhanced transcranial MR-guided focused ultrasound brain hyperthermia: heating mechanism investigation using finite element method

Recently, our group developed a synergistic brain drug delivery method to achieve simultaneous transcranial hyperthermia and localized blood-brain barrier opening via MR-guided focused ultrasound (MRgFUS). In a rodent model, we demonstrated that the ultrasound power required for transcranial MRgFUS hyperthermia was significantly reduced by injecting microbubbles (MBs). However, the specific mechanisms underlying the power reduction caused by MBs remain unclear. The present study aims to elucidate the mechanisms of MB-enhanced transcranial MRgFUS hyperthermia through numerical studies using the finite element method. The microbubble acoustic emission (MAE) and the viscous dissipation (VD) were hypothesized to be the specific mechanisms. Acoustic wave propagation was used to model the FUS propagation in the brain tissue, and a bubble dynamics equation for describing the dynamics of MBs with small shell thickness was used to model the MB oscillation under FUS exposures. A modified bioheat transfer equation was used to model the temperature in the rodent brain with different heat sources. A theoretical model was used to estimate the bubble shell's surface tension, elasticity, and viscosity losses. The simulation reveals that MAE and VD caused a 40.5% and 52.3% additional temperature rise, respectively. Compared with FUS only, MBs caused a 64.0% temperature increase, which is consistent with our previous animal experiments. Our investigation showed that MAE and VD are the main mechanisms of MB-enhanced transcranial MRgFUS hyperthermia.

RGD-coated polymeric microbubbles promote ultrasound-mediated drug delivery in an inflamed endothelium-pericyte co-culture model of the blood-brain barrier

Drug delivery to central nervous pathologies is compromised by the blood-brain barrier (BBB). A clinically explored strategy to promote drug delivery across the BBB is sonopermeation, which relies on the combined use of ultrasound (US) and microbubbles (MB) to induce temporally and spatially controlled opening of the BBB. We developed an advanced in vitro BBB model to study the impact of sonopermeation on the delivery of the prototypic polymeric drug carrier pHPMA as a larger molecule and the small molecule antiviral drug ribavirin. This was done under standard and under inflammatory conditions, employing both untargeted and RGD peptide-coated MB. The BBB model is based on human cerebral capillary endothelial cells and human placental pericytes, which are co-cultivated in transwell inserts and which present with proper transendothelial electrical resistance (TEER). Sonopermeation induced a significant decrease in TEER values and facilitated the trans-BBB delivery of fluorescently labeled pHPMA (Atto488-pHPMA). To study drug delivery under inflamed endothelial conditions, which are typical for e.g. tumors, neurodegenerative diseases and CNS infections, tumor necrosis factor (TNF) was employed to induce inflammation in the BBB model. RGD-coated MB bound to and permeabilized the inflamed endothelium-pericyte co-culture model, and potently improved Atto488-pHPMA and ribavirin delivery. Taken together, our work combines in vitro BBB bioengineering with MB-mediated drug delivery enhancement, thereby providing a framework for future studies on optimization of US-mediated drug delivery to the brain.

Collapsing behavior of spark-induced cavitation bubble in rigid tube

The phenomenon of cavitation within tubes is a common scenario in the fields of medicine and industry. This paper focuses on the effects of rigid circular tube length, diameter and the distance of bubble - tube port on the behavior of bubble in tube. The low-voltage discharge technique was utilized to induce a cavitation bubble in deionized water. The effects of rigid tube lengths, diameters, and bubble-tube port distances on the morphology of bubbles are observed using high-speed camera. It has been found that as the length of the rigid tube increases, so does the period, and this effect is more pronounced in tubes with smaller diameters. Conversely, the cavitation bubble period decreased and then stabilized as the tube diameter increased, the ratio of tube radius and the bubble radius exceeds 4.8, the period of bubble in tube is similar to that of bubble in free field. Further analysis of the influence of tube characteristics on microjets reveals that a pair of oppositely microjets were formed along the tube axis by the bubble near the midpoint of the tube axis. Moreover, when the non-dimensional tube length η < 3.5, the increase tube diameter results in a decrease microjet velocity. It has also been observed that as the bubble gradually approaches the interior of the tube, the velocity of microjets directed inward decreases. Additionally, the smaller the diameter of the tube, the greater the bubble-tube port distance required for the microjets to reach the same level of velocity as bubble near the center of the tube axis. These findings hold theoretical implications for improvement of targeted drug delivery efficiency in medicine and enhance the operational efficiency of inertial micropumps in industries.

Experimental study on damage mechanism of blood vessel by cavitation bubbles

Ultrasound-induced cavitation in blood vessels is a common scenario in medical procedures. This paper focuses on understanding the mechanism of microscopic damage to vessel walls caused by the evolution of cavitation bubbles within the vessels. In this study, cavitation bubbles were generated using the low-voltage discharge method in 0.9% sodium chloride saline, and vessel models with wall thicknesses ranging from 0.7 mm to 2 mm were made using a 3D laminating process. The interaction between cavitation bubbles and vessel models with different wall thicknesses was observed using a combination of high-speed photography. Results show that cavitation bubble morphology and collapse time increased and then stabilized as the vessel wall thickness increased. When the cavitation bubble was located in vessel axial line, pair of opposing micro-jets were formed along the axis of the vessel, and the peak of micro-jet velocity decreased with increasing wall thickness. However, when the cavitation bubble deviated from the vessel model center, no micro-jet towards the vessel model wall was observed. Further analysis of the vessel wall deformation under varying distances from the cavitation bubble to the vessel wall revealed that the magnitude of vessel wall stretch due to the cavitation bubble expansion was greater than that of the contraction. A comparative analysis of the interaction of between the cavitation bubble and different forms of elastic membranes showed that the oscillation period of the cavitation bubble under the influence of elastic vessel model was lower than the elastic membrane. Furthermore, the degree of deformation of elastic vessel models under the expansion of the cavitation bubble was smaller than that of elastic membranes, whereas the degree of deformation of elastic vessel models in the contraction phase of the cavitation bubble was larger than that of elastic membranes. These new findings provide important theoretical insights into the microscopic mechanisms of blood vessel potential damage caused by ultrasound-induced cavitation bubble, as well as cavitation in pipelines in hydrodynamic systems.

An optical and acoustic investigation of microbubble cavitation in small channels under therapeutic ultrasound conditions

Therapeutic focused ultrasound in combination with encapsulated microbubbles is being widely investigated for its ability to elicit bioeffects in the microvasculature, such as transient permeabilization for drug delivery or at higher pressures to achieve 'antivascular' effects. While it is well established that the behaviors of microbubbles are altered when they are situated within sufficiently small vessels, there is a paucity of data examining how the bubble population dynamics and emissions change as a function of channel (vessel) diameter over a size range relevant to therapeutic ultrasound, particularly at pressures relevant to antivascular ultrasound. Here we use acoustic emissions detection and high-speed microscopy (10 kframes/s) to examine the behavior of a polydisperse clinically employed agent (Definity®) in wall-less channels as their diameters are scaled from 1200 to 15 µm. Pressures are varied from 0.1 to 3 MPa using either a 5 ms pulse or a sequence of 0.1 ms pulses spaced at 1 ms, both of which have been previously employed in an in vivo context. With increasing pressure, the 1200 µm channel - on the order of small arteries and veins - exhibited inertial cavitation, 1/2 subharmonics and 3/2 ultraharmonics, consistent with numerous previous reports. The 200 and 100 µm channels - in the size range of larger microvessels less affected by therapeutic focused ultrasound - exhibited a distinctly different behavior, having muted development of 1/2 subharmonics and 3/2 ultraharmonics and reduced persistence. These were associated with radiation forces displacing bubbles to the distal wall and inducing clusters that then rapidly dissipated along with emissions. As the diameter transitioned to 50 and then 15 µm - a size regime that is most relevant to therapeutic focused ultrasound - there was a higher threshold for the onset of inertial cavitation as well as subharmonics and ultraharmonics, which importantly had more complex orders that are not normally reported. Clusters also occurred in these channels (e.g. at 3 MPa, the mean lateral and axial sizes were 23 and 72 µm in the 15 µm channel; 50 and 90 µm in the 50 µm channel), however in this case they occupied the entire lumens and displaced the wall boundaries. Damage to the 15 µm channel was observed for both pulse types, but at a lower pressure for the long pulse. Experiments conducted with a 'nanobubble' (<0.45 µm) subpopulation of Definity followed broadly similar features to 'native' Definity, albeit at a higher pressure threshold for inertial cavitation. These results provide new insights into the behavior of microbubbles in small vessels at higher pressures and have implications for therapeutic focused ultrasound cavitation monitoring and control.

Study on Bubble Cavitation in Liquids for Bubbles Arranged in a Columnar Bubble Group

In liquids, bubbles usually exist in the form of bubble groups. Due to their interaction with other bubbles, the resonance frequency of bubbles decreases. In this paper, the resonance frequency of bubbles in a columnar bubble group is obtained by linear simplification of the bubbles’ dynamic equation. The correction coefficient between the resonance frequency of the bubbles in the columnar bubble group and the Minnaert frequency of a single bubble is given. The results show that the resonance frequency of bubbles in the bubble group is affected by many parameters such as the initial radius of bubbles, the number of bubbles in the bubble group, and the distance between bubbles. The initial radius of the bubbles and the distance between bubbles are found to have more significant influence on the resonance frequency of the bubbles. When the distance between bubbles increases to 20 times the bubbles’ initial radius, the coupling effect between bubbles can be ignored, and after that the bubbles’ resonance frequency in the bubble group tends to the resonance frequency of a single bubble’s resonance frequency. Fluent software is used to simulate the bubble growth, shrinkage, and collapse of five and seven bubbles under an ultrasonic field. The simulation results show that when the bubble breaks, the two bubbles at the outer field first begin to break and form a micro-jet along the axis line of the bubbles. Our methods and conclusions will provide a reference for further simulations and indicate the significance of the prevention or utilization of cavitation.

Ultrasound-based triggered drug delivery to tumors

Over the past few decades, applications of ultrasound (US) in drug delivery have been documented widely for local and site-specific release of bioactives in a controlled manner, after acceptable use in mild physical therapy for tendinitis and bursitis, and for high-energy applications in fibroid ablation, cataract removal, bone fracture healing, etc. US is a non-invasive, efficient, targetable and controllable technique. Drug delivery can be enhanced by applying directed US in terms of targeting and intracellular uptake. US cannot only provide local hyperthermia but can also enhance local extravasations and permeability of the cell membrane for delivery of cell-impermeable and poorly permeable drugs. It is also found to increase the anticancer efficacy of drug against solid tumors by facilitating uniform drug delivery throughout the tumor mass. This review summarizes the mechanism of US; various drug delivery systems like microbubbles, liposomes, and micelles; and biological manifestations employed for improving treatment of cancer, i.e., hyperthermia and enhanced extravasation. Safety issues are also discussed for better therapeutic outcomes of US-assisted drug delivery to tumors. This review can be a beneficial asset to the scientists looking at non-invasive techniques (externally guided) for improving the anticancer potential of drug delivery systems.

Interaction between cavitation microbubble and cell: A simulation of sonoporation using boundary element method (BEM)

Sonoporation has been widely accepted as a significant tool for gene delivery as well as some bio-effects like hemolysis, bringing in high demands of looking into its underlying mechanism. A two-dimensional (2D) boundary element method (BEM) model was developed to investigate microbubble-cell interaction, especially the morphological and mechanical characteristics around the close-to-bubble point (CP) on cell membrane. Based on time evolution analysis of sonoporation, detailed information was extracted from the model for analysis, including volume expansion ratio of the bubble, areal expansion ratio of the cell, jet velocity and CP displacement. Parametric studies were carried out, revealing the influence of different ultrasound parameters (i.e., driving frequency and acoustic pressure) and geometrical configurations (i.e., bubble-cell distance and initial bubble radius). This model could become a powerful tool not only for understanding bubble-cell interactions, but also for optimizing the strategy of sonoporation, such that it could be safer and of higher efficiency for biological and medical studies especially in clinics.

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 6.5 μm, up to 26.95 kPa shear stress could be generated on the vessel wall at a driving pressure of 0.2 MPa, 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 22.79 m/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 26.95 kPa 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.

Molecular Acoustic Angiography: A New Technique for High-resolution Superharmonic Ultrasound Molecular Imaging

Ultrasound molecular imaging utilizes targeted microbubbles to bind to vascular targets such as integrins, selectins and other extracellular binding domains. After binding, these microbubbles are typically imaged using low pressures and multi-pulse imaging sequences. In this article, we present an alternative approach for molecular imaging using ultrasound that relies on superharmonic signals produced by microbubble contrast agents. Bound bubbles were insonified near resonance using a low frequency (4 MHz) element and superharmonic echoes were received at high frequencies (25-30 MHz). Although this approach was observed to produce declining image intensity during repeated imaging in both in vitro and in vivo experiments because of bubble destruction, the feasibility of superharmonic molecular imaging was demonstrated for transmit pressures, which are sufficiently high to induce shell disruption in bound microbubbles. This approach was validated using microbubbles targeted to the αvβ3 integrin in a rat fibrosarcoma model (n = 5) and combined with superharmonic images of free microbubbles to produce high-contrast, high-resolution 3-D volumes of both microvascular anatomy and molecular targeting. Image intensity over repeated scans and the effect of microbubble diameter were also assessed in vivo, indicating that larger microbubbles yield increased persistence in image intensity. Using ultrasound-based acoustic angiography images rather than conventional B-mode ultrasound to provide the underlying anatomic information facilitates anatomic localization of molecular markers. Quantitative analysis of relationships between microvasculature and targeting information indicated that most targeting occurred within 50 μm of a resolvable vessel (>100 μm diameter). The combined information provided by these scans may present new opportunities for analyzing relationships between microvascular anatomy and vascular targets, subject only to limitations of the current mechanically scanned system and microbubble persistence to repeated imaging at moderate mechanical indices.

Ultrasound triggered drug delivery with liposomal nested microbubbles

When ultrasound contrast agent microbubbles are nested within a liposome, damage to the liposome membrane caused by both stable and inertial cavitation of the microbubble allows for release of the aqueous core of the liposome. Triggered release was not accomplished unless microbubbles were present within the liposome. Leakage was tested using fluorescence assays developed specifically for this drug delivery vehicle and qualitative measurements using an optical microscope. These studies were done using a 1 MHz focused ultrasound transducer while varying parameters including peak negative ultrasound pressure, average liposome diameter, and microbubble concentration. Two regimes exist for membrane disruption caused by cavitating microbubbles. A faster release rate, as well as permanent membrane damage are seen for samples exposed to high pressure (2.1-3.7 MPa). A slower release rate and dilation/temporary poration are characteristic of stable cavitation for low pressure studies (0.54-1.7 MPa).

Inertial cavitation threshold of nested microbubbles

Cavitation of ultrasound contrast agents (UCAs) promotes both beneficial and detrimental bioeffects in vivo (Radhakrishnan et al., 2013) [1]. The ability to determine the inertial cavitation threshold of UCA microbubbles has potential application in contrast imaging, development of therapeutic agents, and evaluation of localized effects on the body (Ammi et al., 2006) [2]. This study evaluates a novel UCA and its inertial cavitation behavior as determined by a home built cavitation detection system. Two 2.25 MHz transducers are placed at a 90° angle to one another where one transducer is driven by a high voltage pulser and the other transducer receives the signal from the oscillating microbubble. The sample chamber is placed in the overlap of the focal region of the two transducers where the microbubbles are exposed to a pulser signal consisting of 600 pulse trains per experiment at a pulse repetition frequency of 5 Hz where each train has four pulses of four cycles. The formulation being analyzed is comprised of an SF6 microbubble coated by a DSPC PEG-3000 monolayer nested within a poly-lactic acid (PLA) spherical shell. The effect of varying shell diameters and microbubble concentration on cavitation threshold profile for peak negative pressures ranging from 50 kPa to 2 MPa are presented and discussed in this paper. The nesting shell decreases inertial cavitation events from 97.96% for an un-nested microbubble to 19.09% for the same microbubbles nested within a 2.53 μm shell. As shell diameter decreases, the percentage of inertially cavitating microbubbles also decreases. For nesting formulations with average outer capsule diameters of 20.52, 14.95, 9.95, 5.55, 2.53, and 1.95 μm, the percentage of sample destroyed at 1 MPa was 51.02, 38.94, 33.25, 25.27, 19.09, and 5.37% respectively.

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.

Influence of disjoining pressure on the dynamics of steadily moving long bubbles inside narrow cylindrical capillaries

We study the influence of disjoining pressure for moving long bubbles inside cylindrical capillaries. Towards that end, consistent thin-film equations, for the annular region separating the bubble from the channel surface, are presented with specific emphasis on three different attributes: (a) the van der Waals interaction, formalized by the classical Lifshitz form of disjoining pressure; (b) the nonuniformity in film thickness, accommodated by the necessary corrections in the disjoining pressure; and (c) the electrostatic component of disjoining pressure, reminiscent of the electrostatic interactions in the presence of surface charges. The present thin-film analysis appositely uncovers the existence and the breakdown of the two-thirds power law for minimum film thickness behavior. This is attributed to the alteration in the characteristic length scales governing the underlying physics, as quantitatively established by our consistent scaling analysis. In the breakdown regimes, the characteristic length scales are found to be composed of the suitable combinations of the capillary number and the physics driven intrinsic length scales. The characteristics of the breakdown regime reported by us appear to match excellently with reported experimental data in the low capillary number regime. Towards unveiling the possible implications of slope and curvature dependence of disjoining pressure, our analysis reveals that the consequent correction term endorses an order two-thirds power of the capillary number contribution without alerting the governing length scales. The subsequent asymptotic analysis reveals that this correction may be neglected to the leading order approximation. Finally, we consider the electrostatic component of the disjoining pressure which may be realized in the presence of surface charges. Our analysis reveals that the significance of the electrostatic interaction is realized over a very small capillary number regime, leading towards the departure from the two-thirds power law type behavior. Reasonably good agreement is obtained with reported experimental data over this regime.

In vitro methods for evaluating therapeutic ultrasound exposures: present-day models and future innovations

Although preclinical experiments are ultimately required to evaluate new therapeutic ultrasound exposures and devices prior to clinical trials, in vitro experiments can play an important role in the developmental process. A variety of in vitro methods have been developed, where each of these has demonstrated their utility for various test purposes. These include inert tissue-mimicking phantoms, which can incorporate thermocouples or cells and ex vivo tissue. Cell-based methods have also been used, both in monolayer and suspension. More biologically relevant platforms have also shown utility, such as blood clots and collagen gels. Each of these methods possesses characteristics that are well suited for various well-defined investigative goals. None, however, incorporate all the properties of real tissues, which include a 3D environment and live cells that may be maintained long-term post-treatment. This review is intended to provide an overview of the existing application-specific in vitro methods available to therapeutic ultrasound investigators, highlighting their advantages and limitations. Additional reporting is presented on the exciting and emerging field of 3D biological scaffolds, employing methods and materials adapted from tissue engineering. This type of platform holds much promise for achieving more representative conditions of those found in vivo, especially important for the newest sphere of therapeutic applications, based on molecular changes that may be generated in response to non-destructive exposures.

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)].

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.

Microbubble oscillations in capillary tubes

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

Targeted drug delivery across the blood-brain barrier using ultrasound technique

Effective delivery of therapeutic agents into the brain can greatly improve the treatments of neurological and neurodegenerative diseases. Application of focused ultrasound facilitated by microbubbles has shown the potential to deliver drugs across the blood-brain barrier into targeted sites within the brain noninvasively. This review provides a summary of the technological background and principle, highlights of recent significant developments and research progress, as well as a critical commentary on the challenges and future directions in the field. This review also outlines and discusses the tasks that researchers face in order to successfully translate the technology into a clinical reality, including obtaining improved understanding of the mechanisms, demonstration of therapeutic efficacy and safety for specific applications, and development of methodology for rational design to achieve optimized and consistent outcomes.

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.

Modeling of thermal effects in antivascular ultrasound therapy

Antivascular ultrasound consisting of low-intensity sonication in the presence of circulating microbubbles of an ultrasound contrast agent has been demonstrated to disrupt blood flow in solid cancers. In this study a mathematical framework is described for the microbubble-induced heating that occurs during antivascular ultrasound. Biological tissues are modeled as a continuum of microbubble-filled vasculature, cells, and interstitial fluids with compressibility equal to the sum of the compressibility of each component. The mathematical simulations show that the absorption of ultrasound waves by viscous damping of the microbubble oscillations induced significant local heating of the tissue vasculature. The extent and the rate of temperature increase not only depends on the properties of the microbubbles and the sonication parameters but is also influenced markedly by the blood flow. Slow flow conditions lead to higher tissue temperatures due to a stronger interaction between microbubbles and ultrasound and reduced heat dissipation. Because tumors have slower blood flow than healthy tissue, the microbubble-induced ultrasound antivascular therapy is likely to affect cancerous tissue more extensively than healthy tissue, providing a way to selectively target the vasculature of cancers.

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

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

Regimes of bubble volume oscillations in a pipe

The effect of an acoustically driven bubble on the acoustics of a liquid-filled pipe is theoretically analyzed and the dimensionless groups of the problem are identified. The different regimes of bubble volume oscillations are predicted theoretically with these dimensionless groups. Three main regimes can be identified: (1) For small bubbles and weak driving, the effect of the bubble oscillations on the acoustic field can be neglected. (2) For larger bubbles and still small driving, the bubble affects the acoustic field, but due to the small driving, a linear theory is sufficient. (3) For large bubbles and large driving, the two-way coupling between the bubble and the flow dynamics requires the solution of the full nonlinear problem. The developed theory is then applied to an air bubble in a channel of an inkjet printhead. A numerical model is developed to test the predictions of the theoretical analysis. The Rayleigh-Plesset equation is extended to include the influence of the bubble volume oscillations on the acoustic field and vice versa. This modified Rayleigh-Plesset equation is coupled to a channel acoustics calculation and a Navier-Stokes solver for the flow in the nozzle. The numerical simulations indeed confirm the predictions of the theoretical analysis.

The natural frequencies of microbubble oscillation in elastic vessels

A theoretical model for the dynamics of a bubble in an elastic blood vessel is applied to study numerically the effect of confinement on the free oscillations of a bubble. The vessel wall deformations are described using a lumped-parameter membrane-type model, which is coupled to the Navier-Stokes equations for the fluid motion inside the vessel. It is shown that the bubble oscillations in a finite-length vessel are characterized by a spectrum of frequencies, with distinguishable high-frequency and low-frequency modes. The frequency of the high-frequency mode increases with the vessel elastic modulus and, for a thin-wall vessel, can be higher than the natural frequency of bubble oscillations in an unconfined liquid. In the limiting case of an infinitely stiff vessel wall, the frequency of the low-frequency mode approaches the well-known solution for a bubble confined in a rigid vessel. In order to interpret the results, a simple two-degree-of-freedom model is applied. The results suggest that in order to maximize deposition of acoustic energy, a bubble confined in a long elastic vessel has to be excited at frequencies higher than the natural frequency of the equivalent unconfined bubble.

Acoustic measurement of bubble size in an inkjet printhead

The volume of a bubble in a piezoinkjet printhead is measured acoustically. The method is based on a numerical model of the investigated system. The piezo not only drives the system but it is also used as a sensor by measuring the current it generates. The numerical model is used to predict this current for a given bubble volume. The inverse problem is to infer the bubble volume from an experimentally obtained piezocurrent. By solving this inverse problem, the size and position of the bubble can thus be measured acoustically. The method is experimentally validated with an inkjet printhead that is augmented with a glass connection channel, through which the bubble was observed optically, while at the same time the piezocurrent was measured. The results from the acoustical measurement method correspond closely to the results from the optical measurement.

Linear behavior of a preformed microbubble containing light absorbing nanoparticles: insight from a mathematical model

Microbubbles are used as ultrasonic contrast agents in medical imaging because of their highly efficient scattering properties. Gold nanoparticles absorb specific wavelengths of optical radiation very effectively with the subsequent generation of thermo-acoustic waves in the surrounding medium. A theoretical and numerical analysis of the possibility of inducing radial oscillations in a pre-existing spherical microbubble, through the laser excitation of gold nanoparticles contained within, is presented. A description of such a system can be obtained in terms of a confined two-phase model, with the nanoparticles suspended in a confined region of gas, surrounded by a liquid. The Rayleigh-Plesset equation is assumed to be valid at the boundary between the gas and the liquid. The confined two-phase model is solved in linear approximation. The system is diagonalized and the general solution is obtained. This solution is in the form of exponentially decaying oscillatory functions for the temperature and pressure inside the bubble, and radial oscillations of the bubble boundary. It was found that, for the right size of bubbles, the oscillatory behavior takes place in the low megahertz range, which is ideal for medical applications. This study suggests the possibility of new applications of microbubbles in photoacoustic imaging.

Microbubble-size dependence of focused ultrasound-induced blood-brain barrier opening in mice in vivo

The therapeutic efficacy of neurological agents is severely limited, because large compounds do not cross the blood-brain barrier (BBB). Focused ultrasound (FUS) sonication in the presence of microbubbles has been shown to temporarily open the BBB, allowing systemically administered agents into the brain. Until now, polydispersed microbubbles (1-10 microm in diameter) were used, and, therefore, the bubble sizes better suited for inducing the opening remain unknown. Here, the FUS-induced BBB opening dependence on microbubble size is investigated. Bubbles at 1-2 and 4-5 microm in diameter were separately size-isolated using differential centrifugation before being systemically administered in mice (n = 28). The BBB opening pressure threshold was identified by varying the peak-rarefactional pressure amplitude. BBB opening was determined by fluorescence enhancement due to systemically administered, fluorescent-tagged, 3-kDa dextran. The identified threshold fell between 0.30 and 0.46 MPa in the case of 1-2 microm bubbles and between 0.15 and 0.30 MPa in the 4-5 microm case. At every pressure studied, the fluorescence was greater with the 4-5 mum than with the 1-2 microm bubbles. At 0.61 MPa, in the 1-2 microm bubble case, the fluorescence amount and area were greater in the thalamus than in the hippocampus. In conclusion, it was determined that the FUS-induced BBB opening was dependent on both the size distribution in the injected microbubble volume and the brain region targeted.

Blood-brain barrier (BBB) disruption using a diagnostic ultrasound scanner and Definity in Mice

The objective of this work was to determine whether diagnostic ultrasound and contrast agent could be used to transcranially and nondestructively disrupt the blood-brain barrier (BBB) in mice under ultrasound image guidance and to quantify that disruption using magnetic resonance imaging (MRI) and magnetic resonance (MR) contrast agent. Each mouse was placed under isoflurane anesthesia and the hair on top of its skull was removed before treatment. A diagnostic ultrasound transducer was placed in a water bag coupled with gel on the mouse skull. Definity (ultrasound [US] contrast) and Magnevist (MR contrast) were injected concurrent with the start of a custom ultrasound transmission sequence. The transducer was translated along the rostral-caudal axis to insonify three spatial locations (2mm apart) along one half of the brain for each sequence. T1-weighted MR images were used to quantify the volume of tissue over which the BBB disruption allowed Magnevist to enter the brain, based upon increases in MR contrast-to-noise ratio (CNR) compared with the noninsonified portions of the brain. Ultrasonic frequency, pressure and pulse duration, as well as Definity dose and injection time were varied. Preliminary results suggest that a threshold exists for BBB opening dependent upon both pressure and pulse duration (consistent with reports in the literature performed at lower frequencies). A range of typical diagnostic frequencies (e.g., 5.0-8.0 MHz) generated BBB disruption. Comparable BBB opening was noted with varied delays between Definity injection and insonification (0-2 min) for a range of Definity concentrations (400-2400 microL/kg). The low-pressure, custom sequences (mechanical index [MI]< or =0.65) had minimal blood cell extravasation as determined by histologic evaluation. This study has shown the ability of a diagnostic ultrasound system, in conjunction with Definity, to open the BBB transcranially in a mouse model for molecules approximately 0.5 kDa in size. Opening was achieved at higher frequencies than previously reported and was localized under ultrasound image guidance. A typical, ultrasound imaging mode (pulsed wave [PW] Doppler) with specific settings (transmit frequency=5.7 MHz, gate size=15 mm, pulse repetition frequency=100 Hz, system power=15%) successfully opened the BBB, which facilitates implementation using the most of commercially available clinical diagnostic scanners. Localized opening of the BBB may have potential clinical utility for the delivery of diagnostic or therapeutic agents to the brain.

Ultrasound contrast microbubbles in imaging and therapy: physical principles and engineering

Microbubble contrast agents and the associated imaging systems have developed over the past 25 years, originating with manually-agitated fluids introduced for intra-coronary injection. Over this period, stabilizing shells and low diffusivity gas materials have been incorporated in microbubbles, extending stability in vitro and in vivo. Simultaneously, the interaction of these small gas bubbles with ultrasonic waves has been extensively studied, resulting in models for oscillation and increasingly sophisticated imaging strategies. Early studies recognized that echoes from microbubbles contained frequencies that are multiples of the microbubble resonance frequency. Although individual microbubble contrast agents cannot be resolved-given that their diameter is on the order of microns-nonlinear echoes from these agents are used to map regions of perfused tissue and to estimate the local microvascular flow rate. Such strategies overcome a fundamental limitation of previous ultrasound blood flow strategies; the previous Doppler-based strategies are insensitive to capillary flow. Further, the insonation of resonant bubbles results in interesting physical phenomena that have been widely studied for use in drug and gene delivery. Ultrasound pressure can enhance gas diffusion, rapidly fragment the agent into a set of smaller bubbles or displace the microbubble to a blood vessel wall. Insonation of a microbubble can also produce liquid jets and local shear stress that alter biological membranes and facilitate transport. In this review, we focus on the physical aspects of these agents, exploring microbubble imaging modes, models for microbubble oscillation and the interaction of the microbubble with the endothelium.

Progress and problems in the application of focused ultrasound for blood-brain barrier disruption

Advances in neuroscience have resulted in the development of new diagnostic and therapeutic agents for potential use in the central nervous system (CNS). However, the ability to deliver the majority of these agents to the brain is limited by the blood-brain barrier (BBB), a specialized structure of the blood vessel wall that hampers transport and diffusion from the blood to the brain. Many CNS disorders could be treated with drugs, enzymes, genes, or large-molecule biotechnological products such as recombinant proteins, if they could cross the BBB. This article reviews the problems of the BBB presence in treating the vast majority of CNS diseases and the efforts to circumvent the BBB through the design of new drugs and the development of more sophisticated delivery methods. Recent advances in the development of noninvasive, targeted drug delivery by MRI-guided ultrasound-induced BBB disruption are also summarized.

Blood-brain barrier disruption induced by focused ultrasound and circulating preformed microbubbles appears to be characterized by the mechanical index

This work investigated the effect of ultrasonic frequency on the threshold for blood-brain barrier (BBB) disruption induced by ultrasound pulses combined with an ultrasound contrast agent. Experiments were performed in rabbits using pulsed sonications at 2.04 MHz with peak pressure amplitudes ranging from 0.3 to 2.3 MPa. BBB disruption was evaluated using contrast-enhanced magnetic resonance imaging. The threshold for BBB disruption was estimated using probit regression. Representative samples with similar amounts of contrast enhancement were examined in light microscopy. Results from these experiments were compared with data from previous studies that used ultrasound frequencies between 0.26 and 1.63 MHz. We found that the BBB disruption threshold (value where the probability for disruption was estimated to be 50%) expressed in terms of the peak negative pressure amplitude increased as a function of the frequency. It appeared to be constant, however, when the exposures were expressed as a function of the mechanical index (peak negative pressure amplitude estimated in situ divided by square root of frequency). Regression of data from all frequencies resulted in an estimated mechanical index threshold of 0.46 (95% confidence intervals: 0.42 to 0.50). Histologic examination of representative samples with similar amounts of blood-brain barrier disruption found that the number of regions containing extravasated red blood cells per unit area was substantially lower on average for lower ultrasound frequencies. This data suggests that the mechanical index is a meaningful metric for ultrasound-induced blood-brain barrier disruption, at least for when other parameters that are not taken into account by the mechanical index are not varied. It also suggests that lower frequency sonication produces less red blood cell extravasation per unit area.

Ultrasound-driven microbubble oscillation and translation within small phantom vessels

The use of ultrasound radiation force to manipulate microbubbles in blood vessels has attracted recent interest as a method to increase the efficiency of ultrasonic molecular imaging and drug delivery. However, recent studies indicate that microbubble oscillation is diminished within small blood vessels, and therefore we investigate microbubble oscillation and translation within 12 microm vessels using high-speed photography. With each 0.1- to 1-MPa ultrasound pulse, microbubbles (radius of 1, 1.5 and 2 microm) within 12 microm tubes translate 5 to 10 times less than those within 200 microm tubes. Application of a pulse train with a high pulse repetition frequency displaces bubbles to the wall of 12- and 200-microm tubes within an interval ( approximately 1 s) that is reasonable for clinical translation. Modeling of coupled oscillation and translation for unconstrained microbubbles, based on a modified Rayleigh-Plesset (RP) and the trajectory equations, is compared with experimental observations and demonstrates agreement for the larger displacements observed within the 200 microm tubes. This study has implications for contrast-assisted ultrasound applications, aiding the manipulation of targeted microbubbles and for further theoretical understanding of the complex bubble dynamics within constrained vessel.

Cavitation threshold of microbubbles in gel tunnels by focused ultrasound

The investigation of inertial cavitation in micro-tunnels has significant implications for the development of therapeutic applications of ultrasound such as ultrasound-mediated drug and gene delivery. The threshold for inertial cavitation was investigated using a passive cavitation detector with a center frequency of 1 MHz. Micro-tunnels of various diameters (90 to 800 microm) embedded in gel were fabricated and injected with a solution of Optison(trade mark) contrast agent of concentrations 1.2% and 0.2% diluted in water. An ultrasound pulse of duration 500 ms and center frequency 1.736 MHz was used to insonate the microbubbles. The acoustic pressure was increased at 1-s intervals until broadband noise emission was detected. The pressure threshold at which broadband noise emission was observed was found to be dependent on the diameter of the micro-tunnels, with an average increase of 1.2 to 1.5 between the smallest and the largest tunnels, depending on the microbubble concentration. The evaluation of inertial cavitation in gel tunnels rather than tubes provides a novel opportunity to investigate microbubble collapse in a situation that simulates in vivo blood vessels better than tubes with solid walls do.

The natural frequency of nonlinear oscillation of ultrasound contrast agents in microvessels

Ultrasound contrast agents (UCAs) are under intensive investigation for their applications in physiological and molecular imaging and drug delivery. Prediction of the natural frequency of the oscillation of UCAs in microvessels has drawn increasing attention. To our knowledge, the existing models to predict the natural frequency of oscillation of UCAs in microvessels all apply the linear approximation and treat the blood vessel wall as a rigid boundary. In the potential applications of ultrasound imaging drug and gene delivery, the compliance of small vessels may play an important role in the bubble's oscillation. The goal of this work is to provide a lumped-parameter model to study the natural frequency of nonlinear oscillation of UCAs in microvessels. Three types of the blood vessel conditions have been considered: i.e., rigid vessels, normal compliable vessels and vessels with increasing stiffness that could correspond to tumor vasculature. The corresponding bubble oscillation frequencies in vessels with a radius less than 100 microm are examined in detail. When a bubble with a radius of 4 microm is confined in a compliable vessel (inner radius 5 microm and length 100 microm), the natural frequency of bubble oscillation increases by a factor of 1.7 compared with a bubble in an unbounded field. The natural frequency of oscillation of a bubble in a compliable vessel increases with decreasing vessel size while decreasing with increasing values of vessel rigidity. This model suggests that contrast agent size, blood vessel size distribution and the type of vasculature should comprehensively be considered for choosing the transmitted frequency in ultrasound contrast imaging and drug delivery.

Acoustic response of compliable microvessels containing ultrasound contrast agents

The existing models of the dynamics of ultrasound contrast agents (UCAs) have largely been focused on an UCA surrounded by an infinite liquid. Preliminary investigations of a microbubble's oscillation in a rigid tube have been performed using linear perturbation, under the assumption that the tube diameter is significantly larger than the UCA diameter. In the potential application of drug and gene delivery, it may be desirable to fragment the agent shell within small blood vessels and in some cases to rupture the vessel wall, releasing drugs and genes at the site. The effect of a compliant small blood vessel on the UCA's oscillation and the microvessel's acoustic response are unknown. The aim of this work is to propose a lumped-parameter model to study the interaction of a microbubble oscillation and compliable microvessels. Numerical results demonstrate that in the presence of UCAs, the transmural pressure through the blood vessel substantially increases and thus the vascular permeability is predicted to be enhanced. For a microbubble within an 8 to 40 microm vessel with a peak negative pressure of 0.1 MPa and a centre frequency of 1 MHz, small changes in the microbubble oscillation frequency and maximum diameter are observed. When the ultrasound pressure increases, strong nonlinear oscillation occurs, with an increased circumferential stress on the vessel. For a compliable vessel with a diameter equal to or greater than 8 microm, 0.2 MPa PNP at 1 MHz is predicted to be sufficient for microbubble fragmentation regardless of the vessel diameter; however, for a rigid vessel 0.5 MPa PNP at 1 MHz may not be sufficient to fragment the bubbles. For a centre frequency of 1 MHz, a peak negative pressure of 0.5 MPa is predicted to be sufficient to exceed the stress threshold for vascular rupture in a small (diameter less than 15 microm) compliant vessel. As the vessel or surrounding tissue becomes more rigid, the UCA oscillation and vessel dilation decrease; however the circumferential stress is predicted to increase. Decreasing the vessel size or the centre frequency increases the circumferential stress. For the two frequencies considered in this work, the circumferential stress does not scale as the inverse of the square root of the acoustic frequency va as in the mechanical index, but rather has a stronger frequency dependence, 1/va.

Oscillatory interaction between bubbles and confining microvessels and its implications on clinical vascular injuries of shock-wave lithotripsy

This paper presents a detailed study of the oscillation characteristics of a bubble confined inside a deformable microvessel, whose size is comparable with the bubble size. The vessel's compliance is characterized by a nonlinear relation between the intraluminal pressure and the expansion ratio of the vessel radius, which represents the variation of the vessel stiffness with the pressure of the filling liquid. In this analysis, an initially spherical bubble evolves into an ellipsoid, and the asymmetric oscillation appears immediately after the driving pressure is applied and magnifies with oscillation cycles. Compared with the symmetric oscillation in an unconstrained environment, the vessel constraint makes the bubble contract significantly more and subsequently expand in a more violent rebound, inducing substantially larger peaks of the intraluminal pressure exerted on the vessel wall. A larger initial bubble/vessel radius ratio leads to not only a larger peak but also a higher oscillation frequency of the intraluminal pressure, which are the two most dominating parameters in determining the vessel's failure under cyclic loading. The numerical results have further shown that an increase of the vessel wall stiffness strengthens the asymmetric effect, i.e., a larger peak of the intraluminal pressure with a higher oscillation frequency, and so does a larger pre-existing pressure in the liquid filling the vessel. These findings imply that the asymmetric effect is one of the primary mechanisms for clinical injuries of capillary and small blood vessels and for the higher risk of pediatric and hypertension patients in shock wave lithotripsy.

Bubble pulsations between parallel plates

The dynamic response of an acoustically driven spherical bubble between parallel plates is investigated in the linear approximation. For the case of rigid plates, explicit expressions are provided for the resonance frequency and damping, and the importance of including compressibility of the liquid is discussed. For wide channels, approximate results are presented that account for finite acoustic impedance of the plates.

Targeted disruption of the blood-brain barrier with focused ultrasound: association with cavitation activity

Acoustic emission was monitored during focused ultrasound exposures in conjunction with an ultrasound contrast agent (Optison) in order to determine if cavitation activity is associated with the induction of blood-brain barrier disruption (BBBD). Thirty-four locations were sonicated (frequency: 260 kHz) at targets 10 mm deep in rabbit brain (N = 9). The sonications were applied at peak pressure amplitudes ranging from 0.11 to 0.57 MPa (burst length: 10 ms; repetition frequency of 1 Hz; duration: 20 s). Acoustic emission was recorded with a focused passive cavitation detector. This emission was recorded at each location during sonications with and without Optison. Detectable wideband acoustic emission was observed only at 0.40 and 0.57 MPa. BBBD was observed in contrast MRI after sonication at 0.29-0.57 MPa. The appearance of small regions of extravasated erythrocytes appeared to be associated with this wideband emission signal. The results thus suggest that BBBD resulting from focused ultrasound pulses in the presence of Optison can occur without indicators for inertial cavitation in vivo, wideband emission and extravasation. If inertial cavitation is not responsible for the BBBD, other ultrasound/microbubble interactions are likely the source. A significant increase in the emission signal due to Optison at the second and third harmonics of the ultrasound driving frequency was found to correlate with BBBD and might be useful as an online method to indicate when the disruption occurs.

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 microm 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.