Experimental evidence of nonlinear mode coupling between spherical and nonspherical oscillations of microbubbles

Paganella L, Narciso ML, Supponen O. Cyclic jetting enables microbubble-mediated drug delivery

The pursuit of targeted therapies capable of overcoming biological barriers, including the blood-brain barrier, has spurred the investigation of stimuli-responsive microagents that can improve therapeutic efficacy and reduce undesirable side effects. Intravenously administered, ultrasound-responsive microbubbles are promising agents with demonstrated potential in clinical trials, but the mechanism underlying drug absorption remains unclear. Here we show that ultrasound-driven single microbubbles puncture the cell membrane and induce drug uptake through stable cyclic microjets. Our theoretical models successfully reproduce the observed bubble and cell dynamic responses. We find that cyclic jets arise from shape instabilities, as opposed to classical inertial jets that are driven by pressure gradients, enabling microjet formation at mild ultrasound pressures below 100 kPa. We also establish a threshold for bubble radial expansion beyond which microjets form and facilitate cellular permeation and show that the stress generated by microjetting outperforms previously suggested mechanisms by at least an order of magnitude. Overall, this work elucidates the physics behind microbubble-mediated targeted drug delivery and provides the criteria for its effective and safe application.

Mass and heat transfer in audible sound driven bubbles

Most research on sonoluminescence and sonochemistry has been conducted at acoustic frequencies above ∼20 kHz. Consequently, mathematical models for the dynamics of acoustically-driven bubbles have hardly been examined in the audible frequency spectrum. Here, we develop a new hybrid modelling approach that combines the rigour of the advection-diffusion model whilst retaining the simplicity of a reduced-order boundary layer model to predict phase-change, mass and heat transfer in an inertially collapsing bubble excited by audible sound. Differences in these approaches are explored through a thorough validation against experimental data obtained from ultra-high speed videos of bubble dynamics at 17.8 kHz. Our results indicate that, while the boundary layer model agrees well with the advection-diffusion model at high driving frequencies, there are significant deviations at lower frequencies, where the boundary layer model overpredicts parameters such as bubble size and quantity of trapped vapour while underpredicting others such as temperature and pressure. These deviations at lower frequencies is caused by an inaccurate estimation of the boundary layer thickness originating from the time-scale competition between diffusion and fast bubble wall motion. Our work questions the suitability of existing reduced-order models developed for ultrasonic frequencies when applied to the audible range, reinforcing that further research in the audible range is needed.

Ultrasound-activated microbubbles mediate F-actin disruptions and endothelial gap formation during sonoporation

Locally opening up the endothelial barrier in a safe and controlled way is beneficial for drug delivery into the extravascular tissue. Although ultrasound-induced microbubble oscillations can affect the endothelial barrier integrity, the mechanism remains unknown. Here we uncover a new role for F-actin in microbubble-mediated endothelial gap formation. Unique simultaneous high-resolution confocal microscopy and ultra-high-speed camera imaging (10 million frames per second) reveal that single oscillating microbubbles (radius 1.3-3.8 μm; n = 48) induce sonoporation in all cells in which F-actin remodeling occurred. F-actin disruption only mainly resulted in tunnel formation (75 %), while F-actin stress fiber severing and recoil mainly resulted in cell-cell contact opening within 15 s upon treatment (54 %) and tunnel formation (15 %). F-actin stress fiber severing occurred when the fibers were within reach of the microbubble's maximum radius during oscillation, requiring normal forces of ≥230 nN. In the absence of F-actin stress fibers, oscillating microbubbles induced F-actin remodeling but no cell-cell contact opening. Together, these findings reveal a novel mechanism of microbubble-mediated transendothelial drug delivery, which associates with the underlying cytoskeletal F-actin organization.

Parametrically excited shape distortion of a submillimeter bubble

The existence of finite amplitude shape distortion caused by parametrically excited surface instabilities for a gas bubble in water driven by a temporally periodic, spatially uniform pressure field in an axisymmetric geometry is investigated. Employing a nonlinear coupled system of equations which includes shape mode interactions to third order, the resultant spherical oscillations, translation, and shape distortion of the bubble are modelled, placing no restriction on the size of the spherical oscillations. The model accounts for viscous and thermal damping with compressibility effects. The existence of synchronous and higher order parametrically induced sustained, finite amplitude, periodic shape deformation is demonstrated. The excitement of an odd shape mode via the synchronous mechanism is shown to give rise to linear bubble self-propulsion. For larger driving amplitudes, it is shown that more than one shape mode can be parametrically excited at the same driving frequency but by different resonance mechanisms, leading to more involved shape deformation and the increased possibility of bubble self-propulsion.

Self-propulsion of a periodically forced shape-deforming submillimeter gas bubble

The self-propulsion (translational instability) of a gas bubble in a liquid undergoing parametrically induced axisymmetric shape distortion due to being forced by a temporally sinusoidal, spatially constant acoustic field is investigated. Employing a model which accounts for the nonlinear coupling between the spherical oscillations, the axial translation and shape deformation of the bubble, the parametric excitement of two neighboring shape modes by the fundamental resonance, at the same driving frequency is studied. It is shown that provided pertinent driving pressure threshold values are exceeded, the respective shape modes are excited on different timescales. The growth of the shape mode on the faster timescale saturates giving rise to sustained constant amplitude oscillations, while the growth of the shape mode on the slower timescale is both modulated and unbounded. During the growth of the second shape mode, growing, oscillatory bubble translation is also observed.

Nonspherical oscillations of an encapsulated microbubble with interface energy under the acoustic field

Spherical instability in acoustically driven encapsulated microbubbles (EBs) suspended in a fluid can trigger nonspherical oscillations within them. We apply the interface energy model [N. Dash and G. Tamadapu, J. Fluid Mech. 932, A26 (2022b)] to investigate nonspherical oscillations of smaller radius microbubbles encapsulated with a viscoelastic shell membrane under acoustic field. Using the Lagrangian energy formulation, coupled governing equations for spherical and nonspherical modes are derived, incorporating interface energy effects, shell elasticity, and viscosity. Numerical simulations of governing equations revealed that the parametrically forced even mode excites even modes, while the odd modes excite both even and odd modes. The model demonstrates that finite amplitude nonspherical oscillations are identifiable in smaller radius EBs only when the interface parameters are introduced into the model; otherwise, they are not. Realizing that nonlinear mode coupling is responsible for saturation of instability resulting in stable nonspherical oscillations, we perform a steady-state and stability analysis using the slow-time equations obtained from Krylov-Bogoliubov perturbation method. Analytical expressions for modal amplitudes and stability thresholds are derived in terms of interface and material parameters. The stability curves are invaluable in determining the precise range of excitation pressure and frequency values required for the EB to exhibit finite amplitude nonspherical oscillations.

Memory-friendly fixed-point iteration method for nonlinear surface mode oscillations of acoustically driven bubbles: from the perspective of high-performance GPU programming

A fixed-point iteration technique is presented to handle the implicit nature of the governing equations of nonlinear surface mode oscillations of acoustically excited microbubbles. The model is adopted from the theoretical work of Shaw [1], where the dynamics of the mean bubble radius and the surface modes are bi-directionally coupled via nonlinear terms. The model comprises a set of second-order ordinary differential equations. It extends the classic Keller-Miksis equation and the linearized dynamical equations for each surface mode. Only the implicit parts (containing the second derivatives) are reevaluated during the iteration process. The performance of the technique is tested at various parameter combinations. The majority of the test cases needs only a single reevaluation to achieve 10-9 error. Although the arithmetic operation count is higher than the Gauss elimination, due to its memory-friendly matrix-free nature, it is a viable alternative for high-performance GPU computations of massive parameter studies.

Coupling Two Ultra-high-Speed Cameras to Elucidate Ultrasound Contrast-Mediated Imaging and Therapy

Ultrasound contrast-mediated medical imaging and therapy both rely on the dynamics of micron- and nanometer-sized ultrasound cavitation nuclei, such as phospholipid-coated microbubbles and phase-change droplets. Ultrasound cavitation nuclei respond non-linearly to ultrasound on a nanosecond time scale that necessitates the use of ultra-high-speed imaging to fully visualize these dynamics in detail. In this study, we developed an ultra-high-speed optical imaging system that can record up to 20 million frames per second (Mfps) by coupling two small-sized, commercially available, 10-Mfps cameras. The timing and reliability of the interleaved cameras needed to achieve 20 Mfps was validated using two synchronized light-emitting diode strobe lights. Once verified, ultrasound-activated microbubble responses were recorded and analyzed. A unique characteristic of this coupled system is its ability to be reconfigured to provide orthogonal observations at 10 Mfps. Acoustic droplet vaporization was imaged from two orthogonal views, by which the 3-D dynamics of the phase transition could be visualized. This optical imaging system provides the temporal resolution and experimental flexibility needed to further elucidate the dynamics of ultrasound cavitation nuclei to potentiate the clinical translation of ultrasound-mediated imaging and therapy developments.

Signatures of microstreaming patterns induced by non-spherically oscillating bubbles

In this study, we report recent theoretical and experimental developments dealing with the axisymmetric flow surrounding non-spherically oscillating microbubbles. A wide variety of microstreaming patterns is revealed using a theoretical modeling providing exact analytical solutions of the second-order mean flows. The streaming pattern is highly dependent on the modal content of the bubble interface oscillation, including possibly spherical, translational, and nonspherical modes, as well as any combination of these modes. Experimental results on fluid flow induced by a single, non-spherically oscillating bubble in an unbounded fluid are presented and successfully compared to the theoretical predictions.

Acoustic microstreaming produced by nonspherical oscillations of a gas bubble. IV. Case of modes n and m

This paper is the conclusion of work done in our previous papers [A. A. Doinikov et al., Phys. Rev. E 100, 033104 (2019)10.1103/PhysRevE.100.033104; Phys. Rev. E 100, 033105 (2019)10.1103/PhysRevE.100.033105]. The overall aim of the study is to develop a theory for modeling the velocity field of acoustic microstreaming produced by nonspherical oscillations of a gas bubble. In our previous papers, general equations were derived to describe the velocity field of acoustic microstreaming produced by modes m and n of bubble oscillations. Particular cases of mode interaction were derived, such as the 0-n, 1-1, 1-m, and n-n interactions. Here the general case of interaction between modes n and m, n>m, is solved analytically. Solutions are expressed in terms of complex mode amplitudes, meaning that the mode amplitudes are assumed to be known and serve as input data for the calculation of the velocity field of microstreaming. No restrictions are imposed on the ratio of the bubble radius to the viscous penetration depth. The n-m interaction results in specific streaming patterns: At large distance from the bubble interface the pattern exhibits 2|n-m| lobes, while 2min(m,n) lobes exist in the bubble vicinity. The spatial organization of the recirculation zones is unique for the interaction of two distinct nonspherical modes and therefore appears as a signature of the n-m interaction.

Nonspherical modes nondegeneracy of a tethered bubble

When excited at sufficiently high acoustic pressures, a wall-attached bubble may exhibit asymmetric nonspherical modes. These vibration modes can be decomposed over the set of spherical harmonics Y_{nm}(θ,ϕ) for a degree n and order m. We experimentally capture the time-resolved dynamics of asymmetric bubble oscillations in a top-view configuration. A spatiotemporal modal analysis is performed and allowed recovering the set of zonal (m=0), tesseral (0<m<n), and sectoral (m=n) spherical harmonics that develop at the bubble interface. The analysis of the surface instability thresholds reveals that the frequencies of asymmetric modes differ from the standard Lamb spectrum. In addition, the nondegeneracy of asymmetric modes for a given degree n is evidenced by noncompletely overlapping resonance bands. Finally, the coexistence between zonal and sectoral modes is analyzed through their modal interaction, amplitude interplay and relation of phase, as well as their geometric compatibility.

Acoustic microstreaming produced by nonspherical oscillations of a gas bubble. III. Case of self-interacting modes n-n

This paper is the continuation of work done in our previous papers [A. A. Doinikov et al., Phys. Rev. E 100, 033104 (2019)2470-004510.1103/PhysRevE.100.033104; Phys. Rev. E 100, 033105 (2019)].2470-004510.1103/PhysRevE.100.033105 The overall aim of the study is to develop a theory for modeling the velocity field of acoustic microstreaming produced by nonspherical oscillations of an acoustically driven gas bubble. In our previous papers, general equations have been derived to describe the velocity field of acoustic microstreaming produced by modes m and n of bubble oscillations. After solving these general equations for some particular cases of modal interactions (cases 0-n, 1-1, and 1-m), in this paper the general equations are solved analytically for the case that acoustic microstreaming results from the self-interaction of an arbitrary surface mode n≥1. Solutions are expressed in terms of complex mode amplitudes, meaning that the mode amplitudes are assumed to be known and serve as input data for the calculation of the velocity field of acoustic microstreaming. No restrictions are imposed on the ratio of the bubble radius to the viscous penetration depth. The self-interaction results in specific streaming patterns: a large-scale cross pattern and small recirculation zones in the vicinity of the bubble interface. Particularly the spatial organization of the recirculation zones is unique for a given surface mode and therefore appears as a signature of the n-n interaction. Experimental streaming patterns related to this interaction are obtained and good agreement is observed with the theoretical model.

Subharmonic spherical bubble oscillations induced by parametric surface modes

A potential source of subharmonic bubble emissions is revealed experimentally by high-speed imaging. When an acoustic bubble is driven at sufficiently large pressure amplitudes, energy transfer from surface to volume oscillations can lead to the triggering of subharmonic spherical oscillations. This experimental evidence is in agreement with recent theoretical modeling of nonspherical bubble dynamics accounting for nonlinear mode coupling. Implications for the monitoring of stable cavitation activity are discussed.

Fragmentation of cavitation bubble in ultrasound field under small pressure amplitude

In the present study, dynamic behavior and fragmentation mechanism of acoustic cavitation bubbles are investigated under relatively small pressure amplitudes of ultrasonic wave through a three-dimensional compressive multiphase flow simulation and experimental observations. It is found that the oscillating bubble takes a non-spherical shape soon after occurring the Rayleigh collapse following the sound pressure distribution around the bubble. Then, the amplitude of non-spherical deformation is enhanced during small high-frequent oscillations after the Rayleigh collapse due to the fluid inertial effect. Finally, the oscillating bubble is fragmented into two smaller ones with the Laplace pressure gradient becoming the final trigger of bubble fragmentation. Besides, the results reveal that the temperature of bubble surface is varied when the non-spherical bubble deformation is large, while during spherical bubble oscillations the surface temperature remains almost unchanged.

Acoustic microstreaming produced by nonspherical oscillations of a gas bubble. I. Case of modes 0 and m

A theory is developed that allows one to model the velocity field of acoustic microstreaming produced by nonspherical oscillations of an acoustically driven gas bubble. It is assumed that some of the bubble oscillation modes are excited parametrically and hence can oscillate at frequencies different from the driving frequency. Analytical solutions are derived in terms of complex amplitudes of oscillation modes, which means that the mode amplitudes are assumed to be known and serve as input data when the velocity field of acoustic microstreaming is calculated. No restrictions are imposed on the ratio of the bubble radius to the viscous penetration depth. The present paper is the first part of our study in which a general theory is developed and then applied to the case that acoustic microstreaming is generated by the interaction of the breathing mode (mode 0) with a mode of arbitrary order m≥1. Examples of numerical simulations and a comparison with experimental results are provided.

A Review of Phospholipid Encapsulated Ultrasound Contrast Agent Microbubble Physics

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

Stability mechanisms of oscillating vapor bubbles in acoustic fields

Vapor bubble instability could enhance the sonochemical activities and accelerate the reaction rate. In the present paper, vapor bubble instability in acoustic fields is investigated through combining both the spherical and stiffness stabilities within a wide range of parameter zone (consisting of bubble radius, acoustic frequency and pressure amplitude) in order to determine the stability states of vapor bubbles. The status of bubble oscillations are divided into four zones in terms of their stability characteristics. Influences of several paramount parameters on the bubble stability are demonstrated in detail. Different orders of spherical instability are quantitatively given together with cases in high-frequency and low-frequency limits. The practical applications of the present work are twofold: identification of the parameter zones with rapid sonochemical reactions; validity of the spherical bubble assumption for simplification of the numerical studies.

Dynamics of nonspherical microbubble oscillations above instability threshold

Time-resolved dynamics of nonspherical oscillations of micrometer-sized bubbles are captured and analyzed using high-speed imaging. The axisymmetry of the bubble shape is ensured with certainty for the first time from the recordings of two synchronous high-speed cameras located at 90^{∘}. The temporal dynamics of finite-amplitude nonspherical oscillations are then analyzed for various acoustic pressures above the instability threshold. The experimental results are compared with recent theories accounting for nonlinearities and mode coupling, highlighting particular effects inherent to these mechanisms (saturation of the instability, triggering of nonparametric shape modes). Finally, the amplitude of the nonspherical oscillations is given as function of the driving pressure both for quadrupolar and octupolar bubbles.