Probing the pressure dependence of sound speed and attenuation in bubbly media: Experimental observations, a theoretical model and numerical calculations.

The problem of attenuation and sound speed of bubbly media has remained partially unsolved. Comprehensive data regarding pressure-dependent changes of the attenuation and sound speed of a bubbly medium are not available. Our theoretical understanding of the problem is limited to linear or semi-linear theoretical models, which are not accurate in the regime of large amplitude bubble oscillations. Here, by controlling the size of the lipid coated bubbles (mean diameter of ≈5.4µm), we report the first time observation and characterization of the simultaneous pressure dependence of sound speed and attenuation in bubbly water below, at and above microbubbles resonance (frequency range between 1-3 MHz). With increasing acoustic pressure (between 12.5-100 kPa), the frequency of the peak attenuation and sound speed decreases while maximum and minimum amplitudes of the sound speed increase. We propose a nonlinear model for the estimation of the pressure dependent sound speed and attenuation with good agreement with the experiments. The model calculations are validated by comparing with the linear and semi-linear models predictions. One of the major challenges of the previously developed models is the significant overestimation of the attenuation at the bubble resonance at higher void fractions (e.g. 0.005). We addressed this problem by incorporating bubble-bubble interactions and comparing the results to experiments. Influence of the bubble-bubble interactions increases with increasing pressure. Within the examined exposure parameters, we numerically show that, even for low void fractions (e.g. 5.1×10-6) with increasing pressure the sound speed may become 4 times higher than the sound speed in the non-bubbly medium.

On the threshold of 1/2 order subharmonic emissions in the oscillations of ultrasonically excited bubbles.

The pressure threshold for 1/2 order subharmonic (SH) emissions and period doubling during the oscillations of ultrasonically excited bubbles is thought to be minimum when the bubble is sonicated with twice its resonance frequency (fr). This estimate is based on studies that simplified or neglected the effects of thermal damping. In this work, the nonlinear dynamics of ultrasonically excited bubbles is investigated accounting for the thermal dissipation. Results are visualized using bifurcation diagrams as a function of pressure. Here we show that, and depending on the gas, the pressure threshold for 1/2 order SHs can be minimum at a frequency between 0.5fr≤f≤0.6fr. In this frequency range, the generation of 1/2 order SHs are due to the occurrence of 5/2 order ultra-harmonic resonance. The stability of such oscillations is size dependent. For an air bubble immersed in water, only bubbles bigger than 1 µm in diameter are able to emit non-destructive SHs in these frequency ranges.

Nonlinear dynamics and bifurcation structure of ultrasonically excited lipid coated microbubbles.

In many applications, microbubbles (MBs) are encapsulated by a lipid coating to increase their stability. However, the complex behavior of the lipid coating including buckling and rupture sophisticates the dynamics of the MBs and as a result the dynamics of the lipid coated MBs (LCMBs) are not well understood. Here, we investigate the nonlinear behavior of the LCMBs by analyzing their bifurcation structure as a function of acoustic pressure. We show that, the LC can enhance the generation of period 2 (P2), P3, higher order subharmonics (SH), superharmonics and chaos at very low excitation pressures (e.g. 1 kPa). For LCMBs sonicated by their SH resonance frequency and in line with experimental observations with increasing pressure, P2 oscillations exhibit three stages: generation at low acoustic pressures, disappearance and re-generation. Within non-destructive oscillation regimes and by pressure amplitude increase, LCMBs can also exhibit two saddle node (SN) bifurcations resulting in possible abrupt enhancement of the scattered pressure. The first SN resembles the pressure dependent resonance phenomenon in uncoated MBs and the second SN resembles the pressure dependent SH resonance. Depending on the initial surface tension of the LCMBs, the nonlinear behavior may also be suppressed for a wide range of excitation pressures.

Nonlinear power loss in the oscillations of coated and uncoated bubbles: Role of thermal, radiation and encapsulating shell damping at various excitation pressures.

This study presents the fundamental equations governing the pressure dependent disipation mechanisms in the oscillations of coated bubbles. A simple generalized model (GM) for coated bubbles accounting for the effect of compressibility of the liquid is presented. The GM was then coupled with nonlinear ODEs that account for the thermal effects. Starting with mass and momentum conservation equations for a bubbly liquid and using the GM, nonlinear pressure dependent terms were derived for power dissipation due to thermal damping (Td), radiation damping (Rd) and dissipation due to the viscosity of liquid (Ld) and coating (Cd). The pressure dependence of the dissipation mechanisms of the coated bubble have been analyzed. The dissipated energies were solved for uncoated and coated 2-20 µm in bubbles over a frequency range of 0.25fr-2.5fr (fr is the bubble resonance) and for various acoustic pressures (1 kPa-300 kPa). Thermal effects were examined for air and C3F8 gas cores. In the case of air bubbles, as pressure increases, the linear thermal model looses accuracy and accurate modeling requires inclusion of the full thermal model. However, for coated C3F8 bubbles of diameter 1-8 µm, which are typically used in medical ultrasound, thermal effects maybe neglected even at higher pressures. For uncoated bubbles, when pressure increases, the contributions of Rd grow faster and become the dominant damping mechanism for pressure dependent resonance frequencies (e.g. fundamental and super harmonic resonances). For coated bubbles, Cd is the strongest damping mechanism. As pressure increases, Rd contributes more to damping compared to Ld and Td. For coated bubbles, the often neglected compressibility of the liquid has a strong effect on the oscillations and should be incorporated in models. We show that the scattering to damping ratio (STDR), a measure of the effectiveness of the bubble as contrast agent, is pressure dependent and can be maximized for specific frequency ranges and pressures.

Critical corrections to models of nonlinear power dissipation of ultrasonically excited bubbles.

Current models for calculating nonlinear power dissipation during the oscillations of acoustically excited bubbles generate non-physical values for the radiation damping (Drd) term for some frequency and pressure regions that include near resonance oscillations. Moreover, the ratio of the dissipated powers significantly deviate from the values that are calculated by the linear model at low amplitude oscillations (acoustic excitation pressure of PA=1 kPa and expansion ratio of <≊1.01). In high amplitude oscillation regimes (Pa⩾20 kPa), the dissipated power due to Drd deviates largely from the dissipated power as calculated by the widely accepted approach that uses the scattered power by the bubbles. We provide critical corrections to the present models. The validity of the results was examined in regimes of low amplitude oscillations and high amplitude oscillations. In the low amplitude regime, the ratio of the dissipated powers as calculated by the current and proposed model were compared with the linear model predictions. At higher amplitude oscillations, the dissipated power by radiation loss as calculated by the current and the proposed models were compared with the dissipated power calculated using the scattered power by the bubbles. We show that non-physical values are absent in the proposed model. Moreover, predictions of the proposed approach are identical to the predictions of the linear model and the dissipated power estimated using the scattered pressure by the bubble. We show that damping due to thermal effects, liquid viscosity and radiation heavily depend on the excitation pressure and that the linear model estimations are not valid even at pressures as low as 20 kPa.

Shrinking microbubbles with microfluidics: mathematical modelling to control microbubble sizes.

Microbubbles have applications in industry and life-sciences. In medicine, small encapsulated bubbles (<10 µm) are desirable because of their utility in drug/oxygen delivery, sonoporation, and ultrasound diagnostics. While there are various techniques for generating microbubbles, microfluidic methods are distinguished due to their precise control and ease-of-fabrication. Nevertheless, sub-10 µm diameter bubble generation using microfluidics remains challenging, and typically requires expensive equipment and cumbersome setups. Recently, our group reported a microfluidic platform that shrinks microbubbles to sub-10 µm diameters. The microfluidic platform utilizes a simple microbubble-generating flow-focusing geometry, integrated with a vacuum shrinkage system, to achieve microbubble sizes that are desirable in medicine, and pave the way to eventual clinical uptake of microfluidically generated microbubbles. A theoretical framework is now needed to relate the size of the microbubbles produced and the system's input parameters. In this manuscript, we characterize microbubbles made with various lipid concentrations flowing in solutions that have different interfacial tensions, and monitor the changes in bubble size along the microfluidic channel under various vacuum pressures. We use the physics governing the shrinkage mechanism to develop a mathematical model that predicts the resulting bubble sizes and elucidates the dominant parameters controlling bubble sizes. The model shows a good agreement with the experimental data, predicting the resulting microbubble sizes under different experimental input conditions. We anticipate that the model will find utility in enabling users of the microfluidic platform to engineer bubbles of specific sizes.

Ultrasound-activated microbubble cancer therapy: ceramide production leading to enhanced radiation effect in vitro.

Blood vessels within tumours represent a key component for cancer cell survival. Disruption of these vessels can be achieved by inducing vascular endothelial-cell apoptosis. Moreover, endothelial cell apoptosis has been proven to be enhanced by ceramide-increasing drugs. Herein, we introduce a novel therapeutic approach which uses ultrasound-stimulated microbubbles used in combination with radiation to cause a rapid accumulation of ceramide in endothelial cells in-vitro. We also test this modality directly with other cell types as a general method of killing cancer cells. Human umbilical vein endothelial cells (HUVEC), acute myeloid leukemia cells (AML), murine fibrosarcoma cells (KHT-C), prostate cancer cells (PC3), breast cancer cells (MDA-MB-231) and astrocytes were used to evaluate this mechanism of inducing cell death. Survival was measured by clonogenic assays, and ceramide content was detected using immunohistochemistry. Exposure of cell types to ultrasound-stimulated bubbles alone resulted in increases in ceramide for all cell types and survivals of 12 ±â€…2%, 65 ±â€…5%, 83 ±â€…2%, 58 ± 4%, 58 ±â€…3%, 18 ±â€…7% for HUVEC, AML, PC3, MDA, KHT-C and astrocyte cells, respectively. Results from selected cell types involving radiation treatments indicated additive treatment enhancements and increases in intracellular ceramide content one hour after exposure to ultrasound-activated microbubbles and radiation. Endothelial cell survival decreased from 8 ±â€…1% after 2 Gy of radiation treatment alone and from 12 ±â€…2% after ultrasound and microbubbles alone, to 1 ±â€…1% with combined treatment. In Asmase +/+ astrocytes, survival decreased from 56 ±â€…2% after 2 Gy radiation alone and from 17 ±â€…7% after ultrasound and microbubbles alone, to 5 ±â€…2% when combined. Using ASMase deficient astrocytes (Asmase -/- ) and Sphingosine-1-phosphate (S1P), we also demonstrate that ultrasound-activated microbubbles stimulate ASMase activity and ceramide production. These findings suggest that ultrasound-stimulated microbubbles could be used as a new biomechanical method to enhance the effects of radiation.

High-frequency subharmonic pulsed-wave Doppler and color flow imaging of microbubble contrast agents.

A recent study has shown the feasibility of subharmonic (SH) flow imaging at a transmit frequency of 20 MHz. This paper builds on these results by examining the performance of SH flow imaging as a function of transmit pressure. Further, we also investigate the feasibility of SH pulsed-wave Doppler (PWD) imaging. In vitro flow experiments were performed with a 1-mm-diameter wall-less vessel cryogel phantom using the ultrasound contrast agent Definity and an imaging frequency of 20 MHz. The phantom results show that there is an identifiable pressure range where accurate flow velocity and power estimates can be made with SH imaging at 10 MHz (SH10), above which velocity estimates are biased by radiation force effects and unstable bubble behavior, and below which velocity and power estimates are degraded by poor SNR. In vivo validation of SH PWD was performed in an arteriole of a rabbit ear, and blood velocity estimates compared well with fundamental (F20) mode PWD. The ability to suppress tissue signals using SH signals may enable the use of higher frame rates and improve sensitivity to microvascular flow or slow velocities near large vessel walls by reducing or eliminating the need for clutter filters.