The role of primary and secondary delays in the effective resonance frequency of acoustically interacting microbubbles

Suppressing the jet formation in a bubble pair excited with an ultrasonic pulse

This study numerically explores the suppression of bubble jet formation in oscillating microbubble pairs under excitation with an ultrasonic pulse, focusing on the conditions that lead to bubble collapse without jetting. Bubble jets (i.e., liquid jets penetrating the bubble) are typically observed in collapsing bubble pairs. However, jet formation can be avoided when the distance between the bubbles is kept within a specific range. We investigate identical-sized bubble pairs aligned along an axis and subjected to a single-cycle ultrasound pulse. Simulations are conducted using the axisymmetric assumption with the ALPACA compressible multiphase flow solver. Our findings revealed that the domain where jet formation is suppressed becomes smaller as the bubble compression increases. This is demonstrated by decreasing the bubble size and the excitation frequency, which allows for greater bubble growth. These results indicate that while jet suppression is feasible for bubble pairs with high compression ratios, it becomes increasingly sensitive to distance.

The effect of micro-vessel viscosity on the resonance response of a two-microbubble system

Clinical ultrasound contrast agent microbubbles remain intravascular and are between 1-8 µm in diameter, with a volume-weighted mean size of 2-3 µm. Despite their worldwide clinical utility as a diagnostic contrast agent, and their continued and ongoing success as a local therapeutic vector, the fundamental interplay between microbubbles - including bubble-bubble interaction and the effects of a neighboring viscoelastic vessel wall, remain poorly understood. In this work, we developed a finite element model to study the physics of the complex system of two different-sized bubbles (2 and 3 µm in diameter) confined within a viscoelastic vessel from a resonance response perspective (3-12 MHz). Here, we focus on the effect of micro-vessel wall viscosity on the resulting vibrational activity of the two-bubble system. The larger bubble (3 µm) was not influenced by its smaller companion bubble, and we observed a significant dampening effect across all transmit frequencies when confined within the vessel of increasing viscosity, an expected result. However, the smaller bubble (2 µm) was highly influenced by its larger neighboring bubble, including the induction of a strong low-frequency resonant response - resulting in transmit frequency windows in which its response in a lightly damped vessel far exceeded its vibration amplitude when unconfined. Further, micro-vessel wall dynamics closely mimic the frequency-dependence of the adjacent bubbles. Our findings imply that for a system of multi-bubbles within a viscoelastic vessel, the larger bubble physics dominates the system by inducing the smaller bubble and the vessel wall to follow its vibration - an effect that can be amplified within a lightly damped vessel. These findings have important implications for contrast-enhanced ultrasound imaging and therapeutic applications.

Linear pressure waves in mono- and poly-disperse bubbly liquids: Attenuation and propagation speed in slow and fast and evanescent modes

Using volumetric averaged equations from a two-fluid model, this study theoretically investigates linear pressure wave propagation in a quiescent liquid with many spherical gas bubbles. The speed and attenuation of sound are evaluated using the derived linear dispersion. Mono- and poly-disperse bubbly liquids are treated. To precisely describe the attenuation effect, some forms of bubble dynamics equations and temperature gradient models are employed. Focusing on the dissipative effect, we analyze the stop band that occurs in the linear dispersion relation. In the two-fluid model, even if the dissipation effect is considered, the inconvenience that the wavenumber diverges to infinity in the resonance frequency cannot be resolved. Additionally, the validity of terminating that wavenumber value in the middle of the frequency is demonstrated. To determine a linear dispersion relation that can exactly predict thermal conduction and acoustic radiation, wave propagation velocities and attenuation coefficients are compared with some experimental data and existing models. The results show that thermal conduction and acoustic radiation should be set appropriately to accurately predict the propagation velocity and attenuation except in the high frequency range, the phase velocity in the resonance frequency range, or the attenuation in the high frequency range.

Experimental investigation on the effect of concentration on the resonance frequency of lipid coated ultrasonically excited microbubbles

This study presents an experimental investigation of the influence of MB concentration on the resonance frequency of lipid-coated microbubbles (MBs). Expanding on theoretical models and numerical simulations from previous research, this work experimentally investigates the effect of MB size on the rate of resonance frequency increase with concentration, a phenomenon observed across MBs with two different lipid compositions: propylene glycol (PG) and propylene glycol and glycerol (PGG). Employing a custom-designed ultrasound attenuation measurement setup, we measured the frequency-dependent attenuation of MBs, isolating MBs based on size to generate distinct monodisperse sub-populations for analysis. The resonance frequency of MBs was determined by identifying the attenuation peak in the broadband attenuation ultrasound attenuation measurements. Our experimental findings confirm that larger MBs (≈2.1μm) demonstrate a more significant shift in resonance frequency (≈ 5 MHz, ≈ 40%) as a function of MB concentration. In contrast, smaller MBs (≈1.3μm) show a minor shift in the resonant frequency (≈ 1.8 MHz, ≈ 8%), underlining the importance of size in determining acoustic behavior compared to changes in the lipid shell properties. Additionally, we observed that resonance frequency increase with concentration reaching a saturation point at higher concentrations. This plateau occurs at higher concentrations for larger MBs (≈2.1μm), while smaller MBs (≈1.6μm and ≈1.3μm) reach this saturation point at lower concentrations. Furthermore, the study highlights the small effect of bubble-bubble interactions on the resonance frequency of MB populations, particularly at lower MB concentrations and for smaller MBs. This insight is important for applications utilizing MB clusters, such as contrast-enhanced ultrasound imaging and MB-mediated therapies. While both size and lipid shell composition influence resonance frequency, MB size has a more significant effect. In conclusion, our findings affirm the need to consider both MB size and concentration when utilizing MBs for clinical and industrial ultrasonic applications.

Nanobubble Contrast Enhanced Ultrasound Imaging: A Review

Contrast-enhanced ultrasound is currently used worldwide with clinical indications in cardiology and radiology, and it continues to evolve and develop through innovative technological advancements. Clinically utilized contrast agents for ultrasound consist of hydrophobic gas microbubbles stabilized with a biocompatible shell. These agents are used commonly in echocardiography, with emerging applications in cancer diagnosis and therapy. Microbubbles are a blood pool agent with diameters between 1 and 10 μm, which precludes their use in other extravascular applications. To expand the potential use of contrast-enhanced ultrasound beyond intravascular applications, sub-micron agents, often called nanobubbles or ultra-fine bubbles, have recently emerged as a promising tool. Combining the principles of ultrasound imaging with the unique properties of nanobubbles (high concentration and small size), recent work has established their imaging potential. Contrast-enhanced ultrasound imaging using these agents continues to gain traction, with new studies establishing novel imaging applications. We highlight the recent achievements in nonlinear nanobubble contrast imaging, including a discussion on nanobubble formulations and their acoustic characteristics. Ultrasound imaging with nanobubbles is still in its early stages, but it has shown great potential in preclinical research and animal studies. We highlight unexplored areas of research where the capabilities of nanobubbles may offer new advantages. As technology advances, this technique may find applications in various areas of medicine, including cancer detection and treatment, cardiovascular imaging, and drug delivery.

Numerical investigation of the effect of bubble properties on the linear resonance frequency shift due to inter-bubble interactions in ultrasonically excited lipid coated microbubbles

Ultrasonically excited microbubbles (MBs) have numerous applications in various fields, such as drug delivery, and imaging. Ultrasonically excited MBs are known to be nonlinear oscillators that generate secondary acoustic emissions in the media when excited by a primary ultrasound wave. The propagation of acoustic waves in the liquid is limited to the speed of sound, resulting in each MB receiving the primary and secondary waves at different times depending on their distance from the ultrasound source and the distance between MBs. These delays are referred to as primary and secondary delays, respectively. A previous study demonstrated that the inclusion of secondary delays in a model describing the interactions between MBs exposed to ultrasound results in an increase in the linear resonance frequency of MBs as they approach each other. This work investigates the impact of various MB properties on the change in linear resonance frequency resulting from changes in inter-bubble distances. The effects of shell properties, including the initial surface tension, surface dilatational viscosity of the shell monolayer, elastic compression modulus of the shell, and the initial radius of the MBs, are examined. MB size is a significant factor influencing the rate of linear resonance frequency increase with increasing concentration. Moreover, it is found that the shell properties of MBs play a negligible role in the rate of change in linear resonance frequency of MBs as the inter-bubble distances change.The findings of this study have implications for various applications of MBs in the biomedical field. By understanding the impact of inter-bubble distances and shell properties on the linear resonance frequency of MBs, the utilization of MBs in applications reliant on their resonant behavior can be optimized.

Subharmonic resonance of phospholipid coated ultrasound contrast agent microbubbles

Phospholipid encapsulated ultrasound contrast agents have proven to be a powerful addition in diagnostic imaging and show emerging applications in targeted therapy due to their resonant and nonlinear scattering. Microbubble response is affected by their intrinsic (e.g. bubble size, encapsulation physics) and extrinsic (e.g. boundaries) factors. One of the major intrinsic factors at play affecting microbubble vibration dynamics is the initial phospholipid packing of the lipid encapsulation. Here, we examine how the initial phospholipid packing affects the subharmonic response of either individual or a system of two closely-placed microbubbles. We employ a finite element model to investigate the change in subharmonic resonance under 'small' and 'large' radial excursions. For microbubbles ranging between 1.5 and 2.5 µm in diameter and in its elastic state (σ0 = 0.01 N/m), we demonstrate up to a 10 % shift towards lower frequencies in the peak subharmonic response as the radial excursion increases. However, for a bubble initially in its buckled state (σ0 = 0 N/m), we observe a maximum shift of 8 % towards higher frequencies as the radial excursion increases over the same range of bubble sizes - the opposite trend. We studied the same scenario for a system of two individual microbubbles for which we saw similar results. For microbubbles that are initially in their elastic state, in both cases of a) two identically sized bubbles and b) a bubble in proximity to a smaller bubble, we observed a 6 % and 9 % shift towards lower frequencies respectively; while in the case of a neighboring larger bubble no change in subharmonic resonance frequency was observed. Microbubbles that are initially in a buckled state exert no change, 5 % and 19 % shift towards higher frequencies, in two-bubble systems consisting of a) same-size, b) smaller, and c) larger neighboring bubble respectively. Furthermore, we examined the effect of two adjacent bubbles with non-equal initial phospholipid states. The results presented here have important implications in ultrasound contrast agent applications.

Microbubbles for human diagnosis and therapy

Microbubbles (MBs) were observed for the first time in vivo as a curious consequence of quick saline injection during ultrasound (US) imaging of the aortic root, more than 50 years ago. From this serendipitous event, MBs are now widely used as contrast enhancers for US imaging. Their intrinsic properties described in this review, allow a multitude of designs, from shell to gas composition but also from grafting targeting agents to drug payload encapsulation. Indeed, the versatile MBs are deeply studied for their dual potential in imaging and therapy. As presented in this paper, new generations of MBs now opens perspectives for targeted molecular imaging along with the development of new US imaging systems. This review also presents an overview of the different therapeutic strategies with US and MBs for cancer, cardiovascular diseases, and inflammation. The overall aim is to overlap those fields in order to find similarities in the MBs application for treatment enhancement associated with US. To conclude, this review explores the new scales of MBs technologies with nanobubbles development, and along concurrent advances in the US imaging field. This review ends by discussing perspectives for the booming future uses of MBs.

Resonance behaviors of encapsulated microbubbles oscillating nonlinearly with ultrasonic excitation

The resonance behaviors of a few lipid-coated microbubbles acoustically activated in viscoelastic media were comprehensively examined via radius response analysis. The size polydispersity and random spatial distribution of the interacting microbubbles, the rheological properties of the lipid shell and the viscoelasticity of the surrounding medium were considered simultaneously. The obtained radius response curves present a successive occurrence of linear resonances, nonlinear harmonic and sub-harmonic resonances with the acoustic pressure increasing. The microbubble resonance is radius-, pressure- and frequency-dependent. Specifically, the maximum bubble expansion ratio at the main resonance peak increases but the resonant radius decreases as the ultrasound pressure increases, while both of them decrease with the ultrasound frequency increasing. Moreover, compared to an isolated microbubble case, it is found that large microbubbles in close proximity prominently suppress the resonant oscillations while slightly increase the resonant radii for both harmonic and subharmonic resonances, even leading to the disappearance of the subharmonic resonance with the influences increasing to a certain degree. In addition, the results also suggest that both the encapsulating shell and surrounding medium can substantially dampen the harmonic and subharmonic resonances while increase the resonant radii, which seem to be affected by the medium viscoelasticity to a greater degree rather than the shell properties. This work offers valuable insights into the resonance behaviors of microbubbles oscillating in viscoelastic biological media, greatly contributing to further optimizing their biomedical applications.

The influence of inter-bubble spacing on the resonance response of ultrasound contrast agent microbubbles

Ultrasound-driven microbubbles, typically between 1 and 8 µm in diameter, are resonant scatterers that are employed as diagnostic contrast agents and emerging as potentiators of targeted therapies. Microbubbles are administered in populations whereby their radial dynamics - key to their effectiveness - are greatly affected by intrinsic (e.g. bubble size) and extrinsic (e.g. boundaries) factors. In this work, we aim to understand how two neighbouring microbubbles influence each other. We developed a finite element model of a system of two individual phospholipid-encapsulated microbubbles vibrating in proximity to each other to study the effect of inter-bubble distance on microbubble radial resonance response. For the case of two equal-sized and identical bubbles, each bubble exhibits a decrease between 7 and 10% in the frequency of maximum response (f_MR) and an increase in amplitude of maximum response (A_MR) by 9-11% as compared to its isolated response in free-space, depending on the bubble size examined. For a system of two unequal-sized microbubbles, the large bubble shows no significant change, however the smaller microbubble shows an increase in f_MR by 7-11% and a significant decrease in A_MR by 38-52%. Furthermore, in very close proximity the small bubble shows a secondary off-resonance peak at the corresponding f_MR of its larger companion microbubble. Our work suggests that frequency-dependent microbubble response is greatly affected by the presence of another bubble, which has implications in both imaging and therapy applications. Furthermore, our work suggests a mechanism by which nanobubbles show significant off-resonance vibrations in the clinical frequency range, a behaviour that has been observed experimentally but heretofore unexplained.