Angular dependence of the acoustic signal of a microbubble cloud

Passive Acoustic Mapping for Convex Arrays With the Helical Wave Spectrum Method

Passive acoustic mapping (PAM) has emerged as a valuable imaging modality for monitoring the cavitation activity in focused ultrasound therapies. When it comes to imaging in the human abdomen, convex arrays are preferred due to their large acoustic window. However, existing PAM methods for convex arrays rely on the computationally expensive delay-and-sum (DAS) operation limiting the image reconstruction speed when the field-of-view (FOV) is large. In this work, we propose an efficient and frequency-selective PAM method for convex arrays. This method is based on projecting the helical wave spectrum (HWS) between cylindrical surfaces in the imaging field. Both the in silico and in vitro experiments showed that the HWS method has comparable image quality and similar acoustic cavitation source localization accuracy as the DAS-based methods. Compared to the frequency-domain and time-domain DAS methods, the time-complexity of the HWS method is reduced by one order and two orders of magnitude, respectively. A parallel implementation of the HWS method realized millisecond-level image reconstruction speed. We also show that the HWS method is inherently capable of mapping microbubble (MB) cavitation activity of different status, i.e., no cavitation, stable cavitation, or inertial cavitation. After compensating for the lens effects of the convex array, we further combined PAM formed by the HWS method and B-mode imaging as a real-time dual-mode imaging approach to map the anatomical location where MBs cavitate in a liver phantom experiment. This method may find use in applications where convex arrays are required for cavitation activity monitoring in real time.

Bubble pulsation characteristics in multi-bubble systems affected by bubble size polydispersity and spatial structure

This study seeks to explore the bubble pulsation characteristics in multi-bubble environment with a special focus on the influences of the size polydispersity and the two-dimensional structure of bubbles. Three representative configurations of three interacting bubbles are formed by setting the initial radii of cavitation bubbles and inter-bubble distances appropriately, then the pulsation characteristics of a small bubble are investigated and compared by the bifurcation analysis. The results illustrate that the bubble size polydispersity and two-dimensional structure would greatly affect the bubble pulsations (i.e., the amplitude and nonlinearity of pulsations). Furthermore, the effects of two-dimensional structure are strong at a small inter-bubble distance of the large and small bubbles while the bubble size polydispersity always significantly affects the bubble pulsations for all cases. Moreover, the influences of both bubble size polydispersity and two-dimensional structure can be enhanced as the acoustic pressure increases, which can also become stronger when the large bubble is located at the same side as the small bubble and the initial radius of large bubble increases. Additionally, the effects would also be increased when the tissue viscoelasticity varies within a certain range. The present findings shed new light on the dynamics of multiple polydisperse microbubbles in viscoelastic tissues, potentially contributing to an optimization of their applications with ultrasound excitation.

Theoretical prediction of the scattering of spherical bubble clusters under ultrasonic excitation

Due to the nonlinear vibration of ultrasound contrast agent bubbles, a nonlinear scattered sound field will be generated when bubbles are driven by ultrasound. A bubble cluster consists of numerous bubbles gathering in a spherical space. It has been noted that the forward scattering of a bubble cluster is larger than its backscattering, and some studies have experimentally found the angular dependence of a bubble cluster's scattering signal. In this paper, a theory is proposed to explain the difference of acoustic scattering at different directions of a bubble cluster when it is driven by ultrasound, and predicts the angular distribution of scattered acoustic pressure under different parameters. The theory is proved to be correct under circumstances of small clusters and weak interactions by comparing theoretical results with numerical simulations. This theory not only sheds light on the physics of bubble cluster scattering, but also may contribute to the improvement of ultrasound imaging technology, including ultrasonic harmonic imaging and contrast-enhanced ultrasonography.

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

Acoustically excited microbubbles (MBs) are known to be nonlinear oscillators with complex dynamics. This has enabled their use in a wide range of applications from medicine to industry and underwater acoustics. To better utilize their potential in applications and possibly invent new ones a comprehensive understanding of their dynamics is required. In this work, we explore the effect of bubble-bubble interactions on the resonance frequency of MB suspensions. MBs oscillate in response to an external acoustic wave and since bubbles in a cluster are at different locations compared to the excitation source, they are excited at different times. In this work we refer to these delays as primary delays. Interactions between the scattered pressure fields from adjacent bubbles have also been shown to alter the dynamics of MBs that exist within clusters. These secondary waves generated by MBs reach MBs in their proximity at different times that depend on their spatial location in the cluster. Here we refer to these delays as secondary delays. Inclusion of the secondary delays modifies the class of the differential equations governing the oscillations of interacting MBs in a cluster from ordinary differential equations to neutral delay differential equations. Previous work has not considered the all the delays associated with the bubble distances when modeling the interactions between bubbles. In this work we investigate the effect of both the primary and secondary delays on the effective resonance frequency of MB clusters. It is shown that primary delays cause spreading the resonance frequency of identical MBs within a range where the closest MB to the acoustic source exhibits the lowest resonance frequency and the furthest MB resonates at the highest frequency. This range has been shown to be up to 0.12 MHz for the examples investigated in this work. The effect of secondary delays is shown to be very significant. In the absence of secondary delays, the ordinary differential equation model predicts a decrease of up to 26% in the resonance frequency of 4 identical interacting MBs as the inter-bubble distances are decreased. However, we show that inclusion of the secondary delays result in the increase of the resonance frequency of MBs if they are situated close to each other. This increase is shown to be significant and for the case of 4 identical interacting MBs we show an increase of 58% in the resonance frequency.

The relationship between bubble concentration and the acoustic emission energy of separate frequency bands

This letter presents the relationship between bubble concentration and the energy ratio of low to high frequency bands of their acoustic emissions. Two sensors, placed perpendicular and concentric to a transmitter, captured the emissions from sonicated microbubbles. Emissions from different bubbles arrived at the perpendicular sensor with small time differences. Low frequencies with periods longer than the time differences interfered constructively, while higher frequencies interfered both constructively and destructively. The low-frequency (2nd-3rd harmonics) to high-frequency (7th-12th harmonics) energy ratio increased with the bubble concentration. The relationship was not observed with the concentric sensor, where the time differences were larger.

Time-delayed interactions on acoustically driven bubbly screens

The influence of the compressibility effects is discussed, including the time delays on the dynamics of acoustically excited bubbly screens. In the linear regime, it is shown that the proposed model for the infinite bubbly screen recovers the results predicted by the effective medium theory (EMT) up to the second order without introducing any fitting parameter when the wavelength is large compared to the inter-bubble distance. However, the effect of boundaries on the finite bubbly screens is shown to lead to the appearance of multiple local resonances and characteristic periodic structures, which limit the applicability of the EMT. In addition, a local resonance phenomenon in the liquid spacings between the bubbles is observed for both the infinite and finite bubbly screens with crystal structures, and these effects vanish as the crystal structure is perturbed. In the nonlinear regime, the current model is treated with time-delay effects as a delay differential equation, which is directly solved numerically. The appearance of an optimal distance for the subharmonic emission for the crystal structures is shown, and the accuracy of the EMT in the strong nonlinear regime is discussed.