Microbubble dynamics monitoring using a dual modulation method

Pulsation of bubbles in the viscoelastic medium under dual-frequency ultrasound

The pulsation of bubbles under dual-frequency ultrasound is closely associated with their application in medical diagnostics. In this study, we derive the analytical solution of the bubble dynamic equations in viscoelastic media under dual-frequency ultrasound and compare it with numerical solutions. The effects of the surrounding medium's viscoelasticity, bubble equilibrium radius, incident acoustic frequency, and incident sound pressure ratio on the bubble pulsation and its scattered acoustic waves are analyzed. The results demonstrate consistency between the analytical and numerical solutions. Moreover, our analytical solution reveals that an increase in medium viscosity leads to a decrease in the amplitude of bubble pulsation, even at resonance frequency. Additionally, when the sound pressure ratio is 1, both the difference frequency and sum frequency exhibit maximum amplitude in the spectrum of instantaneous bubble radius. Furthermore, for resonance approximation in sparse bubble cluster detection using sum and difference frequencies, it is necessary for incident frequency f1 to be greater than twice the resonance frequency of the smallest bubble within the cluster.

Equivalent-time-active-cavitation-imaging enables vascular-resolution blood-brain-barrier-opening-therapy planning

Objective. Linking cavitation and anatomy was found to be important for predictable outcomes in focused-ultrasound blood-brain-barrier-opening and requires high resolution cavitation mapping. However, cavitation mapping techniques for planning and monitoring of therapeutic procedures either (1) do not leverage the full resolution capabilities of ultrasound imaging or (2) place constraints on the length of the therapeutic pulse. This study aimed to develop a high-resolution technique that could resolve vascular anatomy in the cavitation map.Approach. Herein, we develop BandPass-sampled-equivalent-time-active-cavitation-imaging (BP-ETACI), derived from bandpass sampling and dual-frequency contrast imaging at 12.5 MHz to produce cavitation maps prior and during blood-brain barrier opening with long therapeutic bursts using a 1.5 MHz focused transducer in the brain of C57BL/6 mice.Main results. The BP-ETACI cavitation maps were found to correlate with the vascular anatomy in ultrasound localization microscopy vascular maps and in histological sections. Cavitation maps produced from non-blood-brain-barrier disrupting doses showed the same cavitation-bearing vasculature as maps produced over entire blood-brain-barrier opening procedures, allowing use for (1) monitoring focused-ultrasound blood-brain-barrier-opening (FUS-BBBO), but also for (2) therapy planning and target verification.Significance. BP-ETACI is versatile, created high resolution cavitation maps in the mouse brain and is easily translatable to existing FUS-BBBO experiments. As such, it provides a means to further study cavitation phenomena in FUS-BBBO.

Time-resolved absolute radius estimation of vibrating contrast microbubbles using an acoustical camera

Ultrasound (US) contrast agents consist of microbubbles ranging from 1 to 10 μm in size. The acoustical response of individual microbubbles can be studied with high-frame-rate optics or an "acoustical camera" (AC). The AC measures the relative microbubble oscillation while the optical camera measures the absolute oscillation. In this article, the capabilities of the AC are extended to measure the absolute oscillations. In the AC setup, microbubbles are insonified with a high- (25 MHz) and low-frequency US wave (1-2.5 MHz). Other than the amplitude modulation (AM) from the relative size change of the microbubble (employed in Renaud, Bosch, van der Steen, and de Jong (2012a). "An 'acoustical camera' for in vitro characterization of contrast agent microbubble vibrations," Appl. Phys. Lett. 100(10), 101911, the high-frequency response from individual vibrating microbubbles contains a phase modulation (PM) from the microbubble wall displacement, which is the extension described here. The ratio of PM and AM is used to determine the absolute radius, R₀. To test this sizing, the size distributions of two monodisperse microbubble populations ( _R = 2.1 and 3.5 μm) acquired with the AC were matched to the distribution acquired with a Coulter counter. As a result of measuring the absolute size of the microbubbles, this "extended AC" can capture the full radial dynamics of single freely floating microbubbles with a throughput of hundreds of microbubbles per hour.

Very Low Frequency Radial Modulation for Deep Penetration Contrast-Enhanced Ultrasound Imaging

Contrast-enhanced ultrasound imaging allows vascular imaging in a variety of diseases. Radial modulation imaging is a contrast agent-specific imaging approach for improving microbubble detection at high imaging frequencies (≥7.5 MHz), with imaging depth limited to a few centimeters. To provide high-sensitivity contrast-enhanced ultrasound imaging at high penetration depths, a new radial modulation imaging strategy using a very low frequency (100 kHz) ultrasound modulation wave in combination with imaging pulses ≤5 MHz is proposed. Microbubbles driven at 100 kHz were imaged in 10 successive oscillation states by manipulating the pulse repetition frequency to unlock the frame rate from the number of oscillation states. Tissue background was suppressed using frequency domain radial modulation imaging (F-RMI) and singular value decomposition-based radial modulation imaging (S-RMI). One hundred-kilohertz modulation resulted in significantly higher microbubble signal magnitude (63-88 dB) at the modulation frequency relative to that without 100-kHz modulation (51-59 dB). F-RMI produced images with high contrast-to-tissue ratios (CTRs) of 15 to 22 dB in a stationary tissue phantom, while S-RMI further improved the CTR (19-26 dB). These CTR values were significantly higher than that of amplitude modulation pulse inversion images (11.9 dB). In the presence of tissue motion (1 and 10 mm/s), S-RMI produced high-contrast images with CTR up to 18 dB; however, F-RMI resulted in minimal contrast enhancement in the presence of tissue motion. Finally, in transcranial ultrasound imaging studies through a highly attenuating ex vivo cranial bone, CTR values with S-RMI were as high as 23 dB. The proposed technique demonstrates successful modulation of microbubble response at 100 kHz for the first time. The presented S-RMI low-frequency radial modulation imaging strategy represents the first demonstration of real-time (20 frames/s), high-penetration-depth radial modulation imaging for contrast-enhanced ultrasound imaging.

Acoustic vibrational resonance in a Rayleigh-Plesset bubble oscillator

The phenomenon of vibrational resonance (VR) has been investigated in a Rayleigh-Plesset oscillator for a gas bubble oscillating in an incompressible liquid while driven by a dual-frequency force consisting of high-frequency, amplitude-modulated, weak, acoustic waves. The complex equation of the Rayleigh-Plesset bubble oscillator model was expressed as the dynamics of a classical particle in a potential well of the Liénard type, thus allowing us to use both numerical and analytic approaches to investigate the occurrence of VR. We provide clear evidence that an acoustically-driven bubble oscillates in a time-dependent single or double-well potential whose properties are determined by the density of the liquid and its surface tension. We show both theoretically and numerically that, besides the VR effect facilitated by the variation of the parameters on which the high-frequency depends, amplitude modulation, the properties of the liquid in which the gas bubble oscillates contribute significantly to the occurrence of VR. In addition, we discuss the observation of multiple resonances and their origin for the double-well case, as well as their connection to the low frequency, weak, acoustic force field.

Chaotic oscillations of gas bubbles under dual-frequency acoustic excitation

Chaotic oscillation of bubbles in liquids reduces the efficiency of the sonochemical system and should be suppressed in the practical applications. In the present paper, a chaos control method based on the dual-frequency approach is numerically investigated and is proved to be an effective method even for cases with intensive energy input. It was found that the chaos could be successfully suppressed by the application of dual-frequency approach in a wide range of parameter zone (even with high acoustic pressure amplitude). Furthermore, influences of power allocation between two waves on the chaos control are quantitatively discussed with clear descriptions of the routes from stable oscillations to chaos.

Combination and simultaneous resonances of gas bubbles oscillating in liquids under dual-frequency acoustic excitation

The multi-frequency acoustic excitation has been employed to enhance the effects of oscillating bubbles in sonochemistry for many years. In the present paper, nonlinear dynamic oscillations of bubble under dual-frequency acoustic excitation are numerically investigated within a broad range of parameters. By investigating the power spectra and the response curves of oscillating bubbles, two unique features of bubble oscillations under dual-frequency excitation (termed as "combination resonance" and "simultaneous resonance") are revealed and discussed. Specifically, the amplitudes of the combination resonances are quantitatively compared with those of other traditional resonances (e.g. main resonances, harmonics). The influences of several paramount parameters (e.g., the bubble radius, the acoustic pressure amplitude, the energy allocation between two component waves) on nonlinear bubble oscillations are demonstrated.