Nonlinear behavior of a liquid containing uniform bubbles: comparison between theory and experiments

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.

Analysis of acoustic nonlinearity parameter B/A in liquids containing ultrasound contrast agents

The acoustic nonlinearity parameter B/A plays a significant role in the characterization of acoustic properties of various biomaterials and biological tissues. It has the potential to be a favorable imaging modality in contrast ultrasound imaging with coated microbubbles. However, the development of effective means for evaluating the nonlinearity parameter of suspensions of ultrasound contrast agents (UCAs, also known as bubbly liquids) remains open. The present paper formulates a new equation based on the thermodynamic method that correlates both attenuation and phase velocity of linear ultrasound. The simplicity of the present method makes the B/A estimation possible with a relatively rigorous mathematical derivation. The calculated nonlinearity parameter contains the contribution of dynamic effects of bubbles, and its low-frequency limit agrees with B/A estimated by the method of mixture law when the volume fraction is below 10^-4. Furthermore, the maximum B/A in bubbly liquids can reach up to10⁵, while the minimum can be as low as -10⁵. The negative nonlinearity parameter indicates significantly different thermodynamic properties of bubbly liquids.

Quasi-phase-matched backward second-harmonic generation by complementary media in nonlinear metamaterials

High efficiency of the second-harmonic and sum-frequency generation can be obtained in optical superlattice by using the conventional quasi-phase-matched (QPM) method. Although this trick can be played on the acoustic wave, the media with negative nonlinear parameters are not common in acoustics. Furthermore, the QPM method used in acoustic metamaterials has been less studied. In this work, a protocol is provided to realize the QPM method by using nonlinear complementary media in acoustic metamaterials in order to obtain large backward second-harmonic generation. Compared with the conventional method, the method gains a broader bandwidth and can be used in both acoustic and electromagnetic waves.

Comparison of EMT and MST approaches in studying linear acoustics in bubbly liquid

Two kinds of approaches have been used in literature to study the linear acoustics in a liquid-bubble mixture: The effective medium theory approach and the multiple scattering theory approach. Theoretical comparisons of mathematical formulations and intrinsic relations between these two approaches are given in this paper and show their consistency in dealing with the linear acoustics in bubbly liquids. Possible applications of these two methods are also generally discussed.

The experimental investigation of ultrasonic properties for a sonicated contrast agent and its application in biomedicine

The ultrasonic properties of a promising ultrasound (US) contrast agent, named SDA (sonicated dextrose albumin) are reported in this paper. SDA is a suspension of stable microencapsulated gas bubbles with average diameter 2.0 microm prepared from sonicated dextrose albumin. The ultrasonic linear and nonlinear parameters, such as acoustic velocity, sound attenuation and acoustic nonlinearity parameter B/A of SDA, as a function of its bubble concentration from 1.0 x 10(7) to 2.05 x 10(8) microbubbles/mL in the frequency range of 2-6 MHz are measured in vitro. The sound attenuation coefficients over 2-6 MHz are linearly proportional to the bubble concentration and frequency. It is important to point out that the acoustic nonlinearity parameter B/A for SDA has a very large value that nonlinearly increases with the increase of bubble concentration.

Temperature rise generated by ultrasound in the presence of contrast agent

Temperature elevation vs. time generated by a focused Gausssian ultrasound beam in the presence of contrast agents has been calculated using a perfect absorbing disc model. The results suggest that, if the contrast agent (Albunex) is introduced into the body intravenously, the temperature rise in the heart, which is 4.5 cm from the transducer, generated by 110-mW (the corresponding acoustic intensity at the transducer front surface is 0.4 W/cm2) 2-MHz ultrasound is about 2 degrees C in 10 s. The relationship between temperature rise and the blood perfusion, acoustic power and focal length is discussed.

Measurements of the nonlinearity parameter B/A of contrast agents

The nonlinearity parameter B/As of two contrast agents (Albunex and Levovist) in a saline solution (Isoton II) were measured. The results show that B/As of both contrast agents were increasing functions of bubble number densities. In general, they are much higher than that of most soft tissues. For Albunex (concentration = 1 microL Albunex: 1 mL Isoton) a B/A of 2000; and for Levovist (concentration = 6.0 mg Levovist powder: 1 mL Isoton), a B/A of 600 was obtained.

Quantitative acoustic characterization of a new surfactant-based ultrasound contrast agent

The acoustic properties of a new ultrasound contrast agent, ST68, have been investigated. ST68 is a sonicated mixture of nonionic surfactants (Span-type and Tween-type) consisting of stabilized microbubbles with a mean diameter of 3.8 microns and a concentrations of 7.1 x 10(8) bubbles/mL. A pulsatile flow system was used to acquire data in vitro. The acoustic properties of ST68, as a function of time, frequency and dose, were calculated. Enhancement changed nonlinearly with contrast agent dose; maximum was 13.1 dB +/- 1.0 dB for a dose of 0.30 microL/mL of suspending medium. Attenuation reached approximately 11 dB/cm for dosages above 0.27 microL/mL and for frequencies between 2.5 and 6.0 MHz. In vivo, i.v. injections of ST68 were given to 4 rabbits (doses from 0.01 to 0.23 mL/kg). A clear increase in flow signal intensity was observed for 1 to 2 min. An in vivo dose-response curve was calculated from audio Doppler signals obtained with a 10-MHz cuff transducer placed around the distal aorta. Maximum enhancement was 18.3 dB +/- 3.13 dB for a 0.13 mL/kg dose. Moreover, ST68 appears to follow a simple relationship between in vivo enhancement and dose. In conclusion, ST68 is capable of producing marked vascular enhancement. Its acoustic properties have been characterized in vitro and in vivo.