Modeling of the acoustic response from contrast agent microbubbles near a rigid wall

In ultrasonic targeted imaging, specially designed encapsulated microbubbles are used, which are capable of selectively adhering to the target site in the body. A challenging problem is to distinguish the echoes from such adherent agents from echoes produced by freely circulating agents. In the present paper, an equation of radial oscillation for an encapsulated bubble near a plane rigid wall is derived. The equation is then used to simulate the echo from a layer of contrast agents localized on a wall. The echo spectrum of adherent microbubbles is compared to that of free, randomly distributed microbubbles inside a vessel, in order to examine differences between the acoustic responses of free and adherent agents. It is shown that the fundamental spectral component of adherent bubbles is perceptibly stronger than that of free bubbles. This increase is accounted for by a more coherent summation of echoes from adherent agents and the acoustic interaction between the agents and the wall. For cases tested, the increase of the fundamental component caused by the above two effects is on the order of 8-9 dB. Bubble aggregates, which are observed experimentally to form near a wall due to secondary Bjerknes forces, increase the intensity of the fundamental component only if they are formed by bubbles whose radii are well below the resonant radius. If the formation of aggregates contributes to the growth of the fundamental component, the increase can exceed 17 dB. Statistical analysis for the comparison between adhering and free bubbles, performed over random space bubble distributions, gives p-values much smaller than 0.05

Modeling of nonlinear viscous stress in encapsulating shells of lipid-coated contrast agent microbubbles

A general theoretical approach to the development of zero-thickness encapsulation models for contrast microbubbles is proposed. The approach describes a procedure that allows one to recast available rheological laws from the bulk form to a surface form which is used in a modified Rayleigh-Plesset equation governing the radial dynamics of a contrast microbubble. By the use of the proposed procedure, the testing of different rheological laws for encapsulation can be carried out. Challenges of existing shell models for lipid-encapsulated microbubbles, such as the dependence of shell parameters on the initial bubble radius and the “compression-only” behavior, are discussed. Analysis of the rheological behavior of lipid encapsulation is made by using experimental radius-time curves for lipid-coated microbubbles with radii in the range 1.2 – 2.5 μm. The curves were acquired for a research phospholipid-coated contrast agent insonified with a 20-cycle, 3.0 MHz, 100 kPa acoustic pulse. The fitting of the experimental data by a model which treats the shell as a viscoelastic solid gives the values of the shell surface viscosity increasing from 0.30×10-8 kg/s to 2.63×10-8 kg/s for the range of bubble radii indicated above. The shell surface elastic modulus increases from 0.054 N/m to 0.37 N/m. It is proposed that this increase may be a result of the lipid coating possessing the properties of both a shear-thinning and a strain-softening material. We hypothesize that these complicated rheological properties do not allow the existing shell models to satisfactorily describe the dynamics of lipid encapsulation. In the existing shell models, the viscous and the elastic shell terms have the linear form which assumes that the viscous and the elastic stresses acting inside the lipid shell are proportional to the shell shear rate and the shell strain, respectively, with constant coefficients of proportionality. The analysis performed in the present paper suggests that a more general, nonlinear theory may be more appropriate. It is shown that the use of the nonlinear theory for shell viscosity allows one to model the “compression-only” behavior. As an example, the results of the simulation for a 2.03- μm-radius bubble insonified with a 6-cycle, 1.8 MHz, 100 kPa acoustic pulse are given. These parameters correspond to the acoustic conditions under which the “compression-only” behavior was observed by de Jong et al. [Ultrasound Med. Biol. 33 (2007) 653–656]. It is also shown that the use of the Cross law for the modeling of the shear-thinning behavior of shell viscosity reduces the variance of experimentally estimated values of the shell viscosity and its dependence on the initial bubble radius

Resonance frequencies of lipid-shelled microbubbles in the regime of nonlinear oscillations

Knowledge of resonant frequencies of contrast microbubbles is important for the optimization of ultrasound contrast imaging and therapeutic techniques. To date, however, there are estimates of resonance frequencies of contrast microbubbles only for the regime of linear oscillation. The present paper proposes an approach for evaluating resonance frequencies of contrast agent microbubbles in the regime of nonlinear oscillation. The approach is based on the calculation of the time-averaged oscillation power of the radial bubble oscillation. The proposed procedure was verified for free bubbles in the frequency range 1–4 MHz and then applied to lipid-shelled microbubbles insonified with a single 20-cycle acoustic pulse at two values of the acoustic pressure amplitude, 100 kPa and 200 kPa, and at four frequencies: 1.5, 2.0, 2.5, and 3.0 MHz. It is shown that, as the acoustic pressure amplitude is increased, the resonance frequency of a lipid-shelled microbubble tends to decrease in comparison with its linear resonance frequency. Analysis of existing shell models reveals that models that treat the lipid shell as a linear viscoelastic solid appear may be challenged to provide the observed tendency in the behavior of the resonance frequency at increasing acoustic pressure. The conclusion is drawn that the further development of shell models could be improved by the consideration of nonlinear rheological laws

Vaporization dynamics of volatile perfluorocarbon droplets: A theoretical model and in vitro validation

Perfluorocarbon (PFC) microdroplets, called phase-change contrast agents (PCCAs), are a promising tool in ultrasound imaging and therapy. Interest in PCCAs is motivated by the fact that they can be triggered to transition from the liquid state to the gas state by an externally applied acoustic pulse. This property opens up new approaches to applications in ultrasound medicine. Insight into the physics of vaporization of PFC droplets is vital for effective use of PCCAs and for anticipating bioeffects. PCCAs composed of volatile PFCs (with low boiling point) exhibit complex dynamic behavior: after vaporization by a short acoustic pulse, a PFC droplet turns into a vapor bubble which undergoes overexpansion and damped radial oscillation until settling to a final diameter. This behavior has not been well described theoretically so far. The purpose of our study is to develop an improved theoretical model that describes the vaporization dynamics of volatile PFC droplets and to validate this model by comparison with in vitro experimental data

Translational instability of a spherical bubble in a standing ultrasound wave

Translational bubble dynamics is much less studied than the dynamics of radial bubble oscillation, while in many scientific and engineering applications the control of space location of cavitation bubbles is of great practical importance. This paper aims at the theoretical study of various aspects of the translational motion of a spherical gas bubble in a high-frequency standing wave. in particular, it is shown that the translational instability that gives rise to the reciprocal translation of a spherical bubble between the pressure antinode and the pressure node is caused by the hysteresis in the main resonance of the bubble. Different types of translational trajectories that can occur in a standing wave are illustrated by numerical simulations. A general classification of the observed translational trajectories is proposed. (C) 2008 Elsevier Ltd. All rights reserved

Radiation dynamics of a cavitation bubble in a liquid-filled cavity surrounded by an elastic solid

International audienceA specific cavitation phenomenon occurs inside the stems of trees. The internal pressure in tree conduits can drop down to significant negative values, which causes the nucleation of bubbles. The bubbles exhibit high-frequency oscillations just after their nucleation. In the present study, this phenomenon is modeled by taking into account acoustic waves produced by bubble oscillations. A dispersion equation is derived, which is then used to calculate the resonance frequency and the attenuation coefficient of the bubble oscillations. Radiation damping is found to be predominant in comparison with viscous damping, except for very small bubbles. A typical number of oscillation cycles before the complete damping of the oscillation is found to be of the order of 10, as observed for cavitation bubbles in biomimetic synthetic trees

Acoustic streaming produced by a cylindrical bubble undergoing volume and translational oscillations in a microfluidic channel

International audienceA theoretical model is developed for acoustic streaming generated by a cylindrical bubble confined in a fluid channel between two planar elastic walls. The bubble is assumed to undergo volume and translational oscillations. The volume oscillation is caused by an imposed acoustic pressure field and generates the bulk scattered wave in the fluid gap and Lamb-type surface waves propagating along the fluid-wall interfaces. The translational oscillation is induced by the velocity field of an external sound source such as another bubble or an oscillatory fluid flow. The acoustic streaming is assumed to result from the interaction of the volume and the translational modes of the bubble oscillations. The general solutions for the linear equations of fluid motion and the equations of acoustic streaming are calculated with no restrictions on the ratio between the viscous penetration depth and the bubble size. Approximate solutions for the limit of low viscosity are provided as well. Simulations of streamline patterns show that the geometry of the streaming resembles flows generated by a source dipole, while the vortex orientation is governed by the driving frequency, bubble size, and the distance of the bubble from the source of translational excitation. Experimental verification of the developed theory is performed using data for streaming generated by bubble pairs