Increasing the nonlinear character of microbubble oscillations at low acoustic pressures

Abstract

The nonlinear response of gas bubbles to acoustic excitation is an important phenomenon in both the biomedical and engineering sciences. In medical ultrasound imaging, for example, microbubbles are used as contrast agents on account of their ability to scatter ultrasound nonlinearly. Increasing the degree of nonlinearity, however, normally requires an increase in the amplitude of excitation, which may also result in violent behaviour such as inertial cavitation and bubble fragmentation. These effects may be highly undesirable, particularly in biomedical applications, and the aim of this work was to investigate alternative means of enhancing nonlinear behaviour. In this preliminary report, it is shown through theoretical simulation and experimental verification that depositing nanoparticles on the surface of a bubble increases the nonlinear character of its response significantly at low excitation amplitudes. This is due to the fact that close packing of the nanoparticles restricts bubble compression.Keywords: bubbles; nonlinear dynamics; microbubbles; nanoparticles; ultrasound THEORETICAL PREDICTIONIn order to predict the effect of particles on the dynamic behaviour of a bubble excited by an acoustic field, a modified Rayleigh-Plesset equation was derived, whereby the radial oscillations of a bubble coated with a surfactant layer containing particles of a given size and concentration are described bywhere R is the instantaneous radius of the bubble; R 0 is its initial value; p 0 is the ambient pressure; s 0 is the initial interfacial tension; G 0 is the initial concentration of the surfactant on the bubble surface; x and K are constants for the surfactant; _ R and € R are the velocity and acceleration of the bubble wall, respectively; r L is the density and m L the viscosity of the surrounding fluid; p A is the pressure due to the applied sound field; p G is the pressure of the gas inside the bubble; R x is the limiting bubble radius beneath which the surface buckles; and B and h s0 are again constants for the individual surfactant. Further details of the treatment of the surfactant coating may be found in Stride (2008). The original equation for an uncoated bubble is given by Plesset & Prosperetti (1977).The effect of the particles is described by the quantity G that is defined aswhere f p is the fractional surface area coverage that defines the limiting radius R lim at which the particles would be expected to reach their square packing density in two dimensions and beyond which the bubble's resistance to further compression would be expected to increase by a factor determined by the compressibility of the particles. This is represented by the quantity X, which is estimated from the ratio of the effective shear moduli of the particles and the surfactant coating. The pressure p rad radiated by the bubble at a distance r from its centre may be predicted using Vokurka (1990) ð1:3Þ Equations (1.1) and (1.3) were solved numerically using purpose-written code in MATLAB R2006b (The Mathworks, Inc., Natick, MA, USA) im...

Nonlinear Shell Behavior of Phospholipid-Coated Microbubbles

“…On the other hand, engineering of bubbles for specific techniques is a promising application. Stride et al (2008) added nanoparticles to the shell restricting the bubbles from compression and to let them behave nonlinearly.…”

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