A model for large amplitude oscillations of coated bubbles accounting for buckling and rupture

Abstract

We present a model applicable to ultrasound contrast agent bubbles that takes into account the physical properties of a lipid monolayer coating on a gas microbubble. Three parameters describe the properties of the shell: a buckling radius, the compressibility of the shell, and a break-up shell tension. The model presents an original non-linear behavior at large amplitude oscillations, termed compression-only, induced by the buckling of the lipid monolayer. This prediction is validated by experimental recordings with the high-speed camera Brandaris 128, operated at several millions of frames per second. The effect of aging, or the resultant of repeated acoustic pressure pulses on bubbles, is predicted by the model. It corrects a flaw in the shell elasticity term previously used in the dynamical equation for coated bubbles. The break-up is modeled by a critical shell tension above which gas is directly exposed to water.

Ultrasound contrast agents : dynamics of coated bubbles

“…In chapter 3 we reveal the origin of the so-called "thresholding" behavior. Furthermore, we show why apparently identical bubbles show completely different behavior by implementing the shell-buckling model by Marmottant et al [12]. In chapter 4 we explore in detail the so-called "compression-only" behavior by means of a weakly nonlinear analysis of the shell-buckling model.…”

“…Note that the effective surface tension in these models is not bound to an upper or lower limit and the effective surface tension can become negative and larger than σ w . Marmottant et al [12] introduced a model which seems to be more applicable for high amplitude oscillations. The model accounts for an elastic shell and also for buckling and rupture of the shell.…”

“…On the other hand expansion of the bubble decreases the phospholipid concentration and leads to rupture. It is assumed that the surface tension will effectively [12] including an elastic regime and buckling and rupture of the shell.…”

Combined optical sizing and acoustical characterization of single freely-floating microbubbles

“…[4][5][6] Previous studies using acoustical or optical techniques to determine the microbubble response to ultrasound excitation, have demonstrated a myriad of nonlinear behaviors specific to lipid-coated microbubbles. These behaviors include asymmetric oscillation due to buckling and rupture of the lipid shell, 7 subharmonic emission, 8 and compression-only behavior. 9 The precedence of these behaviors is influenced by both the microbubble size with respect to the ultrasonic driving frequency (e.g., resonance effects) and the lipid shell properties.…”

“…18,19 The frequency spectrum of e(t) was then derived by applying a Fast Fourier Transform (FFT), from which the following parameters were obtained: e f is the relative oscillation amplitude at the fundamental frequency, i.e., the driving frequency; E 2f is the relative oscillation amplitude at the second harmonic frequency, i.e., at twice the driving frequency; (A exp À A com ) Â 100% (where A exp ¼ jR max À R 0 j/R 0 and A com ¼ jR min À R 0 j/R 0 are the relative amplitude of the expansion and the compression phase), to assess the asymmetry of the dynamic response. 25 To validate the experimental results, the nonlinear bubble dynamics model proposed by Marmottant et al 7 was used to simulate the response of the lipid-coated microbubbles. For the simulation, we chose typical viscoelastic parameters from literature.…”