Dynamical analysis of the nonlinear response of ultrasound contrast agent microbubbles

Abstract

The nonlinear response of spherical ultrasound contrast agent microbubbles is investigated to understand the effects of common shells on the dynamics. A compressible form of the Rayleigh-Plesset equation is combined with a thin-shell model developed by Lars Hoff to simulate the radial response of contrast agents subject to ultrasound. The responses of Albunex, Sonazoid, and polymer shells are analyzed through the application of techniques from dynamical systems theory such as Poincaré sections, phase portraits, and bifurcation diagrams to illustrate the qualitative dynamics and transition to chaos that occurs under certain changes in system parameters. Corresponding calculations of Lyapunov exponents provide quantitative data on the system dynamics. The results indicate that Albunex and polymer shells sufficiently stabilize the response to prevent transition to the chaotic regime throughout typical clinical ranges of ultrasound pressure and frequency. By contrast, Sonazoid shells delay the onset of chaos relative to an unshelled bubble but do not prevent it. A contour plot identifying regions of periodic and chaotic behavior over clinical ranges of ultrasound pressure and frequency is provided for Sonazoid. This work characterizes the nonlinear response of various ultrasound contrast agents, and shows that shell properties have a profound influence on the dynamics.