Numerical study on a polymer-shelled microbubble submerged in soft tissue

Ultrasound contrast agents have been recently utilized in therapeutical implementations for targeted delivery of pharmaceutical substances. Radial pulsations of the encapsulated microbubbles under the action of an ultrasound field are complex and high nonlinear, particularly for drug and gene delivery applications with high acoustic pressure amplitudes. The dynamics of a polymer-shelled agent are studied through applying the method of chaos physics whereas the effects of the outer medium compressibility and the shell were considered. The stability of the ultrasound contrast agent is examined by plotting the bifurcation diagrams, Lyapunov exponent, and time series over a wide range of variations of influential parameters. The findings of the study indicate that by tuning the shear modulus of surrounding medium and shell viscosity, the radial oscillations of microbubble cluster undergoes a chaotic unstable region as the amplitude and frequency of ultrasonic pulse are increased mainly due to the period doubling phenomenon. Furthermore, influences of various parameters which present a comprehensive view of the radial oscillations of the microbubble are quantitatively discussed with clear descriptions of the stable and unstable regions of the microbubble oscillations for typical therapeutic ultrasound pulses.