  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 is inspected \textit{in vivo} 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 over a wide range of variations
of influential parameters. The results imply that the composition of the
surrounding medium alters the microbubble dynamics, strongly. 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.
