Shape stability of a microbubble under the effect of an acoustic field

Therapeutic applications of microbubbles and ultrasound can be used in the field of cancer treatment to improve the treatment efficacy while minimizing side effects. Ultrasound-mediated microbubbles can temporarily increase the permeability of cell membranes to enhance the delivery of drugs and genes to specific target tissues. The non-spherical stable shape oscillation of a microbubble, known as shape modes, is one of the core mechanisms of medical applications. Microbubbles are encapsulated in a lipid or protein shell to increase their lifetime in blood. This study aims to investigate the shape stability of an encapsulated bubble under the effect of an acoustic field. Power law and Kelvin-Voigt constitutive laws are employed for blood and bubble shell, respectively. An external acoustic field is applied to obtain volume oscillations. The spherical interface of the microbubble is perturbed with a harmonic non-spherical perturbation. After the spherical oscillations reach a steady periodic state, Floquet theory is applied to find the eigenvalues of the system. Phase diagrams are obtained for different pressure amplitudes of the acoustic field and initial bubble radius to investigate stable and unstable regions. It is observed that for larger pressure amplitudes of the acoustic field and initial radius values, the bubble becomes unstable, although the detailed structure of the phase diagram is quite complicated.