Ultrasonic bubbles in medicine: influence of the shell

Ultrasound contrast agents consist of microscopically small bubbles encapsulated by an elastic shell. These microbubbles oscillate upon ultrasound insonification, and demonstrate highly nonlinear behavior, ameliorating their detectability. (Potential) medical applications involving the ultrasonic disruption of contrast agent microbubble shells include release-burst imaging, localized drug delivery, and noninvasive blood pressure measurement. To develop and enhance these techniques, predicting the cracking behavior of ultrasound-insonified encapsulated microbubbles has been of importance. In this paper, we explore microbubble behavior in an ultrasound field, with special attention to the influence of the bubble shell. A bubble in a sound field can be considered a forced damped harmonic oscillator. For encapsulated microbubbles, the presence of a shell has to be taken into account. In models, an extra damping parameter and a shell stiffness parameter have been included, assuming that Hooke's Law holds for the bubble shell. At high acoustic amplitudes, disruptive phenomena have been observed, such as microbubble fragmentation and ultrasonic cracking. We analyzed the occurrence of ultrasound contrast agent fragmentation, by simulating the oscillating behavior of encapsulated microbubbles with various sizes in a harmonic acoustic field. Fragmentation occurs exclusively during the collapse phase and occurs if the kinetic energy of the collapsing microbubble is greater than the instantaneous bubble surface energy, provided that surface instabilities have grown big enough to allow for break-up. From our simulations it follows that the Blake critical radius is not a good approximation for a fragmentation threshold. We demonstrated how the phase angle differences between a damped radially oscillating bubble and an incident sound field depend on shell parameters.