Review of shell models for contrast agent microbubbles

Micrometer-scale encapsulated gas bubbles, known as ultrasound contrast agents, are used in ultrasound medical diagnostics for enhancing blood-tissue contrast during an ultrasonic examination. They are also employed in therapy as an activator of drug incorporation or extravasation. Adequate modeling of the effect of encapsulation is of primary importance because it is the encapsulating shell that determines many of the functional properties of contrast agents. In this review, existing approaches to the modeling of the radial motion of an encapsulated bubble are discussed and comparative analysis of available shell models is conducted. The capabilities of the shell models are evaluated in the context of recent experimental observations, such as compression-only behavior and the dependence of shell material properties on initial bubble radius. It is shown that for early shell models, the main problem is that the behavior of encapsulation is described by linear elastic and viscous laws, whereas recent experimental data attest to complicated rheological properties inherent in shell materials. Currently, a trend toward models involving nonlinear laws for shell elasticity and viscosity is observed. In particular, nonlinear models have been proposed that allow one to reproduce compression-only behavior. However, the problem of the radius dependence of shell material parameters remains unsolved.