Physico-mathematical model for multiple ultrasound-contrast-agent microbubbles encapsulated by a visco-elastic shell: Effect of shell compressibility on ultrasound attenuation

Abstract

Owing to its potential for application in ultrasound-based diagnosis and therapy, the dynamics of a microbubble encapsulated by shells has long been theoretically investigated. However, outside of our research group, previous theories have been restricted to the case of single encapsulated bubble, whereas in practical diagnostic scenarios, multiple encapsulated bubbles are used as ultrasound contrast agents. In this study, the most recent theory for a single encapsulated bubble incorporating shell compressibility was extended for multiple encapsulated bubbles. Using the method of multiple scales, weakly nonlinear wave equation for one-dimensional ultrasound in liquids containing multiple encapsulated microbubbles was derived from the set of volumetric averaged equations for bubbly flow. It was found that the shell compressibility significantly increased the advection and dissipation effects of ultrasound. Further, five types of dissipation effects were compared with each other, and showed that the dissipation effects corresponding to shell compressibility were the highest.