Nonlinear ultrasound propagation in liquid containing multiple microbubbles coated by shell incorporating anisotropy

Using microbubbles coated by a thin shell as ultrasound contrast agents for ultrasound diagnosis improves image resolution. Since numerous microbubbles are used in clinical practice, understanding the acoustic properties of liquids containing multiple microbubbles is important. However, interactions between ultrasound and numerous coated microbubbles have not been fully investigated theoretically. Additionally, ultrasound contrast agents with shells made of various materials have been developed. Recently, an equation of motion that considers the anisotropy of the shell was proposed Chabouh et al., “Spherical oscillations of encapsulated microbubbles: Effect of shell compressibility and anisotropy,” J. Acoust. Soc. Am. 149, 1240 (2021), and the effect of shell anisotropy on the resonance of the oscillating bubble was reported. In this study, we derived a nonlinear wave equation describing ultrasound propagation in liquids containing numerous coated microbubbles based on the method of multiple scales by expanding Chabouh's equation of motion for the single bubble. This was achieved by considering shell anisotropy in the volumetric average equation for the liquid and gas phases. Shell anisotropy was observed to affect the advection, nonlinearity, attenuation, and dispersion of ultrasound. In particular, the attenuation effects increased or decreased depending on the anisotropic shell elasticity.