Numerical modeling of the 3D dynamics of ultrasound contrast agent microbubbles using the boundary integral method

Abstract

Ultrasound contrast agents (UCAs) are microbubbles stabilized with a shell typically of lipid, polymer, or protein and are emerging as a unique tool for noninvasive therapies ranging from gene delivery to tumor ablation. While various models have been developed to describe the spherical oscillations of contrast agents, the treatment of nonspherical behavior has received less attention. However, the nonspherical dynamics of contrast agents are thought to play an important role in therapeutic applications, for example, enhancing the uptake of therapeutic agents across cell membranes and tissue interfaces, and causing tissue ablation. In this paper, a model for nonspherical contrast agent dynamics based on the boundary integral method is described. The effects of the encapsulating shell are approximated by adapting Hoff’s model for thin-shell, spherical contrast agents. A high-quality mesh of the bubble surface is maintained by implementing a hybrid approach of the Lagrangian method and elastic mesh technique. The numerical model agrees well with a modified Rayleigh-Plesset equation for encapsulated spherical bubbles. Numerical analyses of the dynamics of UCAs in an infinite liquid and near a rigid wall are performed in parameter regimes of clinical relevance. The oscillation amplitude and period decrease significantly due to the coating. A bubble jet forms when the amplitude of ultrasound is sufficiently large, as occurs for bubbles without a coating; however, the threshold amplitude required to incite jetting increases due to the coating. When a UCA is near a rigid boundary subject to acoustic forcing, the jet is directed towards the wall if the acoustic wave propagates perpendicular to the boundary. When the acoustic wave propagates parallel to the rigid boundary, the jet direction has components both along the wave direction and towards the boundary that depend mainly on the dimensionless standoff distance of the bubble from the boundary. In all cases, the jet directions for the coated and uncoated bubble are similar but the jet width and jet velocity are smaller for a coated bubble. The effects of shell thickness and shell viscosity are analyzed and determined to affect the bubble dynamics, including jet development.