Interaction between encapsulated microbubbles:A finite element modelling study

Theoretical studies on the multi-bubble interaction are crucial for the in-depth understanding of the mechanism behind the applications of ultrasound contrast agents(UCAs) in clinics. A two-dimensional(2 D) axisymmetric finite element model(FEM) is developed here to investigate the bubble–bubble interactions for UCAs in a fluidic environment. The effect of the driving frequency and the bubble size on the bubble interaction tendency(viz., bubbles' attraction and repulsion),as well as the influences of bubble shell mechanical parameters(viz., surface tension coefficient and viscosity coefficient)are discussed. Based on FEM simulations, the temporal evolution of the bubbles' radii, the bubble–bubble distance, and the distribution of the velocity field in the surrounding fluid are investigated in detail. The results suggest that for the interacting bubble–bubble couple, the overall translational tendency should be determined by the relationship between the driving frequency and their resonance frequencies. When the driving frequency falls between the resonance frequencies of two bubbles with different sizes, they will repel each other, otherwise they will attract each other. For constant acoustic driving parameters used in this paper, the changing rate of the bubble radius decreases as the viscosity coefficient increases,and increases first then decreases as the bubble shell surface tension coefficient increases, which means that the strength of bubble–bubble interaction could be adjusted by changing the bubble shell visco-elasticity coefficients. The current work should provide a powerful explanation for the accumulation observations in an experiment, and provide a fundamental theoretical support for the applications of UCAs in clinics.     

包膜黏弹特性及声驱动参数对相互作用微泡动力学行为的影响

关于多气泡相互作用的理论研究对于深入理解超声造影剂在医疗领域中的应用机理具有重要意义。本工作建立了一个2维轴对称有限元模型来研究流体环境中超声造影剂双气泡相互作用,讨论了驱动超声频率和气泡尺寸对气泡之间吸引和排斥趋势的影响,得到了气泡半径与气泡之间距离随时间变化的曲线,以及气泡周围流体速度场的细节,并且研究了气泡包膜参数(即表面张力系数和粘度系数)对气泡相互作用的影响.结果表明,相互作用中的气泡对整体的相对运动趋势由驱动频率和共振频率之间的关系决定;在超声参数固定时,气泡包膜的粘弹特性可用来调控气泡间相互作用强度。结果对实验中观察到的气泡聚集现象进行了合理解释,并为超声造影剂在医疗实践中的应用提供了基础理论支撑.