Boundary Element Analysis of Bubble Oscillations in Elastic Tubes

The interactions between a microbubble and ultrasound in an elastic tube are investigated to understand the bubble dynamics in a blood vessel. The tube wall is modeled with a spring-mass system. A simple bubble model for investigating bubble oscillations in the tube is introduced and is combined with the spring-mass system of the tube: the bubble is represented by a point source for the bubble volume oscillation and a dipole for the translational motion. The natural frequencies of the system are derived by linearizing the governing equations. The influences of an elastic tube on a bubble are mainly discussed by using eigenvalue analysis in the present work. It is shown that the resonance frequency of a bubble in the tube decreases with increasing the mass of the tube wall. The effects of the tube length and the initial location of a bubble are also investigated. The results show that although the resonance frequency decreases monotonically with increase in the tube length when the wall mass is large, it is not changed when the mass is sufficiently small. It is also shown that the resonance frequency is decreased with decreasing the distance between the bubble centroid and the tube wall when the mass is large. However, when the mass is small enough, it is increased with decreasing the distance. We also investigate the influence of the characteristics of an elastic tube on nonlinear oscillations of a bubble. The condition that the harmonic oscillation is enhanced is discussed.