Motivated by various clinical applications of ultrasound contrast agents within blood vessels, the natural frequencies of two bubbles in a compliant tube are studied analytically, numerically, and experimentally. A lumped parameter model for a five degree of freedom system was developed, accounting for the compliance of the tube and coupled response of the two bubbles. The results were compared to those produced by two different simulation methods: (1) an axisymmetric coupled boundary element and finite element code previously used to investigate the response of a single bubble in a compliant tube and (2) finite element models developed in comsol Multiphysics. For the simplified case of two bubbles in a rigid tube, the lumped parameter model predicts two frequencies for in- and out-of-phase oscillations, in good agreement with both numerical simulation and experimental results. For two bubbles in a compliant tube, the lumped parameter model predicts four nonzero frequencies, each asymptotically converging to expected values in the rigid and compliant limits of the tube material.

The dynamic response of bubbles in a liquid that are partially constrained by a surrounding tube or channel is important in a variety of fields, including diagnostic and therapeutic biomedical ultrasound and for microfluidic devices. In this study, numerical simulations, lumped parameter models, and experiments are used to investigate the effects of a surrounding tube on a bubble’s response to acoustic excitation. In particular, a coupled boundary element and finite element model and COMSOL MULTIPHYSICS models have been developed and used to investigate the nonlinear interactions of this three-phase system. Simulation results were compared to experimental measurements obtained using a scaled balloon model. The effects of tube parameters and bubble interactions on a bubble’s natural frequency important for proposed clinical applications of ultrasound are investigated. Resonance frequencies agree well with one-dimensional lumped parameter model predictions for a bubble well within a rigid tube, but deviate for a bubble near the tube end. Simulations also predict bubble translation along the tube axis and the aspherical oscillations and induced tube stresses at higher amplitudes. [Work supported by NIH and NSF CMMI.]