Natural frequencies of two bubbles in a compliant tube: analytical, simulation, and experimental results.

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.

Natural frequency of a gas bubble in a tube: experimental and simulation results.

Use of ultrasonically excited microbubbles within blood vessels has been proposed for a variety of clinical applications. In this paper, an axisymmetric coupled boundary element and finite element code and experiments have been used to investigate the effects of a surrounding tube on a bubble's response to acoustic excitation. A balloon model allowed measurement of spherical gas bubble response. Resonance frequencies match one-dimensional cylindrical 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 aspherical oscillations at higher amplitudes.