title: Natural frequencies of two bubbles in a compliant tube: analytical, simulation, and experimental results.
abstract: 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.
authors.affiliation: Department of Mechanical Engineering, University of Rochester, Rochester, New York 14627, USA.
authors.forename: Neo W
authors.initials: NW
authors.lastname: Jang
authors.forename: Aaron
authors.initials: A
authors.lastname: Zakrzewski
authors.forename: Christina
authors.initials: C
authors.lastname: Rossi
authors.forename: Diane
authors.initials: D
authors.lastname: Dalecki
authors.forename: Sheryl
authors.initials: S
authors.lastname: Gracewski
mesh_terms: D003187:Compliance; D003198:Computer Simulation; D003287:Contrast Media; D004867:Equipment Design; D020342:Finite Element Analysis; D005740:Gases; D016014:Linear Models; D045423:Microbubbles; D008962:Models, Theoretical; D009038:Motion; D017711:Nonlinear Dynamics; D009716:Numerical Analysis, Computer-Assisted; D009991:Oscillometry; D010316:Particle Size; D011312:Pressure; D013499:Surface Properties; D013997:Time Factors; D014465:Ultrasonics / Q000295:instrumentation*
chemical_list: D003287:Contrast Media; D005740:Gases
references.citation: Annu Rev Biomed Eng. 2007;9:415-47
references.pmid: 17651012
references.citation: J Acoust Soc Am. 2003 Sep;114(3):1678-90
references.pmid: 14514221
references.citation: J Acoust Soc Am. 2007 Aug;122(2):1191-200
references.pmid: 17672665
references.citation: Ultrasound Med Biol. 2007 Dec;33(12):1978-87
references.pmid: 17900793
references.citation: J Acoust Soc Am. 2004 Jun;115(6):3235-43
references.pmid: 15237848
references.citation: Front Biosci. 2007 Sep 01;12:5124-42
references.pmid: 17569635
references.citation: Ultrasound Med Biol. 2007 Jul;33(7):1140-8
references.pmid: 17478030
references.citation: J Acoust Soc Am. 2009 Dec;126(6):2963-72
references.pmid: 20000909
references.citation: Ultrasound Med Biol. 2007 Oct;33(10):1651-60
references.pmid: 17590501
references.citation: Phys Med Biol. 2005 Nov 21;50(22):5293-305
references.pmid: 16264254
references.citation: J Acoust Soc Am. 2009 Jul;126(1):EL34-40
references.pmid: 19603851
references.citation: J Acoust Soc Am. 2008 Oct;124(4):2374-84
references.pmid: 19062875
references.citation: Phys Med Biol. 2006 Oct 21;51(20):5065-88
references.pmid: 17019026
references.citation: Adv Drug Deliv Rev. 1999 Apr 5;37(1-3):139-157
references.pmid: 10837732