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2010, 11

Alexander R. Klotz, Kullervo Hynynen

Simulations of the Devin and Zudin modified Rayleigh-Plesset equations to model bubble dynamics in a tube

language: English

received 20.05.2010, published 30.06.2010

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Micron-sized bubbles are used as contrast agents in biomedical ultrasound. While free bubbles are modeled using the Rayleigh-Plesset equation, their dynamics in tubes or vessels are not as well understood. In this paper, the dynamics of a microbubble in a cylindrical tube are simulated by two modified Rayleigh-Plesset equations: one derived by Y. B. Zudin in 1991 but not simulated, and another developed by C. Devin in 1961 but not expressed explicitly. The expressions are manipulated to a common form and shown to be nearly identical. The results of the simulations are compared to each other and various analytical models, as well as to experimental results. Both models show decreased resonant frequency and oscillation amplitude with decreasing tube radius. Agreement is found with established theories and limited experimental results. Thus, the equations may provide an effective tool for simulating bubble behavior in rigid tubes.

Keywords: Ultrasound, contrast agent, bubble, tube, vessel, Rayleigh-Plesset equation

15 pages, 6 figures

Сitation: Alexander R. Klotz, Kullervo Hynynen. Simulations of the Devin and Zudin modified Rayleigh-Plesset equations to model bubble dynamics in a tube. Electronic Journal “Technical Acoustics”,, 2010, 11.


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Alexander R. Klotz is currently a graduate student in the department of physics at McGill University in Montreal. He attained his B.Sc. in physics at Queen's University before researching bubble dynamics for therapeutic ultrasound at Sunnybrook Health Sciences Centre in Toronto. He is currently studying the behavior of DNA in nanofluidic environments.

e-mail: klotza(at)


Kullervo Hynynen is the director of the Department of Imaging Research at Sunnybrook Health Sciences Centre in Toronto. He is also a professor in the Department of Medical Biophysics at the University of Toronto. He attained his B.Sc and M.Sc. degrees at the University of Kuopio in Finland and his Ph.D. at the University of Aberdeen in the United Kingdom. His research interests include therapeutic ultrasound and MRI thermometry.