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Response of constrained and unconstrained bubbles to lithotripter shock wave pulses

The Gilmore formulation for spherical bubble dynamics [F. R. Gilmore, The Growth or Collapse of a Spherical Bubble in a Viscous Compressible Liquid (California Institute of Technology, Pasadena, CA, 1952), Rep. No. 26‐4] is used to investigate the response of air bubbles to a variety of lithotripter... Full description

Journal Title: The Journal of the Acoustical Society of America December 1994, Vol.96(6), pp.3636-3644
Main Author: Ding, Zhong
Other Authors: Gracewski, S. M.
Format: Electronic Article Electronic Article
Language: English
Subjects:
ID: ISSN: 0001-4966 ; DOI: 10.1121/1.410582
Link: http://dx.doi.org/10.1121/1.410582
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recordid: aip_complete10.1121/1.410582
title: Response of constrained and unconstrained bubbles to lithotripter shock wave pulses
format: Article
creator:
  • Ding, Zhong
  • Gracewski, S. M.
subjects:
  • Lithotripsy
ispartof: The Journal of the Acoustical Society of America, December 1994, Vol.96(6), pp.3636-3644
description: The Gilmore formulation for spherical bubble dynamics [F. R. Gilmore, The Growth or Collapse of a Spherical Bubble in a Viscous Compressible Liquid (California Institute of Technology, Pasadena, CA, 1952), Rep. No. 26‐4] is used to investigate the response of air bubbles to a variety of lithotripter shock waveforms. A modification of the Gilmore model is proposed to account for partial constraint of the bubble expansion that can be caused by bubble coatings (such as in echo contrast agents) and by tissues or vessels surrounding bubbles in vivo . In the modified formulation, a viscoelastic membrane is assumed to exist at the bubble interface to include the possible effects of the nonlinear elasticity and strain rate dependent viscosity on the bubble response. The stress induced in the membrane is assumed to be an exponential function of the bubble radius, which tends to restrict the bubble expansion. The viscosity is assumed to increase with the strain rate. In the absence of the membrane, the maximum bubble wall pressure induced by a negative (tensile) pulse is much larger than that induced by a positive (compressive) pulse of the same pressure waveform and amplitude. This difference increases with decreasing initial bubble radius. The addition of the viscoelastic membrane significantly decreases the predicted maximum bubble pressure and the difference in response between the positive and negative pulses. The effect of the time delay between double pulses (positive followed by negative or negative followed by positive) is also investigated for unconstrained bubbles.
language: eng
source:
identifier: ISSN: 0001-4966 ; DOI: 10.1121/1.410582
fulltext: fulltext
issn:
  • 0001-4966
  • 00014966
url: Link


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titleResponse of constrained and unconstrained bubbles to lithotripter shock wave pulses
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descriptionThe Gilmore formulation for spherical bubble dynamics [F. R. Gilmore, The Growth or Collapse of a Spherical Bubble in a Viscous Compressible Liquid (California Institute of Technology, Pasadena, CA, 1952), Rep. No. 26‐4] is used to investigate the response of air bubbles to a variety of lithotripter shock waveforms. A modification of the Gilmore model is proposed to account for partial constraint of the bubble expansion that can be caused by bubble coatings (such as in echo contrast agents) and by tissues or vessels surrounding bubbles in vivo . In the modified formulation, a viscoelastic membrane is assumed to exist at the bubble interface to include the possible effects of the nonlinear elasticity and strain rate dependent viscosity on the bubble response. The stress induced in the membrane is assumed to be an exponential function of the bubble radius, which tends to restrict the bubble expansion. The viscosity is assumed to increase with the strain rate. In the absence of the membrane, the maximum bubble wall pressure induced by a negative (tensile) pulse is much larger than that induced by a positive (compressive) pulse of the same pressure waveform and amplitude. This difference increases with decreasing initial bubble radius. The addition of the viscoelastic membrane significantly decreases the predicted maximum bubble pressure and the difference in response between the positive and negative pulses. The effect of the time delay between double pulses (positive followed by negative or negative followed by positive) is also investigated for unconstrained bubbles.
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descriptionThe Gilmore formulation for spherical bubble dynamics [F. R. Gilmore, The Growth or Collapse of a Spherical Bubble in a Viscous Compressible Liquid (California Institute of Technology, Pasadena, CA, 1952), Rep. No. 26‐4] is used to investigate the response of air bubbles to a variety of lithotripter shock waveforms. A modification of the Gilmore model is proposed to account for partial constraint of the bubble expansion that can be caused by bubble coatings (such as in echo contrast agents) and by tissues or vessels surrounding bubbles in vivo . In the modified formulation, a viscoelastic membrane is assumed to exist at the bubble interface to include the possible effects of the nonlinear elasticity and strain rate dependent viscosity on the bubble response. The stress induced in the membrane is assumed to be an exponential function of the bubble radius, which tends to restrict the bubble expansion. The viscosity is assumed to increase with the strain rate. In the absence of the membrane, the maximum bubble wall pressure induced by a negative (tensile) pulse is much larger than that induced by a positive (compressive) pulse of the same pressure waveform and amplitude. This difference increases with decreasing initial bubble radius. The addition of the viscoelastic membrane significantly decreases the predicted maximum bubble pressure and the difference in response between the positive and negative pulses. The effect of the time delay between double pulses (positive followed by negative or negative followed by positive) is also investigated for unconstrained bubbles.
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abstractThe Gilmore formulation for spherical bubble dynamics [F. R. Gilmore, The Growth or Collapse of a Spherical Bubble in a Viscous Compressible Liquid (California Institute of Technology, Pasadena, CA, 1952), Rep. No. 26‐4] is used to investigate the response of air bubbles to a variety of lithotripter shock waveforms. A modification of the Gilmore model is proposed to account for partial constraint of the bubble expansion that can be caused by bubble coatings (such as in echo contrast agents) and by tissues or vessels surrounding bubbles in vivo . In the modified formulation, a viscoelastic membrane is assumed to exist at the bubble interface to include the possible effects of the nonlinear elasticity and strain rate dependent viscosity on the bubble response. The stress induced in the membrane is assumed to be an exponential function of the bubble radius, which tends to restrict the bubble expansion. The viscosity is assumed to increase with the strain rate. In the absence of the membrane, the maximum bubble wall pressure induced by a negative (tensile) pulse is much larger than that induced by a positive (compressive) pulse of the same pressure waveform and amplitude. This difference increases with decreasing initial bubble radius. The addition of the viscoelastic membrane significantly decreases the predicted maximum bubble pressure and the difference in response between the positive and negative pulses. The effect of the time delay between double pulses (positive followed by negative or negative followed by positive) is also investigated for unconstrained bubbles.
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