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Lithotripsy: The treatment of kidney stones with shock waves

Publication ,  Journal Article
Howle, L; Schaeffer, DG; Shearer, M; Zhong, P
Published in: SIAM Review
January 1, 1998

This paper discusses mathematical models for the response of a small air bubble in water to an ultrasound pulse, a context that arises in the modern treatment for kidney stones. The paper reviews Rayleigh's 1917 theory for bubble response, applies asymptotics to describe large-amplitude solutions of Rayleigh's equations, and briefly discusses effects neglected in the simple model. The style is expository, intended both to introduce this application to mathematicians and to illustrate the use of asymptotic methods to nonmathematicians.

Duke Scholars

Published In

SIAM Review

DOI

ISSN

0036-1445

Publication Date

January 1, 1998

Volume

40

Issue

2

Start / End Page

356 / 371

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4901 Applied mathematics
  • 0906 Electrical and Electronic Engineering
  • 0102 Applied Mathematics
 

Citation

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ICMJE
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Howle, L., Schaeffer, D. G., Shearer, M., & Zhong, P. (1998). Lithotripsy: The treatment of kidney stones with shock waves. SIAM Review, 40(2), 356–371. https://doi.org/10.1137/S0036144597322630
Howle, L., D. G. Schaeffer, M. Shearer, and P. Zhong. “Lithotripsy: The treatment of kidney stones with shock waves.” SIAM Review 40, no. 2 (January 1, 1998): 356–71. https://doi.org/10.1137/S0036144597322630.
Howle L, Schaeffer DG, Shearer M, Zhong P. Lithotripsy: The treatment of kidney stones with shock waves. SIAM Review. 1998 Jan 1;40(2):356–71.
Howle, L., et al. “Lithotripsy: The treatment of kidney stones with shock waves.” SIAM Review, vol. 40, no. 2, Jan. 1998, pp. 356–71. Scopus, doi:10.1137/S0036144597322630.
Howle L, Schaeffer DG, Shearer M, Zhong P. Lithotripsy: The treatment of kidney stones with shock waves. SIAM Review. 1998 Jan 1;40(2):356–371.

Published In

SIAM Review

DOI

ISSN

0036-1445

Publication Date

January 1, 1998

Volume

40

Issue

2

Start / End Page

356 / 371

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4901 Applied mathematics
  • 0906 Electrical and Electronic Engineering
  • 0102 Applied Mathematics