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Lithotripsy: The Treatment of Kidney Stones with Shock Waves
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 solutio...
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| Published in: | SIAM review 1998-06, Vol.40 (2), p.356-371 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c320t-968869ebaf72582804859c0ab1dd6e16659b3ccf3ffc2c179da2851f13c45eb03 |
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| cites | cdi_FETCH-LOGICAL-c320t-968869ebaf72582804859c0ab1dd6e16659b3ccf3ffc2c179da2851f13c45eb03 |
| container_end_page | 371 |
| container_issue | 2 |
| container_start_page | 356 |
| container_title | SIAM review |
| container_volume | 40 |
| creator | Howle, Laurens Schaeffer, David G. Shearer, Michael Zhong, Pei |
| description | 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. |
| doi_str_mv | 10.1137/S0036144597322630 |
| format | article |
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| fulltext | fulltext |
| identifier | ISSN: 0036-1445 |
| ispartof | SIAM review, 1998-06, Vol.40 (2), p.356-371 |
| issn | 0036-1445 1095-7200 |
| language | eng |
| recordid | cdi_proquest_journals_194203370 |
| source | Business Source Ultimate【Trial: -2024/12/31】【Remote access available】; JSTOR Archival Journals and Primary Sources Collection; SIAM美国工业和应用数学学会电子期刊 - Locus过刊全文数据库 |
| subjects | Bubbles Cavitation flow Classical and quantum physics: mechanics and fields Classical mechanics of continuous media: general mathematical aspects Classroom Notes Compressibility Computational methods in fluid dynamics Exact sciences and technology Fluid mechanics: general mathematical aspects Function theory, analysis Kidney stones Kidneys Liquids Lithotripsy Mathematical analysis Mathematical methods in physics Mathematical models Mathematical problems Mathematics Mathematics education Medical procedures Partial differential equations Physics Pressure pulses Sciences and techniques of general use Shock waves |
| title | Lithotripsy: The Treatment of Kidney Stones with Shock Waves |
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