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...

Full description

Saved in:
Bibliographic Details
Published in:SIAM review 1998-06, Vol.40 (2), p.356-371
Main Authors: Howle, Laurens, Schaeffer, David G., Shearer, Michael, Zhong, Pei
Format: Article
Language:English
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
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0036-1445
1095-7200
DOI:10.1137/S0036144597322630