LITHOTRIPSY - THE TREATMENT OF KIDNEY-STONES WITH SHOCK-WAVES

This paper discusses mathematical models for the response of a small a ir bubble in water to an ultrasound pulse, a context that arises in th e modern treatment for kidney stones. The paper reviews Rayleigh's 191 7 theory for bubble response, applies asymptotics to describe large-am plitude solutions of Rayleigh's equations, and briefly discusses effec ts neglected in the simple model. The style is expository, intended bo th to introduce this application to mathematicians and to illustrate t he use of asymptotic methods to nonmathematicians.