Abstract

Unlike shock wave lithotripsy, burst wave lithotripsy (BWL) uses tone bursts, consisting of many periods of sine wave. The fragmentation threshold of a stone depends on the burst frequency or, for a given frequency, on the stone size. In this work, an analytical theoretical approach to modeling mechanical stresses in a spherical stone has been developed. The theory is based on the method previously used to study the acoustic radiation force acting on an elastic stone [Sapozhnikov and Bailey, J. Acoust. Soc. Am. (2013)]. It has been shown that at low frequencies, when the wavelength is much greater than the diameter of the stone, the maximum principal stress is approximately equal to the pressure amplitude of the incident wave. With increasing frequency, when the diameter of the stone begins to exceed about half the wavelength in a surrounding liquid (the exact condition depends on the material of the stone), the maximum stress increases and can reach five times the pressure amplitude or even more. This observation suggests adjusting the BWL frequency depending on the stone diameter in order to comminute it into passable fragments. [Work supported by NIH, Nos. P01-DK043881 and RBBR 20-02-00139.]

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