Modeling of the radiation force imparted on a spherical kidney stone by a focused beam of an ultrasound array

Abstract

Radiation force imparted on an elastic scatterer by a narrow ultrasound beam is different from that imparted by a plane wave, especially when the beam waist is comparable or smaller than the scatterer's diameter. Such a situation exists when a kidney stone is pushed by an acoustic wave emitted by a megahertz frequency ultrasound array. A spherical stone of several millimeters in diameter with elastic properties similar to calcium oxalate monohydrate kidney stones is considered. An acoustic wave is taken in a form of a continuous-wave 2.5 MHz focused ultrasound beam emitted by Philips HDI C4-2 imaging array. To study radiation force, the transducer field is created as a sum of plane waves of various inclinations, and scattering of each plane waves is modeled based on a known solution. Numerical calculations show that within some frequency range both the backscattering from and the radiation force on a kidney stone exceeds the values for absolutely soft or rigid spheres of the same diameter. A vector component of the radiation force can be created in a direction other than the ultrasound propagation by targeting off the stone center. [Work supported by NIH (DK43881, DK092197, and DK086371), RFBR, and NSBRI through NASA NCC 9-58.]