Acoustic radiation force on a sphere in tissue

Abstract

A theory is presented for the acoustic radiation force on a sphere embedded in a soft elastic medium that possesses a shear modulus μ several orders of magnitude smaller than its bulk modulus. Scattering of both compressional and shear waves is taken into account. There is no restriction on the size of the sphere or, apart from axisymmetry, the form of the incident compressional wave. The analysis employs the Piola-Kirchhoff pseudostress tensor and Lagrangian coordinates. In the linear approximation an analytical solution is obtained for the scattered waves. The nonlinear stress and full radiation force are calculated at the next order of approximation. For a small sphere and μ≈0 the classical result for a particle in liquid is recovered. For small but finite shear modulus the radiation force is evaluated for a gas bubble driven at a frequency below resonance. The predicted magnitude of the radiation force on the bubble is found to be less than that in liquid by the factor [1+(4/3)μ/γ P 0]-1, where P 0 is the ambient pressure and γ the ratio of specific heats of the gas. Influence of the scattered shear wave in this limit is negligible. [Work supported by NIH DK070618.]