Acoustic radiation force on a gas bubble in tissue.

Abstract

The motion of a gas bubble subjected to acoustic excitation in a soft elastic medium such as tissue was analyzed previously assuming the radiation force acting on the bubble is the same as in liquid [Ilinskii et al., J. Acoust. Soc. Am. 117, 2338 (2005)]. In the present work we discuss corrections to the acoustic radiation force for finite values of the shear modulus. The analysis is based on the Piola-Kirchhoff equation in Lagrangian coordinates, in which only the stress tensor is nonlinear, and the equation is solved by perturbation. In the linear approximation an analytical solution is obtained for the scattered acoustic wave. The nonlinear stress and full radiation force is calculated at the next order of approximation. For negligible shear modulus the result for a liquid is recovered. For small but finite shear modulus the resulting force differs from that for a liquid by a factor that depends on ktR, where R is bubble radius, kt=ω/ct the wavenumber, ω the angular frequency, and ct the shear wave propagation speed. For ktR>10 the radiation force is practically the same as in liquid, but for ktR<10 its value can be significantly different. [Work supported by NIH DK070618.]