Model for bubble dynamics in liquid near an elastic tissue interface.

Abstract

A model is under development for the weakly nonlinear dynamics of a bubble in a blood vessel surrounded by tissue with elasticity and losses. The model requires knowledge of the radiation impedance of the bubble within the vessel, which is determined by the Green’s function. As a first step toward this objective, the Green’s function is derived for a bubble in a liquid half-space bounded by an elastic half-space. The method used to derive the Green’s function follows an approach described previously for the response of an acoustically driven object in an elastic half-space [Zabolotskaya et al., J. Acoust. Soc. Am. 124, 2514(A) (2008)]. The Green’s function is expressed in terms of its angular spectrum in a plane parallel to the interface, resulting in ordinary differential equations in the coordinate normal to the interface. Boundary conditions are satisfied at the interface and in the plane containing the source to obtain solutions of the differential equations, the inverse spatial Fourier transform of which yields the desired Green’s function. Extension to multiple layers of tissue is straightforward. Calculations will be presented for the radiation impedance of the bubble near the interface. [Work supported by the ASA Hunt Fellowship and NIH DK070618.]