Shock-induced bubble jetting into a viscous fluid with application to tissue injury in shock-wave lithotripsy

Abstract

Shock waves in liquids are known to cause spherical gas bubbles to rapidly collapse and form strong re-entrant jets in the direction of the propagating shock. The interaction of these jets with an adjacent viscous liquid is investigated using finite-volume simulation methods. This configuration serves as a model for tissue injury during shock-wave lithotripsy, a medical procedure to remove kidney stones. In this case, the viscous fluid provides a crude model for the tissue. It is found that for viscosities comparable to what might be expected in tissue, the jet that forms upon collapse of a small bubble fails to penetrate deeply into the viscous fluid "tissue." A simple model reproduces the penetration distance versus viscosity observed in the simulations and leads to a phenomenological model for the spreading of injury with multiple shocks. For a reasonable selection of a single efficiency parameter, this model is able to reproduce in vivo observations of an apparent 1000-shock threshold before wide-spread tissue injury occurs in targeted kidneys and the approximate extent of this injury after a typical clinical dose of 2000 shock waves.

Shock wave–bubble interaction near soft and rigid boundaries during lithotripsy: numerical analysis by the improved ghost fluid method

“…Thus far, the shock wave-bubble interaction has been studied with several numerical methods (Calvisi et al 2008, Freund et al 2009, Johnsen and Colonius 2008, 2009, Takahira et al 2008, 2009). Calvisi et al (2008) calculated the bubble collapse near a rigid boundary using the boundary integral method and clarified that the bubble collapse process with the formation of liquid jet depends on the distance of the bubble relative to the wall when the reflection of the incident wave is taken into account.…”

“…Calvisi et al (2008) calculated the bubble collapse near a rigid boundary using the boundary integral method and clarified that the bubble collapse process with the formation of liquid jet depends on the distance of the bubble relative to the wall when the reflection of the incident wave is taken into account. Freund et al (2009) investigated the problem using the finite volume method. They found that the viscous resistance in tissues can significantly suppress the penetration of the liquid jet induced by the bubble collapse.…”

Nonlinear oscillations following the Rayleigh collapse of a gas bubble in a linear viscoelastic (tissue-like) medium

“…When De 1/Re, the time derivative of stresses in Eqs. (9) and (10) is negligible compared to the rest of the terms. A linear analysis is sufficient to obtain the asymptotic solution.…”

“…Fluids 25, 083101 (2013) tissue lies in the viscoelastic, compressible, and multiphase nature of the problem. Direct simulations of the compressible equations of motion have been performed to study single-bubble dynamics in biomedical applications, many of which have been restricted to inviscid [5][6][7][8] and Newtonian 9 simulations. The few direct simulations in a viscoelastic medium are based on Maxwell fluids, none in which compressibility is included, preventing accurate studies of large-amplitude oscillations.…”

Model for the dynamics of two interacting axisymmetric spherical bubbles undergoing small shape oscillations

“…[15][16][17][18][19][20] In addition, shock-wave induced bubble collapse and jetting near a liquid-solid interface have been studied via direct solution of the Navier-Stokes equations. 21, 22 Blake et al studied bubble deformation near a rigid boundary 23 and a free surface. 24 Modeling the system with the boundary element method (BEM), they found that the liquid jet is directed away from the free surface.…”