Multiphase fluid-solid coupled analysis of shock-bubble-stone interaction in shockwave lithotripsy

A novel multiphase fluid-solid-coupled computational framework is applied to investigate the interaction of a kidney stone immersed in liquid with a lithotripsy shock wave (LSW) and a gas bubble near the stone. The main objective is to elucidate the effects of a bubble in the shock path to the elastic and fracture behaviors of the stone. The computational framework couples a finite volume 2-phase computational fluid dynamics solver with a finite element computational solid dynamics solver. The surface of the stone is represented as a dynamic embedded boundary in the computational fluid dynamics solver. The evolution of the bubble surface is captured by solving the level set equation. The interface conditions at the surfaces of the stone and the bubble are enforced through the construction and solution of local fluid-solid and 2-fluid Riemann problems. This computational framework is first verified for 3 example problems including a 1D multimaterial Riemann problem, a 3D shock-stone interaction problem, and a 3D shock-bubble interaction problem. Next, a series of shock-bubble-stone-coupled simulations are presented. This study suggests that the dynamic response of a bubble to LSW varies dramatically depending on its initial size. Bubbles with an initial radius smaller than a threshold collapse within 1 μs after the passage of LSW, whereas larger bubbles do not. For a typical LSW generated by an electrohydraulic lithotripter (p_max  = 35.0MPa, p_min  =- 10.1MPa), this threshold is approximately 0.12mm. Moreover, this study suggests that a noncollapsing bubble imposes a negative effect on stone fracture as it shields part of the LSW from the stone. On the other hand, a collapsing bubble may promote fracture on the proximal surface of the stone, yet hinder fracture from stone interior.