Wang KG, 2016: Multiphase Fluid-Solid Coupled Analysis of Shock-Bubble-Stone Interaction in Shockwave Lithotripsy.
Department of Aerospace and Ocean Engineering, Virginia Tech, Blacksburg, 24061, VA, USA.
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 two-phase computational fluid dynamics (CFD) solver with a finite element (FE) computational solid dynamics (CSD) solver. The surface of the stone is represented as a dynamic embedded boundary in the CFD 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 two-fluid Riemann problems. This computational framework is first verified for three example problems including a one-dimensional (1D) multi-material Riemann problem, a three-dimensional (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 1μs after the passage of LSW; whereas larger bubbles do not. For a typical LSW generated by an electrohydraulic lithotripter (pmax =35.0MPa, pmin =-10.1MPa), this threshold is approximately 0.12mm. Moreover, this study suggests that a non-collapsing 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.
Int J Numer Method Biomed Eng. 2016 Nov 24. doi: 10.1002/cnm.2855. [Epub ahead of print]
The title of the paper indicates a direct impact on shockwave lithotripsy. Since cavitation and shockwave interaction with bubbles are considered an essential mechanism of stone comminution a better understanding of bubble dynamics is desired. The paper makes use of a noval multiphase fluid-solid coupled computational framework to calculate the interaction of a lithotripsy shockwave (LSW) with a gas bubble near the stone. Some 30 pages of calculation later we get to know how bubbles interact with lithotripsy shock waves in the first 1µs after interaction with the LSW and under which conditions a microjet is generated.
An essential part of a LSW, however, is a tensile pressure lasting several µs. This part is not considered yet but has an extraordinary impact on generation of cavitation bubbles. LSW generated bubbles are similar to a wake vortex following a flying jet. They start as tiny bubbles during the negative pressure phase of the LSW after the short positive pressure peak has passed (see atttached schlierenphotography).
These shock wave-generated cavitation bubbles collaps within several 100 µs and vanish completely after 1 ms. That means, a second LWS will not find cavitation bubbles of a previous shock wave unless it will be fired in less than 1ms delay. Usually clinical application of repetitive LSW is performed with 1-2 Hz, equivalant 500-1000 ms. In real shockwave lithotripsy we, therefore, cannot suppose having sufficient bubbles near the stone to be exposed by the front of the LSW since they follow the front some µs later.
The picture shows a travelling LSW from left to right close to the focus zone in water. Cavitation bubbles appear in the tensile pressure phase (green) and grow within several 10 µs.
Some of the bubbles collapsed already (left) and generated shperical shockwaves.
All comprehensive calculations of this paper are based on pre-existing bubbles near to the stone surface which is, in our mind, not a realistic assumption for shock wave lithotripsy.
This is an excellent paper, on bubble dynamics, however, the relevance for shock wave lithotripsy is limited.