Damage Potential of the Shock-induced Collapse of a Gas Bubble

Numerical simulations are used to evaluate the damage potential of the shock-induced collapse of a pre-existing gas bubble near a rigid surface. In the context of shock wave lithotripsy, a medical procedure where focused shock waves are used to pulverize kidney stones, shock-induced bubble collapse represents a potential mechanism by which the shock energy directed at the stone may be amplified and concentrated. First the bubble dynamics of shock-induced collapse are discussed. As an indication of the damage potential, the wall pressure is considered. It is found that, for bubbles initially close to the wall, local pressures greater than 1 GPa are achieved. For larger stand-off distances, the wall pressure is inversely proportional to the location of bubble collapse. From this relationship, it is found that bubbles within a certain initial stand-off distance from the wall amplify the pressure of the incoming shock. Furthermore, the extent along the wall over which the pressure due to bubble collapse is higher than that of the pulse is estimated. In addition, the present computational fluid dynamics simulations are used as input into an elastic waves propagation code, in order to investigate the stresses generated within kidney stone in the context of shock wave lithotripsy. The present work shows that the shock-induced collapse of a gas bubble has potential not only for erosion along the stone surface, but also for structural damage within the stone due to internal wave reflection and interference. Address all correspondence to this author. INTRODUCTION Shock wave lithotripsy (SWL) is a non-invasive medical procedure in which shock waves are focused on kidney stones in an attempt to break them [2]. A lithotripter pulse consists of a sharp compressive front, followed by a long expansion tail that has a tensile component, as shown in Figure 1. Since kidney stones typically reside in urine and pooled blood, cavitation bubbles form after the passage of the tensile part of the pulse. The exact mechanism responsible for stone comminution has not yet been fully determined; however, two main mechanisms are thought to play an important role: wave propagation within the stone [3,20] and cavitation erosion along the stone surface [5,6]. Wave propagation within the stone leads to several kinds of failure. First, shear waves and surface waves resulting from the different speed of propagation of the shock in the fluid and in the stone interfere constructively to form regions of high stresses [3]. Second, it has been postulated that dynamic squeezing due to the pressure wave in the liquid acts as a compressive hoop stress [7]. Finally, lithotripter pulses propagating through the stone invert their amplitude upon reflection off the distal side of the stone [8, 19]; for stones greater than a certain size, this large negative pressure superposes with the tensile part of the incoming pulse, thus creating a magnified tensile region and breaking the stone near the posterior end. Because of the wave reflection within the stone, both of these phenomena are strongly affected by the geometry and size of the stone. Another process of importance in stone comminution is cavitation erosion. After the passage of the tensile part of the pulse, vapor bubbles grow and gather as a cloud near the stone 1 Copyright c © 2009 by ASME