The collapse of single bubbles and approximation of the far-field acoustic emissions for cavitation induced by shock wave lithotripsy

Abstract

Recent clinical trials have shown the efficacy of a passive acoustic device used during shock wave lithotripsy (SWL) treatment. The device uses the far-field acoustic emissions resulting from the interaction of the therapeutic shock waves with the tissue and kidney stone to diagnose the effectiveness of each shock in contributing to stone fragmentation. This paper details simulations that supported the development of that device by extending computational fluid dynamics (CFD) simulations of the flow and near-field pressures associated with shock-induced bubble collapse to allow estimation of those far-field acoustic emissions. This is a required stage in the development of the device, because current computational resources are not sufficient to simulate the far-field emissions to ranges of O(10 cm) using CFD. Similarly, they are insufficient to cover the duration of the entire cavitation event, and here simulate only the first part of the interaction of the bubble with the lithotripter shock wave in order to demonstrate the methods by which the far-field acoustic emissions resulting from the interaction can be estimated. A free-Lagrange method (FLM) is used to simulate the collapse of initially stable air bubbles in water as a result of their interaction with a planar lithotripter shock. To estimate the far-field acoustic emissions from the interaction, this paper developed two numerical codes using the Kirchhoff and Ffowcs William-Hawkings (FW-H) formulations. When coupled to the FLM code, they can be used to estimate the far-field acoustic emissions of cavitation events. The limitation of the technique is that it assumes that no significant nonlinear acoustic propagation occurs outside the control surface. Methods are outlined for ameliorating this problem if, as here, computational resources cannot compute the flow field to sufficient distance, although for the clinical situation discussed, this limitation is tempered by the effect of tissue absorption, which here is incorporated through the standard derating procedure. This approach allowed identification of the sources of, and explanation of trends seen in, the characteristics of the far-field emissions observed in clinic, to an extent that was sufficient for the development of this clinical device.

Prediction of far-field acoustic emissions from cavitation clouds during shock wave lithotripsy for development of a clinical device

“…Pressures at such distances for propagation through water can readily be calculated using the Gilmore model [40], although this study highlights that, when doing so, it is important to assess whether the assumptions inherent in the Gilmore model are germane to the scenario being simulated (see §4). Even for propagation in water, if the bubble collapses asymmetrically as in this study, the source of the pressure wave is incorrectly modelled by the Gilmore model as being the spherically compressed gas, rather than the blast wave [15,41]. Furthermore, propagation through tissue generates higher absorption than occurs in water.…”

“…Furthermore, propagation through tissue generates higher absorption than occurs in water. There are standard methods for derating predictions made for propagation in water to give estimates of what form the pulse would take if it propagated through tissue, and these have been applied to this problem [15,41]. However, the appropriateness of using the standard method to correct for absorption by the intervening tissue has not been addressed for cases such as the shocks presented here, and this will be also discussed in §4.…”

“…However, account must be taken of absorption in the tissue and the effect of neglecting any nonlinear propagation in this way. Providentially, tissue absorption is the simpler feature to include if standard techniques are followed and are valid (a question discussed further in §4), and its inclusion reduces the importance of nonlinear propagation because high absorption rapidly attenuates the amplitude of the wave [15,41].…”

“…This study forms the third part in a series of simulation studies [14,15] that complement a series of laboratory and clinical studies [16][17][18], which together form a coherent research programme aimed at the development of a passive acoustic device for monitoring the effectiveness of SWL. Following successful clinical trials where its automated response proved to have 94.7 per cent sensitivity in predicting a successful patient outcome, compared with 36.8 per cent achieved by the clinician performing the treatment [18], this device is currently being used for real-time assessment of treatment in the clinic (a typical lithotripsy treatment lasts about an hour).…”

“…Therefore, the second stage of the work developed techniques for predicting the pressure field generated in the far field by the interactions of the incident lithotripter shock, the blast wave and signals reflected from the stone [15]. All of the work in the first and second stages simulated single bubbles.…”