# Exploring the interplay of stone-attached and distant cavitation bubbles during extracorporeal shock wave lithotripsy

Kevin Schmidmayer, Guillaume Thomas Bokman, Armand Sieber, Adedotun

Ade-Onojobi, Bratislav Lukic, Gazendra Shakya, Arvid Kühl, Moritz

Schlötter, Markus Belau, Outi Supponen

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## ► To cite this version:

Kevin Schmidmayer, Guillaume Thomas Bokman, Armand Sieber, Adedotun Ade-Onojobi, Bratislav Lukic, et al. Exploring the interplay of stone-attached and distant cavitation bubbles during extracorporeal shock wave lithotripsy. ICMF 2025 - 12th International Conference on Multiphase Flow, May 2025, Toulouse, France. hal-05070922

HAL Id: hal-05070922

https://inria.hal.science/hal-05070922v1

Submitted on 16 May 2025

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# Exploring the interplay of stone-attached and distant cavitation bubbles during extracorporeal shock wave lithotripsy

Kevin Schmidmayer<fnref n="1" />, Guillaume T. Bokman<fnref n="2" />, Armand Sieber<fnref n="2" />, Adedotun Ade-Onojobi<fnref n="1" />,
Bratislav Lukić<fnref n="3" />, Gazendra Shakya<fnref n="2" />, Arvid Kühl<fnref n="4" />, Moritz Schlötter<fnref n="4" />, Markus Belau<fnref n="4" />, Outi Supponen<fnref n="2" />

**Abstract:**

This study investigates the dynamics of cavitation bubbles around kidney stones during extracorporeal shock wave lithotripsy. Through a combination of *in-situ* experiments and diffuse-interface-method simulations, we observed a peculiar interaction between stone-attached and distant bubbles, resulting in a notable pressure increase at the distant-bubble jet-impact site.

**Keywords:** cavitation, bubble, kidney stone, multiphase flow, shock wave

**Introduction:**

Extracorporeal shock wave lithotripsy (ESWL) is a non-invasive medical procedure aimed at breaking down kidney stones into smaller pieces that can be naturally expelled by the body. The interaction of the shock waves with the stone leads to the formation of cavitation bubbles around it, as depicted in Fig. 1. The collapse of these bubbles plays a crucial role in fragmenting the stone, along with the mechanical effects of the shock wave-stone interaction (Sapozhnikov et al., 2007). To thoroughly understand the contribution of cavitation bubbles, particularly those surrounding the stone, to the fragmentation process, a detailed examination of bubble dynamics and their impact on the stone's surface is necessary. To achieve this, we conducted *in-situ* (ultra-)high-speed X-ray imaging of shock wave-stone interactions at the ID19 beamline of the European Synchrotron Radiation Facility. A medical lithotripter was utilized to generate the shock waves. These visualizations were complemented by numerical simulations to assess the wall-pressure distribution, directly correlated with erosion potential and micro-crack formation.

<figure><img src="image_3.png" /><figcaption>Figure 1: (a-f) Experimental (upper) and numerical (lower) results. The simulation shows the pressure field in log scale, overlaid by the vapour content (black). Experiment at times (a) 0, (b) 80, (c) 100, (d) 220, (e) 340, (f) 380 µs after the distant-bubble maximum radius, and simulation at (a) 0, (b) 97, (c) 116, (d) 187, (e) 312, (f) 350 µs. In the experiment, (a) occurs 90 µs after the passage of the shock wave. (g) Pressure profiles for the dual bubbles (stone attached and distant) and the single, stone-attached bubble cases. Probes are placed on the stone surface at angles $\theta$.</figcaption></figure>

**Experimental and numerical methods:**

Experiments have been conducted by placing a model kidney stone under a commercial medical-grade lithotripter (Storz Medical) employing electromagnetic shock wave technology (Modulith SLK). The lithotripter generated shock waves with peak pressures reaching 92 MPa. The phantom, made of a 15–to–6 mixture of Calcium sulfate hemihydrate (Ca2H2O9S2) plaster and water, is soaked and glued to a spring before being placed in the middle of a tank filled with deionised and degassed water. Dynamics are captured through ultra high-speed X-ray phase contrast radioscopy with inter-frame time of 100 kfps using a FASTCAM SA-Z camera (Photron). This is achieved

<footnote n="1">¹Inria center at the university of Bordeaux, project-team CAGIRE, Université de Pau et des Pays de l'Adour, Laboratory of Mathematics and Applied Mathematics (LMAP), Pau, France, kevin.schmidmayer@inria.fr</footnote>

<footnote n="2">²ETH Zurich, Department of Mechanical and Process Engineering, Institute of Fluid Dynamics, Sonneggstrasse 3, 8092 Zurich, Switzerland</footnote>

<footnote n="3">³ESRF – The European Synchrotron, Grenoble, France</footnote>

<footnote n="4">⁴Storz Medical AG, Lohstampfestrasse 8, 8274 Tägerwilen, Switzerland</footnote>
exploiting high brilliance in the hard X-ray regime (about 30 keV) of the European Synchrotron Radiation Facility (ID19 beamline) and enables visual access to all phase discontinuities along the beam path.

In the context of diffuse interface method, a second-order-accurate MUSCL scheme is used to solve a multi-phase flow model including surface-tension effects (Schmidmayer et al., 2017). This modelling is implemented in ECOGEN (Schmidmayer et al., 2020), and has been validated for numerous problems, including cavitation bubble dynamics and high-speed-flow droplet aerobreakup. The 2D axi-symmetric computational setup shown in Fig. 1(a) is an approximation of the complex real-case scenario to better represent an academic case. Specifically, the initial cavitation growth phase is excluded, focusing solely on modelling the collapse phase from the maximum bubble sizes. A Laplace varying pressure initialization is setup around the two vapour bubbles (2700 Pa to 1 atm). In analogy to the experiment state within the region of interest (red rectangle in Fig. 1(a)), the first bubble is a 3.7 mm-radius-long sphere and surrounds the 1.8 mm-radius-long spherical stone. The second is a 0.5 mm- and 0.65 mm-radius-long ellipsoid and its center is located at 0.7 mm from the interface of the stone-attached bubble.

**Results and Discussion:**

Fig. 1(a-f) presents the experimental and numerical results of the collapsing phase of the bubbles around the stone. Distant bubbles of particular interest are highlighted in Fig. 1(a). The simulation mimics the one indicated with a solid-lined arrow. One can observe in (b) a peculiar jet formation with an almost flat interface on the free field side of the bubble. This is followed by the collapse (c) and jet (d) of the distant bubble. (e) The jet continues during the growth phase of the distant bubble to pierce the larger bubble attached to the stone. The jet eventually impacts the stone while the stone-attached bubble is still collapsing. The latter then collapses and emits a shock wave. (f) This shock wave interacts with the remaining parts of the distant bubble, leading to a greater shock-wave emission.

Finally, the bubble cloud formed enters a new growth phase.
Fig. 1(g) illustrates the pressures measurements from three probes located at 0°, 45° and 90° from the horizontal axis, during two simulations: the dual-bubble case of Fig. 1, and a simulation of a single, stone-attached bubble (no distant bubble). The latter serves as a reference to analyse the impact of peculiar dynamics observed with the dual bubbles. We observe a significant increase in peak pressure at the location of jet impact for the dual-bubble case, with $p_{max} = 70.6$ MPa, compared to $p_{max} = 10.4$ MPa for the reference case. These high-pressure peaks coincide with the collapse time of the stone-attached bubble, whereas the impact of the jet itself is relatively negligible, registering at $p_{impact} = 0.402$ MPa. Additionally, it is worth noting that the upper part of the stone remains unaffected by the dynamics of the distant bubble. We also observe an increase of the pressure impulse $j$ of 313%, calculated as $j = \int_0^t \max[p - p_{ref}, 0] dt$ with $p_{ref} = 10\% p_{max}$, yielding $j_{dual} = 15.33$ Pa s and $j_{single} = 4.90$ Pa s.

**Conclusion:**

Our study sheds light on the intricate dynamics of cavitation bubbles surrounding kidney stones during ESWL. We observed a unique phenomenon where stone-attached and distant bubbles interact with the stone, causing a significant pressure amplification at the jet-impact location. While the presence of dual bubbles leads to higher pressure peaks, the distant-bubble jet's impact alone is minor compared to the collapse of the stone-attached bubble. Our presentation will provide deeper insights into these dynamics, exploring additional configurations to the ones studied here.

**Acknowledgments:**

Authors acknowledge the financial support from ESRF-ID19-ME-1663.

**References**

O. A. Sapozhnikov, A. D. Maxwell, B. MacConaghy, and M. R. Bailey. A mechanistic analysis of stone fracture in lithotripsy. *J. Acoust. Soc. Am.*, 121(2):1190–1202, 2007.

K. Schmidmayer, F. Petitpas, E. Daniel, N. Favrie, and S. L. Gavrilyuk. A model and numerical method for compressible flows with capillary effects. *J. Comp. Phys.*, 334:468–496, 2017.

K. Schmidmayer, F. Petitpas, S. Le Martelot, and E. Daniel. ECOGEN: An open-source tool for multiphase, compressible, multiphysics flows. *Comp. Phys. Com.*, 251:107093, 2020.