Modeling of photoelastic imaging of mechanical stresses in transparent solids mimicking kidney stones

Shock waves generated by toroidal bubble collapse are imperative for kidney stone dusting during Holmium:YAG laser lithotripsy

Holmium:yttrium-aluminum-garnet (Ho:YAG) laser lithotripsy (LL) has been the treatment of choice for kidney stone disease for more than two decades, yet the mechanisms of action are not completely clear. Besides photothermal ablation, recent evidence suggests that cavitation bubble collapse is pivotal in kidney stone dusting when the Ho:YAG laser operates at low pulse energy (Ep) and high frequency (F). In this work, we perform a comprehensive series of experiments and model-based simulations to dissect the complex physical processes in LL. Under clinically relevant dusting settings (Ep = 0.2 J, F = 20 Hz), our results suggest that majority of the irradiated laser energy (>90 %) is dissipated by heat generation in the fluid surrounding the fiber tip and the irradiated stone surface, while only about 1 % may be consumed for photothermal ablation, and less than 0.7 % is converted into the potential energy at the maximum bubble expansion. We reveal that photothermal ablation is confined locally to the laser irradiation spot, whereas cavitation erosion is most pronounced at a fiber tip-stone surface distance about 0.5 mm where multi foci ring-like damage outside the thermal ablation zone is observed. The cavitation erosion is caused by the progressively intensified collapse of jet-induced toroidal bubble near the stone surface (<100 μm), as a result of Raleigh-Taylor and Richtmyer-Meshkov instabilities. The ensuing shock wave-stone interaction and resultant leaky Rayleigh waves on the stone surface may lead to dynamic fatigue and superficial material removal under repeated bombardments of toroidal bubble collapses during dusting procedures in LL.

Improving burst wave lithotripsy effectiveness for small stones and fragments by increasing frequency: theoretical modeling and ex vivo study

INTRODUCTION AND OBJECTIVE

In clinical trial NCT03873259, a 2.6-mm lower pole stone was treated transcutaneously and ex vivo with 390-kHz burst wave lithotripsy (BWL) for 40 minutes and failed to break. The stone was subsequently fragmented with 650-kHz BWL after a 4-minute exposure. This study investigated how to fragment small stones and why varying BWL frequency may more effectively fragment stones to dust.

METHODS

A linear elastic model was used to calculate the stress created inside stones from shock wave lithotripsy (SWL) and different BWL frequencies mimicking the stone's size, shape, lamellar structure, and composition. To test model predictions about the impact of BWL frequency, matched pairs of stones (1-5 mm) were treated at 1) 390 kHz, 2) 830 kHz, and 3) 390 kHz followed by 830 kHz. The mass of fragments greater than 1 and 2 mm was measured over 10 minutes of exposure.

RESULTS

The linear elastic model predicts that the maximum principal stress inside a stone increases to more than 5.5 times the pressure applied by the ultrasound wave as frequency is increased, regardless of composition tested. The threshold frequency for stress amplification is proportionate to the wave speed divided by the stone diameter. Thus, smaller stones may be likely to fragment at higher frequency, but not lower frequency below a limit. Unlike with SWL, this amplification in BWL occurs consistently with spherical and irregularly shaped stones. In water tank experiments, stones smaller than the threshold size broke fastest at high frequency (p=0.0003), whereas larger stones broke equally well to sub-millimeter dust at high, low, or mixed frequency.

CONCLUSIONS

For small stones and fragments, increasing frequency of BWL may produce amplified stress in the stone causing the stone to break. Using the strategies outlined here, stones of all sizes may be turned to dust efficiently with BWL.

Maximizing mechanical stress in small urinary stones during burst wave lithotripsy

Unlike shock wave lithotripsy, burst wave lithotripsy (BWL) uses tone bursts, consisting of many periods of a sinusoidal wave. In this work, an analytical theoretical approach to modeling mechanical stresses in a spherical stone was developed to assess the dependence of frequency and stone size on stress generated in the stone. The analytical model for spherical stones is compared against a finite-difference model used to calculate stress in nonspherical stones. It is shown that at low frequencies, when the wavelength is much greater than the diameter of the stone, the maximum principal stress is approximately equal to the pressure amplitude of the incident wave. With increasing frequency, when the diameter of the stone begins to exceed about half the wavelength in the surrounding liquid (the exact condition depends on the material of the stone), the maximum stress increases and can be more than six times greater than the incident pressure. These results suggest that the BWL frequency should be elevated for small stones to improve the likelihood and rate of fragmentation.

Variations of stress field and stone fracture produced at different lateral locations in a shockwave lithotripter field

During clinical procedures, the lithotripter shock wave (LSW) that is incident on the stone and resultant stress field is often asymmetric due to the respiratory motion of the patient. The variations of the LSW-stone interaction and associated fracture pattern were investigated by photoelastic imaging, phantom experiments, and three-dimensional fluid-solid interaction modeling at different lateral locations in a lithotripter field. In contrast to a T-shaped fracture pattern often observed in the posterior region of the disk-shaped stone under symmetric loading, the fracture pattern gradually transitioned to a tilted L-shape under asymmetric loading conditions. Moreover, the model simulations revealed the generation of surface acoustic waves (SAWs), i.e., a leaky Rayleigh wave on the anterior boundary and Scholte wave on the posterior boundary of the stone. The propagation of SAWs on the stone boundary is accompanied by a progressive transition of the LSW reflection pattern from regular to von Neumann and to weak von Neumann reflection near the glancing incidence and, concomitantly, the development and growth of a Mach stem, swirling around the stone boundary. The maximum tensile stress and stress integral were produced by SAWs on the stone boundary under asymmetric loading conditions, which drove the initiation and extension of surface cracks into the bulk of the stone that is confirmed by micro-computed tomography analysis.