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 the BWL frequency may more effectively fragment stones to dust.Methods: A linear elastic theoretical 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 >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 the 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 a higher frequency, but not at a 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 submillimeter dust at high, low, or mixed frequencies.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.