Sapozhnikov OA. et al., 2021: Maximizing mechanical stress in small urinary stones during burst wave lithotripsy.

Wednesday, 17 August 2022

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Sapozhnikov OA, Maxwell AD, Bailey MR.
Physics Faculty, Moscow State University, Leninskie Gory, Moscow 119991, Russia.
Department of Urology, University of Washington School of Medicine, Seattle, Washington 98195, USA.
Center for Industrial and Medical Ultrasound, Applied Physics Laboratory, University of Washington, 1013 NE 40th Street, Seattle, Washington 98105, USA.

Abstract

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.
J Acoust Soc Am. 2021 Dec;150(6):4203. doi: 10.1121/10.0008902. PMID: 34972267

Comments 1

Othmar Wess on Wednesday, 17 August 2022 10:30

This is another publication of the group (Oleg A. Sapozhnikov, Adam D. Maxwell and Michael R. Bailey) dealing with Burst Wave Lithotripsy (BWL). The recently published paper (1) (Harper et al. 2022) reported BWL on first 19 patients with fragmentation success of 91% and 39% smaller than 2mm. They failed to comminute a small stone (2.6mm) and argued that not enough stress could be generated within the stone to fragmentize.
Rather than Shock Wave Lithotripsy (SWL) which is based on momentum transfer to generate extremely short (microsecond) pulse forces capable to comminute larger as well as smaller stones with the same mechanism (2), BWL is based on resonance phenomena of burst of ultrasound waves of narrow band-width. The problem of BWL with small stones (smaller than ½ wavelengths) is, that waves cannot interfere constructively and destructively in the stone and the required stress enhancement by constructive interference fails.
Generally, the resonance amplification of an oscillatory body (e.g. stone) depends on mass, size, shape, different material properties, wave damping and others. Human urinary stones are different in size, shape and composition and have individual resonance frequencies.
In this work, an analytical theoretical approach to modelling mechanical stresses in a spherical stone was developed to assess the dependence of frequency and stone size on stress generated in the stone. The paper develops the theoretical background for the appropriate frequencies for small stones. The calculations deliver insight into the mechanism of stress generation. It is shown that higher frequencies can excite various vibration modes in different types of defined stones of selected shape and selected composition. Calculated stress enhancements reaches values up to 6 times more than the incident pressure. The use of higher frequencies may enable BWL to fragmentize smaller stones than with lower frequencies as used in current devices.
The analytical calculations confirm that small stones require higher frequencies (higher than efficient for larger stones) to reach high stress amplitudes in their individual vibration modes. Following the results, an additional transducer dedicated to perform on smaller stones has to be integrated within the one for larger stones or, two separate transducer should act one after the other, when coarse fragmentation has left a bulk of smaller fragments requiring further fragmentation. This is not a simple task.
The goal of the group, to develop a small, handheld and easy to use BWL-device still needs some ingenious work to be done.

(1) Harper JD et al., Fragmentation of Stones by Burst Wave Lithotripsy in the First 19 Humans,
J Urol. 2022 May ; 207(5): 1067–1076.
(2) Wess O J, Mayer J., Fragmentation of brittle material by shock wave lithotripsy. Momentum transfer and inertia: a novel view on fragmentation mechanism. Urolithiasis 48, 137-149 (2020)

Othmar Wess

This is another publication of the group (Oleg A. Sapozhnikov, Adam D. Maxwell and Michael R. Bailey) dealing with Burst Wave Lithotripsy (BWL). The recently published paper (1) (Harper et al. 2022) reported BWL on first 19 patients with fragmentation success of 91% and 39% smaller than 2mm. They failed to comminute a small stone (2.6mm) and argued that not enough stress could be generated within the stone to fragmentize.
Rather than Shock Wave Lithotripsy (SWL) which is based on momentum transfer to generate extremely short (microsecond) pulse forces capable to comminute larger as well as smaller stones with the same mechanism (2), BWL is based on resonance phenomena of burst of ultrasound waves of narrow band-width.  The problem of BWL with small stones (smaller than ½ wavelengths) is, that waves cannot interfere constructively and destructively in the stone and the required stress enhancement by constructive interference fails. 
Generally, the resonance amplification of an oscillatory body (e.g. stone) depends on mass, size, shape, different material properties, wave damping and others. Human urinary stones are different in size, shape and composition and have individual resonance frequencies. 
In this work, an analytical theoretical approach to modelling mechanical stresses in a spherical stone was developed to assess the dependence of frequency and stone size on stress generated in the stone. The paper develops the theoretical background for the appropriate frequencies for small stones. The calculations deliver insight into the mechanism of stress generation. It is shown that higher frequencies can excite various vibration modes in different types of defined stones of selected shape and selected composition. Calculated stress enhancements reaches values up to 6 times more than the incident pressure. The use of higher frequencies may enable BWL to fragmentize smaller stones than with lower frequencies as used in current devices. 
The analytical calculations confirm that small stones require higher frequencies (higher than efficient for larger stones) to reach high stress amplitudes in their individual vibration modes. Following the results, an additional transducer dedicated to perform on smaller stones has to be integrated within the one for larger stones or, two separate transducer should act one after the other, when coarse fragmentation has left a bulk of smaller fragments requiring further fragmentation. This is not a simple task. 
The goal of the group, to develop a small, handheld and easy to use BWL-device still needs some ingenious work to be done.

(1) Harper JD et al., Fragmentation of Stones by Burst Wave Lithotripsy in the First 19 Humans, 
J Urol. 2022 May ; 207(5): 1067–1076.
(2) Wess O J, Mayer J., Fragmentation of brittle material by shock wave lithotripsy. Momentum transfer and inertia: a novel view on fragmentation mechanism. Urolithiasis 48, 137-149 (2020)

Othmar Wess

This is another publication of the group (Oleg A. Sapozhnikov, Adam D. Maxwell and Michael R. Bailey) dealing with Burst Wave Lithotripsy (BWL). The recently published paper (1) (Harper et al. 2022) reported BWL on first 19 patients with fragmentation success of 91% and 39% smaller than 2mm. They failed to comminute a small stone (2.6mm) and argued that not enough stress could be generated within the stone to fragmentize. Rather than Shock Wave Lithotripsy (SWL) which is based on momentum transfer to generate extremely short (microsecond) pulse forces capable to comminute larger as well as smaller stones with the same mechanism (2), BWL is based on resonance phenomena of burst of ultrasound waves of narrow band-width. The problem of BWL with small stones (smaller than ½ wavelengths) is, that waves cannot interfere constructively and destructively in the stone and the required stress enhancement by constructive interference fails. Generally, the resonance amplification of an oscillatory body (e.g. stone) depends on mass, size, shape, different material properties, wave damping and others. Human urinary stones are different in size, shape and composition and have individual resonance frequencies. In this work, an analytical theoretical approach to modelling mechanical stresses in a spherical stone was developed to assess the dependence of frequency and stone size on stress generated in the stone. The paper develops the theoretical background for the appropriate frequencies for small stones. The calculations deliver insight into the mechanism of stress generation. It is shown that higher frequencies can excite various vibration modes in different types of defined stones of selected shape and selected composition. Calculated stress enhancements reaches values up to 6 times more than the incident pressure. The use of higher frequencies may enable BWL to fragmentize smaller stones than with lower frequencies as used in current devices. The analytical calculations confirm that small stones require higher frequencies (higher than efficient for larger stones) to reach high stress amplitudes in their individual vibration modes. Following the results, an additional transducer dedicated to perform on smaller stones has to be integrated within the one for larger stones or, two separate transducer should act one after the other, when coarse fragmentation has left a bulk of smaller fragments requiring further fragmentation. This is not a simple task. The goal of the group, to develop a small, handheld and easy to use BWL-device still needs some ingenious work to be done. (1) Harper JD et al., Fragmentation of Stones by Burst Wave Lithotripsy in the First 19 Humans, J Urol. 2022 May ; 207(5): 1067–1076. (2) Wess O J, Mayer J., Fragmentation of brittle material by shock wave lithotripsy. Momentum transfer and inertia: a novel view on fragmentation mechanism. Urolithiasis 48, 137-149 (2020) Othmar Wess

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