An investigation of elastic waves producing stone fracture in burst wave lithotripsy

Abstract

Burst wave lithotripsy is a method to noninvasively fragment urinary stones by short pulses of focused ultrasound. In this study, physical mechanisms of stone fracture during burst wave lithotripsy were investigated. Photoelasticity imaging was used to visualize elastic wave propagation in model stones and compare results to numerical calculations. Epoxy and glass stone models were made into rectangular, cylindrical, or irregular geometries and exposed in a degassed water bath to focused ultrasound bursts at different frequencies. A high-speed camera was used to record images of the stone during exposure through a circular polariscope backlit by a monochromatic flash source. Imaging showed the development of periodic stresses in the stone body with a pattern dependent on frequency. These patterns were identified as guided wave modes in cylinders and plates, which formed standing waves upon reflection from the distal surfaces of the stone model, producing specific locations of stress concentration in the models. Measured phase velocities compared favorably to numerically calculated modes dependent on frequency and material. Artificial stones exposed to bursts produced cracks at positions anticipated by this mechanism. These results support guided wave generation and reflection as a mechanism of stone fracture in burst wave lithotripsy.

Figures

FIG. 1.

Waveforms recorded by fiber optic probe hydrophone at 170 kHz (top), 340 kHz (middle), and 800 kHz (bottom) with peak negative pressure of 6.5 MPa. The 170 and 340 kHz waveforms are captured at the focus, while the 800 kHz waveform is captured 1 cm prefocally along the acoustic axis of the transducer.

FIG. 2.

(Color online) Stone holders for each model in this study. The top shows a schematic diagram and the bottom shows a photograph of each. (A) A rectangular stone model held by a small amount of epoxy attached to a 22-gauge wire. These models were directly submerged in degassed water. (B) A chamber for containing an optical-matching fluid and fixing a cylindrical stone model. An acoustically transparent membrane is placed over the front face to contain the liquid while the optical windows on the side allow visualization with a camera. The model is held by three spring-loaded pins in the center of the chamber. ML = Matching liquid. (C) A small plastic frame (black) extending from a tissue-mimicking material holding a cylindrical artificial stone made from Begostone Plus plaster. This holder was used to suspend and support the length of the stone during fracture formation.

FIG. 3.

Experimental setup with the stone model aligned with the transducer focus in a water bath. A high-speed camera is used to record stroboscopic images of the stone model, backlit by a 450 nm LED flash source. A timing board controls triggering of the ultrasound pulse, light source, and camera with staggered triggers for the camera and light producing stroboscopic images of the ultrasound pulse interaction with the stone.

FIG. 4.

(A) Schematic of the formation and progression of guided waves modes during BWL. Red denotes the incident wave in the liquid travelling at angle θi, and blue denotes transmitted or reflected wave in the stone model traveling at θt. The blue dots indicate positions of constructive interference of the propagating guided wave mode. (B) Impinging focused ultrasound waves transmit into a stone and form a guided wave mode (i)–(ii). The modes travel towards the distal end of a stone (iii) and reflect from the surface, forming periodic stress points (iv)–(v). The green dots indicate antinodes with higher stress due to reflection from the distal surface. After the pulse, elastic waves reverberate at a lower amplitude within the stone and decay from attenuation or radiation (vi). (C) Photoelastic images showing the development of elastic waves in a 26-mm epoxy plate at 340 kHz, with the BWL pulse incident from the left and propagating to the right. The images are subtraction images from a still frame at the start of the sequence. Between 1 and 15 μs, the formation of the guided wave mode is seen propagating through the plate, with areas of brightness indicating intensity. The red arrows indicate locations where the transmitted waves converge at the center and opposing edges of the model. By 20 μs, the mode reflects from the distal surface and a periodic standing wave is formed that remains until the end of the pulse (67 μs). During this time, the photoelastic intensity is further increased in the distal area of the stone, appearing as a dark fringe within each bright zone (black arrowhead), indicating an optical birefringent shift greater than π/2 radians in phase (i.e., greater photoelastic effect). These are differentiated from stress minima, the areas between the bright circular regions (white arrowhead). After the pulse, the photoelastic intensity declines. For a more complete visualization of the progression, see the accompanying video Mm. 1.

FIG. 5.

Temporal sequences of elastic wave propagation in rectangular models 26 mm length at (A) 170, (B) 340, and (C) 800 kHz. The images show the development of wave modes in the model at each frequency, with the BWL pulse incident from the left and propagating to the right. The images are subtraction images from a still frame at the start of the sequence, and brightness indicates photoelastic intensity. Each pulse is 50–60 μs in duration (10 cycles at 170 kHz, 20 cycles at 340 kHz, and 40 cycles at 800 kHz). A mode forms and propagates down the acoustic axis in the model, reaching the end at 10–15 μs. After reaching the distal surface, the spatial pattern near the distal end becomes constant for the remainder of the pulse (for example, compare images at 32 and 67 μs for 170 kHz pulse). Then energy then dissipates after the end of the pulse (last three frames in each sequence). The dissipation is faster at 800 kHz likely due to greater attenuation in the material at that frequency. The video sequence for (A) is available as Mm. 2. The video sequence for (C) is available as Mm. 3.

FIG. 6.

Guided wave mode phase velocities for an infinite (A) and 1-mm finite thickness (center) rectangular plate. On the left, the symmetric (Sn) and antisymmetric (An) Lamb wave modes are listed for each curve. The black diamonds denote measured phase velocities for different rectangular models of varying length at 170, 340, and 800 kHz. In (B), the same experimental data are plotted over the finite (1-mm thick) plate, indicating close agreement with specific modes in the model used in experiments. Illustrations in (C) show the displacement patterns for the identified guided wave modes in an infinite plate (scaled in magnitude for visibility).

FIG. 7.

(Color online) (A) Temporal progression of photoelastic patterns in 6.35-mm diameter 22-mm length epoxy cylinders exposed to BWL pulses with 170, 340, and 800 kHz frequency. Similar stress patterns as those observed in the rectangular plates are seen, although the photoelastic effect is greater, because of the larger thickness particularly on axis. Images are shown with ultrasound incident from the left. (B) Phase velocities vs frequency calculated by GUIGUW in epoxy stone models. Extensional modes are displayed in red and flexural modes are displayed in blue. Experiments show higher phase velocities in epoxy cylinders as those in plates. Diamonds indicate initial phase velocity estimate during propagation and squares indicate standing wave estimate from measured wavelength. A video of the photoelastic imaging sequence in (A) at 340 kHz is available as Mm. 4.

FIG. 8.

(Color online) (A) Temporal progression of photoelastic patterns in 26 mm length glass cylinders exposed to BWL pulses with 170, 340, and 800 kHz (subtraction images). Note at 170 kHz the progression of the stress pattern from about 1 wavelength (10 μs) along the length of the cylinder to about 3/2 wavelengths (55 μs). The 340 kHz pattern similarly shows about 3/2-wavelength pattern, indicative of a higher phase velocity than the final pattern at 170 kHz. (B) Phase velocities vs frequency calculated by GUIGUW and estimated from initial wave speeds (diamonds) or standing wave patterns (squares) in glass stone models. Extensional modes are displayed in red and flexural modes are displayed in blue. Measurements indicate multiple significant modes for a given frequency. For instance, at 170 kHz, it is apparent that the initial propagation is extensional but undergoes mode conversion to a flexural state after repeated reflections. At 800 kHz, two separate modes traveling at different speeds are visible. A video of the photoelastic imaging sequence in (A) at 340 kHz is available as Mm. 5.

FIG. 9.

Time-averaged photoelastic intensity in rectangular models of different lengths and frequencies. Ultrasound is incident from the left. Time averaging emphasizes areas where the amplitude is constant vs time, thus areas of localized standing wave antinodes appear bright and nodes appear dark. The images show strong constructive interference near the distal surface in most models with similar spacing for a given frequency.

FIG. 10.

Integrated (time-averaged) photoelastic effect in star (A) and “N shaped” (B) models exposed to 340 kHz BWL burst. Ultrasound impinges from the left side of the models. Both show photoelastic stresses strongest near the distal surfaces of the model (arrows), indicating standing wave formation due to reflections from these surfaces. The distance from the interfaces is similar to that for the rectangular and cylindrical interfaces. The scale bar shows a 1 mm distance.

FIG. 11.

(A) Schematic diagram of the alteration of stress patterns caused by cracks in the stone. The pattern is shifted forward as a crack is generated, creating a new position for the peak stress just in front of the crack. (B) Photoelastic images in an 18 mm cylinder intact (top), with an artificially created crack at 4 mm (upper center) and 1 mm (lower center) from the back surface and with the 1-mm back section broken off (bottom). The photos show brightfield images of the stone models prior to insonation and the photos in (C) show a transient photoelastic image during the last cycle of the ultrasound pulse. The black bars in the middle of each image are pins holding the cylinder in place. The red lines in the right image indicate axial positions of peak photoelastic effect in the intact cylinder, while the blue arrowheads indicate the positions of peak stress in the modified cylinders. When a crack was introduced, the peaks shift to be proximal to the crack, indicating significant reflection from the crack which was similar to that formed when the back section is removed (bottom).

FIG. 12.

(Color online) (A) An artificial stone containing several cracks after initial BWL exposure. The vertical arrow shows the location of the distal crack. (B) Position of the distal circumferential crack observed during a short BWL exposure vs stone length. A linear regression fit indicates minimal variation between lengths. (C) Simulated phase velocity curves and anticipated phase velocity based on the measured position of the crack, assuming a soft boundary condition at the distal stone surface. An example video of stone fracture over the first 100 s of an exposure is available as Mm. 6.

FIG. 13.

Brightfield photoelasticity images of a cylindrical epoxy stone with 26 mm length exposed to 170 kHz BWL with a symmetric (A) and asymmetric (exposure) angle relative to the cylinder axis. Similar modes appear in both cases, although the photoelastic amplitude and exact distribution of stresses differs. The scale bar is 1 cm.