Bubble proliferation in the cavitation field of a shock wave lithotripter

In shock wave lithotripsy (SWL) for the treatment of kidney stones, it has been observed that stones break better when shock waves (SWs) are delivered at slow rate than at fast rate—that is, stones break better at 0.5–1 Hz compared to 2 Hz pulse repetition frequency (PRF).¹ The precise mechanism for this effect is, as yet, not entirely clear, but appears to involve bubble proliferation.^2,3 Even though the growth-collapse cycle of cavitation bubbles is short compared to the interval between SWs, more bubbles are generated at fast PRFs resulting in a reduction in delivery of SW energy to the stone.^1,2,4–6 We sought to characterize the growth of bubble clouds produced by lithotripter SWs and looked for evidence that bubble proliferation at fast PRF is due to SWs interacting with cavitation nuclei generated by previous SWs.

This study was conducted with a Dornier DoLi-50 electromagnetic lithotripter (Dornier MedTech Systems, Germany). The DoLi-50 has six power levels (PL1–6) and can deliver SWs at PRF up to 2 Hz. The treatment head of the lithotripter was coupled to the test tank through a Mylar membrane as previously described.⁷ The majority of experiments were performed in non-degassed tap water. The dissolved oxygen content was measured using an YSI DO200 oxygen meter (YSI, Inc., Yellow Springs, OH) and was at about 8 ppm or near 100% of saturation.

Cavitation bubbles were studied using a high-speed camera (HS camera) and a conventional frame-rate camcorder. The HS camera (Imacon 200, DRS Hadland, Inc., Cupertino, CA) records fourteen 1280 × 1024 pixels frames using seven sensors (Sony ICX085). Because each sensor is used twice, there can be faint artifacts in the second frame of a pair. For example, a bubble captured in frame 2 can show a faint shadow visible in frame 9 of the same series (as seen in Mm. 1). HS-camera frames were post-processed in Adobe Photoshop (Adobe Systems, Inc.). Background noise was diminished by subtracting the frame recorded by the same channel without bubbles and readjusting brightness and contrast of the images.

A conventional frame-rate camcorder (Sony HDR-HC3) was used for continuous recording of cavitation bubbles over successive SWs. The camcorder images (1920 × 1080 pixels) were captured as 1080 interlaced lines, that is, the camera recorded 540 lines during one scan (odd field), and then the alternate lines on the next scan (even field). Odd and even fields were captured alternately at about 60 (59.94) frames per second (fps) and, if interlaced together into single frames, gave standard NTSC rate of about 30 (29.97) fps. Because transient cavitation bubbles were captured in only one of the two interlaced fields, we used both the odd and even fields as individual frames to produce the 60 fps movies. The missing 540 spatial lines in each frame were interpolated using the de-interlace video filter in Adobe Photoshop. De-interlaced frames were renamed to the relative time in seconds using a program written in LabVIEW (National Instruments, Austin, TX) and converted into QuickTime movies using the H.264 video compressor. The reader is encouraged to examine the movies frame-by-frame while reading the text.

As the camcorder assembles frames from (1920 pixel) lines progressively scanned top to bottom, the bottom lines were captured slightly later in time than the top lines. This yielded a visual artifact in which transient cavitation bubbles within the cloud were partitioned between two consecutive frames (e.g., frames 1.485 s and 1.502 s in Mm. 3). Because the frame-rate of the camcorder (59.94 fps) did not match the SW rates of the lithotripter (0.5 or 2 Hz), the position of the partition line was different for different pairs of frames. When this artifact occurred, bubbles in movies started to appear at the bottom of one frame, and then appeared at the top of the next frame. With these considerations—slight progression in time from top to bottom in the recorded frames—the images are readily interpretable.

Because the acoustic axis of the lithotripter is at 45° from vertical,⁷ the camcorder was tilted so that the SW would be seen to propagate from right to left in the images. In the HS camera movies, SWs propagated diagonally from the bottom right corner of the images. The HS-camera and camcorder images were calibrated by positioning a ruler in the field of view of the cameras. The field of view of the camcorder was 45 × 25 mm—providing a spatial resolution of about 23 μm/pixel. The resolution of the HS camera was about 4 μm/pixel.

SWs were measured using a fiber-optic probe hydrophone (FOPH-500, RP Acoustics, Germany). The 100 μm glass fiber tip of the hydrophone was positioned at the focus (F) of the lithotripter⁷ and is faintly visible in camcorder images. The temporal profile of a lithotripter pulse consisted of a ∼2 μs leading positive-pressure phase followed by a ∼5 μs negative-pressure phase and trailing residual oscillations. The residual pressure oscillations are understood to be due to fading oscillations of electric current during the discharge of the high-voltage capacitor through the coil of the SW generator.⁶ 

Passage of the shock pulse gave rise to inertial cavitation in which bubble growth was followed by collapse and rebound. The HS-camera sequence of the growth–collapse–rebound cycle of a cavitation bubble is shown in Fig. 1. The first frame was recorded at ∼4 μs after the passage of the shock front through the focus F of the lithotripter. By this time, the positive-pressure phase of the SW (0–2 μs) had passed through the field of view of the camera, and the bubble began to grow under the tensile phase of the SW.

The bubble continued to grow after the passage of the SW due to inertia, reaching maximum radius (R_max ≈ 1.3 mm) near frame 164 μs (Fig. 1). Then, driven by atmospheric pressure, the bubble began to contract, leading toward collapse. The first inertial collapse occurred between frames 284 and 324 μs. Frames 324 μs to 404 μs captured a microjet emanating from a bubble during the first rebound cycle. The second inertial collapse occurred between frames 444 μs and 484 μs followed by a short second rebound cycle in which subsequent collapse appeared to be accompanied by breakup of the bubble.

Further analysis of images showed that clouds of microbubbles emerged from cavitation jets and from the collapse of single cavitation bubbles. A jet breaking up into ∼25 microbubbles is shown in the left panel of Fig. 2. The three frames of the right panel of Fig. 2 show a different cavitation bubble in which the growth-collapse-rebound cycle (Mm. 1) produced more than 100 daughter microbubbles (frame 788 μs).

Movie Mm. 1 shows the growth–collapse–rebound cycle of two cavitation bubbles. The bubbles were recorded independently at the focus of the lithotripter (SWs delivered minutes apart) but are shown here side by side. The bubble in the left panel of Mm. 1 reached its maximum radius (R_max ≈ 0.7 mm) near the third frame (128 μs, Mm. 1), and then, began to collapse. The precise moment at which the bubble began to break up was not imaged, but frame 4 (248 μs) captured a liquid jet that breached the bubble wall to extend ∼0.5 mm into the surround. As the liquid jet is visible in the surrounding liquid, the jet presumably entrained some of the gas-vapor mixture from the bubble. In subsequent frames, the bubble and the jet broke up into microbubbles. More than 100 daughter microbubbles can be counted in the last frame (788 μs) but there are likely more of these very small bubbles beyond the field of view.

The right panel of Mm. 1 shows a bubble with R_max ≈ 0.2 mm. Because of its smaller size, this bubble collapsed earlier than the bubble in the left panel, somewhere near the second frame (68 μs). A liquid jet is faintly visible inside the bubble during the rebound in the third frame (128 μs). Subsequent frames show that this small bubble created about 40 microbubbles. These daughter bubbles continued to rebound, attaining maximum size near frame 368 μs and reappeared with smaller diameter in the last frame (788 μs). It is possible that the reappearance of the daughter bubbles was intensified by a wave scattered from the original bubble and then reflected from a tank boundary or the surface of the water.

Mm. 1 also shows spatial translation of the daughter microbubbles. The spatial translation was more evident with longer time steps for imaging. Movies Mm. 2 and Mm. 3 show bubble dynamics recorded at 0.017-s steps using a conventional 60 fps camcorder. Because the exposure time (∼17 ms) was longer than the entire growth—collapse–rebound cycle (∼1 ms, Mm. 1), a single 0.017-s frame captured bubbles at all stages throughout the cavitation cycle. Thus, camcorder images show bubbles at their maximum expansion. Because the bubbles emit jets and spawn smaller bubbles (Mm. 1), they appear as comet-tailed structures in which the “comet tail” marks the direction of the jet and spatial translation of the microbubbles.

Mm. 2 shows the evolution of cavitation bubbles during seven consecutive lithotripter pulses at 0.5 Hz PRF. A bubble can be seen briefly to be moving diagonally upward (direction of buoyancy force) in the upper right quadrant of the field during the first three frames. At frame 0.050 s, the bubble is hit by the SW (SW propagates from right to left in these images) and in subsequent frames is seen to spawn numerous smaller bubbles. Starting at 0.234 s, one can see a pair of bubbles somewhat larger than the rest, drifting diagonally toward the top of the field (buoyancy); while smaller bubbles are moving toward the middle of the field. As one tracks the bubbles across the field between successive SWs (frames 2.052 s, 4.054 s, 6.056 s, 8.058 s), it is seen that daughter bubbles seed the proliferation of cavitation and that the subsequent bubble clouds are located 2–3 cm from where the first bubble was struck by the first SW. As the daughter microbubbles (cavitation nuclei) continued to drift beyond the focal point of the lithotripter (F), no new bubbles were generated prefocally (to the right of F in these images). Starting at 9.693 s, another bubble is seen floating diagonally upward in the prefocal region of the lithotripter and the process of bubble proliferation repeats.

The cavitation generated at a firing rate of 0.5 Hz was relatively sparse compared to the extensive bubble clouds that were observed when the lithotripter was fired at 2 Hz (as seen in Mm. 3, in the following text). This is likely due to the increased time for bubble dissolution at slow PRF. As seen in Mm. 2, about 65 microbubbles can be identified after the collapse of a parent bubble (frame 10.043 s, Mm. 2), but only ∼15 nuclei are visible at the arrival of the next lithotripter pulse 2 s later (frame 12.045 s, Mm. 2).

Movie Mm. 3 shows an example of bubble proliferation at 2 Hz PRF. A single bubble—seen on the right at the beginning of the movie—gave rise to a bubble cloud that grew from shot to shot. Eventually, the daughter bubbles occupied the whole field of view.

Figure 3 shows six frames of Mm. 2 (top) and Mm. 3 (bottom) recorded at 2-s intervals. As Mm. 2 was recorded at 0.5 Hz and Mm. 3 at 2 Hz, the top row shows consecutive SWs at 0.5 Hz (Mm. 2) while the bottom row show every fourth SW at 2 Hz (Mm. 3). Arrows in the first frames point to the single bubbles that gave rise to the bubble clouds seen in subsequent frames. Note that information presented in Fig. 3 alone, that is without seeing the movies Mm. 2 and Mm. 3, does not adequately demonstrate the dynamic nature of cloud formation or the fact that solitary bubbles give rise to numerous cavitation nuclei, which in turn generate bubble clouds.

Figure 3 also shows that after several SWs the cavitation field at 2 Hz consisted of a myriad of bubbles. How these bubbles affected the lithotripter SWs is shown in Fig. 4. The leading positive-pressure phase (0–2 μs, left plot) remained virtually unchanged but the negative-pressure phase (2–7 μs) and trailing residual oscillations (visible after 7 μs) decreased in amplitude as the number of bubbles increased from pulse-to-pulse (Mm. 3). The increase of number of bubbles for the first six SWs is shown in the right panel of Fig. 4. The first two SWs produced only a few bubbles, so the negative-pressure phase remained robust for these SWs. As bubbles proliferated from shot to shot, the amplitude of the negative-pressure phase declined.

The middle plot of Fig. 4 shows peak positive and negative pressures for this series of 23 SWs (Mm. 3). The peak positive pressure (P+, top) remained unchanged (40 ± 2 MPa), but the peak-negative pressure (P-, bottom) decreased from about −5.5 to −1.5 MPa (within the noise level of the FOPH). As the energy for bubble growth is provided by the negative-pressure phase of SWs, the decrease of P- diminished the proliferation of bubbles. Subsequent SWs (shots 23–30, movie not shown) showed no apparent increase in number of bubbles.

It was observed that the growth-collapse-rebound cycle of individual bubbles generated dozens of smaller bubbles (Fig. 2, Mm. 1). Possible mechanisms of bubble breakage include the so-called microjet mechanism and the spherical equivalent of Rayleigh–Taylor instability.⁸ We observed that the first inertial collapse can produce a microjet (e.g., frame 324 μs in Fig. 1) that breaks up into smaller bubbles (left panel of Fig. 2). The fluid microjet destroys the spherical symmetry of the bubble (Fig. 1, Mm. 1). Sometimes during the first cycle of the rebound the bubbles came close to regaining spherical shape (frame 128 μs, right panel of Mm. 1). However, subsequent collapses disintegrate the bubble into numerous smaller bubbles.⁹ 

Breakup is likely due to the spherical equivalent of Rayleigh–Taylor instability of the gas/water interface.⁸ The gas/water interface can become unstable when bubble wall acceleration reaches very large numbers and is directed outward from the bubble center, that is, directed from gas (lighter liquid) toward water (denser liquid). This instability leads to the growth of non-spherical distortions and disintegration and breakup of the bubble—a process that generated numerous smaller bubbles.

Continuous recording with a conventional frame-rate camcorder was used to track cavitation bubbles over successive SWs. The clouds of bubbles that were generated resembled the pattern of the smaller bubbles that seeded them. That is, bubbles migrated across the field and seeded the proliferation of cavitation upon being hit by successive SWs. Stepping through frame by frame (Mm. 2 and Mm. 3), bubbles could be tracked from their origin to the clouds they spawned.

The cavitation generated at a firing rate of 2 Hz was more dense than at 0.5 Hz (Fig. 3). This is most likely due to the increased time for bubble dissolution at slow PRF. Numerical simulations show that micrometer-sized bubbles are expected to grow to an equilibrium radius of 25-30 μm after exposure to a single SW.⁵ This growth is due to the diffusion of non-condensable gases in a saturated liquid. From Fig. 1 (middle) of Sapozhnikov et al.,⁵ a 25-μm radius bubble can be expected to dissolve in 80-90 s at atmospheric pressure. This dissolution time would obviously span the time between SWs at either 2 or 0.5 Hz PRF. However, if a 25-μm bubble were to break into 100 daughter bubbles (Movie Mm. 1), each daughter bubble would be about 5.4 μm in radius. For such daughter bubbles, Epstein–Plesset calculations¹⁰ suggest a dissolution time of just over a second. This dissolution time is consistent with the observed difference in bubble proliferation between 0.5 and 2 Hz PRF. Moreover, the bubble breakup behavior documented here (i.e., the number of observed daughter bubbles) provides a clear explanation for why this difference in PRF can be significant.

Bubble proliferation with successive SWs was associated with a gradual decrease in the negative-pressure phase of the lithotripter SW (Fig. 4). The fall in negative pressure provided progressively less energy for bubbles to grow,² and subsequent proliferation of bubbles diminished. Eventually—in dense cavitation clouds, such as in the last frames of Mm. 3—the negative-pressure phase of SWs became so small (Fig. 4) that there was no apparent increase in number of bubbles in subsequent SWs. Bubble coalescence and bubble-bubble interactions within a dense cloud can also contribute to the diminished proliferation of bubbles.

In summary, cavitation bubble jetting and the break up of bubbles upon collapse are key events in the proliferation of cavitation nuclei in SWL. These results support the idea that bubbles hit by a lithotripter SW can spawn smaller bubbles and help to explain how lithotripter SWs fired at fast PRF produce more bubbles than at slow PRF. With the caveat that this work was performed using non-degassed water in vitro, the implication is that it may take very few bubbles (perhaps only one bubble) to seed a substantial cavitation cloud at SW rates used in clinical SWL.

This work was supported by a grant from the National Institutes of Health (DK 43881).