Suppression of large intraluminal bubble expansion in shock ... - NTU

Suppression of large intraluminal bubble expansion in shock wave lithotripsy without compromising stone comminution: Refinement of reflector geometry Yufeng Zhou and Pei Zhonga) Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708

共Received 15 June 2002; revised 12 October 2002; accepted 21 October 2002兲 Using the Hamilton model 关Hamilton, J. Acoust. Soc. Am. 93, 1256 –1266 共1993兲兴, the effects of reflector geometry on the pulse profile and sequence of the shock waves produced by the original and upgraded reflector of an HM-3 lithotripter were evaluated qualitatively. Guided by this analysis, we have refined the geometry of the upgraded reflector to enhance its suppressive effect on intraluminal bubble expansion without compromising stone comminution in shock wave lithotripsy. Using the original HM-3 reflector at 20 kV, rupture of a standard vessel phantom made of cellulose hollow fiber (i.d.⫽0.2 mm), in which degassed water seeded with ultrasound contrast agents was circulated, was produced at the lithotripter focus after about 30 shocks. In contrast, using the upgraded reflector at 24 kV no rupture of the vessel phantom could be produced within a 20-mm diameter around the lithotripter focus even after 200 shocks. On the other hand, stone comminution was comparable between the two reflector configurations, although slightly larger fragments were produced by the upgraded reflector. After 2000 shocks, stone comminution efficiency produced by the original HM-3 reflector at 20 kV is 97.15⫾1.92% (mean⫾SD), compared to 90.35⫾1.96% produced by the upgraded reflector at 24 kV (p⬍0.02). All together, it was found that the upgraded reflector could significantly reduce the propensity for vessel rupture in shock wave lithotripsy while maintaining satisfactory stone comminution. © 2003 Acoustical Society of America. 关DOI: 10.1121/1.1528174兴 PACS numbers: 43.80.Ev, 43.80.Gx, 43.25.Yw 关FD兴

I. INTRODUCTION

Reducing vascular injury in shock wave lithotripsy 共SWL兲 is becoming an increasing clinical concern and a primary challenge for basic research,1 especially with the much higher pressure output of the third-generation lithotripters.2 Following SWL, although most young adult patients recover well, a subgroup of patients, such as pediatric and elderly patients, and patients with preexisting renal function impairment, are at much higher risk for SWL-induced chronic injury.1,3,4 Therefore, it is highly desirable to improve lithotripsy technology to ameliorate renal injury while maintaining successful stone comminution. Previous studies using in vitro phantom systems and in vivo animal models have demonstrated that cavitation, the formation and subsequent expansion and collapse of gas/ vapor bubbles in an acoustic field, is an important mechanism for vascular injury in SWL.5–7 Theoretical analyses have shown that in free field the tensile pressure of a lithotripter shock wave 共LSW兲 can cause preexisting cavitation nuclei in the range of 10 nm–10 ␮m to expand rapidly in about one hundred microseconds to bubbles of 1 – 2 mm in diameter, which then collapse violently.8,9 It has been postulated that SWL-induced rupture of capillaries and small blood vessels, in which bubble oscillation is severely constrained, is caused by the rapid, large dilation of the vessel wall from expanding intraluminal bubbles,5,9 whereas dama兲

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J. Acoust. Soc. Am. 113 (1), January 2003

age in large blood vessels may be caused by high-speed microjets or secondary shock waves produced by the violent collapse of cavitation bubbles, either with or without the aid of an impinging LSW.10,11 Based on the results of these previous studies, various strategies have been proposed to reduce tissue injury in SWL. Overall, these strategies can be categorized into two groups. The objective for the first group of strategies is to minimize or eliminate cavitation nuclei in the medium so that bubbles will not be induced by LSW. This includes the use of overpressure,12,13 low pulse repetition rate,14 –16 and staged SWL treatment combining low- and high-amplitude shock wave exposures.17 In contrast, the second group of approach relies on the modification of the profile of LSW to actively suppress cavitation, and thus to reduce its damage potential to surrounding tissues. This later approach includes inversion of the lithotripter pressure waveform by the use of a pressure-release reflector18 or by inverting the polarity of input excitation voltage to piezoceramic transducers19 and various pulse superposition techniques.20–23 Among these approaches, the in situ pulse superposition technique that we developed recently23 has the advantage of reducing tissue injury without compromising stone comminution or increasing treatment time. The basic principle of the in situ pulse superposition technique is to use a relatively weak compressive wave to superimpose onto the trailing tensile component of a LSW to suppress the expansion of cavitation bubbles induced in a lithotripter field.23 To implement this technique in an HM-3 lithotripter, a thin shell ellipsoidal reflector insert with its

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© 2003 Acoustical Society of America

inner surface sharing the same first focus (F 1 ) with the original HM-3 reflector, but its second focus shifted 5 mm proximal to the shock wave generator was designed and fabricated as previously described.23 The reflector insert, with its lower edge extending to the focal plane across F 1 and perpendicular to the lithotripter axis, covers a large portion of the original HM-3 reflector. Therefore, the reflector insert becomes the primary reflecting surface to form a leading LSW after each spark discharge, whereas a second weakly focused shock wave, delayed by about 4 ␮s, is produced by wave reflection from the uncovered bottom surface of the original HM-3 reflector.23 In vitro phantom tests have shown that stone comminution produced by the upgraded reflector at 24 kV is comparable to that produced by the original HM-3 reflector at 20 kV. However, the upgraded reflector significantly reduces the potential for vascular injury. At corresponding output voltages, rupture of a standard hollow fiber vessel phantom 共perfused with degassed water seeded with ultrasound contrast agents兲 around the lithotripter beam focus was produced after about 30 shocks using the original HM-3 reflector, yet no rupture could be produced by the upgraded reflector even after 200 shocks. The only exception is at the geometric focus of the reflector insert where the tensile pressure of the LSW reaches its maximum and rupture of the vessel phantom could be produced after about 130 shocks.23 Apparently, refinement of the upgraded reflector is needed to further suppress intraluminal bubble expansion and to reduce the potential of vascular injury in SWL without compromising stone comminution. In this work, we analyzed qualitatively the effect of reflector geometry on the profile of LSW produced by the upgraded reflector, using a linear wave propagation model developed by Hamilton.24 Guided by this analysis, we have refined the geometry of the reflector insert and characterized the resultant acoustic field and bubble dynamics using a fiber optic probe hydrophone and high-speed imaging technique. The performance of the refined upgraded reflector in vitro was evaluated using established stone and vessel phantom systems; and the dynamics of cavitation bubbles induced by the original and upgraded HM-3 lithotripter were analyzed using the Gilmore model. All together, it was found that with refinement in geometry the upgraded reflector can further reduce the potential of vascular injury in SWL while maintaining satisfactory stone comminution. II. THE EFFECT OF REFLECTOR GEOMETRY ON WAVEFORM PROFILE ALONG LITHOTRIPTER AXIS

To increase the strength of the second shock wave, the original reflector insert23 needs to be further truncated to increase the area for the uncovered bottom surface of the original HM-3 reflector. However, truncation of the reflector insert also reduces the reflecting surface area for the leading LSW. Therefore, a balance needs to be reached between reducing vascular injury and maintaining successful stone comminution using the upgraded reflector. For this purpose, it would be helpful to understand the relationship between the geometry of the upgraded reflector and the pressure field produced at the lithotripter beam focus. In this work, we used a linear wave propagation model that was developed by J. Acoust. Soc. Am., Vol. 113, No. 1, January 2003

FIG. 1. A schematic diagram of the geometry of a reflector insert, in relation to the original HM-3 reflector. Note that the reflector insert shares the same first focus with the original HM-3 reflector (F 1 ⫽F 1⬘ ), but its second focus (F ⬘2 ) is 5 mm proximal to the shock wave source relative to that of the original HM-3 reflector (F 2 ).

Hamilton to describe small-amplitude wave reflection, focusing, and diffraction from an ellipsoidal reflector.24 An unique feature of the Hamilton model is that it describes the contribution and evolution of different wave components to the pressure waveform produced along a lithotripter axis. Therefore, the Hamilton model was used to provide a qualitative assessment of the effect of reflector insert geometry on the pressure amplitude at the reflector focus, and to facilitate the interpretation of the pressure waveforms measured experimentally. It should be note that optimization of the reflector insert design would require a quantitative prediction of the pressure waveform in a lithotripter field based on nonlinear shock wave propagation models in an electrohydraulic lithotripter,25–27 which is beyond the scope of this work. A. The Hamilton model

Let’s consider the situation where an outgoing omnidirectional spherical pressure wave, centered at the first focus (F 1 ), is reflected and refocused towards the second focus (F 2 ) of an ellipsoidal reflector 共see Fig. 1兲. Based on a geometrical acoustics approximation, the reflected pressure field p 2g can be expressed by24

冉冊冉

冊

p 2g 1⫹␧ r 0 r 2 ⫺2a ⫽D 共 z s 兲 f t⫹ , p0 1⫺␧ r 2 c0

共1兲

where p 0 is the pressure amplitude at a fixed but arbitrary distance r 0 from F 1 , D(z s ) is the directivity function with z s denoting the coordinate on the surface of the ellipsoidal reflector, ␧ the eccentricity of the ellipsoidal reflector, r 2 the distance from F 2 , f (t) a dimensionless function of time representing the source waveform, and c 0 sound speed in water. The directivity function, corresponding to the density of rays Yufeng Zhou and Pei Zhong: Refinement of reflector geometry

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where H c , H e , and H w are the impulse strengths for the center wave, the edge wave, and the wake, respectively, and ␶ c , ␶ e , t 1 , and t 2 are the retarded times for the corresponding waves. Detailed expressions of these parameters can be found in the original reference.24 Moreover, it has been shown that at beam focus of the ellipsoidal reflector the pressure can be expressed by

冉冊

r0 d 2a p2 f t⫺ ⫽F , p0 c 0 dt c0

z⫽z 2 ,

共5兲

where F is the focusing factor defined by F⫽

FIG. 2. Angular dependence of the directivity function D( ␪ ) in the reflected pressure field predicted by geometrical acoustics with four different eccentricity values (␧⫽0.2, 0.5, 0.83, and 0.84兲.

reflected from different regions of the ellipsoidal reflector, is given by

冋

D 共 ␽ 兲 ⫽ 1⫹

4␧ sin2 共 ␽ /2兲共 1⫺␧ 兲 2

册

⫺1

,

共2兲

共 0⭐␧⬍1 兲 ,

共3兲

in which, ␧ is defined by ␧⫽ 冑1⫺ 共 b/a 兲 2 ⫽c/a

where a, b, c are the semimajor axis, semiminor axis, and half-focal length of the ellipsoidal reflector, respectively, and ␪ is an angle between the ray normal to the reflected wavefront and the lithotripter axis, which is defined as the z-axis in Fig. 1. The directivity function determines the amplitude shading of the pressure field across the aperture of the lithotripter reflector. As shown in Fig. 2, the directivity decreases monotonically with ␪ and it also depends on the eccentricity of the reflector. When ␧→0 共i.e., for a spherical reflector兲, the reflected wave becomes spherically converging, whereas as ␧ →1, the reflected field becomes increasingly localized along the z-axis. For the original and upgraded HM-3 reflectors (␧⫽0.826 and 0.842, respectively兲, their directivity functions are similar and the amplitude of the pressure reflected from the edge of the reflector aperture is about 10% of that reflected from the bottom along the reflector axis 共see Fig. 2兲. Using the Kirchhoff integral, the reflected pressure along the z-axis can be determined.24 The solution, accounting for the effect of wave diffraction at the aperture of the ellipsoidal reflector, can be expressed by two closed form expressions, representing the center wave and the edge wave, respectively, and a convolution integral over time representing the wake: c0 p2 ⫽H c 共 z 兲 f 共 ␶ c 兲 ⫹H e 共 z 兲 f 共 ␶ e 兲 ⫹ p0 a

冕

t2

t1

H w 共 z,t ⬘ 兲

⫻ f 共 t⫺t ⬘ 兲 dt ⬘ , 588

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共4兲

冉冊冉

冊

1⫺␧ 2 a⫹␧d/ 共 1⫺␧ 兲 ln , 2␧ a⫺␧d/ 共 1⫹␧ 兲

共6兲

in which d is the depth of the ellipsoidal reflector 共see Fig. 1兲. The Hamilton model describes linear wave propagation in a truncated ellipsoidal reflector such as in the HM3 lithotripter. To determine the pressure waveform produced by the upgraded reflector, the Hamilton model was used to calculate pressure waveforms 共PW兲 produced by three different truncated ellipsoidal reflectors, namely, 共1兲 PW 1 from the reflector insert that is assumed to be not truncated at the bottom 共thus covering completely the original HM-3 reflector兲, 共2兲 PW 2 from the truncated bottom of the reflector insert, and 共3兲 PW 3 from the uncovered bottom surface of the original HM-3 reflector. Because of the linear wave propagation described by the Hamilton model, the pressure waveform produced by the upgraded reflector can be calculated by ( PW 1 ⫺ PW 2 )⫹ PW 3 .

B. The effect of reflector geometry on focusing factor

It can be seen from Eq. 共6兲 that, for a given ␧, F is only a function of the depth of the reflector. Therefore, for small amplitude waves, F represents the influence of reflector geometry on the pressure produced at F 2 . On a first order approximation, F may be used to evaluate qualitatively the influence of the reflector insert geometry on the leading LSW and the second shock wave produced by the upgraded reflector. Figure 3 shows the relative change in F associated with the reflecting surfaces for the leading LSW and the second shock wave, respectively, when the truncation depth of the reflector insert (d T , see Fig. 1兲 increases from 0 to 10 mm. Here, the results were normalized with respect to the corresponding values for the prototype upgraded reflector,23 in which the lower edge of the reflector insert was extended to the focal plane across F 1 . It can be seen that, as the truncation depth increases 共i.e., the lower edge of the reflector insert retracts toward the reflector aperture兲, the focusing factor for the leading LSW will decrease and the corresponding value for the second shock wave will increase. The magnitude of the relative change in F for the second shock wave is about twice that for the leading LSW. Considering that the leading LSW is much stronger than the second shock wave, this result suggests that a small truncation of the reflector Yufeng Zhou and Pei Zhong: Refinement of reflector geometry

FIG. 3. Normalized value of the focusing factor 共F兲 associated with the reflector insert and uncovered bottom surface of the original HM-3 reflector in relation to the truncation depth (d T ) of the lower rim of the reflector insert. The focusing factor is normalized by the corresponding value when the lower rim of the reflector insert is extended to the focal plane across the first focus of the original HM-3 reflector.

insert will significantly increase the pressure amplitude of the second shock wave without affecting greatly the leading LSW. C. The effect of reflector geometry on waveform profile

Using the Hamilton model, we calculated the pressure waveforms along the lithotripter axis produced by the original HM-3 and the upgraded reflectors. The incident wave from the spark discharge at F 1 is assumed to be a triangle pulse of 4 ␮s duration and 0.75 ␮s rise time, similar to the

values used in previous studies.24 –26 To facilitate comparison, the pressure waveform was normalized by the maximal pulse amplitude at each location and the retarded time for the wave propagation was used. A cross-sectional view of the original and upgraded reflector is shown in Fig. 1. The geometric parameters of the reflectors are described in the next section. Figure 4 shows the evolutions of three main components of the waveform along the z-axis in the original HM-3 lithotripter. Hereinafter, ⌬z 2 is used to denote the distance between the location where the waveform is calculated and the beam focus on the z-axis, z 2 . At ⌬z 2 ⫽⫺43.8 mm, the center wave and edge wave 共produced by wave diffraction at the reflector aperture兲 are clearly separated, and the wake contributes to the tensile pressure immediately following the center wave. As the waveform propagates towards the focus the edge wave catches up with the wake, generating a large tensile pressure before F 2 共see ⌬z 2 ⫽⫺27.3 mm). Subsequently, the edge wave and wake overlap with the center wave near F 2 , and eventually, they overtake the center wave far beyond F 2 共see ⌬z 2 ⫽65.7 mm). As shown by Hamilton, the polarity of the wake is the same as that of the edge wave, but opposite to the center wave.24 That is, in the pre-focal region, the center wave is compressive, yet the wake and edge wave are tensile. However, in the post-focal region the polarities of all the wave components are reversed. Using the upgraded reflector, two waves that travel in tandem are predicted 共Fig. 5兲. Because the reflector insert has both an upper and a lower rim, two edge waves associated with the leading LSW are produced at different time instants. At ⌬z 2 ⫽⫺63.3 mm, the edge wave produced by the lower rim of the reflector insert 共which is close to the spark discharge at F 1 ) has already merged with the wake of the LSW.

FIG. 4. Theoretical prediction of the pressure waveforms along the lithotripter axis using the original HM-3 reflector. Here, t denotes the propagation time of a reflected sound pulse originated from the first focus of the lithotripter reflector, and ⌬z 2 is the distance from the second focus of the original HM-3 reflector on the z-axis (z 2 ). C: center wave, W: wake, and E: edge wave. J. Acoust. Soc. Am., Vol. 113, No. 1, January 2003

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FIG. 5. Theoretical prediction of the pressure waveforms along the lithotripter axis using the upgraded reflector. Here, t denotes the propagation time of a reflected sound pulse originated from the first focus of the lithotripter reflector, and ⌬z 2 is the distance from the second focus of the original HM-3 reflector on the z-axis (z 2 ). Arrows indicate the edge waves, originated from the lower 共L兲 and upper 共U兲 rim of the reflector insert.

In comparison, the edge wave produced by the upper rim of the reflector insert 共which is distal from the spark discharge at F 1 ) arrives later; however, it converges to the center wave faster than the edge wave from the lower rim. Beyond F 2 both edge waves and the wake overtakes the center wave, with the edge wave from the upper rim diverging away from the center wave faster than its counterpart from the lower rim 共see ⌬z 2 ⫽65.7 mm in Fig. 5兲. Because of the shallow depth of the uncovered bottom surface of the HM-3 reflector, the second shock wave is weakly focused with a resultant long beam size along the lithotripter axis. Consequently, the center wave and the edge wave of the second shock wave overlap with each other most of the time when propagating along the lithotripter axis. For the same reason, the rate at which the edge wave diverges away from the wake and center wave beyond the focus is much faster for the first shock wave than for the second shock wave. In comparison, it is interesting to note that around the beam focus, the waveform profiles of the leading LSWs produced by the original HM-3 reflector and the upgraded reflector 共whose geometrical foci are separated by 5 mm兲 are quite similar. III. EXPERIMENTAL MATERIALS AND METHOD A. Lithotripter

The experiments were carried out in a Dornier HM-3 lithotripter with a 80 nF capacitor and a truncated brass ellipsoidal reflector with semimajor axis a⫽138 mm, semiminor axis b⫽77.5 mm, and half-focal length c⫽114 mm. In our previous study, to produce in situ pulse superposition we fabricated a thin shell ellipsoidal reflector insert that had an outer surface matching with the original HM-3 reflector and an inner surface with a ⬘ ⫽132.5 mm, b ⬘ ⫽71.5 mm, and c ⬘ 590


⫽111.5 mm. 23 The lower edge of the reflector insert was extended to the focal plane across F 1 where the tips of the spark electrode are centered. In this study, the lower edge of the original reflector insert23 was truncated by 4 mm in order to increase the pressure amplitude of the second shock wave without weakening significantly the LSW 共see Fig. 3兲. In addition, to reduce the effect of wave diffraction the lower edge of the reflector insert was trimmed into a conical shape of 11.8° angle with respect to the lithotripter axis, extending to the focus of the original HM-3 reflector 共see Fig. 1兲. B. Pressure waveform measurements

The pressure waveforms produced by the HM-3 lithotripter using either the original or upgraded reflector were measured using a fiber optic probe hydrophone 共FOPH 300, Universita¨t Stuttgart, Germany兲 that can accurately record both the compressive and tensile components of the LSW.28 The sensing probe of the FOPH 300, a 100-␮m optical fiber, was placed inside a holder and attached to a three-axis translation stage titled at 14° so that the probe could be aligned parallel to the lithotripter axis. Accurate alignment of the probe tip with F 2 was aided by a mechanical pointer that coincides with the beam focus of the HM-3 lithotripter. The probe tip of the hydrophone was scanned along the lithotripter axis in 5-mm steps (⫺15 mm⬍⌬z 2 ⬍15 mm) around the beam focus. At each location, at least four pressure waveforms were recorded using a digital oscilloscope 共LeCroy 9314M, Chestnut Ridge, NY兲 operated at 100 MHz sampling rate. C. High-speed shadowgraph imaging

Based on the design principle used in our previous studies,5,29 a high-speed shadowgraph imaging system was Yufeng Zhou and Pei Zhong: Refinement of reflector geometry

FIG. 6. Experimental setup for high-speed shadowgraph imaging in an HM-3 lithotripter. See text for details.

set up to capture the dynamics of cavitation bubbles produced in the HM-3 lithotripter field 共Fig. 6兲. A Lucite chamber (73.7⫻29.2⫻15.2– 21.6 cm,L⫻W⫻H), consisting of a wet test chamber at the center and two dry chambers on the lateral side to accommodate various imaging components, was constructed and fixed firmly inside the water tub of the HM-3 lithotripter. An illumination pulse, produced by a Nd:YAG laser 共MiniLaseI, New Wave Research, Sunnyvale, CA, ␭⫽512 nm and t p ⫽6 ns), was collimated using a combination of a concave lens and a Schlieren mirror that were mounted on an optical breadboard placed on top of the HM-3 tub. Using a steering mirror, the collimated laser beam was passed through the test chamber, and the image was projected through a combination of lenses and mirror onto a CCD camera. By adjusting the trigger delay to the camera and the Nd:YAG laser with respect to the spark discharge of the lithotripter, a series of images of shock wave propagation and bubble dynamics could be captured. In addition, a sponge was placed at the water surface inside the test chamber to reduce wave reflection and its influence on bubble dynamics at the lithotripter focus. D. Stone comminution

For stone comminution tests, spherical stone phantoms (D⫽10 mm) made of BegoStone 共BEGO USA, Smithfield, RI兲 were used. The acoustic properties of BegoStone have been characterized and found to be similar to those of calcium oxalate monohydrate stone,30 which is the most frequently observed kidney stone in patients.31 Following our established protocol, the fragmentation test was carried out by using a phantom system that mimics stone comminution in the renal pelvis.17 However, in contrast to our previous study in which stone comminution was compared after 100 shocks, we evaluated the progression of stone comminution produced by the original HM-3 and upgraded reflector within the typical clinical dose of 2000 shocks at a pulse repetition rate of 1 Hz. Moreover, after each 100 shocks the position of the stone fragments with respect to F 2 was checked using the bi-planar fluoroscopic imaging system of the HM-3 lithotripter. If necessary, re-positioning was carried out to ensure that the largest fragment was aligned with F 2 . After 1000 J. Acoust. Soc. Am., Vol. 113, No. 1, January 2003

shocks, most of the original stone phantom was reduced to small fragments that accumulated around several large residual pieces, which were difficult to discern from each other in fluoroscopic images. Therefore, after 1000 shocks, the lithotripter focus was scanned every 100 shocks throughout the fragments to ensure sufficient shock wave exposure to all the residual large fragments. At the end of each experiment, all the fragments were carefully removed from the holder, spread out on paper, and dried in air for 24 hours. The dry fragments were then filtered through a series of ASTM standard sieves 共No. 5, No. 10, No. 18, No. 35, W. S. Tyler, Mentor, OH兲 with 4, 2, 1, and 0.5 mm grids, respectively. Stone comminution efficiency was determined by the percentage of fragments less than 2 mm, which can be discharged spontaneously in urine following clinical SWL.32 Six samples were used under each test configuration. E. Vessel phantom rupture

The potential for vascular injury produced by the upgraded reflector was evaluated using a vessel phantom made of a single regenerated cellulose hollow fiber (i.d. ⫽0.2 mm) following our established protocol.5,23 Briefly, the hollow fiber was immersed in the test chamber filled with highly viscous fresh castor oil and placed on the lithotripter axis around F 2 . Degassed water seeded with 0.1% ultrasound contrast agent Optison was circulated inside the hollow fiber to ensure that intraluminal cavitation could be produced consistently by each shock wave. A slow pulse repetition rate of ⬃0.1 Hz was used so that before the next shock any visible bubbles outside the hollow fiber could be carefully removed. The experiment was stopped either when a rupture was produced or when the total number of shocks delivered to the hollow fiber reached 200. IV. RESULTS A. Pressure waveforms

Figure 7 shows representative pressure waveforms produced along the lithotripter axis. Using the original HM-3 reflector, a typical shock wave consisting of a leading compressive wave followed immediately by a tensile wave was Yufeng Zhou and Pei Zhong: Refinement of reflector geometry

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FIG. 7. Representative pressure waveforms measured along the lithotripter axis by using a fiber optic probe hydrophone, FOPH 300. 共a兲 Original HM-3 reflector at 20 kV and 共b兲 upgraded reflector at 24 kV. Here, ⌬z 2 denotes the distance from the second focus of the original HM-3 reflector on the z-axis (z 2 ). Arrows indicate the double-peak structure in the second shock wave.

produced. In addition to the leading shock front, a second positive pressure peak was also observed in the compressive wave. This double-peak structure is most obvious and consistently observed in an HM-3 lithotripter,33–35 whose ellipsoidal reflector is truncated on the lateral sides to accommodate the bi-planar fluoroscopic imaging system for stone localization. In contrast, pressure waveforms produced by other experimental electrohydraulic lithotripters with similar 592


reflector geometry yet without truncation on the lateral sides reveal less distinct second peak in the compressive wave.18,35 This second positive pressure peak, much smaller in amplitude than the leading shock front, may be related to the superposition of the edge wave originated from wave diffraction at the aperture of the reflector and the center wave, which are opposite to each other in phase polarity. Truncation of the lateral sides of the HM-3 reflector strengthens the Yufeng Zhou and Pei Zhong: Refinement of reflector geometry

FIG. 8. Representative high-speed shadowgraph images of shock wave propagation and bubble dynamics produced in water around the lithotripter focus 共center of each frame兲. 共a兲 Original HM-3 reflector at 20 kV and 共b兲 upgraded reflector at 24 kV. The number above each image frame indicates the time delay from the spark discharge of the lithotripter electrode. LSW: lithotripter shock wave, 2nd SW: second shock wave generated from the uncovered bottom surface of the original HM-3 reflector, 2 0 SW: secondary shock wave produced by the collapse of cavitation bubbles.

edge wave when portions of the reflector become shallower.24 The strong edge wave causes a significant ditch on the compressive wave following the shock front, leading to the appearance of the second positive peak. In comparison, the pressure waveform produced by the upgraded reflector has a leading compressive wave following by a modified trailing tensile component. An edge wave preceding the lithotripter shock front is apparent when the pressure waveforms were measured at locations beyond the geometrical focus of the reflector insert. More importantly, a second shock wave produced by wave reflection from the uncovered bottom surface of the original HM-3 reflector is observed, which superimposes on the trailing tensile component of the LSW. The amplitude of the second shock wave at F 2 is estimated to be 15.6 MPa, compared to 10.4 MPa produced by our prototype upgraded reflector.23 The higher amplitude of the second shock wave produced by the refined upgraded reflector is consistent with the increased reflecting surface area for the second shock wave. Interestingly, a double-peak structure 共indicated by arrows in Fig. 7兲 was also observed for the second shock wave before its geometric focus, F 2 , which may relate to the strong edge wave produced by the shallow, uncovered bottom surface of the HM-3 reflector. Beyond F 2 , the edge wave overtakes the center wave 共Fig. 7兲. J. Acoust. Soc. Am., Vol. 113, No. 1, January 2003

B. High-speed shadowgraph imaging

Figure 8 shows two representative sequences of bubble dynamics produced in water (O2 concentration: ⬍2.0 mg/L兲 by the original HM-3 reflector at 20 kV and the upgraded reflector at 24 kV, respectively. With the original reflector, the leading focused shock front, and, following immediately behind it, the convex edge waves propagating laterally and crossing each other on the lithotripter axis can be clearly observed 关 t⫽178 ␮ s and t⫽180 ␮ s in Fig. 8共a兲兴. Subsequentally, cavitation bubbles were induced in the wake of the shock front by the trailing tensile component of the LSW. The initial bubble expansion was quite large. With only 10 ␮s after the passage of the shock front, some bubbles have grown to a size of about 0.8 mm 关 t⫽190 ␮ s in Fig. 8共a兲兴. Although initially individual bubbles appeared to expand spherically, bubble aggregation might occur later on near the lithotripter axis 关 t⫽330 ␮ s in Fig. 8共a兲兴. Following the maximum expansion, most bubbles collapsed violently, generating secondary shock waves 关440 ␮s in Fig. 8共a兲兴. The collapse of rebound bubbles appeared to be affected by the secondary shock wave, leading to microjet formation along the propagation direction of the secondary shock wave 关 t⫽550 ␮ s in Fig. 8共a兲兴. Using the upgraded reflector, a leading focused shock Yufeng Zhou and Pei Zhong: Refinement of reflector geometry

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FIG. 9. Photographs of BegoStone fragments after exposure to 50–2000 shocks produced by 共a兲 the original HM-3 reflector at 20 kV and 共b兲 the upgraded reflector at 24 kV.

front with the accompanying edge waves were observed, and their arrival time at F 2 is about 4 ␮s earlier than the LSW produced by the original HM-3 reflector 关Fig. 8共b兲兴. In addition, a second shock wave produced by wave reflection from the uncovered bottom surface of the orginal HM-3 reflector was observed 关 t⫽176 ␮ s in Fig. 8共b兲兴. Interestingly, the edge wave, separated from the leading shock front by about 1 ␮s, could be identified from the shadowgraph imaging, which correlates well with the double-peak structure of the second shock wave measured by the FOPH 300 hydrophone 共Fig. 7兲. In comparison to the bubble dynamics produced by the original HM-3 reflector, three major differences were identified. First, the second shock wave significantly suppressed the initial bubble expansion produced by the leading LSW. Smaller bubbles were observed at 10 ␮s after the passage of the leading LSW front 关 t⫽186 ␮ s in Fig. 8共b兲兴. Second, the perturbation of the second shock wave on the initial bubble expansion largely disrupted the spherical geometry of the bubbles, which appeared uneven at the boundary 关 t ⫽190 ␮ s and t⫽260 ␮ s in Fig. 8共b兲兴. Third, although these disrupted bubbles could continue to expand to a maximal size, their subsequent collapse appeared to be very weak with few microjets produced as a result of the secondary shock wave-bubble interaction 关 t⫽550 ␮ s in Fig. 8共b兲兴.

tween the two reflector configurations when the exposure was less than 500 shocks (p⬎0.05, Fig. 10兲. From 500 to 1500 shocks, the original HM-3 reflector was found to produce better stone fragmentation than the upgraded reflector. Yet, towards the end, after a typical clinical dose of 2000 shocks, stone comminution produced by the two reflector configurations were again close to each other, i.e., 97.15 ⫾1.92% (mean⫾SD) for the original HM-3 reflector at 20 kV and 90.35⫾1.96% for the upgraded reflector at 24 kV, although the difference is statistically significant (p⬍0.02). D. Rupture of vessel phantoms

Using the upgraded reflector with refined geometry, no rupture of the hollow fiber vessel phantom could be produced around the lithotripter beam focus (⫺10 mm⬍⌬z 2 ⬍10 mm) even after 200 shocks at 24 kV 关Fig. 11共a兲兴. In comparison, consistent and spatial position-dependent rupture of the vessel phantom was produced by the original HM-3 reflector at both 20 and 24 kV.17 Previously, rupture of the vessel phantom was produced using our prototype up-

C. Stone comminution

Figure 9 shows the dose-dependent stone comminution produced by the original HM-3 reflector at 20 kV and the upgraded reflector at 24 kV, respectively. In both cases, a progressive fragmentation of the BegoStone phantom was produced as the number of shocks delivered increased. It is noted that although only about 500 shocks were needed to disintegrate each stone phantom into a distribution of fragments of various sizes, a much higher number of shocks 共up to 1500 additional pulses兲 was required to reduce the fragments to small and passable sizes. In comparison, the upgraded reflector was found to produce a slightly higher number of large fragments than the original HM-3 reflector 共Fig. 9兲. This observation is expected because the upgraded reflector suppresses cavitation, which, in addition to its role in vascular injury, is also critical for producing small and passable fragments in SWL.36 Quantitatively, no statistically significant difference in stone comminution was observed be594


FIG. 10. Dose-dependent fragmentation efficiency produced by the original HM-3 and upgraded reflector. The fragmentation efficiency was determined by the weight percentage of fragments less than 2 mm in size following shock wave treatment. A Student’s t-test was performed to determine statistically significant differences (p⬍0.05) between the results produced by the original HM-3 reflector at 20 kV and that from the upgraded reflector at 24 kV. The significance levels 共p values兲 are shown in the figure. Yufeng Zhou and Pei Zhong: Refinement of reflector geometry

FIG. 11. 共a兲 Relationship between the number of shocks to cause a rupture of a cellulose hollow fiber (N r ) and the axial position of the fiber in the lithotripter field (n⫽6). Here, ⌬z 2 denotes the distance from the second focus of the original HM-3 reflector on the z axis (z 2 ). A Student’s t-test was performed for each location between the results of 20 kV and 24 kV using the original HM-3 reflector. The significance levels 共p-values兲 are shown in the figure, 共b兲 a cellulose hollow fiber (i.d.⫽0.2 mm) at lithotripter focus before shock wave exposure, and 共c兲 and 共d兲 maximum intraluminal bubble expansion produced by the original HM-3 reflector at 20 kV and the upgraded reflector at 24 kV, respectively.

graded reflector at ⌬z 2 ⫽⫺5 mm where the highest tensile pressure was induced.17 Therefore, refinement of the reflector geometry has resulted in further suppression of the large intraluminal bubble expansion around the lithotripter focus, and concomitantly, a further reduction of the potential for vascular injury in SWL. The maximum bubble expansion produced inside a hollow fiber vessel phantom by the original HM-3 and upgraded reflector was captured using the high-speed shadowgraph imaging system shown in Fig. 6. While substantial circumferential dilation of the vessel wall was observed using the original HM-3 reflector, minimal dilation was produced by the upgraded reflector 关Figs. 11共c兲 and 共d兲兴. This observation is consistent with the significantly reduced potential for vessel phantom rupture by the upgraded reflector 关Fig. 11共a兲兴. All together, these results suggest that compared to the original HM-3 reflector, the upgraded reflector can produce satisfactory stone comminution with greatly reduced potential for vascular injury. E. Bubble dynamics predicted by the Gilmore model

To confirm theoretically that the upgraded reflector can suppress cavitation, bubble dynamics in response to the pressure waveforms measured by the FOPH 300 at F 2 were calculated using the Gilmore model.8 No gas diffusion was conJ. Acoust. Soc. Am., Vol. 113, No. 1, January 2003

sidered in the model calculation because we were mainly interested in the expansion phase of the bubble oscillation.17 The results, shown in Fig. 12共a兲, revealed a dramatic reduction in the maximum bubble expansion. For the original HM-3 reflector at 20 kV, a maximum bubble radius (R max) of 866 ␮m with an associated collapse time (t c ) of 163 ␮s was predicted. In comparison, corresponding values of R max ⫽161 ␮ m and t c ⫽12 ␮ s were predicted for the upgraded reflector at 24 kV. Although the model prediction is comparable to the experimental results 共see Fig. 8兲 for the original HM-3 reflector, there is an apparent discrepancy for the upgraded reflector. This discrepancy may be caused in part by the fact that a bubble induced in the acoustic field of the upgraded HM-3 lithotripter tends to expand non-spherically as a result of in situ pulse superposition. In addition, the variation in pressure waveform profile off-axis and away from F 2 may also contribute to the differences between the theoretical prediction and experimental results. Nevertheless, on a qualitative basis, both the theoretical prediction and the experimental results strongly suggest that the upgraded reflector can significantly suppress bubble expansion and, therefore, greatly reduce the propensity for vessel rupture in SWL.23 From the phase diagram shown in Fig. 12共b兲, it is noted that the bubble expansion produced by both the original Yufeng Zhou and Pei Zhong: Refinement of reflector geometry

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FIG. 12. Computed bubble dynamics of a cavitation nucleus (R 0 ⫽3 ␮ m) in response to the pressure waveforms measured at the lithotripter focus using a fiber optic probe hydrophone 共see Fig. 7兲. 共a兲 Bubble radius 共R兲 vs time and 共b兲 phase plot of bubble wall velocity 共U兲 vs R.

HM-3 and the upgraded reflector reaches a maximal outward speed at a bubble radius of about 80 ␮m. Therefore, capillaries that have a typical inner diameter on the order of 10 ␮m are still at high risk for rupture due to intraluminal bubble expansion even when the upgraded reflector is used. However, the propensity for the rupture of small blood vessels should be greatly reduced by the upgraded reflector.

wave significantly suppresses the initial bubble expansion and reduces the dilation of the vessel wall by the intraluminal bubbles. Based on the pressure waveforms measured by using an optical fiber probe hydrophone, numerical simulation of bubble dynamics also predicts a substantial reduction in maximum bubble expansion due to in situ pulse superposition. All together, these findings corroborate the experimental observation that the upgraded reflector can greatly reduce the propensity for vessel rupture. Furthermore, preliminary results from animal studies have also demonstrated a significant reduction in gross and microscopic renal injury using the upgraded reflector.37 After a typical clinical dose of 2000 shocks, histology evaluation revealed more than threefold reduction in tissue injury in the kidney treated by the upgraded reflector at 24 kV, compared to that produced by the original HM-3 reflector at 20 kV. Microscopically, although extensive hemorrhages were produced throughout the thickness of the kidney using the original HM-3 reflector, only discrete microblooding spots were generated by the upgraded reflector.37 Although the overall profile and sequence of the pressure waveforms along the lithotripter axis can be evaluated qualitatively by the Hamilton model, an accurate prediction of the peak pressure at the beam focus will require the use of nonlinear wave propagation models that also accounts for thermoviscous absorption and dispersion in tissue.25–27 However, an accurate description of the initial pressure distribution around the spark discharge at F 1 needs to be determined before one can use these nonlinear models to guide the optimization of the HM-3 reflector geometry to achieve the most desirable bubble activity in SWL.27 Finally, it is interesting to note that the upgraded reflector produces slightly larger fragments than the original HM-3 reflector 共see Figs. 9 and 10兲. This finding is consistent with the results of our recent study, which suggests that although stress waves play an important role in the initial disintegration of kidney stones, cavitation is necessary to produce small and passable fragments, which is most critical for the success of clinical SWL.36 Because the upgraded reflector suppresses cavitation, it has the tendency to produce larger residual fragments and therefore reduce slightly 共⬃7%兲 the concomitant fragmentation efficiency after a clinical dose of 2000 shocks. Such a small loss in fragmentation efficiency, however, may be compensated by selectively enhancing the collapse of cavitation bubbles near the stone surface produced by the upgraded HM-3 lithotripter using an auxiliary shock wave source, such as a piezoelectric annular array shock wave generator.38

V. DISCUSSION

By refining the geometry of the reflector insert, we have strengthened the second shock wave and, consequently, further suppressed the intraluminal expansion of cavitation bubbles induced by LSW. Comparing to our prototype design, the refined reflector insert prevents the rupture of the hollow fiber vessel phantom throughout a large area around F 2 (⫺10 mm⬍⌬z 2 ⬍10 mm) while maintaining satisfactory stone comminution. In addition, we have demonstrated via high-speed shadowgraph imaging that the second shock 596


ACKNOWLEDGMENTS

This work was supported in part by NIH through Grants Nos. RO1-DK52985 and RO1-DK58266. The authors are grateful to Thomas Dreyer and Marko Liebler from Universita¨t Karlsruhe, Germany for their help in pressure waveform measurements using a fiber optic probe hydrophone 共FOPH 300兲. The authors are also grateful to Dr. Songlin Zhu, who designed and fabricated the test chamber and set up the highspeed imaging system in the HM-3 lithotripter. Yufeng Zhou and Pei Zhong: Refinement of reflector geometry

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