Using an experimental system that mimics stone fragmentation in renal pelvis, we have investigated the role of stress waves and cavitation in stone comminution in shock wave lithotripsy (SWL). Spherical plaster-of-Paris stone phantoms (D=10 mm) were exposed to 25, 50, 100, 200, 300, and 500 shocks at the beam focus of a HM-3 lithotripter operated at 20 kV and a pulse repetition rate of 1 Hz. The stone phantoms were immersed either in degassed water or in castor oil to delineate the contribution of stress waves and cavitation to stone conuninution. It was found that while in degassed water there is a progressive disintegration of stone phantoms into small pieces, the fragments produced in castor oil are fairly sizable. From 25 to 500 shocks, the clinically passable fragments (< 2 mm) produced in degassed water increases from 3% to 66%, whereas in castor oil the corresponding values are from 2% to 1 1 %. Similar observations were confmned using kidney stones of primarily calcium oxalate monohydrate compositions. After 200 shocks, 89% of the fragments of the kidney stones treated in degassed water become passable, while only 22% of the fragments of the kidney stone treated in castor oil are less than 2 mm in size. This apparent size limitation of the stone fragments produced by stress waves alone (in castor oil) is likely caused by the destructive superposition of the stress waves reverberating inside the fragments when their sizes are less than half of the compressive wavelength in the stone material. On the other hand, if a stone is only exposed to cavitation bubbles induced in SWL, the resultant fragmentation is much less effective compared to that produced by the combination of stress waves and cavitation. It is concluded that while stress wave-induced fracture is important for the initial disintegration of kidney stones, cavitation is necessary to produce fine, passable fragments which is most critical for the success of clinical SWL. Stress waves and cavitation work synergistically rather than individually to produce effective and successful disintegration of renal calculi in SWL.

Key words: Shock wave lithotripsy, mechanisms of stone comminution, stress waves, and cavitation.

Disintegration of renal calculi in a lithotripter field is the consequence of dynamic fracture of stone materials due to the mechanical stresses produced either directly by the incident lithotripter shock wave (LSW) or indirectly by the collapse of cavitation bubbles (Lokhandwalla and Sturtevant, 2000). In shock wave lithotripsy (SWL), two basic mechanisms of stone fragmentation have been well documented, namely, spalling at the posterior surface and at internal crystalline-matrix interfaces of a stone due to reflected tensile waves (Chaussy 1982, Khan et al. 1986), and cavitation erosion at the anterior surface of a stone due to violent collapse of bubbles (Coleman et al. 1987, Crum 1988, Sass et al. 1991, Zhong and Chuong, 1993, Zhong et al. 1993). The damage patterns produced by these two mechanisms, however, are distinctly different (Chuong et al. 1989) and their relative contribution to the overall success of stone conuninution in SWL has not been determined.

When a LSW impinges on a stone surface at least two types of stress waves (longitudinal and transverse waves) will be generated at the wave entry site and propagate into the stone material (Gracewski et al. 1993, Dahake and Gracewski, 1997, Xi and Zhong, 2001). Upon reaching the posterior surface of the stone, the leading longitudinal stress wave, which has a pressure profile similar to the LSW in water, will be partially reflected and undergone a phase inversion due to the decrease in acoustic impedance from the stone to surrounding tissue/urine. The reflected tensile wave, propagating back towards the shock wave source, will subsequently superimpose with the remaining tensile component of the incident longitudinal stress wave, producing a strong tensile stress near the posterior surface of the stone (Chaussy 1982, Xi and Zhong, 2001). Since most kidney stones are brittle materials (Jodrde and Cocks, 1985, Zhong et al. 1993a), they fail much more easily under tension than under compression. In general, spalling damage refers to stone fragmentation initiated and facilitated by the reflected tensile waves. In addition to wave superposition, strong tensile stresses can also be produced by the focusing and crossing of wave fronts near the posterior surface of the stone (Xi and Zhong, 200 1, Gracewski et al. 1993). Using photoelastic imaging technique and ray-tracing analysis, these basic features of stress wave propagation, evolution, and resultant damage in stone phantoms of different size and geometries have been confirmed (Xi and Zhong, 2001). In addition, it was found that the transmitted transverse (or shear) wave could facilitate the extension and propagation of microcracks initiated by the reflected tensile waves (Xi and Zhong, 2001).

Alternatively, the production of characteristic fracture patterns in stone models has been described by the squeezing mechanism (Eisenmenger, 2001). Based on this theory, circumferential compression of a stone by a LSW of large beam diameter will generate maximum dilatational strain perpendicular to the wave propagation direction both at the anterior and posterior surface of the stone, and parallel to the wave axis in the center of the stone. Theoretically, if the stone structure is weak (i.e., with numerous pre-existing flaws or fissures) it may also fail readily under the influence of the transmitted compressive and tensile waves (Brace and Bombolakis 1963; Bombolakis 1968, Lokhandwalla and Sturtevant, 2000). Although conceptually the progressive disintegration of kidney stones in SWL may be best described based on the principle of dynamic fatigue in brittle materials (Ortiz, 1988, Lokhandwalla and Sturtevant, 2000), such an analysis is difficult to carry out under practical SWL conditions because of the complexity in stone composition, geometry, and internal structure (Sutor, 1972). It should be noted that a simplified model based on the concept of binary fragmentation has been shown to predict the progression of stone phantom fragmentation in vitro (Eisenmenger, 2001).

In comparison to stress wave-induced fragmentation, cavitation damage in SWL is characterized by surface erosion with numerous minute pits produced either by the secondary shock waves or microjet impingement due to the violent collapse of bubbles near a stone surface (Coleman et al. 1987, Crum 1988, Zhong et al. 1993, Philipp and Lauterbom 1998, Xi and Zhong, 2000). The fragments produced by cavitation damage are usually small, due to the highly localized stresses generated by a collapsing bubble (Church, 1989, Zhong et al. 1993). This is in great contrast to the large fragments produced by spalling mechanism (Chuong et al. 1989, Gracewski et al. 1993, Xi and Zhong, 2001). Furthermore, when cavitation was inhibited either by increasing the viscosity of the medium or by excessive overpressure, the fragmentation of gallstones by LSWs (presumably stress waves) was found to be significantly reduced (Delius et al. 1988, Delius, 1997). The effect of LSW-induced cavitation alone on stone comminution in SWL, however, has not been investigated. Considering that about 2,000 shocks are generally employed for the successful comminution of kidney stones in patients (Bierkens et al. 1992), a better understanding of the contribution of stress, waves and cavitation to stone comminution in SWL could be helpful in developing strategies to improve the treatment efficacy of SWL.

In this work, a series of experiments were carried out using a phantom system that mimics in vivo stone comminution in renal pelvis. Emphasis is placed on delineating the contribution of various working mechanisms to the overall success of stone comminution, and on understanding of the progressive development of stone comminution in SWL in relation to the contributing mechanisms. It was found that both stress waves and cavitation play critical roles in the comminution of kidney stones; they act synergistically rather than individually to ensure an effective and successful fragmentation of renal calculi in SWL.

Lithotripter
In this study, we used a Dornier HM-3 lithotripter with a truncated ellipsoidal reflector (semi-major axis a = 138 mm, semi-minor axis b = 77.5 mm, and half-focus length c = 114 mm). The lithotripter was operated at the typical clinical setting of 20 kV and I Hz pulse repetition rate. Based on measurements using a fiber optical probe hydrophone, the pressure waveform (see Fig. 1) at the beam focus (F2) of the HM-3 lithotripter has a typical peak positive/negative pressure of 45/-8 MPa, a zero-crossing positive and negative pulse duration of 2 and 9 its, and a -6 dB beam size of 75 x 8 nun along and transverse to the lithotripter axis, respectively.

Fig. 1. A representative pressure wavefonn produced at the focal point of a HM-3 lithotripter operated at 20 kV. The pressure waveforrn was measured using a fiber optical probe hydrophone with the recording digital oscilloscope triggered by the spark discharge of the lithotripter electrode.

Stone samples
Spherical stone phantoms (D = 10 mm) were made of plaster-of-Paris (powder/water ratio = 2 : 1 by weight), using a specially designed mold (Zhu et al. 2000). The acoustical properties of the plaster-of-Pairs stone phantom are comparable to that of magnesium ammonium phosphate hydrogen (or struvite) stones (Chuong et al. 1992, Zhong et al. 1993). In addition, six pairs of kidney stones of different compositions, surgically removed from patients, were used for comparison of stone comminution in different fluid media. Each pair of the stones were selected based on their similarity in composition, size, color, and weight (Table 1), with their primary chemical composition determined to be calcium oxalate monohydrate (COM), the most commonly observed crystalline material in kidney stones (Sutor, 1972).

Experimental protocol
To mimic stone comminution in renal pelvis, a phantom system developed recently (Zhong and Zhou, 2001) was used. Figure 2 shows the experimental setup. The stone sample was placed in a plastic holder with disposable finger cot (VWR Scientific Products, Suwanee, GA) at the end. The holder was filled with either degassed water (a cavitation supportive medium) or freshly poured caster oil (a cavitation inhibitive medium) to delineate the contribution of stress waves and cavitation to stone comminution. Using this set up, the finger cot and the test fluid inside the sample holder can be replaced easily following each test. The stone holder was immersed in an acrylic testing chamber (254x254xl52~216 mm, LxWxH) filled with caster oil and with a slab of 25-mm thick tissue-mimicking phantom placed at the bottom to simulate tissue attenuation on the incident LSWs (Zhong and Zhou, 2001).

Fig. 2. Schematic diagram of the experimental set up for mimicking stone comminution in renal pelvis.

The stone phantoms were randomly divided into two populations for shock wave treatments either in degassed water or in castor oil. To determine the dose dependency in stone comminution, samples in each population were further subdivided into six groups (n = 6 in each group) and exposed to 25, 50, 100, 200, 300, and 500 shocks, respectively. For kidney stones, the comparison was made at 200 shocks only. Before the experiment, the weight,-of each sample in dry state was measured. Prior to shock wave treatment, each stone sample was immersed in the prospective test fluid (degassed water or caster oil) for at least 20 minutes until no visible bubbles could be seen at the stone surface. Based on our experience, prolonged immersion of the sample beyond 20 minutes does not change the fragmentation results significantly. Alignment of the stone phantom to F2 was aided by a pointer and verified by the fluoroscopic imaging system of the HM-3 lithotripter. Following the shock wave treatment, all the fragments in the finger clot was carefully removed and spread into a layer on a dry paper. For samples treated in castor oil, facial tissue was used to gently absorb any excessive oil left on the specimen surface. After drying in air for 48 hours, the fragments were collected and their size distribution was determined by sequential sieving (Akers et al. 1987). Briefly, the fragments were filtered through a set of four sieves (W.S. Tyler) placed vertically in a rack with descending order of pore size from 4.0 mm to 0.5 mm. The fragments were then removed from each sieve and weighed.

To identify the contribution of cavitation alone to stone comminution in SWL, another set of experiments was performed using the plaster-of-Paris stone phantoms in an experimental HM3 lithotripter. This laboratory lithotripter is equipped with a transparent water tank, so that high-speed shadowgraphs can be recorded to visualize the transient shock waver-stone interaction (Xi and Zhong, 2001). To eliminate the contribution of stress waves, the stone phantom was placed in the focal plan but with its center shifted transversely by a 13-mm distance from the shock wave axis to position the stone just outside the lithotripter beam focus (see Fig. 7b). Cavitation bubbles, however, were still produced at F2 in water and collapsed near the lateral surface of the stone. In the fragmentation tests, the stone sample was placed inside a thin-wire net affixed to an inverted U-shape holder, and exposed to LSWs in degassed water without tissue-mimicking materials. For comparison, another group of stone phantoms was treated at F2.

Stone phantoms

Dose-dependency of stone comminution in degassed water
In degassed water, stone phantoms break up progressively as the number of shocks increases (Fig. 3). The size distribution of the fragments at different number of shocks is shown in Fig. 4a. Initially, after 25 to 50 shocks the stone was broken into several large pieces (> 4 mm), which accounts for more than 90% of the fragments by weight. As the shock number increased, more medium- (2 ~ 4 mm) and small-size (<2 mm) fragments were produced, indicating a progressive comminution of the initial large fragments. After 200 shocks, the large fragments was reduced to 28% of the total weight, while the medium fragments reached a maximum of 36%, and the small fragments contributed to the remaining 36%. As the shock wave exposure continued, the percentage of small fragments increased further while the percentage of large and medium fragments decreased.

Fig. 3. Photographs of fragments of plaster-of-Paris stone phantoms treated in water after exposing to 25 - 500 shocks at 20 kV using a HM-3 lithotripter.

Figure 4b shows the dose dependency in stone comminution using the 2-mm criterion for passable fragments, based on the clinical observation that stone fragments less than 2 mm can be discharged spontaneously following SWL (Chaussy, 1982). It can be seen that initially (< 50 shocks) stone comminution increases slowly with the shock number, between 50 and 300 shocks, there is a rapid, linear increase in fragmentation, and after 300 shocks, the comminution rate slows down again. One important reason for this reduced rate of stone comminution at large number of shocks is the scattering of LSWs by residual small fragments. During the experiments, it was observed that small fragments tend to settle down at the bottom of the finger clot. When a significant portion (> 50%) of the stone was fragmented, a layer of small fragments could be accumulated underneath the residual large pieces, which would significantly attenuate the ensuing LSWS, and thus decreasing stone comminution efficiency subsequently. Similar effect of residual fragments on the comminution of ureteral stones has been reported previously (Mueller et al. 1986).

Fig. 4. Dose-dependent size distribution of the fragments of plaster-of-Paris stone phantoms in water after shock wave treatment in a HM-3 lithotripter at 20 kV.

The contribution of stress waves
To determine the contribution of stress waves, stone phantoms were immersed in castor oil to suppress cavitation (Howard and Sturtevant, 1997, Zhong 'et al. 2001). Under this circumstance, stone phantoms could only be fragmented by the stress waves produced by the incident LSWs (Gracewski et al. 1993, Xi and Zhong, 2001, Lokandwalla and Sturtevant 2000). The result, shown in Fig. 5, demonstrates that although stone phantoms were disintegrated into multiple pieces in castor oil, the fragments remained fairly sizable even after 500 shocks. Quantitatively, large and medium fragments were produced after 25 shocks accounting for 75% and 20% of the stone weight, respectively (Fig. 6a). With continued shock wave exposure, the large fragments were reduced to medium-size pieces, which, however, were not further comminuted into small fragments. For example, after 500 shocks only 1.5% of the stone mass was reduced to less than I mm and no fragments less than 0.5 mm were produced (Fig. 6a). This is in great contrast to the progressive comminution of stones into fine fragments in degassed water (Fig. 3 and Fig. 4). Using the 2-mm criterion, it is clear that if stone comminution in SWL were produced by the stress waves alone most fragments would not pass spontaneously following the treatment (Fig. 6b). From 25 to 500 shocks, the percentage of passable fragments increases only slightly from 2% to 1 1%. Clearly, under the influence of stress waves alone there is an apparent limitation on the smallest fragments that can be produced.

Fig. 5. Photographs of fragments of plaster-of-Paris stone phantoms treated in castor oil after exposing to 25 - 500 shocks at 20 kV using a HM-3 lithotripter.

Fig. 6. Dose-dependent size distribution of the fragments of plaster-of-Paris stone phantoms in castor oil after shock wave treatment in a HM-3 lithotripter at 20 kV.
 

The contribution of cavitation
To isolate the contribution of cavitation alone to stone comminution in SWL, a plaster-of-Paris stone phantom was placed off-axis transversely from F2 by 13 mm. As shown in Fig. 7b, the incident LSW propagated through F2 in water sweeping by the lateral surface of the stone. With this arrangement, stress waves produced inside the stone could be minimized. Yet, cavitation bubbles were still generated by the incident LSW around F2. The bubbles first expand to a maximum size in about 200 ms and then collapsed violently near the lateral surface of the stone, emitting secondary shock waves (see circular rings at 600 ms in Fig. 7b). Some bubbles were also seen to aggregate on the lateral surface of the stone, and their subsequent collapse could be asymmetric with resultant formation of microjets impinging towards the stone (Coleman et al. 1987, Crum 1988). Overall, the bubble dynamics in the off-axis arrangement is similar to that generated when the stone is placed at F2 (Fig. 7a), except that in the later case the bubbles collapse primarily near the proximal surface of the stone facing the incident LSW (frames at 500 m s and 680 ms in Fig. 7a).

Fig. 7. Representative high-speed image sequences of shock wave-cavitation bubbles-stone interaction produced by a laboratory HM-3 lithotripter in water at 24 kV. The plaster-of-Paris stone phantom (I 0 mm in diameter) was placed a) at F2, b) at a 13 mm transverse distance from F2. The number above each image frame indicates the time  delay in its after the spark discharge of the lithotripter electrode.

When the stone phantom was placed off-axis, only 3% of the stone mass were fragmented to be less than 2 mm after 30 shocks at 24 kV in the experimental HM-3 lithotripter (Fig. 8). In comparison, when placed at F2, 27%,of the stone mass was disintegrated into passable fragments. Macroscopically, damage to the stones placed off-axis was primarily surface erosion produced by the collapse of cavitation bubbles without any bulk disintegration of the stone. Whereas stones placed at F2 were fragmented into pieces of different sizes. These results suggest that with cavitation alone, although damage to the stone (primarily surface erosion) can be produced, the comminution efficiency is significantly reduced compared to that produced by the combination of stress waves and cavitation.

Fig. 8. Comparison of stone fragmentation at the beam focus of a laboratory HM-3 lithotripter and at a 13 mm transverse distance from the beam focus. The lithotripter was operated at 24 kV.

Kidney stones

Paired kidney stones of similar composition, size, shape, and weight were exposed to 200 shocks at 20 kV in the HM-3 lithotripter either in degassed water or in castor oil. The results, shown graphically in Fig. 9 and quantitatively in Fig. 10, revealed that in water most stones were comminuted into passable pieces whereas in castor oil most fragments remained in large size. For example, in water no fragments were larger than 4 mm and the residual weight for 2 ~ 4 mm, 1 ~ 2 mm, and < 1 mm fragments were 11%, 37%, and 52%, respectively. In contrast, in caster oil the fragments > 4 mm and 2 ~ 4 mm were 51% and 28%, respectively (Fig. 10a). Using the Z-mm criterion, about 89% fragments of the kidney stones in water could be passed spontaneously after 200 shocks whereas in caster oil the passable fragments were only 22% (Fig. 10b). These results are consistent with the observations from stone phantoms (Figs. 3, Fig. 4, Fig. 5 and Fig 6). All together, these experimental findings confirm that with stress waves alone, kidney stones can only be disintegrated into large, impassable pieces.

Fig. 9. Photographs of original pairs of kidney stones and their corresponding fragments after being treated by 200 shocks produced by a HM-3 lithotripter at 20 kV, a) in water and b) in castor oil.

Fig. 10. Size distribution of the kidney stone fragments after being treated by 200 shocks

The fragmentation of kidney stones in SWL is the consequence of dynamic fracture of stone materials in response to the mechanical stresses produced either by LSW or cavitation (Lokhandwalla and Sturtevant, 2000). Kidney stones, likely most crystalline materials, have preexisting flaws or microcracks randomly distributed at the crystalline-matrix interface or at the grain boundary of the crystalline materials. Under the mechanical stresses imposed by the LSWS, these pre-existing microcracks may extend if the accumulated stress-intensity factor at the crack tip exceeds a threshold value, also known as the fracture toughness of the material (Lokhandwalla and Sturtevant, 2000). The fracture toughness for kidney stones of various compositions has been measured in the range of 0.056 MPa*m^1/2 for magnesium ammonium phosphate hydrogen (or struvite) stones to 0.120 - 0.136 MPa*m^1/2 for brushite and COM stones, corresponding to their varying fragilities in SVYT (Zhong et al. 1993a). These values are an order of magnitude lower than the fracture toughness of ceramic materials (Hertzberg, 1989). It has been suggested that the nucleation, growth, and coalescence of the microcracks in the stone material under repeated bombardments of the LSWs eventually leads to the fragmentation of kidney stones in SWL (Lokhandwalla and Sturtevant, 2000).

The observation that stone phantoms and kidney stones immersed in castor oil cannot be fragmented into passable pieces (see Fig. 5 and Fig. 9b) indicates that there is a size limitation on the fragments produced by stress waves alone in SWL. Among various proposed mechanisms, this finding is most consistent with the spalling mechanism. A simple analysis of the wave reflection and superposition at the stone boundary may provide some critical insights to the problem. Let's consider the reflection of a transmitted longitudinal wave at the posterior surface a kidney stone, a critical process involved in the production of spalling damage (Gracewski et al. 1993, Xi and Zhong, 2001). Because of the decrease in acoustic impedance from stone material to surrounding tissue or fluid, the leading compressive component of the wave will be inverted in phase, generating a reflected tensile wave. This reflected tensile wave, propagating back into the stone material, will first superimpose with the remaining portion of the compressive component of the incident wave, resulted in a mutual reduction of their respective amplitudes (Xi and Zhong, 2001). Subsequently, as the reflected tensile wave propagates further into the stone and superimposes with the trailing tensile component of the incident wave, a strong tensile stress will be produced at some distance from the posterior surface of the stone. This is the reason why in cylindrical stone phantoms (LSW propagating along the axis of the cylinder), spalling damage always occurs at a distance from the posterior surface of the stone (Xi and Zhong, 2001). On a first order approximation, the reflected tensile wave has to travel at least half of the positive pulse duration (t⁺) of the incident longitudinal wave in order to built up a sufficient tensile stress. Taking a typical value of t⁺ = 2.0 [ts for a HM-3 LSW (see Fig. 1) and the longitudinal wave speed (C_L) in kidney stones (Zhong et al. 1993a), this minimal distance (- C_L * t⁺/2) is estimated to be in the range from 2.7 mm for struvite to 4.5 mm for COM stones, which are greater than the 2-mm critical size for spontaneous discharge following clinical SWL. When the size of the residual fragments becomes less than this minimal distance, there will be destructive superposition of the stress waves reverberating inside the fragment. Consequently, the net stress imposed on the stone material will be significantly reduced. If the corresponding stress-intensity factor at the tip of pre-existing microcracks in the fragment falls below the fracture toughness of the stone material, subsequent shock wave exposure will not cause the microcracks to extend and, therefore, no further disintegration of the fragment will occur. Based on this analysis, if only stress waves contribute to stone comminution in SWL most renal calculi will not be comminuted to fragments small enough (< 2 mm) for spontaneous discharge, as demonstrated by the stone comminution results in castor oil (see Figs. 5 and Fig. 9b).

On the other hand, when cavitation is the only contributory force for stone comminution the resultant fragmentation efficiency is very low, compared to that produced by the combination of stress waves and cavitation (see Fig. 8). Cavitation-induced damage is primarily surface erosion and it does not penetrate much into the bulk of the stone material. Despite this, cavitation damage may weaken the surface structure of the residual large fragments (Fig. 11), making them much more fragile to the impact of subsequent LSWS. With the progression of shock wave exposure, liquid may enter into the bulk of the stone material through the crevices produced on the surface (Sass et al. 1991). The expansion of a bubble inside the stone by ensuing shock waves may generate large tensile stress at the crevice root, leading to crack expansion (Field 1991, Delius 1997). The analogy in SWL-induced tissue injury is the tensile rupture of small blood vessels due to the large intraluminal bubble expansion (Zhong et al. 2001). As the number of fragments increases, the total surface area of the fragments will increase much more rapidly, which would favor the progression of cavitation-facilitated damage. Although the contribution of each individual cavitation bubble to the overall stone comminution is small, the accumulative effect from numerous bubbles generated during the course of SWL treatment could be significant. It is conceivable that while stress wave-induced fracture, such as spalling and squeezing damage, is responsible for the initial fragmentation of the stone, cavitation is necessary to produce fine, passable fragments which is most critical for the success of clinical SWL treatment. All together, it appears that while individually both stress waves and cavitation have limitations in producing satisfactory or effective stone comminution, when combined they work synergistically to produce efficient and successful stone fragmentation.

As observed this and other studies (Mueller et al. 1986; Whelan and Finlayson, 1988), the scattering of LSWs by small fragments surrounding the large residual stone pieces is a significant efficiency-limiting factor for the successful of SWL treatment. As shown in Figs. 3 and Fig. 4, while only a few hundred shocks are needed to break up the stone into distributed fragments, clinically it usually requires a few thousand shocks to completely reduce the size of the fragments below 2 mm (Bierkens et al. 1992). Therefore, strategies to alleviate the scattering of LSWs by small fragments surrounding the large residual stone pieces should be explored in future investigations to improve the treatment efficiency of SWL.

Stress waves and cavitation are found to be both important for the success of stone comminution in SWL. While stress waves are important initially for breaking up kidney stones into distributed pieces, their effectiveness is hindered when the size of the residual fragments becomes less than half of the compressive wavelength in the stone material, due to destructive superposition of the reverberating waves inside the residual fragments. Cavitation, on the other hand, while working at a much slow rate of stone comminution, can significantly weaken the structure of the stone surface, making it much more fragile to the impact of ensuing LSWs and associated bombardments of cavitation bubbles. Therefore, stress waves and cavitation work synergistically rather than individually to produce effective and successful disintegration of renal calculi in SWL. Optimal utilization of the stress waves and cavitation in SWL may help to improve treatment efficiency while reducing adverse tissue injury.

This work was supported in part by NIH through Grants No. ROI-DK52985 and ROIDK58266, and by a Research Grant from the Whitaker Foundation. The authors would like to acknowledge the technical assistance of Yufeng Zhou in fabricating the test chamber and tissuemimicking phantom. The authors also want to express their gratitude to Thomas Dreyer and Marko Liebler from the University of Karlsruhe, Germany for their collaboration on the pressure wavefonn measurements in a HM-3 lithotripter using a fiber optical probe hydrophone.

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Table 1. Dimension and chemical compositions of the kidney stones

		Dimension (LxWxH, mm)	Initial Weight (g)	Component
				COM	MAPH	CaPO4	UA	COD	CA	PTN
Stone Group 1	A	9.23x8.48x7.28	0.4860	50	20	30
	B	10.77x9.03x7.03	0.6768
Stone Group 2	A	13.18xlO.18x5.96	0.7157	88			12
	B	9.64x6.93x7.46	0.9871
Stone Group 3	A	9.64x6.93x7.46	0.3817	88			12
	B	9.54x8.17x5.12	0.3163
Stone Group 4	A	14.17x 11.03x7.40	0.7620	90		10
	B	14.4x 11.87x7.79	0.8983
Stone Group 5	A	13.25x10.28x10.55	1.1968	60	15	25
	B	16.76x9.51x10.32	1.1281
Stone Group 6	A	11.03x7.05x6.84	0.3912	42				38	17	3
	B	10.99x7.22x5.14	0.2830

COM, calcium oxalate monohydrate; MAPH, magnesium ammonium phosphate hydrogen; CaPO₄, Calcium phosphate; UA, uric acid; COD, calcium oxalate dehydrate; CA, carbonate apatite; and PTN, platinum triamine ion.