The two-frequency ultrasound wave of the C-C waveform used in this study is shown in Fig. 7.2. The acoustic pressure is recorded using a membrane hydrophone (MHB200B, NTR systems, Seattle, WA, United States) placed at the focus of a concave lead zirconium titanate (PZT) transducer.

First, the high frequency ultrasound wave (3.82 MHz, 175 cycles in this case) is transmitted. Immediately after the high frequency wave is stopped, a short pulse of a low-frequency wave (545 kHz, 6 cycles) follows. For the high frequency wave in Fig. 7.2, the focal pressure is the maximum positive pressure |P + | = 10.0 MPa, and the maximum negative pressure |P−| = 6.0 MPa. For the low frequency part; |P+| = 16.0 MPa and |P−| = 6.5 MPa. High frequency ultrasound is designed to produce a localized cavitation bubble cloud on a stone, and low frequency ultrasound triggers the bubble cloud into violent collapse.

Cloud cavitation is a densely populated cluster of cavitation bubbles that has lost the characteristics of individual bubble behavior and the global behavior as a cluster increases. Bubbles are dynamically coupled through fluid motion and acoustic wave propagation inside the cloud (d’Agostino and Brennen 1988, 1989). Cloud collapse has been shown to be more destructive to high speed turbo-pumps and ship propellers than the collapse of individual bubbles. Numerous experimental studies (Knapp 1955; Soyama et al. 1992; Kato et al. 1996; Reisman and Brennen 1996; Reisman et al. 1998; Konno et al. 2002) and analytical/numerical studies (van Wijngaarden 1964; Mørch 1981; Omta 1987; Chahine and Duraiswami 1992; d’Agostino and Brennen 1988, 1989; Wang and Brennen 1995, 1999) have been conducted to investigate the dynamics of cloud collapse and to calculate the pressure generated in a cloud. The indirect experimental measurements of the maximum pressure inside a cloud of up to O(10⁸ ~ 10⁹) Pa have been reported (Kato et al. 1996; Reisman et al. 1998). Shimada et al. (2000) used a numerical model for a spherical bubble cloud considering the individual oscillating bubbles to investigate the converging shock wave within the cloud. They argued that the shock wave convergence inside the cloud led to a center bubble collapse pressure of O(10⁹) Pa, when a bubble cloud with bubbles of radius 20 μm and a cloud radius of 5 mm was subjected to stepwise pressure decrease and increase. Their work has been extended for initial and boundary conditions appropriate for focused ultrasound applications (Yoshizawa et al. 2004; Matsumoto and Yoshizawa 2005), although the model was restricted to lower ultrasound pressure amplitudes than those used clinically. They investigated the behavior of spherical cloud cavitation with uniform bubble size and distribution excited using medical ultrasound. They also showed that a violent cavitation cloud collapse occurs with a frequency range much less than the resonance frequency of the individual bubbles inside the cloud, with a collapse pressure up to 1000 times the ultrasound pressure amplitude, which forces the cloud into strong collapse. They also showed a broadening of the resonance bandwidth when the cloud was subjected to relatively large pressure amplitude. Their results provide the basis for our method for eroding kidney stones. A one-frequency wave is used to generate a cloud of bubbles, and then a lower frequency wave excites the cloud at its broad resonance to create high collapse pressure. Due to the broad resonances of the cloud, the low and high frequencies do not need to be precisely fixed.

The cavitation phenomenon at the focus of the focused ultrasound is recorded with a high speed image converter camera, Imacon 200 (DRS Hadland; at present, DRS Data & Imaging Systems, Oakland, NJ, USA). The Imacon 200 can take 8 photographs at a rate of up to 200 million frames/s, with a 5 ns minimum exposure. This is suitable for observing cavitation in the frequency bandwidth of the experiment (0.5–4 MHz), as this corresponds to a comparably shorter exposure time than the ultrasound cycle (250 ns–2 μs) and a faster frequency than ultrasound. Interframe and exposure time are varied by the software control, and the double shutter mode of Imacon 200 can obtain 16 frames with time intervals between frames of greater than 300 μs. An air-backed ultrasound transducer with a concave PZT ceramic element (C-213, Fuji Ceramics, Japan) was fixed in an acrylic water tank. Both the aperture and focal length of the PZT element were 80 mm.

Stone-erosion tests were conducted to investigate the applicability and efficiency of C-C waveform for lithotripsy applications. The erosion rate was also determined to investigate the efficiency of cavitation erosion in stone disintegration. The model stones are the test materials that were previously developed for research with commercial SWL machines. The U-30 stones were supplied by McAteer et al. (2005). These stones were cylindrical and longer (6.4 ~ 10.1 mm) than the wavelength of ultrasound (0.38 ~ 3.0 mm), and a -6 dB beam width of the focused ultrasound (0.6 ~ 4.0 mm). It took 72 h to completely rehydrate the U-30 stones in the atmospheric pressure (McAteer et al. 2005). Since the trapped gas inside the stone potentially affects the amount of erosion and distorts the acoustic profile, every stone was dipped in a desiccator filled with degassed water maintained at 10 kPa. They were left to stand for more than 48 h until there were no observable gas bubbles rising from the stone surfaces.

The acoustic waves for the stone-erosion tests were designed to demonstrate the advantage of the C-C waveform, which has combined high and low frequency waves. The C-C waveform was compared with waves with only a high or low frequency wave. The test waves for stone erosion were as follows: (a) High frequency alone (3.82 MHz, 175 μs), (b) low frequency alone (545 kHz, 6 cycles), and (c) high frequency and low frequency combined (C-C waveform). The ultrasound wave of the C-C waveform is shown in Fig. 7.2, and was also used in the experiment shown in Fig. 7.5.

In each case, the pulse repetition frequency (PRF) of the waves transmitted from the PZT transducer was fixed at 25 Hz, such that a 39.94 ms interval elapsed before the next pulse of the C-C waveform (c) (39.95 ms for (a) and 39.99 ms for (b)).

The upper graphs in Fig. 7.6 show the measured weight losses of the U-30 stones for each wave. The ultrasound irradiation time was 3, 6, 12, 18 min. Two samples were tested for each wave and irradiation time. The lower photographs correspond to the eroded model stones for each ultrasound irradiation time for the C-C waveform. In this experiment, each stone was moved in an attempt to achieve erosion over the entire stone surface. Two operators moved the stones while monitoring them with a microscope equipped with an ocular ruler with 0.1 mm resolution. In the transverse direction, the operators moved the stone so that the focus entirely covered the whole area of the stone’s base circle. The round trip of diameter scanning was maintained at 4 s. In the axial direction, the stones were also moved as the ultrasound focus was maintained on the base circle. This stone-erosion test protocol was applied for every sample (48 samples). The erosion rate was calculated using the least square fit of linear regression between the weight loss and ultrasound irradiation time. The calculated erosion speeds of the C-C waveform, low frequency alone and high frequency alone were 0.3, 2.2 and 5.0 mg/min, respectively. The determination coefficient R ² between the weight loss and ultrasound irradiation time was 0.66, 0.91 and 0.99, respectively.

As shown in Fig. 7.6, the C-C waveform eroded the stones more efficiently compared with the high frequency alone and low frequency alone waves. The calculated erosion rate reveals that the erosion rate of the C-C waveform (c) is double the rate of the sum of the high frequency alone (a) and low frequency alone (b). The high frequency causes localized cloud cavitation on the stone surface, but the amount of erosion is small, possibly because the cloud cavitation shields the stone surface. The low frequency wave alone creates a wider region of cavitation bubbles, so the eroded region is wider than the high frequency alone case. These bubbles collapse independently, such that the maximum pressure is not as high in comparison to the collapse of the cloud cavitation. The C-C waveform, with the high and low frequency in combination, forces the bubble cloud into a violent collapse, and the C-C waveform’s advantage might be a result from the controlled cloud cavitation collapse on the stone surface.

Ultrasound irradiation of the C-C waveform was applied to two types of natural kidney stones: Cystine and staghorn. The ultrasound wave was the same as that in Fig. 7.2, and the PRF of the cycle was 25 Hz. The upper photographs in Fig. 7.7 are of the eroded stones and their fragments, (a) cystine stone and (b) staghorn stone.

Erosion holes can be seen in both. The lower figures are the size-frequency of the number-size distribution of the fragment diameter D _p for (a) cystine stone and (b) staghorn stone. The D _p was calculated from the binary processed image of photographed stone fragments. From the area and peripheral length of the fragments, the D _p was calculated for each particle. For the cystine stone, the mean diameter was 0.13 ± 0.070 mm for 756 fragments, and 0.187 ± 0.120 mm for 1393 fragments of the staghorn stone. Every cystine stone particle was less than 0.8 mm. Almost all the staghorn fragments were less than 1.0 mm, although three fragments of D _p =1.2 mm, and one particle of D _p = 1.5 mm, were observed. The size distribution for each stone had slightly different characteristics. The staghorn stone fragments had a typical size-frequency distribution of fragments, with a long tail for increasing fragment size. The cystine stone’s distribution also had a long tail for the larger fragment sizes, whereas the small fragments did not have a local maximum. This is possibly due to the fact that very small fragments could not be completely collected due to water convection in the tank, so they did not all fall into the beaker placed just beneath the stone.

Almost all the eroded fragments were less than D _p = 1 mm, except the three fragments of D _p = 1.2–1.5 mm for the staghorn stone. These results show one of the main advantages of using cavitation erosion. Using cavitation erosion, fragmentation is expected to result in small stone fragments (1–2 mm) of clinically passable size from the initial stage of treatment. Cystine stones have been reported to be the most difficult to break by SWL. Zhong et al. (1992) argues that cystine stones are non-breakable due to their ductility in spite of their small surface hardness value. Figure 7.7 shows that the cystine stone was eroded by cavitation from the surface into small fragments of less than 1 mm.

Finally, the estimated acoustic power of the C-C waveform is in the range between the intensity of the Power Doppler (15 W/cm²) and typical HIFU for the treatment of tumors (500–2000 W/cm²) (ter Haar 2001; Bailey et al. 2001). Although the intensity was small compared with that of HIFU treatment, and there is the large time interval between C-C waveform pulses, the effect of unwanted tissue heating should be examined through in-vivo studies.

In the experiment discussed in Sect. 7.2, the cavitation activity in the C-C waveform sequence was well visualized and seemed to be well controlled in-vitro in degassed and distilled water. Whereas in the human body, the cavitation phenomena should be different and unpredictable because the physical property of the medium in which the stone exists is totally different. Thus, specially designed cavitation monitoring is necessary to optimize stone comminution under in-vivo conditions.

Passive and active cavitation detection has been investigated through SWL (Coleman et al. 1996; Cleveland et al. 2000a, b; Bailey et al. 2005). In two-frequency ultrasound lithotripsy using the C-C waveform, it is important to detect cavitation generation as stone erosion efficiency by the low frequency ultrasound wave depends on the state of cavitation bubbles induced by the high frequency wave. Cavitation bubbles were generated on a stone in a small region from the high frequency wave, as shown in Fig. 7.3, and acoustic emission intensity from the bubbles during high frequency exposure was much lower than that of the reflected ultrasound from the stone surface. Therefore, a sensitive detection method is required. The subharmonic ultrasound signal is a specific frequency component emitted from highly, nonlinear scatter, such as cavitation bubbles. The subharmonic detection method and the relation between the signal amplitude and stone erosion volume (Yoshizawa et al. 2009) are introduced in this section.