High-efficiency shock-wave generator for extracorporeal lithotripsy

S Biomedical engineering

High-efficiency shock-wave generator for extracorporeal lithotripsy P. Broyer

D. Cathignol

Y. Theillere

J . L . Mestas

INSERM U281, 151 cours Albert Thomas, 69424 Lyon Cedex 03, France

Abstractmln extracorporeal lithotripsy, the electro-acoustic efficiency of electrohydraulic generators is limited by the inductance of the electrical discharge circuit. A new shockwave generator is described that uses a coaxial discharge line enabling electro-acoustic efficiency to be greatly increased. The line is built using a para-electric ceramic with a relative dielectric constant of 1700, manufactured for use in high-voltage impulse mode. A coaxial spark gap, with minimal inductance, has been developed to obtain the triggered breakdown of the discharge line. Shock waves are created with a coaxial electrode plugged directly into the spark gap and immersed in an electrolyte of degassed saline. Electrode gap and electrolyte resistivity are adjusted to match the resistivity of the electrolyte volume between the underwater electrodes to the characteristic impedance of the line. The discharge line generates in the medium a rectangular current pulse with an amplitude of about 6000 A and a rise time of 50 ns. Compared with conventional generators, measurements of the expansive peak pressure pulse show an increase of 105% at tO kV, 86.5% at 12 kV and 34.5% at 14 kV charging voltage. Electro-acoustic efficiency is found to be 11% instead of 5.5% for a conventional discharge circuit.

KeywordsmCurrent rise time, Discharge line, Electro-acoustic efficiency, Electrolyte, Extracorporeal lithotripsy, Shock-wave generator, Spark gap, Underwater discharge Med. & Biol. Eng. & Comput., 1996, 34, 321-328

1 Introduction

THEASSOCIATIONof two concepts, i.e. the generation of extracorporeal focused shock waves and the endoscopic fragmentation of renal stones by micro-explosions (KIERFELDe t aL, 1969; WATSON, 1970), has led to the development of a extracorporeal renal lithotriptor (FORSSMANN et al., 1977). Commercial lithotriptors using electrohydraulic techniques are routinely used to break up kidney or gall bladder stones. In terms of fragmentation efficacy, the electrohydraulic principle has become the gold standard. The basic principle of an electrohydraulic generator is largely described elsewhere (CATHIGNOLet aL, 1991a). The electrohydraulic generator consists of a semi-ellipsoidal bowl with two electrodes located at its first focus and connected to a capacitor bank via a high-voltage switch, called a spark gap. The reflector is filled with degassed water to limit acoustic attenuation and avoid cavitation phenomena along the path way. When the spark gap is triggered, plasma forms between the two electrodes, which leads to vaporisation of the water. The energy released produces a vapour bubble that instantaneously grows and acts on the liquid as a spherical piston, thus creating an expanding acoustic wave. After reflection off the walls of the semi-ellipsoid, the acoustic wave converges at the second focus of the reflector. The pressure is then strong enough to disintegrate kidney stones located at the focal point.

First received 14 August 1995 and in final form 23 April 9 IFMBE:1996 Medical & Biological Engineering & Computing

1996.

The shock-wave amplitude can be varied by adjusting the charging voltage of the capacitor. Until the 1990s, this shock-wave device was considered the reference, although it has considerable drawbacks. The nonreproducible formation of the plasma between the electrodes in degassed water induces great variations in the pressure pulse amplitude and in the location of the focal point, increasing pain and risk for the patient (EISENBERGERe t aL, 1991; DELIUS, 1990), and it also leads to considerable wear of the electrodes. This problem has been solved by replacing deionised water with degassed saline of concentration 100 g 1-1, corresponding to an electrical resistivity of 7.78 Q cm -1 (CATHIGNOL et al., 1991a). This electrolyte allows a critically damped electrical discharge, leading to a great improvement in the pressure pulse reproducibility, fragmentation efficacy and electrode wear; This is because in the electrolyte the plasma and consequently the origin of the shock wave are always located in the same place. Lithotriptors developed by Technomed Medical Systems (TMS) are based on these electroconductive properties. Nevertheless, as with other types of generator (piezoelectric or electromagnetic), the absolute electro-acoustic efficiency, calculated as the ratio of the energy of the pressure wave to the electrical energy stored in the capacitor bank, shows that only a small part of the initial energy is contained in the expanding pressure wave created at the first focus. Most energy is lost in the indifferent physical phenomena of underwater discharge. In the best case, i.e. with the electroconductive technique, this ratio is 5-5%. It is a well known fact that in this type of generator the value of its efficiency increases in proportion to the electrical discharge frequency (GAVRILOV et al., 1971).

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321

Therefore, the discharge circuit used in the conventional shock-wave device is made with the minimum inductance. For example, in the case of the TMS Sonolith 4000 lithotriptor, which uses the electroconductive technique, the inductance of the discharge circuit is about 85 nil; this value may be considered a technical limit. With the present configuration of this generator, it is not possible to decrease this value because connecting wires between the capacitor and electrodes cannot be shortened. Consequently, it became necessary to find a new discharge circuit with a lower inductance to increase the electro-acoustic efficiency of electrohydraulic shock-wave devices. The theory of underwater discharge phenomena suggests that the amplitude of shock waves increases with the reduction in the time taken to release electrical energy in the medium for a given inter-electrode gap (RYABIN1Nand RYABININ, 1976; ONUS, 1971; SKVORTSOV et al., 1961). The shorter the release time, the higher is the pressure pulse amplitude. We therefore hope that a reduction in the plasma duration will lead to an increase in the electro-acoustic efficiency and will enable the same fragmentation efficiency to be obtained at a lower charge voltage, decreasing the patient's pain and electrode wear. To release the initial electrical energy in the shortest time, we propose a new electrohydraulic generator based on the discharge line principle. The original feature of this electrical circuit is to release the stored energy into the liquid in the minimum time possible.

2 Theory To produce shock waves, conventional electrohydraulic generators always use the same discharge circuit, shown in Fig. la. The electrical energy is released through an RLC discharge circuit. The current rise time is then dependent on the inductance value Ltot, which corresponds to the connecting wire between all the elements of the circuit plus the internal inductance of the capacitors used. The discharge line, as described in Fig. Ib, enables (in a load) an electrical rectangular pulse with very sharp rise time to be delivered, instead o f a critical damped oscillation (MCDONALD and BENIN6, 1965). Discharge lines are a well known technical application of transmission lines and are widely used in triggered laser circuits where very low inductance is required. Transmission lines are composed of two parallel conductors separated by a dielectric. In the case of a dielectric without losses, transmission lines can be considered as perfect and only described by their capacitance C and

Fig. 1

322

inductance L per unit of length l (METZEGERand VABRE, 1966). For a coaxial line, L and C can be expressed as C--

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(1)

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(2)

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(3)

z = I(LC) 1/2

(4)

The production of a rectangular electrical pulse by a discharge line (Fig. 1) can be briefly explained by considering the input and output reflection coefficients. Reflection coefficients are expressed for the input AA' and the output BB' of the line by F i --

Fo

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(5)

(6)

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& Biological

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September

1996

where S is the area of the sphere where p was measured, and tp+ is the time after which the pressure value was negative or zero. The electrical energy stored in the transmission line is 0.5 fro t V 2, where Ctot is the total capacitance of the line and V is the voltage applied. We is defined as the total electrical energy dissipated in the medium, and Wep is the partial electrical energy dissipated during the positive part of the current and voltage pulses. The total and partial electrical energy dissipated in the innerspace of the electrodes are, respectively, given by relationships.

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4 Results 4.1 Electrical character&ation o f the discharge line

To study the influence of the electrolyte conductivity and electrode gap on the electrical pulse characteristics, the adjustable electrode plugged into the spark gap and immersed in electrolyte was used (Figs. 2 and 3). Current and voltage pulses generated by the line in the electrolyte are given in Figs. 4a-d, for four different resistivities: 13.54 f~ cm -1, 10.66 Q cm -1, 7.78 ~ cm -1 and 7.1 lf~ cm -1, respectively. The line was charged at 12 kV, and the electrode gap was 0.20 ram. The curves shown were smoothed by a second-order 9.5 MHz low-pass filter. It should be noticed that, for a given electrode gap, current and voltage amplitudes depend on electrolyte resistivity. For a resistivity ranging from 13.54 f~ c m - I to 7.11 f ~ c m -~, the maximum current amplitude increased from 4500 A to 6000 A, whereas the maximal voltage ampli-

tude decreased from 6000 V to 4500 V. With a resistivity of 13.54 f2 cm -1 (Fig. 4a), we observed a descending stairshaped front caused by the wave reflections in the line. These reflections were caused by the mismatching between the characteristic impedance of the line and the load constituted by the electrolyte resistivity (R > Re). For a resistivity of 7.78 f) c m - t , current and voltage time waveforms are very similar and it can be considered that the line is correctly matched to the load (Fig. 4c). The electrical energy Wep dissipated by the electrodes as a function of the inter-electrode space was studied in the particular case of a 12 kV charging voltage. As studied in Fig. 5, for a resistivity of less than 13.54 f~ cm - t , more than 80% of the energy stored in the line is released during the first positive part of the current discharge time waveform. If the resistivity is greater than 13.54 ~ cm - t , we have demonstrated previously (CATHIGNOL et al., 1991b) that the current does not appear exactly inside the electrode space, but appears as a plasma between the edges of the two electrodes. In this latter case, the inter-electrode resistivity during the discharge is in the order of mO, and so the line is unmatched to the load and the energy is released over several periods. For example, for an electrolyte resistivity of 22.04 Q c m - 1, the energy dissipated in the first positive period of the discharge current waveform is less than 50% of the initial energy stored in the transmission line (shaded area of Fig. 5). The maximum energy released (white area of Fig. 5) was obtained for an electrolyte resistivity of 7.78 f~ c m - 1 and a 0.20 mm electrode gap. In these experimental conditions, calculation of the total and partial energy dissipated in the medium, according to eqns. I0 and 11, gives 6.53 J and 6.47 J, respectively, meaning that all the stored energy can be considered as released in the first half-period. These values correspond to 85-5% and 84-7%, respectively, of the stored energy in the transmission line. The typical discharge current and voltage time waveforms are illustrated in Fig. 6. Electrical discharge reproducibility in the electrolyte was evaluated at 12 kV charging voltage over ten consecutive pulses. The inter-electrode gap was 0.20 mm, and the resistivity was 7.78 f~ cm-1. Fig. 7 shows the superposition of four current discharge time waveforms. As can be seen, the reproducibility is spectacular and has never been seen before in the case of an electrohydraulic generator. Width and amplitude standard deviations of the current discharge time waveforms were 1.2% and 1%, respectively.

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Fig. 5 Influence of electrolyte resistivity and electrode interspacing on the rate of electrical energy release during first positive power pulse (Wep); values noted represent the percentage of the initial energy stored in the line Medical & Biological Engineering & Computing

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September 1996

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characteristics

current

voltage

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As the resistivity is less than or equal to 13.54 f~ c m - t , the standard deviation on the amplitude, width, rise and fall times of the electrical pulses does not exceed 4%. Mean values of current and voltage pulses are given in Table 1 for 12 kV charging voltage. Owing to a non-zero inductance in the measuring circuit o f the voltage, a difference between the current and the voltage rise time may be noticed. 4.2 Acoustic characterization o f pressure wave generated by discharge line Fig. 8 shows the peak pressure values measured at 98 mm from the electrodes for resistivities ranging from 22.04 f~ cm -1 to 6-45 f~ cm - l , and for inter-electrode space variations from 0.15 mm to 0.25 mm. The line was charged at 12 kV. It can be seen that pressure was maximum in the white area, which corresponds approximately to a distance o f 0.15-0.20 mm and a resistivity of 10.54 cm - 1 7.51 c m - x. This white area corresponds to the optimal working conditions o f the discharge line. The maximum pressure value was 27.9 l0 s Pa for a 0.15 mm inter-electrode space

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and a 7- ~ c m - 1 resistivity. The same pressure values was obtained for 0.20 mm and 10.66 Q cm - ' . The reproducibility was evaluated in the following conditions: charging voltage was 12 kV, resistivity was 7.78 Q cm - " and inter-electrode distance was 0-20 mm. Fig. 9 shows the superposition o f four consecutive expanding pressure curves. The excellent reproducibility o f the shockwave generation is obvious. The peak pressure value averaged over ten shocks was 25-1 x 105 Pa, with a standard deviation of 1.9%, and the pulse width was 1.38 p.s, with a standard deviation of 2%. Pressure rise time was less than 50 ns. 4.3 Comparison o f pressure values compared with a conventional generator Peak pressure values and electro-acoustic efficiency were compared with the TMS results for the same distance between the electrodes and the hydrophone (98 mm) and three different charging voltages. We used the adjustable (Elect) and the TMS (Elec2) electrodes, with an electrode gap chosen at 0.15 mm and an electrolyte resistivity of 7.78 Q cm - t . The curves in Fig. 10 show a spectacular improvement in the shock-wave amplitude. With the TMS electrode, we obtained a maximum peak pressure o f 24 x l0 s Pa, 30.2 x 105 Pa and 35-2 x 105 Pa for charging voltages of 10 kV, 12 kV and 14 kV, respectively. Pressure values were therefore increased by 105% at 10 kV charging voltage, 86-5% at 12 kV and 34.5% at 14 kV. Pressure values measured with the adjustable

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Fig. 8 Peak pressure values relative to electrode distance and resistivity at 12 kF charging voltage 326

Peak pressure values obtained with the discharge line for the adjustable electrode (Elecl) and the TMS electrode (Elecz) were much higher than mean pressure values given by TMS; with the discharge line, the pressure at 98 m m is approximately proportional to the voltage charge

Medical & Biological Engineering & Computing

September

1996

electrode were lower than with the TMS electrode, by approximating 20%, due to their different geometrical characteristics. It can be seen that pressure values were nearly proportional to the charging voltage, whereas they are not in the case of other electrohydraulic generators. The acoustic energy calculated from the pressure curve p(t), measured at 98 mm from the electrodes and according to eqn. 9, was 1.12 J. The electrical energy dissipated at 14 kV in the medium calculated according to eqn. 10 was 6.44 J. The relative electro-acoustic efficiency index was 12-8%, and the absolute electro-acoustic efficiency index was 11%. For comparison, with the DIATRON III from TMS, relative and absolute electro-acoustic index were 6% and 5.5%, respectively.

5 Discussion 5.1 Electrical results The electrical measurements made for discharges occurring in an electrolyte show that the constructed line discharge enables the stored energy to be released in the form of an electrical pulse, with characteristics close to those of the theoretical rectangular pulse. As the rise and fall times are of finite duration, the average current and voltage pulse time (Table 1) differs from the theoretical time of 217 ns by 20% and 24.4%, respectively. When the line is adapted, the amplitude of the voltage pulse is close to half the load voltage. Superposing the current and voltage pulses (Figs. 4a-d) shows that the volume of electrolyte between the electrodes behaves, throughout the discharge, as a resistive element, the value of which varies around 1 f2 depending on the resistivity and the chosen gap between the electrodes. The current characteristics are practically identical to those of the voltage, and the respective amplitudes of the current and voltage pulses vary in inverse proportion to the resistance of the electrolyte. The lower resistivity, the lower is the equivalent resistance of the medium (R < 1 f2). Calculating Wep as a function of the gap between the electrodes and resistance shows that approximately 80% of the initial energy is released in a single pulse if the resistivity 9 is less than or equal to 13.54 f~ c m - . 1 The correlation between the best line adaptation (R ~ Re) and the maximum amount of energy released to the liquid appears fairly clear. The current and voltage pulses are closest to the adaptation for resistivities of 10-66 and 7.78 f~ c m - t , resistivities for which we obtained a ~'rep value very close to the W e value (all the energy is dissipated in a single pulse). Measurements made with resistivities of 6.45 and 5.78 f2 cm - l would be of interest to bring out this correlation even more clearly. It can also be noted that, in the best case, there exists a loss of approximately 15% compared with the energy initially stored in the line. This loss can be explained by a considerable consumption of energy by the arc created in the spark gap (SUNKA et al., 1993). In addition, as the measurements made were difficult, the energy actually released into the electrolyte may be slightly underestimated. The study of the reproducibility of the pulses shows that it is necessary to work with resistivities of less than or equal to 13.54 f~ cm to take advantage of the conductive properties of the electrolyte. The discharges made with a resistivity of 22.04 f~ cm -1 are not reproducible (standard deviation of approximately 15%), because the discharges are made by an arc and a current conduction. For resistivities of less than or equal to 13.54 f~ cm -1, reproducibility of electrical pulses generated in the electrolyte is excellent, whatever the gap between the electrodes (standard deviation < 4%). However, the electrical reproducibility of the line will have to be

Medical & Biological Engineering & Computing

assessed over a number of discharges corresponding to a treatment, to find the influence of electrode wear on the current and voltage pulse characteristics. The average characteristics of the electrical pulses given in Table 1 show a difference between the current and voltage rise times of approximately 50 ns, whereas they ought to be equal. The small overshoot is certainly due to the length of the connecting wires from the electrodes to the voltage probe. 5.2 Acoustic results The study of the amplitude of the incident pressure as a function of electrode gap and resistivity enabled us to determine the optimum adjustment of our generator. The maximum pressure amplitude is obtained with gaps of 0.20 mm and 0.15 mm, and with resistivity values of 10.66 f~ cm -1 and 7.78 f~ cm - l , respectively. We observed that the pressure increases when the electrode gap is reduced. However, a gap of 0-15 mm appears to be the minimum distance for the line to operate in a reproducible manner. Even with an electrolyte with a very low resistivity (6.45 f~ c m - l ) , a gap of 0-10 mm causes a non-reproducible arc discharge and makes the average incident pressure drop significantly. It is probable that the surface condition of the electrode plane may be at fault in this arc discharge process when the gaps are too small. Comparison between Fig. 5 and 8 does not show a significant correlation between the maximum energy released into the medium and the maximum amplitude of the shock wave. Whatever the gap, Wep values are very close for resistivities of less than or equal to 13-54 f~ c m - l , whereas the average incident pressure values Pm vary noticeably with gap size and resistivity. Nevertheless, for resistivity values in excess of 13.54 f2 c m - l , the correlation between Wep and Pm can be seen, as a lower amount of energy released does in fact lead to a significant drop in shock-wave amplitude. The pressure values Pm obtained at I0, 12 and 14 kV show that the use of a discharge line allows a very great increase in shock-wave amplitude, and therefore a great improvement in the electro-acoustic output of the generator (11%). Reproducibility of the shock waves is excellent (standard deviation--2%). It has been attempted to find the cause of this improvement by comparing the electrical characteristics of the Sonolith 4000 with those of the discharge line. No significant different that might show the cause of the increase in pressure Pm was observed. Calculation of the energy released during the first half-period of oscillation (Wep) on the TMS generator and on the line shows that the two values are not significantly different (8.33 J and 8-36 J, respectively). The current rise times are also 81 ns and 120 ns for the discharge line and TMS generator, respectively. However, these electrical readings previously performed on the Sonolith 4000 were taken with a very large time base and do not enable the discharge current rise time to be determined accurately. In addition, we may doubt the accuracy of these measurements on account of the cancelling of the voltage well before the discharge current after the first half-period of oscillation. It is possible that the current was over-estimated (electromagnetic coupling), leading to an over-estimated value of We. 5.3 Improvement in current rise time According to eqn. 8 and with the approximation that the resistance of the electrolyte R is constant during the discharge time and equal to I fl the total inductance of our discharge line was found to be 98 nil. This value corresponds to the specific inductance due to the generator geometry (spark gap and electrodes) and to the plasma created in the spark gap and in the electrolyte. Experiments performed with the spark gap

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short-circuited (without plasma channel) and a 1 f2 resistor wire connected on the tips o f the electrodes to discharge the line gave a mean current rise time of 12 ns. We computed a total inductance of 25 nil. Furthermore, geometrical spark gap inductance estimated with eqn. 2 gives a value o f 5.6 nil. This value is similar to the inductance calculated for other spark gaps with the same design (GOLNABI et al., 1992; KETO et al., 1980). Consequently, the main part of the inductance is due to the plasma channel in the spark gap and between the electrodes during the discharge. To improve the current rise time, it is necessary to decrease the creation time of the plasma between the electrodes o f the spark gap. One solution is to reduce the interspacing electrodes to obtain a shorter plasma channel length (BLANCHET, 1990). We chose an electrode gap of 0-8 mm,, i.e. 2 mm less than the initial interspacing electrodes. With this distance, the spark plug modifies the formation of the plasma channel, leading to large oscillations in the current rise time. To be able to measure the current rise time accurately, the spark plug was suppressed and the spark gap was pressurised at 6 x 105 Pa and triggered by depression via an electrovalve. Pressure measurements were conducted in electrolyte using Elecl with a resistivity of 7.78 f2 c m - l and an electrode interspacing o f 0-5 mm. The mean value of the current rise time was found to be about 50 ns. This improvement in the rise time leads to an increase in the mean pressure Pm o f the expanding wave of 14% and 4.5% at 10 kV and 12 kV, respectively.

6 Conclusions Replacing the conventional discharge circuit with a discharge line results in a very large increase in the mean pressure o f the expanding wave. In comparison with conventional shock-wave generators, electro-acoustic efficiency was increased by a factor of two. To obtain maximum expanding wave pressure, the electrode distance must be minimum (0.15 mm), and it is necessary to match the electrolyte resistivity to the characteristic impedance o f the line (1 f2). For an electrode distance o f between 0-15 mm and 0-25 ram, the resistivity must be less than 13-54f~ cm - 1 , to take advantage o f the electroconductive properties o f the electrolyte. In this case, the reproducibility o f the expanding wave is excellent, with a standard deviation in the order o f 1%. The large improvement in the expanding pressure values may be caused by a shorter transfer time o f electrical energy into the medium. It can be hoped to obtain the same fragmentation efficacy for conventional generators at lower charging voltage and, consequently, with less pain for the patient. Acknowledgment--The authors would like to thank Mr A. Matias for his technical contribution.

CATHIGNOL, D., MESTAS, J. L., GOMEZ, F. and LENZ, P. (1991a): 'Influence of water conductivity on the efficiency and the reproducibility of electrohydraulic shock wave generation,' Ultrasound in Med. BioL, 17, (8), pp. 819-828 CATHIGNOL,D., MESTAS, J. L. and GOMEZ, F. (1991b): 'Reproducibility of the shock waves improves when electrolyte is used in electrohydraulic generators, why?. Proc. Ultrasonics 91 Int. Conf., pp. 65-68 COLE, H. R. (1948): 'Underwater explosions' (Dover Publications, Inc., New York) DELIUS, M. (1990): 'Effect of lithotriptor shock waves on tissues and materials' in: HAMILTON, M. F. and BLACKSTOCK,D. T. (Eds): 'Frontiers of nonlinear acoustics.' Proc. 12th Int. Symp. on Nonlinear Acoustics (Elsevier Science Publishers Ltd., London) pp. 31-47 EISENBERGER, F., MILLER, K. and RASSEILER, J. (199l): 'Stone therapy in urology' (Thieme Medical Publishers, New York) p. 131 FORSSMANN, B., HEPP, W., CHAUSSY, C. H., EISENBERGER,F. and WANNER, K. (1977): 'Einde methode zuer beriihrungsfreien zertrtimmerung von nierensteinen durch stosswellen,' Biomed. Tech., 22, p. 164 GAVRILOV, G. N., PETUKHOV, V. V., RYABININ,A. G. and BRUBLEVSI~YA, T. V. (1977): 'Total hydrodymamic efficiency of an underwater electric discharge,' Soy. Phys. Tech. Phys., 22, pp. 868-870 GOLNABI, H. (1992): 'Reliable spark gap switch for laser triggering,' Rev. Sci. Inst., 63, (12), pp. 5804-5805 KETO, J. W., RAYMOND, T. D. and WALSH, S. T. (1980): 'Low inductances spark gap switch for bluemlein-driven lasers,' Ibid., 51, (1), pp. 42-43 KIERFELD, G., MELLIN, P. and DAUM, H. (1969): 'Blasensteinzertriimmerung durch hydraulische schlagwellenwirkung in tierexperiment,' Der Urologe, 8, pp. 99--106 McDONALD, D. F. and BENNING, C. J. (1965): 'Subnanosecond risetime multikilovolt pulse generator,' Rev. Sci. Inst., 36 (4), pp. 504-606 MESTAS and CATHIGNOL,D. (1990): 'Capteur de pression pour les contrrles de g~nrraeturs d'ondes de choc 61ectrohydrauliques.' Colloque de physique, colloque C2, supplrment au no~ 2, tome 51, pp. 1287-1290 METZGER, G., and VABRE, J. P. (1966): 'Electronique des impulsions---circuits fi ~l~ments r~partis' (Masson Eds) pp. 1-20 OKUN, I. Z. (197l): 'Generation of compression waves by a pulsed discharge in water," Soy. Phys. Tech. Phys., 16, pp. 219--226 PELLINEN, D. G., D1 CAPUA, M. S., STEPHEN, E., SAMPAYAN,E., GERBRACHT, H. and WANG, M. (1980): 'Rogowski coil for measuring fast, high-level pulsed currents,' Rev. Sci. Inst., 51, (11), pp. 1535-1540 RYABININ,A. G. and RVABrNrN,A. G. (1976): 'Gas-bubble energy in an underwater electrical discharge,' Rev. Sci. Inst., 21, (4), pp. 512-514 SKVORTSOV, Yu. V., KOMEL'KOV, V. S. and KUZNETSOV, V. N. (1961): 'Expansion of a spark channel in a liquid,' Soy. Phys. Tech. Phys., 5, p. I100 SUNK& P., BABICKY,V., CLUPEK, M. and STUKA, C. (1993): 'New discharge circuit for efficient shock wave generation.' Proc. Int. Symp. on Shock Waves, 93, pp. 232-232 WATSON, B. W. (1970): 'Urat 1: Instrument for crushing calculi in the urinary bladder by electrohydraulics,' Biomed. Eng., pp. 21-22

References BLANCHET, M. (1990): 'Production d'impulsions de haute tension br~ves par ~clateurs fonctionnant dans le domaine de la centaine de picosecondes.' Symp. Commutation rapide d'~nergie ~levres, Club 26 SEE, 28 September 1990 BOURLION, M., DANCER, P., LACOSTE, F., MESTAS, J. L. and CATHIGNOL, D. (1994): 'Design and characterization of a shock wave generatore using canalized electrical discharge: Application to lithotripsy,' Rev. Sci. lnst., 65, (7), pp. 2356-2363 BROYER, P., CATHIGNOL,D., TEILLERE,Y. and MESTAS,J. L. (1995): 'Amelioration du rendement 61ectroacoustique des grn~rateurs d'ondes de choc par l'itilisation d'une ligne ~ d~charge: application fi la lithotritie extraeorporelle,' Innov. Tech. Biol. Med., 16, (1), pp. 67-82

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Author's biography Patrick Broyer was born in Amb~rieu, France, in 1968. He received his MS in Biomedical Technology from the University of Luminy, Marseille, France, in 1990, and his Docteur es Sciences from the Lyon I University, Lyon, France, in 1995. He is currently working as an acoustic engineer in the EDAP Technomed Group on several applications of therapy transducers. His research interests are lithotripsy and high-intensity focused ultrasound (HIFU).

Medical & Biological Engineering & Computing

September 1996