Acoustic Field

Lithotripters can use a number of methods of generating shock waves. Our research is an electrohydraulic lithotripter which uses a spark source placed at the first focus (F1) of an ellipsoidal reflector, shown in Fig. 1. The ellipsoid reflects the energy and focuses it at the second focus (F2) of the ellipse where the kidney stone should be positioned. Figure 1 shows the ray paths emanating from the spark plug and focusing on F2. Our research machine is patterned after the Dornier HM3 lithotripter which was the original clinical lithotripter. The first HM3 was installed in the United States in 1984 and many HM3s are still in wide use. hm3web

webwaveform Figure 2 shows a typical waveform recorded at the focus of a lithotripter using a PVDF membrane hydrophone. The waveform consists of a compressive spike with peak amplitude of about 40 MPa and duration 1 µs. The front of the waveform is shocked and the measured rise time of 30 ns is limited by the hydrophone. Theoretically it should be less than 1 ns. The spike is followed by a tensile tail that lasts more than 3 µs and has a peak negative pressure of about 10 MPa. It is the tensile tail that is responsible for the cavitation generated by a lithotripter.

Figure 3 shows the distribution of the peak positive pressure in the field of an HM3 based on calculations using the KZK equation. Contours for 10, 20, and 30 MPa are shown. The geometrical focus is at 12.8 cm. Note that the maximum in the peak positive pressure actually occurs just beyond the focus because of self-refraction associated with nonlinear propagation. Figure 4 shows the peak negative pressure which achieves a maximum in front of the geometrical focus. kzkpp kzkpm

Movie Frame Click on the image to view a short animation of the calculated pressure field of the HM3. The radius has been normalised to the 77.5 mm, the axial distance by 128 mm and the pressure by 6 MPa.

Reference: M. A. Averkiou and R. O. Cleveland, "Time domain numerical modeling of an electrohydraulic lithotripter with the KZK equation," J. Acoust. Soc. Am., 106: 102--112 (1999).


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Last Updated July 1999