Estimation of transient temperature elevation in lithotripsy and in ultrasonography

Transient solutions of the thermal conductivity equation for the two-dimensional case of an elongated cylindrical focus in the ultrasonic beam were derived and applied for lithotripsy and obstetrical ultrasonography. Assuming uniform and Gaussian distributions in the focus of the beam cross section, it was possible to estimate the temperature elevation arising in lithotripsy for various repetition frequencies of shock-wave pulses and for various radii of the beam. In obstetrical ultrasonography where the blood perfusion is difficult to determine, the authors suggested that the insonation time be used as the decisive factor for the temperature determination. Values of focal intensities were found necessary to increase the tissue temperature by 1 degree C as a function of the insonation time and the beam radius which exclude the possibility of any hazardous effect caused by temperature elevation.