Thermal effects in soft tissues developed under the action of ultra¬sonic fields of long duration *)

The thermal effect arising from the sonification of soft tissues by an ultrasonic beam, cylindrical in shape, with the assumption of an even distri¬bution of heat sources in the beam, has been considered.
The analysis is based on the solution of the thermal conductivity equation, using the Laplace transformation as in the author's paper [1]. The formulae obtained permit determination of the rise in and distribution of temperature inside and outside the ultrasonic beam for sonification times longer than 20 s.
The formulae have been applied to estimate the temperature changes encountered in ultrasonic continuous wave Doppler methods used in medical diagnosis. For example, with a cylindrical ultrasonic beam of radius 2.2 mm, frequency 5 MHz, mean spatial intensity of 0.1 W/cm2 and sonification time of 100 s, the estimated value of the temperature increase at the centre of the beam was 1.8 °C.
The values obtained are overestimated since they do not consider the transfer of heat by the circulating blood or the thermal conductivity along the ultrasonic beam, which is particularly evident for higher frequencies.