Temperature elevation in a beam of ultrasound

Computations are made of the temperature elevation expected at points along the axis of an unfocussed beam of ultrasound in a homogeneous absorbing medium. A simplified model is used in which the intensity is assumed uniform over a cross section. Heat conduction is taken into account, but not convection or perfusion. Results are presented for frequencies from 1 to 10 MHz and beam diameters from 0.2 to 2.4 cm. The results include limiting temperatures, reached at infinite time, as well as temperature vs time characteristics. As an example for certain conditions (transducer diameter 1.2 cm, frequency 4 MHz, intensity at the transducer 0.1 W/cm2, tissue acoustically similar to liver, transducer thermal conductivity similar to that of tissue) the temperature elevation produced at a distance 2 cm from the transducer is calculated to be 0.61 degrees C after 253 s; it then increases more and more slowly, approaching, but never exceeding 1.46 degrees C.