Thermal effects in soft tissues developed under the influence of focused ultrasonic fields of short duration - FILIPCZYŃSKI, Leszek (Archives of Acoustics, 1976)
Temperature increases in soft tissues developing under the influence of a concentrated ultrasonic beam, as used in ultrasonography, have been analytically determined. By solving the heat conductivity equation and subsequent use of the Laplace transformation, formulae have been obtained (30), (38) which permit the calculation of the approximate value and distribution of the temperature in the focus of the beam, perpendicular to the direction of propagation, as a function of time.In the case of an ultrasonic impulse with a duration of 1 μs the intensity of 20 W/cm^2, in soft tissue with an attenuation of 3 dB/cm and simplified shape of ultrasonic beam (Fig. 2); a maximum temperature increase equal barely to 3.3 · 10^-6°C has been obtained. The temperature increase calculated for an ultrasonic impulse of 1 s duration gives a value of the same order as that obtained by other authors. In the case of an ultrasonic exposure of an intensity of 200 W/cm^2 and a duration of 1 s, which corresponds to the threshold from curves for irreversible changes in the brain published in the literature, a value of temperature increase in the tissue of 33°C has been obtained.