Non-invasive estimation of a non-linear temperature gradient using spectral analysis of multi-echo ultrasonic signals

An spectral analysis technique, that establishes a linear relation between the temperature changes in a body and the frequency displacement in the overtone peaks being displayed in the power spectral density (PSD) of ultrasonic echo-signal, has been improved and applied by the paper authors to estimate temperature gradients induced inside a biological phantom by means of ultrasonic therapeutic radiation. In order to evaluate the technique results under controlled conditions, multi-pulse ideal waveforms are properly simulated, considering a non-linear temperature gradient as the thermal distribution induced on this simulated body. The results obtained by means of a very accurate spectral analysis are contrasted, at different depths, with the established increasing-decreasing temperature gradient. The adequacy of the technique to effectively estimate such a realistic temperature spatial distribution, inside a body, is evaluated regarding to selected frequency peaks behavior in comparison with thermal distribution along the central axis of the simulated body, under ultrasonic radiation.