NARX structures for non-invasive temperature estimation in non-homogeneous media

The safe and effective application of thermal therapies are limited by the existence of precise non-invasive temperature estimators. Such estimators would enable a correct power deposition on the region of interest by means of a correct instrumentation control. In multi-layered media, the temperature should be estimated at each layer and especially at the interfaces, where significant temperature changes should occur during therapy. In this work, a non-linear autoregressive structure with exogenous inputs (NARX) was applied to non-invasively estimate temperature in a multi-layered (non-homogeneous) medium, while submitted to physiotherapeutic ultrasound. The NARX structure is composed by a static feed-forward radial basis functions neural network (RBFNN), with external dynamics induced by its inputs. The NARX structure parameters were optimized by means of a multi-objective genetic algorithm. The best attained models reached a maximum absolute error inferior to 0.5degC (proposed threshold in hyperthermia/diathermia) at both the interface and inner layer points, at four radiation intensities. These models present also a small computational complexity as desired for real-time applications. To the best of ours knowledge this is the first non-invasive estimation approach in multi-layered media using ultrasound for both heating and estimation.