Adaptive Estimation of Pennes' Bio-Heat Equation

This paper reports on a novel approach for adaptive estimation of uncertain parabolic reaction-diffusion Partial Differential Equations (PDEs), specifically focusing on the Pennes' bio-heat Equation. The core concept involves observing heat transfer in biological tissues and achieving real-time temperature estimation within the interior of a spatial domain using boundary measurements. The study is motivated by the clinical need to improve the accuracy of oncology hyperthermia treatments to enhance the efficacy of chemo and radiotherapy. To this aim, the temperature estimation provided through the proposed method is meant to be used as feedback information in robot-assisted hyperthermia treatments. The proposed method demonstrates its effectiveness in estimating the system solution and accurately recovering the reaction coefficient. An innovative observer employing Neural Networks to predict PDE states eliminates the need for online integration, thus overcoming the limitations observed in classical numerical simulation tools. The preliminary results show the method's effectiveness within the studied problem and its potential for extension to larger classes of problems and higher dimensions.