Published October 20, 2023
| Version v1
Conference paper
Open
Adaptive Estimation of Pennes' Bio-Heat Equation
Description
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.