Identifying the heat source of biomedical heat transfer from final measurement data in the biological thermal-wave...

This study investigates the inverse problem of spatial heat source identification in biomedical heat transfer. Departing from conventional parabolic biomedical heat transfer models, our research focuses on more sophisticated and clinically relevant hyperbolic models, which offer enhanced suitability for biomedical engineering applications. Firstly, the uniqueness of the heat source was proved through the energy variational approach. Subsequently, the inverse problem is reformulated as an optimal control problem by employing total variation regularization within the framework of optimal control theory. Theoretical contributions include rigorous proofs of the existence of optimal solutions and their corresponding necessary conditions, complemented by the establishment of criteria for solution uniqueness and stability. Building upon these theoretical foundations, we have developed an innovative gradient algorithm, the efficacy of which has been validated through comprehensive numerical experiments utilizing clinically relevant electromagnetic radiation tissue heat transfer parameters commonly encountered in hyperthermia treatments.