NATIONAL PHD IN ARTIFICIAL INTELLIGENCE

Thesis title: AI-based solution methods for PDEs with application to Oncological Hyperthermia

This thesis explores the observability of temperature distribution in the Gross Tumor Volume of a patient undergoing superficial hyperthermia treatment. The treatment is used in combination with Radiotherapy or Chemotherapy, especially for recurrences and hard-to-treat tumors. The motivation for this study lies in the challenges associated with real-time temperature assessment at the target site, which is crucial for providing feedback during treatment. The current standard approach relies on direct measurements using thermocouples, a highly invasive method that poses significant discomfort to patients. Moreover, these measurements offer limited clinical utility due to their discrete nature and imprecise localization. The situation is complicated by the presence of uncertainties in the properties of the patients, particularly the blood perfusion rate, which can vary when the tissue undergoes heating. We investigate then the necessary information and conditions to predict the temperature distribution inside the domain, relying only on boundary measurements and the knowledge of the patient’s anatomy. Given the uncertainties in the patient’s properties, this study is framed as a state estimation problem of the governing physical law of heat transfer in biological systems—Pennes’ Bio-Heat Equation—rather than a direct solution of the equation itself. We developed an approach for the adaptive estimation of Pennes’ Bio-Heat Equation using a backstepping observer design. The validation process has highlighted some limitations in traditional numerical simulation methods, which we propose to handle through the implementation of the estimator relying on Deep Learning. Among the wide range of Deep Learning solutions, we focused on Physics-Informed learning, which is well-suited for scenarios where the governing physical law is known, but training data is scarce or difficult to obtain. This approach eliminates the need for discretizing the spatiotemporal domain, allowing for continuous probing, in contrast to conventional numerical methods that compute solutions on a predefined grid. Moreover, it enables real-time estimation of the partial differential equation’s solution and offers the potential for seamless scalability to higher-dimensional input spaces. The final part of this study focuses on solving the wave equation for the simulation of soft materials, with applications in surgical training within mixed reality environments. This research brings together applied mathematics, computer sciences, and engineering disciplines to solve challenging real-world problems. Keywords: Physics-informed learning, Adaptive state estimation, Oncological hyperthermia, Bio-heat transfer, Mixed reality