Survey of Inverse Methods to Estimate Thermal Properties for Adaptive Treatment Planning during Thermal Therapies

Thermal therapies are minimally invasive cancer treatments that raise tumor temperatures to induce damage while minimizing heat exposure to surrounding healthy tissue. These therapies typically involve remotely activated or minimally inserted heat sources. Due to variability in tumor geometry across patients, patient specific adaptive treatment plan is required. As a result, estimating patient-specific thermal properties in real time is critical. Previous studies have attempted such estimations, often focusing on a single method. This limits the robustness and general applicability of the results, as no single method suits all input conditions in inverse modeling. In this study, we surveyed both deterministic methods: Gradient Descent, Gauss-Newton, Levenberg–Marquardt, and Tikhonov Regularization and probabilistic methods: Offline Bayesian and Markov Chain Monte Carlo with Metropolis–Hastings. We assessed their performance under varying sensor noise levels, sensor-to-source distances, initial conditions, prior assumptions, and inverse method-specific parameters. Two types of heat sources were considered: line sources, representing laser interstitial thermal therapy, and point sources, representing magnetic nanoparticle hyperthermia. Estimations within 1 [%] accuracy were deemed acceptable. Our findings indicate that sensor noise must remain below 0.7 [°C] and the sensor should be positioned at least 0.5 [cm] from the heat source for all the methods to achieve reliable thermal conductivity estimate. Future work will focus on validating these results on tissue mimicking phantoms.