A physics-informed neural network approach to diffusion and auto-oxidation in Fricke gel dosimeters

Precise dose quantification is critical for advanced radiation-based medical applications, particularly in emerging high dose-rate and mini-beam therapies. Fricke gels (FGs) are promising tissue-equivalent dosimeters based on the radiation-induced oxidation of \\(Fe^{2+}\\) to \\(Fe^{3+}\\) , which can be quantified through magnetic resonance imaging (MRI) or optical absorption (OA) spectroscopy to reconstruct three-dimensional dose distributions (DDs). However, spatial accuracy is degraded by ion diffusion, while the incorporation of chelating agents such as methylthymol blue (MTB) introduces competing auto-oxidation kinetics, both of which significantly limit clinical translation. The combined reaction–diffusion ion dynamics can be described by diffusion equations with source terms, but inversion of these processes to recover the initial DD constitutes an ill-posed backward-time problem. In this work, we address this challenge using Physics-Informed Neural Networks (PINNs), which embed the governing reaction–diffusion equations into the learning framework to regularize the inverse reconstruction. PINNs were trained to infer pre-diffusion DDs in MTB-based FGs from OA measurements acquired up to 8 hours post-irradiation. Model predictions were validated against experimental data from irradiated MTB gels, yielding Mean Squared Errors in the range \\(10^{-4}-10^{-5}OD^2\\) ( OD , Optical Density) and gamma analysis passing rate > \\(90\\%\\) at \\(2\\%/2mm\\) . These results demonstrate the capability of physics-constrained learning to reconstruct the initial condition of a coupled reaction–diffusion system, mitigating diffusion-driven degradation and enhancing the spatial reliability of FG dosimetry.