Deep learning approach for diffusion correction in Fricke hydrogel dosimeters

Abstract

In recent years studies on Fricke gel dosimeters have demonstrated their potential in performing fast measurements of 3D spatial dose distributions. These dosimeters work by oxidising ferrous (𝐹 𝑒2+) ions to ferric (𝐹 𝑒3+) ions, which can be read by magnetic resonance or optical techniques. However, the accuracy of these measurements can be affected by the diffusion of 𝐹 𝑒3+ ions within the gel matrix, causing image blurring. To overcome this issue, the study proposes a computational method using artificial intelligence (AI) and specifically deep learning (DL). The method is based on Physics Informed Neural Networks (PINNs), which are effective in solving partial differential equations, especially in inverse problems. The PINNs are optimised using physical equations as loss functions, allowing them to predict real-life phenomena like ion diffusion in Fricke gel. The idea is to solve the backward diffusion equation using a PINN model and predict the initial condition, providing as input the spatial distribution of 𝐹 𝑒3+ ions at measurement time T, the boundary conditions and the diffusion coefficient D of 𝐹 𝑒3+ ions inside the medium. The method was first tested using 1D simulated data in diffusion processes, achieving a mean squared error of 1 − 4 × 10−4𝑎.𝑢. in step-wise and rectangular distributions. It was then tested using experimental data, achieving a mean squared error of 2 × 10−4𝑂𝐷2 . The technique here proposed is very promising for overcoming the limits due to the diffusion of 𝐹 𝑒3+ ions in Fricke gel dosimeters.