An improved position reconstruction method for radioactive particle tracking

This work introduces a novel reconstruction method exploiting the inverse of Finite Element Method (FEM) to reconstruct positions from ray tracing experimental measurement such as those obtained by radioactive particle tracking. FEM based Position Reconstruction (FEM-PR) relies on shape function evaluation within simplex elements (i.a tetrahedron) for position reconstruction using a mean-square problem, which has proven to be robust, accurate, and fast. Tracer positions are reconstructed under the condition that least-squares compatibility is maintained between experimental counts and interpolated values within inverse elements. This approach is implemented in a module within the open-source software, Lethe-RPT, enabling user to carry out radioactive particle tracking (RPT) experiments from calibration to tracer position reconstruction. The test benchmark and experimental setup are described. For the same test cases, the reconstruction error is investigated using an increasing number of inverse elements and Monte Carlo (MC) iterations. The accuracy and robustness of FEM-PR concerning the inevitable measurement errors due to calibration, measurement systems, and the quantized nature of γ-rays is demonstrated. This approach provides a new view for immediate and precise position reconstruction. FEM-PR reconstructs the tracer position with an accuracy of 0.08 mm. Approximately 3.37 ms is required to reconstruct one position on a desktop computer, which is less than the sampling time for experimental data collection.