Analytical positron range model for PET with cross-code Monte Carlo benchmarking

Introduction: The positron range (PR) effect is a significant factor limiting spatial resolution in positron emission tomography (PET), particularly for high-resolution systems and non-standard isotopes. Objective: This study introduces a novel analytical model to accurately and rapidly describe positron range distributions (PRd) for various PET radioisotopes. Approach: The proposed model explicitly incorporates the Coulomb repulsion effect, the multi-branch nature of certain β + emitters, and the scaling of PR with electronic density. To minimise bias, we used a histogram-free statistical method to derive the cumulative PRd from Monte Carlo (MC) simulated annihilation datasets, avoiding arbitrary histogram binning. A comparative analysis of PR estimates was conducted across three major MC radiation transport algorithm packages: PENELOPE (via PenEasy/PeneloPET), GEANT4 (via GATE), and EGS5 (via PHITS), revealing notable discrepancies between codes, versions, and input configurations, especially at short distances from the source. Main results: The new analytical model demonstrated an excellent reproduction of the simulated data for isotopes including C-11, N-13, O-15, F-18, Cu-64, Ga-68, Rb-82, and I-124, achieving in general coefficients of determination (R 2 ) greater than 0.995 and mean absolute percentage errors (MAPE) < 20%. Compared to previous methods, our model provides a more accurate description of PRd at short and long distances and offers improved R 2 values. Significance: This work provides a robust framework for generating accurate annihilation point spread function (aPSF) kernels, facilitating improved PR correction in quantitative Nuclear Medical imaging and supporting research with diverse radioisotopes.