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 PR distributions (PRd) for various PET radioisotopes to better include its effect in PET reconstruction algorithms.Approach.The proposed model explicitly incorporates the Coulomb repulsion effect, the multi-branch nature of certainβ+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 including11C,13N,15O,18F,64Cu,68Ga,82Rband124I, achieving in general coefficients of determination (R²) greater than 0.995 and mean absolute percentage errors≲20%. Compared to previous methods, our model provides a more accurate description of PRd at low distances and offers improvedR²values.Significance.This work provides a robust framework for generating accurate annihilation point spread function kernels, facilitating improved PR correction in quantitative Nuclear Medical Imaging and supporting research with diverse radioisotopes.