Condensed-History GPU Positron Range Simulator in Heterogeneous Media for PET Resolution Modelling

Positron range (PR) degrades spatial resolution in positron emission tomography (PET), with its effect being radionuclide- and medium-dependent. Current accurate PR simulators are computationally intensive and cannot be used in clinical time frames. This work presents the Hybrid Monte Carlo (HMC) PR simulator, a GPU-accelerated condensed-history code in CUDA Fortran for 3D annihilation imaging in heterogeneous voxelised geometries derived from CT images and μ-maps. Pre-computed look-up interaction tables (LUTs) covering 24 reference-tissue materials and support for arbitrary β+ emitters up to 3.55 MeV end-point energies (68Ga, 82Rb, 124I, etc.) allow both GPU and CPU implementations. Maximum speeds reach 4.77·105 (Intel i9-14900KF) and 3.32·108 (NVIDIA RTX 5080) histories/s, surpassing prior CPU-only PenEasy 2024 by up to 4 orders of magnitude. A fixed step of 0.5 mm was chosen for LUT generation with a uniform ±10% variation each HMC step that allowed reducing aliasing effects. These values are consistent with our previous cross-code benchmark for the isotopes studied. Close agreement with PenEasy 2024 is demonstrated: point-source FWHM and FWTM residuals using 18F, 68Ga, 124I and 82Rb are below 0.3 mm at 107 histories, and voxelwise R2=0.995, SSIM=0.995 and PSNR ≈36.4 dB are achieved simulating 82Rb uptake from a human-scale [18F]FDG myocardium acquisition, while decreasing the simulation time from almost 9 h to roughly 1 s using HMC GPU. The resulting annihilation maps enable PET resolution modelling and patient-specific PR correction within clinically practical time frames.