Using radial distribution functions to calculate cellular cross-absorbed dose for β emitters: comparison with reference methods and application for 18 F-FDG cell labelling

To further improve the understanding ofinvitrobiological effects of incorporated radionuclides, it is essential to accurately determine cellular absorbed doses. In the case of β-emitters, the cross-dose is a major contribution, and can involve up to millions of cells. Realistic and efficient computational models are needed for that purpose. Conventionally, distances between each cell are calculated and the related dose contributions are cumulated to get the total cross-dose (standard method). In this work, we developed a novel approach for the calculation of the cross-absorbed dose, based on the use of the radial distribution function (rdf) that describes the spatial properties of the cellular model considered. The dynamic molecular tool LAMMPS was used to create 3D cellular models and compute \textit{rdfs} for various conditions of cell density, volume size, and configuration type (lattice and randomized geometry). The novel method is suitable for any radionuclide of nuclear medicine. Here, the model was applied for the labelling of cells with18F-FDG used for PET imaging, and first validated by comparison with other reference methods. Mean Scrossvalues calculated with the novel approach versus the standard method agreed very well (relative differences less that 0.1%). Implementation of therdf-based approach with LAMMPS allowed to achieved results considerably faster than with the standard method, the computing time decreasing from hours to seconds for 1.106cells. Comparison of mean Scrossfor the different configuration types was done varying the cell density and the volume size, allowing to investigate the impact of the geometric configuration on the cross absorbed dose. Finally, the usefulness of therdf-based method and the tool LAMMPS to handle more complex cellular models was highlighted through the application to the18F-FDG radiolabelling experiment, assuming random distributions of clusters and single cells.