Electron Absorbed Fractions and S Factors for Intermediate Size Target Volumes: Comparison of Analytic Calculations and Monte Carlo Simulations

The absorbed fraction and the S factor represent fundamental quantities in MIRD-based dosimetry of radiopharmaceutical therapy (RPT). Although Monte Carlo (MC) simulations represent the gold standard in RPT dosimetry, dose point kernels (DPK) obtained from analytic range-energy relations offer a more practical alternative for charged-particle dosimetry (beta- or alpha-emitters). In this work, we perform DPK- and MC-based calculations of the self-absorbed fractions and S factors for monoenergetic electrons uniformly distributed in intermediate-size target volumes (similar to mm to cm) relevant to micrometastasis and disseminated disease. Specifically, the aim of the present work is as follows: (i) the development of an analytic range-energy relation, effective over a broad energy range (100 keV-20 MeV) covering most applications of radiotherapeutic interest; (ii) the application of the new formula to DPK-based calculations of the absorbed fraction and S factor and comparison against MC simulations (both published and present work data) as well as the MIRDcell V2.0.16 software, which uses a similar analytic methodology; and (iii) the study of the influence of simulation parameters (step-size, tracking/production cut-off energies, and ionization model) in Geant4-based calculations of S factors. It is shown that the present DPK-based calculations are in excellent agreement (within 1.5%) with the MIRDcell software, while also being in fair agreement with published MC data as well as with the new Geant4 simulations, with average differences of similar to 20% for the (sub) mm-sized volumes and similar to 10% for the cm-sized volumes. The effect of the choice of Geant4 simulation parameters was found to be negligible for the examined target volumes (similar to mm), except for the use of the Penelope ionization model, which may exhibit noticeable discrepancies (up to similar to 20%) against the Standard and Livermore models. The present work provides quantitative information that may be useful to both the MC- and DPK-based beta dosimetry of micrometastasis and disseminated disease, which represents an important field of application of RPT.