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

Abstract

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 (β- or α-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 (~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 ~20% for the (sub) mm-sized volumes and ~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 (~mm), except for the use of the Penelope ionization model, which may exhibit noticeable discrepancies (up 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.

Keywords

• absorbed fraction
• S factor
• internal dosimetry
• electron dosimetry
• Geant4