Assessing the influence of microdosimetric formalism on calculations of relative biological effectiveness in carbon ion radiotherapy

Microdosimetry enables precise quantification of energy deposition in microscopic domains and aids in RBE prediction for particle therapy. Different methods for calculating microdosimetric spectra have unique assumptions, which can impact RBE estimates. This study examines how variations in microdosimetric calculation method, including microdosimetric formalism and domain geometry, impact RBE estimates in carbon radiotherapy. Microdosimetric spectra were calculated using two versions of the analytical microdosimetric function (AMF, 2006 and 2023), implemented in PHITS to reproduce track structure simulations in spherical water targets. Additional spectra were generated using the Kiefer-Chatterjee (KC) radial dose distribution, originally implemented for cylindrical domains and subsequently used as the foundation of the modified Microdosimetric Kinetic Model (mMKM). To enable geometrically consistent comparisons with the AMF, a novel application of the KC model was developed for spherical domains. These four microdosimetric functions were further compared with track structure simulations using the GEANT4 based TOPAS-nBio platform and benchmarked against published in vitro data. With each approach, RBE10% was calculated using the mMKM with fixed cell and reference radiation parameters, varying only the method of calculating microdosimetric input. Finally, mMKM parameters were tuned for each approach to determine whether RBE predictions could align with those obtained using the KC model for cylindrical domains as a reference. Qualitative comparisons of microdosimetric spectra across all calculation methods revealed important differences, particularly in the variations of delta ray contributions at low LETs. In contrast, the predictions from all four functions became increasingly consistent with each other and with track structure simulations at higher LET. Notably, the recent AMF version (2023) showed the strongest agreement with TOPAS-nBio, with remaining discrepancies attributed to the simulation stopping power models. Overall, variations in domain geometry and microdosimetric function impacted RBE predictions by up to 10%. Nevertheless, by optimizing mMKM parameters such as the nuclear radius, RBE estimates obtained with alternative functions and geometries were made consistent with those of the KC model implemented for cylindrical domains, reflecting the original model basis. Both the choice of microdosimetric formalism and the assumed domain size and geometry substantially affect RBE predictions in carbon radiotherapy. To ensure accurate modeling of biological effectiveness, these factors must be explicitly accounted for within RBE models. In particular, changes in the underlying microdosimetric formalism require careful parameter tuning to preserve consistency across clinical applications and computational frameworks.