Microdosimetry calculations in situ for clinically relevant photon sources and their correlation with the early DNA damage response

Background: Radiobiological data suggests variations in relative biological effectiveness (RBE) between clinically used photon-based sources. A microdosimetric formalism using Monte Carlo (MC) methods can mechanistically describe the photon RBE. Experimentally derived RBE based on DNA double-strand breaks ((Formula presented.)) has been shown to scale with the microdosimetry quantity dose-mean lineal energy ((Formula presented.)). Purpose: To calculate microdosimetric spectra for clinically relevant photon sources, spanning from soft x-rays produced by a 50 kVp x-ray source through various brachytherapy sources up to a 6 MV medical linac. Furthermore, we investigated the correlation between (Formula presented.) and (Formula presented.) of different photon sources. Methods: Photon sources simulated include low-energy x-rays (50 kVp), orthovoltage x-rays (225 kVp), high-dose-rate brachytherapy sources (⁷⁵Se, ¹⁹²Ir and ⁶⁰Co), and a 6 MV medical linac. Secondary electron spectra at the cellular level were calculated for in vitro cell irradiation setups using Geant4 MC-based packages, RapidBrachyMCTPS and RapidExternalBeam. The obtained spectra were used in MicroDose, a microdosimetry simulation software, to obtain microdosimetric quantities, including single-event lineal energy ((Formula presented.)) and specific energy ((Formula presented.)) spectra, and dose-mean and frequency-mean quantities ((Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.)). Uniform spherical targets (1–14 (Formula presented.) radius) and realistic HeLa and PC3 cell nucleus models were simulated using cell size data obtained from literature and nuclei size data from confocal microscopy imaging. Radiobiological experiments using (Formula presented.) foci quantified DNA double-strand breaks for HeLa and PC3 cells after irradiations with 50 and 225 kVp, ¹⁹²Ir, and 6 MV linac, and (Formula presented.) was determined using 225 kVp as the reference. Results: The calculated (Formula presented.) ((Formula presented.)) is within the 3.5–1.2 keV/ (Formula presented.) range (1.8–0.2 keV/ (Formula presented.)) for 1 (Formula presented.) simulated target size between the lowest energy 50 kVp x-ray source and the highest energy 6 MV linac source, respectively. For the HeLa and PC3 cell nuclei models based on microscopy data, (Formula presented.) ((Formula presented.)) spans from 1.6 to 0.6 keV/ (Formula presented.) (0.7 to 0.2 keV/ (Formula presented.)). When compared between different target sizes, (Formula presented.) ((Formula presented.)) ranges from 3.5 to 1.0 (1.8–0.4) keV/ (Formula presented.) between 1 and 10 (Formula presented.) radius targets for the 50 kVp x-ray source. A smaller change is observed for 6 MV linac, ranging from 1.2 to 0.5 keV/ (Formula presented.) and 0.23 to 0.22 keV/ (Formula presented.) for (Formula presented.) and (Formula presented.), respectively. For the simulated ⁷⁵Se source currently under investigation, the calculated (Formula presented.) values are 11%–24% higher relative to those of ¹⁹²Ir in the range of target sizes between 1 and 14 (Formula presented.) in radius. (Formula presented.) for HeLa cells was 1.4 (Formula presented.) 0.7 for 50 kVp x-rays, 0.5 (Formula presented.) 0.2 for ¹⁹²Ir, and 0.7 (Formula presented.) 0.4 for 6 MV linac irradiations. For PC3 cells, (Formula presented.) was 1.3 (Formula presented.) 0.6, 0.8 (Formula presented.) 0.4 and 0.5 (Formula presented.) 0.3 for 50 kVp, ¹⁹²Ir and 6 MV linac, respectively. Measured (Formula presented.) values are consistent with (Formula presented.) ratios of the corresponding photon sources for HeLa and PC3 nucleus models. Conclusions: Microdosimetric spectra strongly depend on the simulated energy of photon sources and target size, with (Formula presented.) and (Formula presented.) decreasing by a factor of (Formula presented.) 2–3 between diagnostic 50 kVp and 6 MV therapeutic x-rays for target sizes from 1–14 (Formula presented.) in radius. The early damage (Formula presented.) indicates this stochastic change in energy density between various photon sources as the yields of (Formula presented.) foci per nucleus scale with (Formula presented.) of the source.