A phenomenological model of proton FLASH oxygen depletion effects depending on tissue vasculature and oxygen supply - Zou, Wei; Kim, Haram; Diffenderfer, Eric S.; Carlson, David J.; Koch, Cameron J.; Xiao, Ying; Teo, BoonKeng K.; Kim, Michele M.; Metz, James M.; Fan, Yi; Maity, Amit; Koumenis, Costas; et al. (Frontiers in Oncology, 2022)
Introduction: Radiation-induced oxygen depletion in the tissue is assumed as a contributor to the FLASH sparing effects. In this study, we simulated the heterogeneous oxygen depletion distribution in tissue surrounding vessels and calculated the proton FLASH Effective Dose Modifying Factor(FEDMF) which could be used for biology-based treatment planning. Methods: The dose and dose-weighted LET of a small animal proton irradiator were simulated with the Monte Carlo simulation. We deployed a parabolic partial differential equation to account for the generalized radiation oxygen depletion, tissue oxygen diffusion, and metabolic processes to investigate oxygen distribution in 1D, 2D and 3D solution space. Dose and dose rates, particle LET, vasculature spacing and blood oxygen supplies were considered. Using a similar framework for the hypoxic reduction factor(HRF) developed previously(1), the FEDMF was derived as the ratio of the cumulative normoxic-equivalent dose(CNED) between CONV and UHDR deliveries. Results: Dynamic equilibrium between oxygen diffusion and tissue metabolism can result in tissue hypoxia. The hypoxic region displays enhanced radio-resistance and results in lower CNED under UHDR deliveries. In 1-D solution, comparing 15 Gy proton dose delivered at CONV 0.5 and UHDR 125 Gy/s, 61.5% of the tissue exhibits ≥20% FEDMF at 175 um vasculature spacing and 18.9 uM boundary condition. This percentage reduces to 34.5% and 0% for 8 and 2 Gy deliveries. Similar trends are observed in 3D solution space. The FLASH versus CONV differential effect remains at larger vasculature spacings. Higher FLASH dose rate shows an increased region with ≥20% FEDMF. Higher LET near the proton Bragg Peak region does not appear to alter the FLASH effect. Conclusion: We developed 1D, 2D and 3D oxygen depletion simulation process to obtain the dynamic HRF and derive the proton FEDMF related to the dose delivery parameters and the local tissue vasculature information. The phenomenological model can be used to simulate or predict FLASH effects based on tissue vasculature and oxygen concentration data obtained from other experiments.