Incorporating oxygenation levels in analytical DNA–damage models — quantifying the oxygen fixation mechanism

Purpose: To develop a framework to include oxygenation effects in radiation therapy treatment planning which is valid for all modalities, energy spectra and oxygen levels. The framework is based on predicting the difference in DNA–damage resulting from ionising radiation at variable oxygenation levels. Methods: Oxygen fixation is treated as a statistical process in a simplified model of complex and simple damage. We show that a linear transformation of the microscopic oxygen fixation process allows to extend this to all energies and modalities, resulting in a relatively simple rational polynomial expression. The model is expanded such that it can be applied in for polyenergetic beams. The methodology is validated using microdosimetric Monte Carlos simulations (MCDS). This serves as a bootstrap to determine relevant parameters in the analytical expression, as MCDS is shown to be extensively verified with published empirical data. Double strand break induction as calculated by this methodology is compared to published proton experiments. Finally, an example is worked out where the Oxygen Enhancement Ratio (OER) is calculated at different positions of a clinically relevant SOBP dose deposition in water is presented. This dose deposition is obtained using a general Monte Carlo code (FLUKA) to determine dose deposition and locate fluence spectra. Results: For all modalities (electrons, protons), the damage categorised as complex could be predicted parameterised to within 0.3% of the value calculated using microdosimetric Monte Carlo. The proton beam implementation showed some variation in oxygen enhancement ratios which differed slightly depending on where the assessment was made; before the SOBP, mid–SOBP or at the distal edge. Environment oxygenation was seen to be the more important variable. Conclusions: An analytic expression calculating complex damage depending on modality, energy spectrum, and oxygenation levels was shown to be effective and can be readily incorporated in treatment planning software, to take into account the impact of variable oxygenation, forming a first step to an optimised treatment based on biological factors