Using oxygen dose histograms to quantify voxelised ultra-high dose rate (FLASH) effects in multiple radiation modalities.

Purpose. To introduce a methodology to predict tissue sparing effects in pulsed ultra-high dose rate radiation exposures which could be included in a dose-effect prediction system or treatment planning system and to illustrate it by using three published experiments. Methods and materials. The proposed system formalises the variability of oxygen levels as an oxygen dose histogram (ODH), which provides an instantaneous oxygen level at a delivered dose. The histogram concept alleviates the need for a mechanistic approach. At each given oxygen level the oxygen fixation concept is used to calculate the change in DNA-damage induction compared to the fully hypoxic case. Using the ODH concept it is possible to estimate the effect even in the case of multiple pulses, partial oxygen depletion, and spatial oxygen depletion. The system is illustrated by applying it to the seminal results by Town (Nat. 1967) on cell cultures and the pre-clinical experiment on cognitive effects by Montay-Gruel et al (2017 Radiother. Oncol. 124 365-9). Results. The proposed system predicts that a possible FLASH-effect depends on the initial oxygenation level in tissue, the total dose delivered, pulse length and pulse repetition rate. The magnitude of the FLASH-effect is the result of a redundant system, in that it will have the same specific value for a different combination of these dependencies. The cell culture data are well represented, while a correlation between the pre-clinical experiments and the calculated values is highly significant ( p  < 0.01). Conclusions . A system based only on oxygen related effects is able to quantify most of the effects currently observed in FLASH-radiation.