How quickly does FLASH need to be delivered? A theoretical study of radiolytic oxygen depletion kinetics in tissues.

Radiation delivered over ultra-short timescales ("FLASH" radiotherapy) leads to a reduction in normal tissue toxicities for a range of tissues in the preclinical setting. Experiments have shown this reduction occurs for total delivery times less than a "critical" time that varies by two orders of magnitude between brain (∽0.3 s) and skin (≳ 10 s), and three orders of magnitude across different bowel experiments, from ∽0.01 s to ≳ (1-10) s. Understanding the factors responsible for this broad variation may be important for translation of FLASH into the clinic and understanding the mechanisms behind FLASH.
Methods. Assuming radiolytic oxygen depletion (ROD) to be the primary driver of FLASH effects, oxygen diffusion, consumption, and ROD were evaluated numerically for simulated tissues with pseudorandom vasculatures for a range of radiation delivery times, capillary densities, and oxygen consumption rates (OCR's). The resulting time-dependent oxygen partial pressure distribution histograms were used to estimate cell survival in these tissues using the linear quadratic model, modified to incorporate oxygen-enhancement ratio effects. 
Results. Independent of the capillary density, there was a substantial increase in predicted cell survival when the total delivery time was less than the capillary oxygen tension (mmHg) divided by the OCR (expressed in units of mmHg/s), setting the critical delivery time for FLASH in simulated tissues. Using literature OCR values for different normal tissues, the predicted range of critical delivery times agreed well with experimental values for skin and brain and, modifying our model to allow for fluctuating perfusion, bowel. 
Conclusions. The broad three-orders-of-magnitude variation in critical FLASH radiation delivery times observed in vivo can be accounted for by the ROD hypothesis and differences in the oxygen consumption rate amongst simulated normal tissues. Characterization of these may help guide future experiments and open the door to optimized tissue-specific clinical protocols. &#xD.