  Background: Experiments have reported low normal tissue toxicities during
FLASH radiation, but the mechanism has not been elaborated. Several hypotheses
have been proposed to explain the mechanism. The oxygen depletion hypothesis
has been introduced and mostly studied qualitatively. Methods: We present a
computational model to describe the time-dependent change of oxygen
concentration in the tissue. The kinetic equation of the model is solved
numerically using the finite difference method. The model is used to analyze
the FLASH effect with the oxygen depletion hypothesis, and the brain tissue is
chosen as an example. Results: The oxygen distribution is determined by the
oxygen consumption rate of the tissue and the distance between capillaries. The
change of oxygen concentration with time after radiation has been found to
follow a negative exponential function, and the time constant is determined by
the distance between capillaries. When the dose rate is high enough, the same
dose results in the same change of oxygen concentration regardless of dose
rate. The analysis of FLASH effect in the brain tissue based on this model does
not support the explanation of the oxygen depletion hypothesis. Conclusions:
The oxygen depletion hypothesis remains controversial because oxygen in most
normal tissues cannot be depleted by FLASH radiation according to the
mathematical analysis with this model and experiments on the expression and
distribution of the hypoxia-inducible factors.
