A mathematical model of the evolution of free radical concentrations in a cell under ionizing radiation

A probabilistic mathematical model that describes the evolution of the free radical concentration in a cell under ionizing radiation is proposed. The model is of a stochastic character and allows one to describe the generation of free radicals in the process of radiolysis, as well as the interaction between the radicals of different types and between the radicals and the cell constituents (the latter is responsible for radiobiological effect). The possibility of the presence in the cell of a certain equilibrium quantity of radicals of nonradiative origin at the moment that the irradiation begins is taken into account. The results thus obtained show that under certain values of the model’s free parameters the total number of free radicals in a cell under radiation may decrease. This effect can explain the “positive” influence of small doses of ionizing radiation.