Repair dependent radiation survival: a stochastic model with Euler gamma function solutions

The probability of survival of cells or viruses exposed to various forms of radiation is expressed as a function of the probability that a given cell will receive a certain number of lethal damages, the average probability that each such damage is repairable, and an upper bound on the repair capacity of each cell. All lethal damages are presumed induced as a linear function of dose. The probability of survival is found to be the product of a single exponential, which reflects inactivation by unrepairable lethal damages and dominates at low doses, and an Euler gamma function, which reflects inactivation due to repairable damages formed in excess of the upper bound on repair capacity. Computational procedures obtain stochastic parameters from published survival data for the inactivation of bacterial, yeast and mammalian cells exposed to ionizing or ultraviolet radiation, including split-dose experiments. The survival of cells exposed to photodynamic therapy is analysed assuming that lethal damages cannot be repaired, but more than one may be required for inactivation.