Models for Cell Survival with Low LET Radiation

We develop a model for cell survival under low LET irradiation in which the cell is considered to have$N_{0}\text{-independent}$ sensitive sites, each of which can exist in either an undamaged state (state A) or one of two damaged states. Radiation can change the sensitive sites from the undamaged state to either of two damaged states. The first damaged state (state B) can either be repaired or be promoted on the second damaged state (state C) which is irreparable. The promotion from the first damaged state to the second can occur due to any of the following: (1) further radiation damage, (2) an abortive attempt to repair the site, or (3) the arrival at a part of the cell cycle where the damage is "fixed." Subject to the further assumptions that radiation damage can occur either indirectly (i.e., through radiation products) or due to direct interaction, and that repair of the first damaged state is a one-step process, we derive expressions for P($N_{{\rm A}},\ N_{{\rm B}}$, t) = probability that after time t a cell will have$N_{{\rm A}}$ sites in state A and$N_{{\rm B}}$ in state B. The problem of determining P($N_{{\rm A}},\ N_{{\rm B}}$, t) is formulated for arbitrary time dependences of the radiation field and of all rate coefficients. A large family of cell-survival models can be described by interpreting the sensitive sites in different ways and by making different choices of rate coefficients and of the combinations of numbers of sites in different states that will lead to cell death.