A simple new alternative to the linear-quadratic model (and where the LQ model comes from)

I present a new dose-survival equation for fitting clonogenic assay data collected for irradiated cells, one motivated by the hypothesis that all cellular activities can be partitioned into two states (“state R” and “state Q”) which differ in their sensitivity to low-LET radiation. The LQ model can be derived from it by taking a Taylor expansion. The empirical observation that rapidly proliferating cancer cells have a straighter dose-survival relationship, while slowly proliferating cancer cells and normal cells have a curvier one featuring a shoulder region, is explained in terms of state R and state Q. The new equation (1) provides a convention for classifying cells as radioresistant, (2) provides a means of reducing, or possibly eliminating, cell cycle phase as a variable in treatment outcome, and (3) may enable standardization of the results reported for clonogenic assays. Finally, a novel hypothesis is offered for the “oxygen enhancement ratio” phenomenon.