Equivalence of the linear-quadratic and two-lesion kinetic models

Double strand breaks (DSBs) are widely accepted as the main type of DNA damage responsible for cell killing in the range of doses and dose rates relevant to radiation therapy. Although the standard linear-quadratic (LQ) model with one first-order repair term often suffices to explain the results of some radiobiological experiments, converging lines of evidence suggest that DSBs are rejoined at two or more distinct rates. A two-lesion kinetic (TLK) model has been proposed to provide a direct link between biochemical processing of the DSBs and cell killing. A defining feature of the TLK model is that the family of all possible DSBs is subdivided into simple and complex DSBs, and each kind may have its own unique repair characteristics. Break-ends associated with both kinds of DSB are allowed to interact in pairwise fashion to form irreversible lethal and non-lethal chromosome aberrations. This paper examines the theoretical and practical linkages between the TLK and LQ models. The TLK formalism is used to derive an LQ formula with two first-order repair terms (dose protraction factors) and to relate the intrinsic radiosensitivity parameters used in one model to the parameters used in the other. Two extensive radiobiological datasets, one for CHO 10B2 cells and one for C3H 10T1/2 cells, are analysed using the TLK and LQ models. The LQ with two repair terms and the TLK are equally capable of explaining the CHO 10B2 and C3H 10T1/2 cell survival data. For the doses and dose rates most relevant to radiation therapy, tests of model equivalence indicate that an LQ formula with two first-order repair terms is an excellent approximation to the TLK model. We find the LQ and TLK models useful complementary tools for the analysis and prediction of radiobiological effects.