Use of the LQ model with large fraction sizes results in underestimation of isoeffect doses

Purpose: To test the appropriateness of the linear-quadratic (LQ) model to describe survival of jejunal crypt clonogens after split doses with variable (small 1–6 Gy, large 8–13 Gy) first dose, as a model of its appropriateness for both small and large fraction sizes. Methods: C3Hf/KamLaw mice were exposed to whole body irradiation using 300 kVp X-rays at a dose rate of 1.84 Gy/min, and the number of viable jejunal crypts was determined using the microcolony assay. 14 Gy total dose was split into unequal first and second fractions separated by 4 h. Data were analyzed using the LQ model, the lethal potentially lethal (LPL) model, and a repair-saturation (RS) model. Results: Cell kill was greater in the group receiving the larger fraction first, creating an asymmetry in the plot of survival vs size of first dose, as opposed to the prediction of the LQ model of a symmetric response. There was a significant difference in the estimated bs (higher b after larger first doses), but no significant difference in the as, when large doses were given first vs small doses first. This difference results in underestimation (based on present data by approximately 8%) of isoeffect doses using LQ model parameters based on small fraction sizes. While the LPL model also predicted a symmetric response inconsistent with the data, the RS model results were consistent with the observed asymmetry. Conclusion: The LQ model underestimates doses for isoeffective crypt-cell survival with large fraction sizes (in the present setting, >9 Gy).