An ‘Incomplete-repair’ Model for Survival after Fractionated and Continuous Irradiations

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Abstract
An incomplete-repair (IR) model of survival after fractionated or continuous irradiation is derived from the concept of ‘dose-equivalent’ of incomplete repair. The model gives reasonably good predictions of the effect of interfraction interval, dose per fraction, and dose rate on cell survival in vivo and on tissue responses. This model is compared to the ‘lethal, potentially lethal’ (LPL) model after the latter has been generalized to an arbitrary number of fractions and to low dose-rate, continuous exposures. It is shown that the two models are equivalent, given certain constraints on the size of dose per fraction and dose rate. For example, in a particular cell line the equivalence of fractionation models breaks down if dose per fraction is well in excess of 4 Gy (the IR model employs the linear-quadratic survival model). The equivalence of low dose rate models breaks down for dose rates well in excess of 20 cGy/min. The assumptions on which the generalized LPL model is based are used to give a radiobiological interpretation to the incomplete-repair model. The larger β/α ratio characteristic of late-responding normal tissues is interpreted in terms of the relatively faster fixation of potentially reparable lesions in the target cells of acutely responding tissues, on account of progression in the cell cycle. According to this interpretation the β/α ratios estimated from isoeffective fractionation regimens are directly related to the parameters of clonogenic cell killing.