Derivation and Application of Equations Describing the Effects of Fractionated Protracted Irradiation, Based on Multiple and Incomplete Repair Processes. Part I. Derivation of Equations

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Abstract
A general model is developed where the induction and interaction rates of sublethal radiation damage with subsequent irradiation are represented as polynomial functions of the dose-rate. The effect of incomplete multiple repair processes is also included. Equations are evaluated for fractionated protracted irradiation where the dose-rate is constant during each fraction. However, both the dose-rate and the fractional dose are permitted to change from fraction to fraction. The resultant equations show that the apparent α/β ratio derived from the analysis of equivalent protocols may be protocol dependent. Also, the α/β ratio calculated from experimental data, assuming a single repair half-life, will appear to be protocol dependent if in reality more than one repair process is involved in the repair of sublethal damage. It is possible that the effects due to the induction of sublethal damage or its subsequent interaction may be distinguished by designing experiments in which the dose-rate is not constant throughout the whole protocol; also that the underlying processes governing the conversion of sublethal damage may be analysed by fitting experimental data to the equations.