A New Incomplete-repair Model Based on a 'Reciprocal-time' Pattern of Sublethal Damage Repair

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Abstract
A radiobiological model for closely spaced non-instantaneous radiation fractions is presented, based on the premise that the time process of sublethal damage (SLD) repair is 'reciprocal-time' (second order), rather than exponential (first order), in form. The initial clinical implications of such an incomplete-repair model are assessed. A previously derived linear-quadratic-based model was revised to take account of the possibility that SLD may repair with time such that the fraction of an element of initial damage remaining at time t is given as 1/(1 + zt), where z is an appropriate rate constant; z is the reciprocal of the first half-time (tau) of repair. The general equation so derived for incomplete repair is applicable to all types of radiotherapy delivered at high, low and medium dose-rate in fractions delivered at regular time intervals. The model allows both the fraction duration and interfraction intervals to vary between zero and infinity. For any given value of z, reciprocal repair is associated with an apparent 'slowing-down' in the SLD repair rate as treatment proceeds. The instantaneous repair rates are not directly governed by total dose or dose per fraction, but are influenced by the treatment duration and individual fraction duration. Instantaneous repair rates of SLD appear to be slower towards the end of a continuous treatment, and are also slower following 'long' fractions than they are following 'short' fractions. The new model, with its single repair-rate parameter, is shown to be capable of providing a degree of quantitative explanation for some enigmas that have been encountered in clinical studies. A single-component reciprocal repair process provides an alternative explanation for the apparent existence of a range of repair rates in human tissues, and which have hitherto been explained by postulating the existence of a multi-exponential repair process. The build-up of SLD over extended treatments is greater than would be inferred using a single-exponential repair model and this has important implications in several areas of radiotherapy.