Determination of the optimum dose per fraction in fractionated radiotherapy when there is delayed onset of tumour repopulation during treatment.

Abstract

The choice of fractionation in radiotherapy involves a compromise between a number of competing radiobiological factors. The severity of late normal tissue effects may be highly dependent on fraction size, thus requiring the dose per fraction to be relatively small. This in turn leads to more fractions being used in order to maintain the tumour effect, resulting in a longer overall treatment time. In contrast, tumours possessing short clonogen doubling times ideally require shorter treatment times for improved tumour cell kill in order to reduce the impact of tumour cell repopulation. A mathematical model has been previously developed to investigate ways of optimizing the theoretical treatment outcome by estimating the optimum dose per fraction required for a given set of radiobiological parameters [1, 2]. The earlier model assumed that tumour repopulation proceeds at a constant rate right from the initiation of treatment, i.e. that there is no delay time before the repopulation process begins. However, especially for head and neck tumours, there is evidence for the existence of a lag time before the onset of compensatory re-growth [3, 4]. This report describes a modification to the earlier model and which provides a non-analytical, re-iterative, method for deriving the optimum dose per fraction which produces the maximum biologically effective dose (BED) to the tumour in the presence of a delayed start to repopulation.