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Abstract: Aims: A previous paper in this journal (part I) concluded that there was no pronounced optimum overall time, at least up to 70 fractions of 1.15Gy at two fractions/day in 50 days. The maximum tolerable tumour doses increased only 2% from the best short schedules of 21 or 23 days to those of 50 days. Only this range was modelled in part I because it covered the fewest and the most fractions, and the longest overall times that will probably be used in practice. Most UK schedules, typically using five fractions a week, yield tumour effective doses about 10% less than the best schedules in other developed countries. The present paper covers a much wider range of fraction numbers from one to 115, and from 1 to 80 days. Some numerical errors in the Tables in part I are also corrected in the present appendix. These made no difference to the main conclusions just described. Materials and methods: Standard linear quadratic modelling was used, assuming at first α/β=10Gy, α=0.35 ln/Gy, Tk=21 days, Tp=3 days for tumours, but with Tk=7 days, Tp=2.5Gy for acute mucosal reactions, as before. A late complications constraint of 70Gy was accepted, and an acute constraint of 51Gy (both at 2Gy fractions). Alternative values of more rapid or slower repopulation were also explored (Tp=2 days or Tp=5 days, respectively). Results: Optimal values were shown at 22–32 days for one fraction/day five times a week, and at 42–49 days for two fractions/day at 10 fractions/week. Repopulation caused a rapid fall in tumour dose after 30 days with one fraction/day, but not until after 50 days with two fractions/day, and so was not seen in part I with its too-practical end time. Conclusions: Biological modelling can extrapolate calculations outside the borders of published treatment schedules to clarify borderline situations. Optimum schedules in radiotherapy can reliably give more tumour control if two fractions/day are used. The potential gains are equivalent to about two fractions of 2Gy as given by this modelling. However, the late complications will be less with some nearly tumour equivalent shorter schedules if optimally designed. [Copyright &y& Elsevier]

Abstract: Aims: To test by modelling whether a non-standard fractionated schedule giving optimum log cell kill could be expected, between short (accelerated) and longer multiple fraction/day schedules. Materials and methods: Linear quadratic modelling was carried out for many schedules, with biologically effective doses converted to normalised total doses (NTDs; in 2Gy fractions). Late complication and acute mucosal NTDs were calculated as constraint doses for each schedule, and the highest tumour NTDs and log cell kill values within both constraints were calculated. This modelling is robust and agrees with conclusions in a very recent meta-analysis (Bourhis J, Overgaard J, Audry H, et al. Hyperfractionated or accelerated radiotherapy in head and neck cancer: a meta-analysis. www.thelancet.com. Published online August 17, 2006). Results: The six schedules that gave the highest tumour log cell kill deliver a narrow range of 11.1–11.2log10 cell kill in the present parameters. Other regularly used schedules give closer to 10log10. Using one fraction/day fails to achieve the highest therapeutic ratios. Suggestions are made for escalating certain UK schedules. Fractionated radiotherapy results in a nearly constant tumour cell kill if the acute mucosal NTD is held constant. However, a small (3%) gain in tumour cell kill occurs from 3 weeks to 73 fractions of 1.15Gy in 7 weeks. That is how fractionation works, within both acute and late constraints. Short accelerated schedules enable fewer late complications, but do not do as well for the minority of head and neck tumours that repopulate slowly. Conclusions: Schedules of 4–6 weeks overall time could be chosen to give at least 11log10 cell kill, which are safe. Most tumours would require two fractions/day, until routine monitoring of repopulation rates becomes feasible to select individual tumours. There is no ‘optimum schedule’, but each chosen schedule can be balanced against its own risk of excessive acute or late complications, as shown in these examples. [Copyright &y& Elsevier]