How worthwhile are short schedules in radiotherapy?: A series of exploratory calculations

Abstract

A series of calculations is presented of log cell kill for most of the fractionated schedules that could conceivably be devised using 1, 2 or 3 fractions per day and 3, 5 or 7 treatment days per week, in overall times of 1 to 7 weeks inclusive. The basic assumption is that late reactions are kept constant, and that repair of sublethal damage is complete, i.e. intervals are at least 6 h. A wide range of effective doubling times of tumor cells is assumed: 2, 3, 5, 7, 10, 20 days and infinity. The results show that optimum overall times depend primarily on (1) the doubling time for cells in the tumor and (2) the intrinsic radio sensitivity alpha (which is proportional to α/β in one of the assumptions made here). Optimum overall times are proportional to (1) but can increase even more steeply with increasing radiosensitivity or α/β Short overall times are required for tumors with low α/β and/or fast proliferation. Optimum overall times are, interestingly, relatively independent of the number and frequency of fractions. However, therapeutic ratios are higher if larger numbers of smaller fractions are used within the selected overall time. This is a critical factor in achieving adequate tumor cell kill. For median potential doubling times of 5 days, and median radiosensitivity, overall times of 2.5 to 4 weeks would be optimal. More slowly proliferating tumors, possibly about half of many types of carcinoma, should be treated with longer overall times, but selection is necessary. Doubling or halving the cell doubling time would mean 5–8 or 1.2–2 weeks overall time, respectively. Similarly, for a 5 day doubling time, a tumor with α/ β = 5 Gy should be treated in less than a week; but if α/ β = 20 Gy the optimum overall time could exceed 7 or 8 weeks. A tumor with cells that double in 3 days would require overall times of 0.3, 2.5 and 6.5 weeks for α/β values of 5, 10 and 20 Gy, respectively. Acute effects (excluded in the analysis) would disqualify some of the shorter schedules. We can hope to know potential doubling times (from flow cytometry) and eventually values of alpha (and α.β). It is important that assays of both should continue to be developed. When such individual values are available, optimum overall times can be chosen, as described here, within which the maximum practicable number of small fractions can be given. Without such selection, clinical trials will continue to be as diluted as if staging were not taken into account.