EXTRA LETHAL DAMAGE DUE TO RESIDUAL INCOMPLETELY REPAIRED SUBLETHAL DAMAGE IN HYPERFRACTIONATED AND CONTINUOUS RADIATION TREATMENT

In the conventional linear-quadratic model of single-dose response, the alpha and beta-terms reflect lethal damage created during the delivery of a dose, from two different presumed molecular processes, one linear with dose, the other quadratic. With the conventional one-fraction-per-day (or less) regimens, the sublethal damage (SLD), presumably repairing exponentially over time, is essentially completely fixed by the time of the next dose of radiation. If this assumption is true, the effects of subsequent fractions of radiation should be independent, that is, there should be little, if any, reversible damage left from previous fractions, at the time of the next dose. For multiple daily fractions, or for the limiting case, continuous radiation, this simplification may overlook damaged cells that have had insufficient time for repair. A generalized method is presented for accounting for extra lethal damage (ELD) arising from such residual SLD for hyperfractionation and continuous irradiation schemes. It may help to predict differences in toxicity and tumor control, if any, obtained with "unconventional" treatment regimens. A key element in the present model is the finite size and the dynamic character of the pool of sublethal damage. Besides creating the usual linear and quadratic components of lethal damage, each new fraction converts a certain fraction of the existing SLD into ELD, and creates some new SLD. The expressions developed by Thames [Int. J. Radiat. Biol. 47, 319-339 (1987)] for fractionated treatment (the IR model) and by Dale [Br. J. Radiol. 58, 515-528 (1985); 59, 919-927 (1986)] for protracted and fractionated treatment are found to be similar to our results in the limiting case where the pool of SLD is very large (infinite). Calculations with the present model suggest that enhancement of radiation effect with hyperfractionation due to conversion of sublethal damage to lethal damage should be modest within current clinical schedules, because of the judicious use of 4-h or preferably longer interfraction times, which permit sufficient repair of SLD. Shorter interfraction times would increase conversion of SLD to ELD and might lead to an unacceptable increase in toxicity. In continuous radiation, use of the ELD concept enables fitting computed survival curves to published experimental survival curves demonstrating decrease of effectiveness of a given total dose for dose rates below a certain level: low dose rate effect. Inclusion of proliferation will help in gaining insight into the limiting dose rate at which irradiation becomes ineffective.