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Mathematical models of the effect of ionizing radiation on tumours have not, so far, received general acceptance, and Wheldon (1989) warns of the dangers of over-generalization. Nevertheless, the construction of models may have a certain value, in that we are forced to define our assumptions with clarity. It is interesting to compare two models which have been described in the columns of the BJR: “Misonidazole in fractionated radiotherapy: are many small fractions best?” (Denekamp et al, 1980) and “The linear-quadratic formula and progress in fractionated radiotherapy” (Fowler, 1989). The former gives a detailed description of the possible effect of reoxygenation on tumour response, but excludes repopulation. The latter is much concerned with repopulation, but excludes reoxygenation. Evidence that hypoxic cells may be important in the clinical response of tumours has been published recently (Gatenby et al, 1988; Whittle et al, 1990), and it would appear to be logical to combine the two models. Denekamp et al give a full description of their model, and any computer-literate reader could reconstruct the programs from which they worked. The addition of repopulation is a simple matter, but the marriage of the two programs forces us to face an interesting question: which class of cells repopulates, the oxic or the hypoxic? The work of Tannock (1968), also quoted by Suit et al (1977), suggests that cells deprived of both oxygen and nutrients in a tumour cord are less likely to divide.

The K values for two cell strains with differing intrinsic GSH concentrations have been measured with the yield of DNA breaks as end-point of the radiation effect. The K value of the strain with reduced GSH content was decreased (1.59 microM O2) in comparison to the K value (3.01 microM O2) for the strain with a normal GSH content. The significance of the observation is discussed in relation to competition models. All variants of the competition model agree in predicting a reduction of K, if GSH is reduced.

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The frequency of X-ray-induced DNA breaks was determined in human cell lines which are deficient in glutathione synthetase and have a greatly reduced glutathione content. Hydroxyapatite chromatography was used for the estimation of the DNA breaks in cell cultures, which were derived either from lymphoblasts transformed by infection with EB virus or from fibroblasts. The dose-effect relationship for the induction of breaks when radiation exposure was made in argon, was similar to that found when exposure was made in air. In control cultures with normal glutathione content, the induction of breaks was enhanced when irradiation was made under aerobic, instead of anaerobic, conditions. Treatment of the glutathione-deficient cells with the hypoxic radiosensitizer misonidazole did not enhance the induction of breaks by radiation delivered either in air or in argon. In control cultures, radiation induction of breaks was enhanced by misonidazole under anaerobic but not under aerobic conditions. When the glutathione-deficient cells were pretreated with cysteamine however, irradiation in the absence of oxygen resulted in a decreased frequency of DNA breaks.

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