Mathematical models of repopulation and reoxygenation in radiotherapy

Source abstract

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.