Consideration of tissue response in the application of the two-mutation model to radiation carcinogenesis

The Moolgavkar-Venzon-Knudson (MVK) two-mutation model of carcinogenesis is an analytical model that predicts the variation of cancer yield-rate with time, and with dose of a carcinogen. The model is biologically based, and assumes that a specific mutation in a stem-cell will increase its rate of proliferation compared with that of unmutated cells, so that a clone of pre-malignant cells develops; a second specific mutation in any one of these will make it malignant, and a cancer will start to grow. The model has been used in recent years to analyse a number of sets of epidemiological data on carcinogenesis. The purpose of this paper is to point to a problem in the use of this model for radiation-induced carcinogenesis, namely that ionizing radiation causes reproductive death of stem cells, which leads to regenerative division and hence a change in the number of stem-cells at risk. The possible effects of such changes on the predictions of the model are discussed. At low dose-rates of continuous or chronic irradiation and at low doses of acute irradiation, it is expected that pre-malignant cells will be killed along with the unmutated cells, and that the regenerative division of the surviving pre-malignant cells will restore the numbers of both stem cells and pre-malignant cells to what they would have been in the absence of cell killing; hence, no net effect of the tissue regeneration is expected. At high dose-rates, the initial delay in regenerative division and subsequent faster proliferation are expected to lead to an initial reduction in tumour yield-rate with time (compared with that predicted by the MVK model) followed by a faster increase. For acute irradiation, in the particular case of beta-particle irradiation of the skin, at high doses where there are practically no surviving cells in the irradiated area, repopulation by unirradiated cells from the margin is predicted to lead to a decrease in tumour yield-rate with dose. The predictions have been compared with published data on the induction of osteosarcoma in mouse by repeated injection of 89Sr, the induction of skin tumours in rat by acute and chronic irradiation with electrons, and the induction of skin tumours in mouse by acute irradiation with beta-particles. At low doses and dose-rates the basic MVK model fitted the data well. At higher doses and dose-rates the expected effects of tissue regeneration were observed qualitatively, although there were some discrepancies in detail; these are discussed.