New insights into factors influencing the clinically relevant oxygen enhancement ratio

Abstract

Background and purpose: This paper deals with the variations in the oxygen enhancement ratios that could be observed ( OER′) when comparing oxic and hypoxic cells in different types of fractionated experiments as a consequence of the non-linearity of the underlying cell survival curves. Calculations have been made of the OER′ that would be obtained for fractionated irradiations with a series of small doses to allow the comparison of isoeffective doses in oxic and hypoxic conditions. Two styles of fractionated experiment were modelled. In one, the dose per fraction was kept constant in the oxic and hypoxic arms of the experiment, necessitating more fractions in hypoxia to achieve the same level of cell kill. In the other the number of fractions was kept constant and the fraction size was varied to obtain equal levels of damage. The first is the relevant design for the clinic, whereas the second is the design most commonly used in animal studies. Materials and methods: Three models of the survival curve were used to simulate the response of cells to radiation injury, all based on the linear quadratic model, but with various added assumptions. A simple classical LQ model is compared with two models in which the concept of inducible repair is added. In one of these the induction dose for `switching on' the more resistant response is assumed to be increased in hypoxia and in the other it is assumed to be independent of the oxygen tension. Results: These calculations show a clear and previously unsuspected dependence of the measured OER′ on the design of the fractionated experiment. The values obtained in the clinical and animal types of study differ considerably with all three models. The direction and magnitude of that difference depends critically on the assumptions about the fine structure of the survival curve shape. The authors suggest that the inducible repair version with an oxygen-dependent induction dose is probably the most relevant model. Using this, the measured OER′ is reduced at doses around 2 Gy for the clinically relevant design of constant sized fractions to the oxic and hypoxic cells. It may even, in certain model assumptions, fall below unity resulting in an increased sensitivity, not resistance, from the hypoxia. Conclusions: These calculations indicate the urgent need for more knowledge about the fine structure of the low dose region of the survival curves for human tumour cells and especially for comparisons in the presence and absence of oxygen. The extent of the hypersensitivity at very low doses, the trigger dose needed to induce the repair and its oxygen modification may be dominant factors in determining the response of tumour cells to clinically relevant fractionation schedules.