Dose-effect models for risk-relationship to cell survival parameters.

There is an increased interest in estimating the induction of cancers following radiotherapy as the patients have nowadays a much longer life expectancy following the treatment. Clinical investigations have shown that the dose response relationship for cancer induction following radiotherapy has either of two main characteristics: an increase of the risk with dose to a maximum effect followed by a decrease or an increase followed by a levelling-off of the risk. While these behaviours have been described qualitatively, there is no mathematical model that can explain both of them on mechanistic terms. This paper investigates the relationship between the shape of the dose-effect curve and the cell survival parameters of a single risk model. Dose response relationships were described with a competition model which takes into account the probability to induce DNA mutations and the probability of cell survival after irradiation. The shape of the curves was analysed in relation to the parameters that have been used to obtain them. It was found that the two main appearances of clinical data for the induction of secondary cancer following radiotherapy could be the manifestations of the particular sets of parameters that describe the induction of mutations and cell kill for fractionated irradiations. Thus, the levelling off appearance of the dose response curve could be either a sign of moderate to high inducible repair effect in cell survival (but weak for DNA mutations) or the effect of heterogeneity, or both. The bell-shaped appearance encompasses all the other cases. The results also stress the importance of taking into account the details of the clinical delivery of dose in radiotherapy, mainly the fractionated character, as the findings of our study did not appear for single dose models. The results thus indicate that the shapes of clinically observed dose response curves for the induction of secondary cancers can be described by using one single competition model. It was also found that data for cancer induction may be linked to in vivo cell survival parameters that may be used for other modelling applications.