A generalization of the clonal survival models: equations for the families of curves obtained with fractionated irradiation.

The survival curves obtained when cellular recovery follows various first radiation dose deliveries DI seem, when semi-logarithmically plotted, to be translated from the part of the curve corresponding to an unfractionated irradiation beyond a dose DR. A possible assumption consistent with such experimental observations is proposed which allows the generalization of any survival model S = f (D). The derived equation S = f (DR + D - DI) f (DI)/f (DR) is convenient for the whole family of experimental survival curves involving cellular damage repairs when the first radiation doses vary. All the parameters of the family equation can be simultaneously fitted so that their reliability is increased. The generalized equations are given for the four following models: two-hits targets, Chadwick and Leenhouts, Green and Burki, Wideröe. As an example, the Chadwick and Leenhouts generalized model parameters are fitted to a family of experimental survival curves concerning Chlorella cells exposed to fractionated and continuous gamma irradiation. The fittings are presented with their confidence limits and are briefly discussed.