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

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Abstract
The survival curves obtained when cellular recovery follows various first radiation dose deliveriesDI seem, when semi-logarithmically plotted, to be translated from the part of the curve corresponding to an unfractionated irradiation beyond a doseDR. A possible assumption consistent with such experimental observations is proposed which allows the generalization of any survival modelS = f(D). The derived equationS = 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 concerningChlorella cells exposed to fractionated and continuous gamma irradiation. The fittings are presented with their confidence limits and are briefly discussed.