A new model of shouldered survival curves

Recently, the linear-quadratic equation has been used to construct the dose-response relationships of ionizing radiation. The radiobiological theory on which this relationship is based indicates that at low doses, the risk of a biological lesion being formed should depend linearly on dose if a single event is required or quadratically on dose if two events are required. The same approach has also been used to construct the shouldered survival curves, which indicate a lower response of cell killing at low doses of low linear energy transfer (LET) radiation than at high doses because of repair. However, a different approach is possible, derived from the concept of generating the hybrid lognormal distribution, in which the hybrid form of linear and logarithmic components of a random variable is used. The hybrid form is a formulation of the phenomenon in which there is a feedback mechanism against the large change in the random variable. This paper presents a new model of shouldered survival curves, called a hybrid scale model, which has two parameters: the inactivation constant and the protective factor. In the model, the surviving fraction, normalized by a protective factor plotted in a hybrid scale, is assumed to be linear against the dose. This simple model provides an implication of the shoulder of survival curve and the effect of recovery time of radiation damage, as well as giving a good to the well-known data of split-dose experiments with mammalian cells.