where ted (I) is the survival time following duration-of-life exposure at dose-rate I and ecis a dose-rate dependent constant. These basic trends of the actuarial parameters in irradiated mammalian populations are schematically represented in Figure I. 21. The assumptions underlying such interpretations are that the Gompertz function is a measure of the amount of aging injury present at any given time. Acute exposure would increase this amount of injury once and for the rest of life. However, if any new amount of injury induced summates to the residual injury present at any given time and to the underlying aging injury, one should expect a change in slope by chronic irradiation with a divergence from control slope proportional to the amount of daily dose administered. It should be clear that such characteristics of the actuarial functions are not necessarily related to the form of the dose-effect relationships, which may them- selves be linear or not, as discussed in the next chapter. 22, In 1952 ([B2, B3] and again later in a more complete form [B4, B5] Blair formulated a "theory" of the relationships between radiation dose and lifeshortening. This model postulates that total injury is linearly propor- tional to dose and that such injury is only in part reparable. Recovery from reparable injury would proceed exponentially at a rate proportional to its magnitude, while, on the contrary, the irreparable portion of injury would accumulate linearly with dose. Finally, reparable and irreparable injuries would add in all proportions and death would occur when their sum is propor- tional to the remaining life expectancy. Starting from these premises, Blair developed simple equations relating dose and injury under different conditions of exposure and showed that some of them conformed to the then avail- able data. Blair's formulation stimulated much research to ascertain under a variety of experimental conditions the amount of reparable injury and the kinetics of repair but was recognized later as an oversimplification of reality, leading to incorrect estimates and as such inadequate to account for the form of the dose-injury functions. 23. Mewissen et al. [M5] developed a complex equation relating life- shortening to chronic whole-body irradiation and applied this formula to the irradiation of the burro. The formula is based on an analysis of the injury, which is also assumed to consist of a reparable and an irreparable fraction.