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.