wh,
At higher dose-rates the life-shortening continues to increase but,
owing to the progressive reduction of life, the dose accumulated decreases and
the curve bends over towards the origin.
described by Lorenz et al.
{B5| and Sacher [S1].
Such an effect had previously been
[L6] and may be predicted by the theories of Blair
Although this observation is not immediately apparent
from Figure X it may be noted that all along the curve the data obtained at
approximately similar dose rates are reasonably well clustered together.
This
immediately points to a relationship between the three quantities under study
in the graph: dose, dose-rate and life-shortening effect.
145.
Simply in order to describe the data with a maximum of precision, an
attempt was made to fit a curve where the three quantities cited would all
contribute to determine the final shape of the relationship.
The following
equation was assumed to interpolate the phenomenon reasonably
where
y
is the percentage of life-span-shortening,
dose-rate,
b
and
ce
D
being proportionality constants.
the dose and
A
the
Such a relationship
could not be fitted adequately in the absence of some function relating dose
and dose-rate.
In order to find such a function the simplifying assumption of
an exponential decrease of the life-span with increasing dose-rate was made
for any given total absorbed dose
r= pt ° eA,
(2h)
Since the total absorbed dose is given by the product of the duration of life
and the dose-rate
D=
AT
(25)
it follows that
D=
AT
enA/A,
(26)
A plot of total absorbed dose versus dose-rate for data belonging to the same
experiments in Figure IX was found to agree reasonably well with an expression
of the above type.
Therefore, the previous relationship was fitted to the ex-
perimental data, yielding
D
with an
Re
=
0.98.
=
664.11 Ae
-0.0351
(27)