108
THE SHORTER-TERM BIOLOGICAL HAZARDS OF A FALLOUT FIELD
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QUANTITIVE ESTIMATION OF RADIATION INJURY AND LETHALITY
sequences of the fundamental postulate that
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radiation lethality is a consequence of physi-
ologic injury. Therefore a correct, description
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of lethality can only follow from correct conceptions of the nature of physiologic injury
and recovery. Despite the complexities that
have been pointed out (and others that have
not been considered) the prediction of lethal
effects in man is possible if we can identify the
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Frours 5.—Cumulant lethalily functions for several experimental species, based on all available data.
DETERMINATION OF TILE CUMULANT
LETHALITY FUNCTION FROM DATA
ON TIME-DEPENDENT EXPOSURES
In the previous gection, lethality functions
for several species were obtained from data on
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physiologic correlates of the various components of the lethality function.
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ever, the validity of the basic postulates of the
exposure patterns,
In this section it is shown that the cumulant
lethality function may be deduced from data on
time-dependent exposures. The comparison of
the derived cumulant function with one determined directly permits a test of the consistency
of the model.
To simplify the derivation, the integral
equation for injury will be solved for timedependent exposure on the assumption of linear
effectiveness (Equation 12).
The exposure intensity function, f(, will be
written as a sum of exponentials ?
platted on @ log-log grid. Note (a) lack of apectes differences in first 7 days, (b) existence of a plateau region indicating
partial equilibration of the recoverable injury, (c) large species differences in the plateau level of injury, (d) appearance
=P Aun
of non-recoverable injury, aa indicated by final rising branch, after a latent period of several hundred days.
The contribution of the empirical analysis
presented thus far is to suggest that these
parameters are independent and must be deter-
mined separately. According to present evidence, the LDj is a poor predicter of the later
phase of the recovering injury, and there is as
yet no evidence that it has predictive value
(16)
with
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representation
frome retained isotopes.
+ [1-40|
(18)
Equation 2 then becomes, with Y(é) 1,
Z=f)DAc exp [—auctt~ | dr
e
= 3 de" f(oredr
(19)
(20)
Thereis no need for the general solution because
the limitations of the empirical data preclude
the use of more than two exponential terms in
Ff). The case that f() has two exponentials is
nowconsidered.
Let us define the new variable
PaAef"ere"dr
(21)
The derivative of P, with respect to ¢* may be
written
DPy=aAef“pnedr+Awlt*) (22)
0
=PtAp
where
(23)
_d
p=t,
(24)
$=o(t*)
(25)
With 2=2, Equation 20 becomes
Z=P,+P2
(26)
Wealso obtain readily
DZ=~—mP,\—mP2+¢
(27)
D°Z=a/P\+07P2—(aArtorzd2¢+D¢ (28)
for the true chronic injury, which is expressed
in neoplasia and degenerative disease.
There would appear to be only one methodologically sound approach to the problem of
predicting lethality, that of pursuing the con-
Zz
duration-of-life exposure at a constant rate.
It was possible to determine thereby some
general properties of the injury process. Howlinear model was not tested thereby. The
postulate of linearity of mechanism can be
tested by using date from a numberofdifferent
109
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Otherclasses of exposure patterns (Hnear rise or
(all, aquare wave, powerfunction, etc.) can also be solved.
We can eliminate P, and P, between these to
obtain
(D+ (ay a) + 00)Z = (D-ronAy +aAa)e (29)