THE SHORTER-TERM BIOLOGICAL HAZARDS OF A FALLOUT FIELD
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QUANTITIVE ESTIMATION OF RADIATION INJURY AND LETHALITY
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90
50
{00
MEAN
50
AFTER- SURVIVAL
200
( days}
the lethality functions cannot be adequately
sions,
Thus, the impulse lethality function
(fig. 4) for the ABC mouse does not agree well
with the formule of the type offered by Blair
(19, 20) to describe this function
X=Ce" +O,
(13)
zero.
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0
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50
100
TIME
I
(doys)
1
150
200
250
for the impulse function which is of the catenary form
recovering injury is not present in the Blair
formulation.
Since the nonrecovering injury
where 8 is the recoveryrate.
This expression would perhaps give a fair
description of an individual injury process, but
an adequate description of the empirically
determined impulse function during the first
thality functions for man. This does not mean
an explicit formula is to assume that injury
fact the important parameters necded can be
reduced to a set such as the following.
becomes manifest as an exponentially decreasing function of the time after exposure [21],
Vi) = evet
(14)
where V(t) is the amount of injury that appears
at time ¢ after exposure to unit dose. If this
This ex-
Blair acknowledges the existence of a
2A modification of Blair's theory based on this consideration has been
developed by Dr. D. Mewlessen (personal communication),
pression would put the peak of injury at time
0
fe
disease, the delay in its appearance, as seen in
Figures 3, 4, and 5, is the expected behavior.
Our actual problem is to estimate the Ie-
is combined with the assumptions that (a)
recovery is linear, and (4) there is a non-recovering component, we obtain an expression
where C,, C, and & are constants.
oooh
(1s)
matical developments. A simple way of introducing the delayed appearance of injury in
tepresonted by simple mathematical expres-
0008
{19] but does not take account ofit in his mathe-
lants for different species differ in form.
First,
-0010
is manifested in neoplasia and degenerative
delay in the appeerance of recoverable injury
vations for the mathematical theory?
0012
Fiaurs 4,-—Impulse lethality function, obtained by graphical differentiation of the curve in Figure 3.
It is evident that the lethality cumulant is
What are the implications of these obser-
107
250
Frevre 3.—-Cumulant lethality function, for ABC male mice exposed to daily dosages ranging from 20 te 1000 r/day.
species-characteristic, for each species has a
consistent pattern of behavior, and the cumu-
DERIVED SINGLE DOSE LETHALITY FUNCTION (r7~')
106
X=O(e!—e404
100 days (fig. 4) would require at least two
catenary terms.
Even this more elaborate
expression would fail to describe events accurately between 50 and 200 days, in view of
evidence that the non-recovering lethal effect
has a mean latent time of about 200 days for
the mouse and rat, and a greater magnitude
for the dog and guineapig [14]. This accounts
for the extended plateau region in the cumulant
functions of the various species shown in
Figure 5. This latency property of the non448020 O—S8—_—8
that we need to trace « complicated curve. In
1. The sensitivity of the recoverable injury,
as measured by the plateau level of the
cumulant function.
2. The sensitivity of the nonrecoverable
injury, as measured by the constants of
of thefinal rising branch of the cumulant
function.
3. The meanlatent timeof the recoverable
injury.
4. The mean latent time of the nonrecoverable injury.