THE SHORTER-TERM BIOLOGICAL HAZARDS OF A FALLOUT FIELD
In this differential equation, the a, and «4, are
known constants of the exposure function. In
application to experimental daia, Z is a known
numerical function of the dosages, survival
times and the ageing function.
We therefore
havea first-order linear differential equation in
the unknown impulse lethality function, #(@).
Now let
7
f Z(tdt=¥
a
(30)
A, Daily X-ray
Meon daily
dove * {r)
(8)
Wefind
DEZ+ (oy +n) Z+ ana ¥ = (D+-yAgt+ mA,
(31)
This is solved for C, as
B. Rutt njeetlone
Moun after-| Camulant
survival
lethality 4
(days)
(rAlayi-1
andintegrate term by term, remembering that
f $(t)dt= C4, (4)
QUANTITIVE ESTIMATION OF RADIATION INJURY AND LETHALITY
TaBse 2.-CUMULANT LETHALITY VALUES
FOR CARWORTH FEMALE MICK (A) EXPORED TO CONSTANT DAILY DOSE OF XRAYS FOR THE DURATION OF LIFE AND(B)
INJECTED WITH Ru® V7A TAIL VRIN
103... ....
LTA
425
63. 1
36.4)
21,91
16.4;
13.4)
Mean
Median
injected
afterdose
survival
facie)
(days)
Cumulant
lethality +
Kueyt
se ee een} O
500 |...
0. 0256
1. 42
140
2. 047
. 0182 3.21
37
- 704
.0142 4.96
18
~ 418
.0093 8 94
12
~151
. 0056 |... ----) 22.2 eae
Exposures given § days per week.
.
> Using Equation 16 with E(Z}«2 and A(t*) =p
s
* Thebiologic decay of Ru! was found by Walton [22] to be
JAE} 3e- WOAHGe 10881
‘This was used to deseribs the time-course of exposure,
Ce"f* PYDZ+-(ayten)Z-+eyn¥dt (32)
o
.035
7
where B equals a,4,+ 0.4).
We * have evaluated C, from some data obtained
by the late Mr. Howard Walton [22] on the
toxicity of Ru’ for CF-1 mice. Equation 32
was evaluated numerically, using the data given
in Table 2.
Figure 6 represents the numerical
estimates of C, based on the rutheniumdata,
and also an estimate of C, obtained from data
on CF~1 mice given constant daily dosages.
In both cases A(t) and E(1) were assumed to
be given by Equations 11 and 12 respectively.
The scaling factor for best adjustment of the
+The assistance of Mr. Robert Schweisthal is grate-
fully acknowledged.
030
/
CONCLUSION
1 uc/g equivalent to 38.5 rep/day
lethality was discussed briefly. The formal
theory of lethality developed here was presented as an approach devised for the purpose
was found to be
The present status of the theoryof radiation
The tissue dose received from retained Rul was
estimated by Walton to be
of obtaining information about. lethality, re-
garded as a physiologic process. It was shown
that the lethality process is polyphasic, and
1 ue/g==41.6 rep/day
The estimated RBEof Ru with respect to 200
kvp X-rays istherefore
RBE=0.925
7
4
015
7,
O10 f—
when they can be given a correct physiologic
exposure pattern from the effects of a known
pattern, if the patterns do not differ too greatly
in form. This comparison is of some interest,
validity must first be determined by experiments with such patterns.
in predicting the lethal effects of an unknown
because Ruhas a fairly uniform distribution
in the body. However, experiments with time-
dependent exposures to external radiations are
°
9
methods described here can equally well be
However, the argument [23]
that
only fractionated exposure patterns should be
used in lethality studies, in order to avoid the
‘wasted radiation” received in the last days of
life, has no basis. The lethality functions exhibited above are estimates of the actual
makes its properly weighted contribution to
{
i
!
20
40
60
60
1oo
MEAN AFTER- SURVIVAL (doys)
Fiaure 6.—-Cumulant lethality functions for Carworth
female mice.
Fractionated exposure patterns are particular
cases of time-dependent exposure, to which the
amount of injury present as a function of time
after exposure. Hence, the injury arising
from exposures received shortly before death
.005
Solid line—directly determined Jrom
data on survival at constant daily X-ray dosages.
Dashed line—calculated from date on the survival
Jollowing dosages of Ru™, by use of Equation $2.
parameters, The estimation of these parameters by nondestructive methods will be possible
at 140 days is perhaps somewhat high.
It would appear from these results that the
linear model, despite its shortcomings, is useful
applied.
020
that the several species studied appear to show
considerable independent variation in the
amplitudes of the different phases. The construction of an adequate lethality function for
manrequires knowledge of several independent
The two estimates of the cumulant function also
agree in shape, although the C, value from Ru!
needed.
.025 r
>
CUMULANT LETHALITY (esdoy)™!
The integral may be evaluated numerically,
using numerical data to specify X(t), or it may
be evaluated analytically by first fitting Z(¢)
with a graduation formula.
In the event that the model is validated for
application in a given range of conditions, and
given also that an acceptable estimate of C,
exists, then Equation 32 becomes a formula for
estimating the expected relation of dose and
survival time for a given time-pattern of exposure.
il!
Rucumulant to the daily X-ray cumulant
the lethal injury.
Inspection of Figure 4 will
show also that this contribution in the first few
days ig actually comparatively small. Fractionated exposure, like time-dependent exposures in general, have an important role in the
development of the theory of lethality, but this
contribution will come from considerations
quite unrelated to the wasted radiation concept.
interpretation.
The linear model may have
utility for prediction of the effects of timedependent exposure patterns, but its range of
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Rate of Repair of Radiation Damage
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I. Recovery after single large doses of radiation.
British Journ. Radiol. 29, 563-569, 1956.
TI. Recovery during and after daily irradiation.
Tbid., 90, 40-46, 1957.
a. Kress, J. 8. Ro. W. Braver, and H. Kaupace.
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Fractionation and protraction of Cogamma
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(Abstract) Radzatton Research, 6, 601, 1956.
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IL, Specific aspects of the physiology of radiation
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a
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I, part 2, pp. 959-1028,
Alexander Hollaender,
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