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MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS -1963
83
CONH
MASTER
A DOSE ESTIMATE BASED
ON STABLE-ISOTOPE DATA*
DEC 21 10965
W. S. Snyder
Health Physics Division
Oak Ridge National Laboratory
Oak Ridge, Tennessee
Data on intake and on concentration of stable elements in human tissue have
been used in many cases as a check on the adequacy of inetabolic models for radio-
active isotopes. It is clear that if individuals in the population are supposed to have
a nearly constant intake and to be nearly in a state of equilibrium with respect to a
given element, then the amounts in grams of the element in the various tissues die a
direct measure of average gram-days of residence of the isotope in those tissues for
the given level of intake. If a radioactive isotope of this element is taken into the
body in similar chemical form, the number of microcurie-days of residence in the
tissue will be less than that indicated by the data on the stable isotope because of
radioactive decay. However, it is clear that neglect of decay will produce an over-
NAME
estimate of dose rate and that it may be possible to make some correction for the
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decay. Although all this is quite obvious, the question does not seem to have been
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treated quantitatively in the literature until quite recently.
Brues and Tyler have discussed the variation of dose and dose rate in a
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multicompartment system which is in a state of equilibrium. They find that "there
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Research sponsored by the U. S. Atomic Energy Commission under contract
with the Union Carbide Corporation.
LEGAL NOTICE
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RMITASID FOR ANNOUNCEMENT
The report ms prepared n mooount of Govarura sponsored work, Mathar the United
Matea, nor the Commission, nor my person acting a bhall at the Commisedom:
A. Makes my warranty or representation, aproaped or implied, with respect to the scou.
racy, completament, or wentalnom of the information contained to the report, or that the we
of any information, apparatus, method, or procons declared to the report may not latringe
privately owned right of .. .
B. Asunou may liabilities with respect to the who, or for dumnguo nowotny from the
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As mund te the shova, "pernon noting on behalf of the contentor" Includes my
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deron train, or provides nomas 10, any information pursuant to wo employment of contract
with the Commission, or wo employment with each ontractor.

IN NUCLEAR SCIENCE ABSTRACTS
MNAASIUM
have the image
the delivered be

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is a predictable max imum radiation given by any compartment of any steady-state
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multicompartment open system in which the 'external compartment is specified as
to its specific activity in time." Marshall has generalized the argument of Brues and
Tyler in his discussion of the metabolism of the alkaline earths. (2) However, his dis-
cussion applies almost without change for other elements. In the present note a related
result is obtained without the assumption of a multicompartment or mammillary system,
and the final estimate of dose does not directly involve the rate constants of the
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various compartments. Thus the present result appears soinewhat more general than
those mentioned above. On the other hand, the argument presented here demands a
knowledge of the daily intakes and of the mean concentrations in the organs involved
of a stable isotope of the radionuclide in question. In this sense, the argument may
be more special than that of Brues and Tyler or that of Marshall.
1
Assume an individual is taking in a stable element E and is in a state of
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equilibrium with respect to this element, and consider that this individual takes in
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an amount A (in microcuries) of a radioactive isotope of E, the latter being designated
by E*. It is assumed that E* enters the body by the same route as does the stable
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element E and that the chemical forms of E and E* are similar or, preferably, iden-
tical. If this is the case, one can expect that E and E* will metabolize in similar or
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identical fashion. It is desired to estimate the total dose delivered to an arbitrary
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tissue T of mass M in the body of this individual. The tissue in question need not be
a complete organ or physiological entity. For example, one may choose it to be the
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lower third of the heart, or the tissue in a sphere with its center at the center of
gravity of the body and radius 5 cm, etc.
Lot Rat! be the retention function for element E in tissue T; that is, if I g
of stable element E is taken in at time 0, then + days later, R(t) g of element E
is present in tissue T. Since the route of entry and chemical form in which E is
encountered are assumed to be similar or identical to those for E*, the same function
R(+) describes the fraction of an intake of E* which is present in tissue T, + days
following intake, corrected for radioactive decay.
The total microcurie-days accumulated in T during the first L days following
exposure due to the intake of A pc of E* is given by
A So Ret) e Atdt microcurie-days,
(1)
where is the radioactive decay constant for E*. The dose delivered to tissue T
during these L days is then
-> dt x 3.2x10° x < x 1.6x1078
M
- rads,
(2)
where
3.2x10° - dis day-Ruc,
E
= energy (Mev) absorbed in T per
disintegration of E*,
TA
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1.6x 10^8 = gram-rad/Mev, and
M = mass of tissue T in grams.
In many cases, R(t) is not known or is not known very precisely.
If the hypothetical individual is taking in I g of stable element E per day,
then, at equilibrium, tissue I should contain So r(t) dt g of element E. The
integration over an infinite range is purely symbolic, and one may substitute any
finite number of days, say I days, for infinity, provided L is so large that equilibrium
is attained effectively within days. Mathematically, this means that so r(t) dt
and SoR(t) dt are effectively equal. That is, I must be specified as a number of
days so great that the individual will be effectively in equilibrium when maintained
on a constant daily intake of E for a period of L days.
With L so specified, the equilibrium concentration of stable element E in
tissue T is given approx imately by
grams of E
M grams of T•
One may solve (3) for M and substitute in (2), obtaining
51 AEC
SR(t) e =At dt
Do
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R(+) dt
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From (4) one has the immediate overestimate of dose
O $ 51€ rack.
(5)
The estimate will be of most interest when E* has a radioactive half-life which is
long compared with the time for an individual to reach effective equilibrium, that is,
long compared to L days. Under these conditions et ~ 1 for 0 <+<L, and the
estimate in (5) should be a good approximation to the actual dose.
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As a first application of this result, consider the exposure of an infant to
Sr.
Comary has suggested that in early infancy the bone is remodeling rapidly and that
effective equilibrium on a steady diet should be reached in a matter of a few weeks or
perhaps a month. The infant is growing during this period, and doubtless a true and
precise state of equilibrium is not attained. However, growth during a month usually
would not be so great as to be a considerable factor in dose estimation, and we may
suppose that there is a state of transient equilibrium. Applying formula (5), one finds
that an intake of 1 pc of Sr in a very young infant would produce an estimated dose.
to bone of 1.7 rads. This estimate is obtained by using
E = 1.1 Mev, (4)
C = 1.5x10-5 = concentration of stable Sr in infant bone,
= 5x10-4 9 = daily intake of stable Sr by the infant.
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The value of C is found by assuming that the skeleton of the one-year-old child
contains 100 g of Ca and weighs 1.30 kg and by using the value 200 Mg of Sr per
gram of Ca in the skeleton obtained from ref. 5. The value of I is taken from ref..
6. This estimate is somewhat lower than a similar estimate given by Rivera and
by Mayslo) who give estimates of about 9 rads and 7 rads, respectively. The rather
low value obtained by the present argument may be due in part to the imprecision of
the data on intake and bone content of Sr, or it may be due to a significant departure
from equilibrium.
If formula (5) is applied for an adult, one obtains
DL = 2.8 rads per microcurie of intake.
This value is obtained by using
C = 5x 10-5 g of Sr per gram of bone,"
i = 10-3g of Sr per day. (6)
The use of (5) for the adult is questionable since the very long retention time of Sri
year radioactive half-life of Osr. Thus the exponential factor e-** in (5) may be
significantly less than 1 during a part of the residence time. Putting this another way,
(5) neglects the effect of radioactive decay and thus. may produce an overestimate of
DLAccording to the ICRP rule," a yearly intake of 'Osr will produce a dose of
Derived from ref. 5.
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30 roms or, equivalently, of 6 rads over the ensuing 50 years. Using the latest MPC
value recommended by ICRP of 4x1000 pc/cc for continuous occupational exposure by
Ingestion, a yearly intake is found to be 3.2 pc. Thus, I wc of intake should, by this
rule, deliver 2 rads to bone. It is gratifying that the estimate from (5) is so close and
that it is high as would be expected.
Finally, the case of an intake of 'H'HO will be discussed. In the 1964 annual
reportivo) a human exposure was reported for which R(t) seemed to involve two expo-
nentials. This suggests that some tissues other than the body water are involved and
may accumulate a greater dose than that received by body water. According to (5),
any tissue I would receive a total dose of 1.8 rads per microcurie of intake. This is
obtained by assuming
C
= 0.1 g of H per gram of soft tissue
and
1 = 2500 g of H20 per day,
which is equivalent to 278 g of H per day. The value of I is probably an underestimate
since some hydrogen will be taken in with the solids of the diet. This is essentially
the same as the dose to body water. In fact, all soft tissues for which data have been
found show a concentration of hydrogen close to 10% and thus have essentially the
same dose according to (5). The concentration of hydrogen in bone is approximately
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5%, and thus bone should receive a smaller dose. Tritium is, perhaps, the isotope
least favorable for this type of estimation. The ratio of the masses of Hand 'H is
far greater than in the case of other isotopes, and so it is questionable as to how
nearly the retention function for 'H corresponds to the retention function for H.
The argument assumes 'H and ⓇH have the same retention function in the body when
they are taken in as H, Oor 'H'HO, respectively. No doubt there are differences
in the metabolism of 'H and H, but it does not seem easy to obtain an indication
of the degree of disparity that might exist. Except for this factor, (5) yields essen-
tially the same estimate for all tissues. In the case of other elements where this
difference in mass ratio is much smaller, one may use (5) with more confidence.
However, even for tritium it seems unlikely that the retention would differ by orders
of magnitude, and thus (5) may serve to allay any fears that some tissue might receive
a dose which is orders of magnitude greater than the dose to body water.
References
1. A. M. Brues and S. A. Tyler, Atomprax is 5, 253 (1959).
2. J. H. Marshall, J. Theoret. Biol. 6, 386 (1964).
3. C. L. Comar et al., Health Phys. 11, 609 (1965).
4. ICRP Publication 2 (Pergamon, Oxford, 1964).
5. Medical Research Council, Assay of sp90 in Human Bone in the United Kingdom
Results for 1963, Part II (H. M. Stationery Office, London, 1964).
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6. F. J. Bryant and J. F. Loutit, Human Bone Metabolism Deduced from
Strontium Assay, AERE-R 3718 (1961).
7.
Joseph Rivera, Second AEC Conference on Radioactive Fallout from Nuclear
Weapons Tests, Germantown, Maryland, Nov. 3-6, 1964, CONF-765 (1965),
Paper No. 7.
Charles W. Mays and Ray D. Lloyd, w90sr and 89 Sr Dose Estimates for the
Fetus and Infant, " (In press).

ICRP Publication 6 (Pergamon, Oxford, 1959).
10. Health Phys. Div. Ann. Progr. Rept. July 31, 1964, ORNL-3697, p. 173.
END

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