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ORNL
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11.25 1.1.4 1.1.6
MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS - 1963
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MASTERP
A COMPUTER CODE FOR ESTIMATION OF BODY BURDEN OF POSR
BASED ON O.R. AND BONE REMODELING WHICH ARE AGE DEPENDENT*

DEC 2 1 03
Henry L. Fisher, Jr. **
Health Physics Division
Oak Ridge National Laboratory
Oak Ridge, Tennessee
RIKTILLSID FÖR ANILOVICH
DI MGUMA NOINIOS ABSTRAONG
The principal concern in occupational exposure to internal ionizing radiation
is with adult man. However, in extending the concept of radiation protection to a
population consisting of all ages of people, one is faced with additional problems.
For an adult, many of the physiological parameters such as body weight, water intake,
and absorption or uptake of an element into an organ may be considered practically
constant with time. It is not always possible to use such simplifying assumptions for the
general population. Therefore, the model we choose to apply to this case should allow
us the freedom of choosing or determining the necessary metabolic parometers as a
function of age of the individual.
Kulp" has derived such a model for estimating the skeletal burden of Osr from
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oral ingestion. Since 'Sr is chemically similar to calcium, a biologically essential
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element, it may be expected that they act similarly but not identically. From this
point of view, we will show a derivation of Kulp's model which is, in fact, based on
calcium metabolism. The skeleton will be considered to be a compartment from which
calcium and strontium enter and leave. These elements gain entrance by way of the
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Research sponsored by the U.S. Atomic Energy Commission under contract with
the Union Carbide Corporation.
On assignment from U. S. Public Health Service, Washington, D. C.
HE PATA

T
RKIMSIW POR ANNOUNCEMENT
IN NUCLEAR SCIENCE ABSTRACTS
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diet, specific fractions of that in the diet being deposited in the skeleton. In this
model, we will assume that there is no recycling between the skeleton and other
compartments, i.o., when a portion of the calcium or strontium in the skeleton
leaves the skeleton, it is excreted. The differential equation describing the material
balance of Pºsr in the skeletal compartment is given in Fig. 1. From this figure we
see that the rate of change of Sr in the skeleton is equal to the negative of the
rate of loss plus a gain rate. The first term in the right member of the equation is
com.com
the loss rate due to radioactive decay. In the model, let us assume that a certain
fraction, f(t), of the skeletal calcium, Calt), is absorbed from the skeleton and
excreted. The loss rate of calcium from the skeleton is, therefore, f(t)Calt). It is
assumed that Sr will be excreted along with this Ca in the same proportion as that
of 'Sr to Ca in the skeleton. The second term on the right represents this elimination
or loss of Osr from the skeleton. This excreted calcium must be replaced with an
identical quantity of new calcium. In addition, if the skeleton is changing its net
size with respect to calcium, the term Calt) must be added to the replacement term
to obtain the total calcium input rate to the skeleton. The Post to Ca ratio in this
new calcium going to the skeleton, or new bone, is equal to that in the diet multiplied
by the observed ratio K(t). The third term in the equation, or the rate of Osr input,
is the product of the Sr to Ca ratio in new bone and the total calcium input rate.
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In order to solve this differential equation for S(t), using specified functions
Calt), f(t), k(t), and Z (t), the equation was converted to a difference equation and
LEGAL NOTICE
The report wuo prepared an isoon of Government sponsored work. Mother the Outud
mato, nor the Commission, Mor my porton sotto
of the Commons ,
A. Makes my warranty or representation, promod or implied, with n ot to the mont-
racy, complemous, or watelnous of the tubormation contained on the report, or that the wo
of my taformation, apparatua, mothod, a procon deloved in this report may not mange
: patrately owned ar
B. Assumes say liabilities with respect to the use of, or for damage resulting from the
un at taformation, apparatuur, method, or you dealmond la roport
As wed in the above, porno rothea What the Commandoton mode meny to
ployw or contractor of the Commission, a play of wool contractor, he took that
work employus or contractor of the Couledom, was playas of will contractor prepares,
decombates, or provides Mona to, aby tormation puremat w Memployment or contract
with the counterton, or we oployment with much ontructor.
ORNL DWG. 65-10222
METABOLIC MODEL FOR STRONTIUM METABOLISM
st) = -As(t) – r(t)Calt) (sete) + Kleszce) (it) cact) + di cact)
s(t) = 90Sr Skeletal Burden
Ca(t) = Skeletal Calcium Content
f(t) = Turnover Rate for Calcium in the Skeleton,
K(t) = {Sr/Ca]gone/[sr/Ca Diet
z(t) = (sr/Ca Diet
Fig. 1.
solved numerically. This difference equation is shown in Fig. 2. Beginning with
an initial value for the body burden of Sr, one may apply the difference equation
repeatedly and determine the body burden, Sne for each value of n. The body burden
for the fetus was not determined; however, the body burden at birth is determined by
the relationship
28.0 K'Z
where
Bone Newborn
Mother's Diot
K' = [cheldono Newborated Morther's Diet
2 - Casa Mother's Dier
"Mother's Diet
The skeleton of the newborn is assumed to contain an average of 28.0 grams of calcium.
K' is taken as 0. 1 in this paper, this being the value assumed in FRC Report No. 7.17
The average dose rate over the skeleton at time n is given by
where w, is the weight of the skeleton and k is a constant which for Osr is
20.54 x 10-6 yad o
In Fig. 3 the skeletal calcium content, Ca, and skeletal weight, W, as used in the
calculation are shown for the age range considered. The skeletal calcium content is
ORNL DWG. 65-6044
METABOLIC MODEL FOR CALCULATING
ODY BURDEN
IC
Inn
Sn = $n-1 - (f+ )Sn-1
+ (Con-Com-1))
where
s = pc Sr90 Body Burden in Period n
f = Fractional Bone Turnover Rate per Period
À = sr°° Radiological Decay Constant per Period
nov
nunca vs Sic
Water Intake (liters/day)
C = spº° Concentration in Water (pc/liter)
G = Calcium Intake (grams/day)
Ca = Calcium Content of Body (grams)
Fig. 2.
ORNL-DWG. 66-5337

PARAMETERS FOR STRONTIUM
BONE BURDEN MODEL
SKELETAL CALCIUM CONTENT (GRAMS)
SKELETAL WEIGHT
SKELETAL WEIGHT (KILOGRAMS)
-SKELETAL CALCIUM
CONTENT
N
6
8
16
18
20
22
24
10 12 14
AGE (YEARS)
Fig. 3.
given by Mitchell;(3) the skeletal weight is from Spector; (C) and the observed ratio,
K(1), and the turnover rate, f(t), were estimated by Riveral) by applying Kulp's
model in roverso. From the measurements of Sr in bono, s(t), and from estimations
of the dietary Osr to calcium ratio, Z(+), Rivera determined the turnover rate and
observed ratio at yearly intervals. These functions are shown in Fig. 4. The estimated
valuos at birth were obtained by extrapolation from the values found for the one- and
two-year-old children.
The difference equation was coded for computer solution using a step interval
of one month from zero to two years of age, every quarter year from two to 24 years
of age, and yearly increments thereafter.
In order to compare the results of this model with others, we have applied it
to several simple cases. In Fig. 5 dose rate to the skeleton as a function of time for
an intake of one picocurie of Osr is given by the solid curves for intakes occurring
at various ages. The dashed curve indicates the initial dose rate for such an intake
at any age. Therefore, all solid curves begin on the dashed curve. Furthermore, all
solid curves have exactly the same shape. Thus one may move the solid curve for the
newborn in a vertical manner and generate a family of curves giving dose rate as a
function of time for all ages when the intake occurs. From this graph it is apparent
that the adult has the lowest initial dose rate. Excluding the 0-to-3-year age group,
the initial dose rate for any age does not exceed four times the initial dose rate for
adults. For ages less than three years, the initial dose rate increases until at birth
Wandversaire

ORN - DWG. 65-9449 10
PARAMETERS FOR STRONTIUM
BONE BURDEN MODEL
** BONE TURNOVER RATE ( Yr."')
TURNOVER RATE
OBSERVED RATIO
0
2
4
6
8
10
12
18
20
22
24
14 16
AGE ( YEARS)
26
28
Fig. 4.

WNL-OWE 66-9047
SKELETAL DOSE RATE AFTER INTAKE OF 1 pc "Sr: INTAKE
PERIOD 1 MONTH AT INDICATED AGE
HNITIAL DOSE RATE
DOSE RATE IM RAD/YR.)
· 002
لللللللللللللللللللللللللللللللللاوه
0
5
·
10
· 15
25
30
O
35
20
AGE (YEARS)
.
Fig. 5.
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It is about 26 times that for an adult. For this same intake condition, the lifetime
dose is given in Fig. 6. Variability in the lifetime dose is not as great as that in
the initial dose rate. Again, excluding the 0-to-3 year old, the lifetime dose for
intakes at any age does not vary by more than a factor of 1.4 from the lifetime dose
received by the 25 year old. The newborn receives a lifetime dose some 16 times
that of the 25 year old. With this model and these parameters, the results for short-
term intakes of Osr at all ages except the 0-to-3 year old indicate some uniformity
of exposure between the various ages.
Another mathematical test case is that of chronic exposure, beginning at
various ages, i.e., to place an individual on a diet containing 1 pc sr/g Ca for
the remainder of his life. The dose rate as a function of time for this case is shown
in Fig. 7. Excluding the 0-to-1 year old, the equilibrium dose rate for adults, for
all practical purposes, is the maximum dose rate obtainable. Those that exceed this
value do so by only about 12 per cent. For the newborn we see a sharp increase in
dose rate as he is placed on this diet. His max imum dose rate is about 1.7 times the
adult equilibrium value. This maximum occurs when he is one year old. Figure 8 gives
the lifetime dose for the individuals on this diet. The lifetime dose is a decreasing
function of age because the exposure time is shorter for older individuals. As a point
of comparison, the lifetime dose for the 25 year old is about 22 m rad/(pc *° sr/g Ca),
whereas the newborn is approximately 42 m rad/(pc 90Sr/g ca).
ORNL-DWG 65-9848
CS
SKELETAL DOSE TO AGE 70 YEARS AFTER
INTAKE OF Ipc SOS. AT VARIOUS AGES.
INTAKE PERIOD: 1 MONTH
DOSE (H RAD)
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10
25
30
35

15 20
AGE (YEARS)
Fig. 6.
kishin mbeturinationem
home
bit
ORNL-DWG. 65-9451
DOSE RATE TO THE SKELETON FROM THE CONTINUOUS
ORAL INGESTION OF A DIET CONTAINING I pc so Sr/g Ca.
BEGINNING AT VARIOUS AGES
(RIVERA MODEL)
(MILLIRAD / YEAR )
EQUILIBRUM VALUE FOR ADWS
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DOSE RATE
2
4
8
10
12
18
20
22
24
26
28
30
14 16
AGE (YEARS)
stimento do
ORNL-DWG. 65-9450
40
LIFETIME DOSE TO THE SKELETON FROM THE CONTINUOUS
ORAL INGESTION OF A DIET CONTAINING I pc so Sr. /g Ca
BEGINNING AT VARIOUS AGES
( RIVERA MODEL)
30
.........................
26
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...
vercome of the con

10+
o
4
8
12
16
44
48
52
56
60
20 24 28 32 36 40
AGE AT BEGINNING OF EXPOSURE (YEARS)
Fig. 8.

commitment
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test and
the la
in
. . While these cases allow simple generalizations, this model has been applied
to other situations such as the consumption of Clinch River water containing Sr
beginning at various ages.)
in the
nature
There are three major limitations of this model that should be borne in mind:
(1) The skeleton is considered as a single compartment with a simple constant turn-
over rate coefficient for each oge of the individual;
(2) Any recycling or exchange of strontium between various parts of the body is
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tistics
neglected;
isini
a
(3) Even if the model were perfectly valid, the turnover rate and observed ratio
as a function of age are known imperfectly at this time.
However, this model is the only one that provides a means of estimating body burden
of Osr for individuals of all ages and can be considered to be based on data derived
from direct study of the exposure of man to 'Osr in the diet.
hominisanominend
References
1. J. L. Kulp, TID-7632, p. 457.
2.
Background material for the development of radiation protection standards
Protective action guides for strontium-89, strontium-90 and cosium-137,
Federal Radiation Council Report No. 7 (May 1965).
3. H. H, Mitchell et al., J. Biol. Chem. 158, 625 (1945).
4. W. Spector, Handbook of Biological Data (National Academy of Sciences, 1956).
5.
Joseph Rivera, TID-7701 (1965); HASL-163 (1965).
6.
K. E. Cowser and W. S. Snyder, Safety Analysis of Radionuclide Release to the
Clinch River, Supplement No. III to Status Report No. 5 on Clinch River Study,
ORNL (1965).
-95RCERIAKA
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