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NATIONAL BUREAU OF STANDARDS -1903
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: NOV 29 1966
DISTRIBUTION OF DOSE IN THE BODY
FROM A SOURCE OF GAMMA RAYS DISTRIBUTED UNIFORMLY IN AN ORGANI,2
CISTI DI
H. L. Fisher, Jr., and W. S. Snyder
Health Physics Division
Oak Ridge National Laborciory H.C. $2.00 mW 150
Oak Ridge, Tennessee, USA

II.
MASTER
When a gamma emitter is present in an organ of the body, only a fraction of
the emitted gamma energy is absorbed in that organ. Many evaluations of the absorbed
fraction have been published, mostly for highly idealized and perhaps cversimplified
cases. The use of an effective radius and a spherical geometry is one instance of such
drastic simplification. Although an exact theory of gamma photon intera 'on with
matter is known in detail, application of this theory is usually difficult since an
enormous amount of mathematical computation is involved. However, by use of a
high-speed digital computer these calculations become feasible. A Monte-Carlo-type
calculation has been used to estimate the dose in 22 orguns and 100 subregions of an
adult human phantom for four initial gamma energies. This report is divided into three
sections; in section one is a description of the phantom, in section two are some details
.
of the Monte-Carlo method used, and in section three are the dose estimates from a '
.
gamma source distributed uniformly in (1) the total body and (2) the skeleton.
'Research sponsored by the U. S. Atomic Energy Commission under contract
with Union Carbide Corporation.
• "For presentation at the First International Congress of the International Radiation
Protection Association.
On loan from the USPHS.
LEGAL NOTICE

RELEASED FOR ANNOUNCEMENT
IN NUCLEAR SCIENCE ABSTRACTS
This roport was propared as an account of Govornment sponsored work, Neither the United
States, nor the Commission, nor any person doting on behalf of the Commissions
A. Makos aay warranty or representation, expressed or implied, with respect to the accu-
racy, comploledoos, or usefulness of the information contained in this report, or that the use
of any information, apparatus, method, or procoas disclosed in this report may not Infringe
privately owned righto; or
B. Assumes any llabilities with rospect to the use of, or for damages resulting from the
use of any information, apparatus, method, or proceso disclosed in this report,
i Ao used in the above, "person acting on behalf of the Commission" Includes any em-
:ployee or contructor of the Commission, or employee of such contractor, to the extent that
such employee or contractor of the Commiosion, or employec of such contractor proparos,
disseminates, or provides Acoous to, any information pursuant to his omployment or contract
with the Commission, or his omployment with such contractor,
..........
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1. The Phantom
.. Shown in Fig. 1 is the phantom and subregions in which dose was determined.'
The dimensions of the phantom were chosen after consideration of the average size and
designed
weight of humans (1,2,3) and the phantoms esant by Hayes and Brucer. (4) in
order to describe the various regions, a coordinate system is needed. As shown in
the figure, the origin of the rectangular coordinate system is located at the center
of the base of the trurk. The positive z-ax is extends vertically through the head,
the left side of the phantom will be iaken along the positive x-axis, and the rear will
be taken along the positive y-axis. All units of length are given in centimeters.
Using the coordinate system in Fig. 1, the body of the phantom may be described
as follows. The trunk is an elliptical cylinder given by
(a) + (%)*si
s
1 :
...0 Sz 570.
The head is also an elliptical cylinder
(*) (*) si
<
1
:
70 < 2 S 94.
The legs are considered together to be a truncated elliptical cone
(*) (*)* (10)
100
:- 80 < z <0.
C.
4
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It is now a simple matter for the computer to take any point (x, y, z), substitute it
into these inequalities, note whether the inequalities are satisfied, and thereby
determine whether this point is inside or outside the phantom and whether it is in the
head, trunk, or legs of the phantom. Except for the head, this phantom is convex.
Account ras been taken of the photons which transverse the void between trunk and
.
head.
The arbitrary subregions into which the phantom was sectioned and in which
dose was determined are outlined in Fig. 1. The legs were cut into four layers by
equidistant horizontal planes; the trunk was divided into five layers by equidistant
horizontal planes. Two vertical planes, intersecting ar right angles along the central
axis of the trunk and having an angle of 45 degrees from either the x-or y-axis, cut
these layers. The final volume element is obtained by four vertical, concentric, elliptical
cutting cylinders. The major axes of these elliptical cylinders are 4, 8, 12, and 16 cm,
and the minor axes are 2, 4, 6, and 8 cm. The innermost elliptical cylinder was not
cut by the vertical planes.' The head was sectioned into two layers equal in thickness
and was cut by the same two vertical planes which cut the trunk. Although dose was
determined in these arbitrary regions, the results are not presented in this report since
the principal purpose is to give organ doses. However, results from the arbitrary regions
permit an approximation of the variation of dose throughout the phantom. In particular,
if an organ is very small, e.g., ovary, thyroid, pituitary, etc., the dose estimate may
be statistically unreliable on a given calculation, and one may use instead an average
dose over one of these layer regions.
-
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.
.
-. .
.
.
.
.
-
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.
.
1
.
2.
,
6
.
SER
Mathematical descriptions of the organs were formulated after consideration
of the descriptive and schematic material from several general anatomy references.
The scaled cross sections of the human body by Eycleshymer and Schoemaker" were
helpful in locating the positions at which to place the organs as well as aiding in the
construction of the organs. The representations of the organs by the mathematical
equations given herein are only approx imate, and many other geomatrically simple
approx imations might be used. The goal in constructing these mathematical organs
was to obtain the approximate size and shape of an avero je organ through the use of
a few simple mathematical equations. If the size and shape approximate those of the
real organ, the dose estimate shouid be correspondingly accurate. To minimize running
time and, therefore, cost, the formulas used should be as simple as possible.
The composition of the phantom is tissuel) of density 1 g/cm3 There is no Irow
density area for the lung nor is there a high density region with modified mass absorption
coefficient for bone. However, for gamma energies between 0.2 and 4 Mev, the mass
absorption coefficients for bone and soft tissue are essentially the same within several
percent. Below 0.2 Mev the photoelectric cross section for bone rises much more rapidly
than that for soft tissue. This is one of the major limitations of the present approach. The
volume in cubic centimeters of most marhenatical organs will be equal to the weight of
an average organ in grams. This is not true for the lungs or for regions of bone. The
linear dimensions of all organs including lungs and bones have been used as the primary
basis for developing the mathematical equations.
Spil
AT!
.
-5-
In Fig. 2 is an anterior view of some of the larger organs end their positions
in the phantom. In the following account, a brief description of each mathematical
organ will be given followed by the mathematical inequalities which must be satisfied
for the point (x, y, z), in the coordinate system of Fig. 1, to be in the organ. The
volumes which are given were determined by integration.
The volumes of the head, tiunk, legs, and total body are 5,278 cm,
43,982 cm”, 20,776 cm", and 70,036 cm°, respectively. When there are left and
right organs, the equations for only one, the left, will be given. The equations for
the other may be obtained by replacing x by -x in the inequalities.
Adrenals. Each adrenal is half an ellipsoid sitting atop a kidney. The left
adrenal is given by
(**)+(359) + (**)'s!
.*LY
<
1
z
39
The volume of both adrenals is 15. 71 cm.
Bladder (urinary). The bladder plus contents when moderately full is an
ellipsoid given by
(8)* +(****)? + (%)'s!
The volume is 508.9 cm”.
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Brain. The brain is an ellipsoid given by
(P + (7) + (28.6.5) - 1.
The volume is 1470 cm.
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--
2.99
Gastrointestinal Tract. The form of the gastrointestinal (GI) tract given
here represents the mass of the tract itself plus the 24-hour average mass of contents,
This is a particularly difficult organ to fix since its volume and location are subject
-
-
.
.
.
.
.
to change between individuals as well as in the same individual. The intestines are
taken to be in the somewhat-idealized standard positions. The stomach is the most
difficult to represent since its volume will change by nearly an order of magnitude,
several rimes in 24 hours. The constant-sized and fixed-position stomach given here
is, therefore, not very realistic but should suffice for estimating an approximare dose
in that region. The stomach is an ellipsoid,
and has a volume of 402. 1 cm.
The small intestine has not been constructed in detail. Instead the volume
occupied by the coils of the small intestine is used. This volume, which lies in the
pelvic regicn, is a section of a circular cylinder given by .
x? + (y+3.832 < (11.32
. -7 Śy s3
Pit
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Exclude large intestine volume.
The upper large intestine is simulated by two cylinders, one cylinder with
its ax is vertical representing the ascending colon and an elliptical cylinder with its ::
ax is horizontal representing the transverse colon. The upper large intestine is the
region satisfying
?: (+8.5)2 + (y + 4.5)= (2.532
15.4 5 ¿ < 24
2. (279) + (* 1951
- 10.5 ** 10.5,
and its volume is 416.3 cm? ..
The lower large intestine is composed of an elliptical cylinder and an S-shaped
figure formed from half of a torus. It is the region satisfying
1. (b) =(444.3) 51
13.
4
2
24
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2. 0 sz s 13.4
2+(2-6.7+ 6.7 m2 -0.7) + p? 5 (1.6)
where
E
E = 4x - 4.75) 0.7090 - (y - 0.4252) 0.7053
- F = (x - 4.75) 0,7053 + (y - 3.4252) 0.7090
m = 1 if E 20
m = -1 if Eco
and has a volume of 275.8 cm”.
Heart. The heart is h i an ellipsoid caped by a hemisphere which is cut by
a plane. A rotation and translation are then effected. The heart,
-
LIST
IP
:
*, = 0.6943 (x + 1) - 0.3237 (y + 3) - 0.6428 (z - 51)
y = 0.4226.(x + 1) + 0.9063 (y + 3)
24 = 0.5826 (x + 1) - 0.2717 (y + 3) + 0.7660 (z - 51)
ii
(39** (7)** (31) si
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has a volume of 603. 1 cm?
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Kidneys. Each kidney is an ellipsoid cut by a plone. The left kidney is given
.by
het + 43*1* (***Psi
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E
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The volume of both kidneys is 288.0
Liver: The region of the liver is defined by an elliptical cylinder cut by a
plane as follows:
'..
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Bš +
27 5 z 5 43.
Its volume is 1,614 cm?
Lungs. Each lung is half an ell'ipsoid with a section in front removed. The
defining inequalities for the left tung are
.
z - 42
(****** (**********
.z > 43.5
(*2:5* + (73)** (*1935) ? 1 #ty.co.
The volume of both lungs is 3,378 cm?
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Ovary. Each ovary is an ellipsoid. The left ovary is given by
!
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The volume of both ovaries is 8.378 cm”.
Pancreas. The pancreas is half an ellipsoid with a section removed. It is
defined by :
x
> 0
2 2 37 if x > 3
and has a volume of 61.07 cm”.
:.. . Skeleton. The skeleton consists of six parts-the leg bones, the arm bor.es,
..the pelvis, the spine, the skull, and the ribs. Each piece will be described separately.
. Each arm bone is the frustrum of an elliptical cone. The left one is defined by
(z - 69) + (x - 18.4)
1.4
Osz Ś 69
-
The volume of both arm bones is 956.0 cm”.
E The pelvis is a volume between two nonconcentric circular cylinders described.
:
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x2 + (y + 3)2 = (12)
x2 + (y+3.852 2 (11.32
y +3?0 .
o Szs 22
Ys 5 if z14.
Its volume is 606. 1 cm?.
The spine is an elliptical cylinder given by
1.5
L
in
22 {z < 78.5
and has a volume of 887.5 cm.
The rib volume is that region between two concentric, right, vertical, elliptical
cylinders. This region is sliced by a series of equispaced horizontal planes into slabs,
every other slice being a rib. The statements that must be satisfied are
2
.
2
IZ - 35. 1'
35.1 52 567.3
· Integer (24) is even
The total rib volume is 694.0 cm?
is even.
.mindroid
.:
T
12
Each leg bone is the frustrum of a circular cone. The left one is
( - 1 - 2
x
10
tỷ 2 (1.5 đ)
::: -79.8 << < 0.
The volume of both is 2,799 cm”.
The skull is the volume between two nonconcentric ellipsoids defined by
IZ-8
(+*+ (8*+436.5*31
XIO
.
and has a volume of 846.6 cmº.
Dose to the entire skeleton is determined by adding together the energies deposited
in each part of the skeleton and dividing by the volume of the skeleton as follows. Let
E, be the energy in Mev deposited in region i having a volume V;. Then the dose in :
-rads to n such regions is ::
.
.
Timo TMB :
DN = 1.6 x 10-8
The proportion of marrow in each bone of the skeleton has been given by Mechanic."
Using average values for this proportion, fi, and assuming that the marrow in each region
receives the average dose received by that region, the marrow dose is
.
.
-
1
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1
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-
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.
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DN = 1.6x 10-8
i=1
in
V
The proportions, fi, are skull 0.2, spine 0.5, leg bones 0.4, arm bones 0:3, rib 0.4,
and pelvis 0.45. . :
-
Skin. The so-called skin of the phanton was constructed to give the dose at the
surface. This region is a layer about 0.2--сm thick just inside the surface of the phantom.
:
sunt
.
For a point to be located in skin, it must be in one of the following six subregions:
1. z ? 93.8
2. 70 << < 93.8
(21
ile * (*)*21
3. z ? 69.8
.
:
4.0 < z < 69.8
... 5. z 5-79.8
6. -79.8 czso .
(1990) * (o me (2015: 7)?
The total 'volume of i-in is 2,677 cm
Spleen. The spleen is defined by the ellipsoid
and has a volume of 175.9 cm.
Testes. The left testis, an ellipsoid, is given by
Iz + 2.3
1:3
1.5
The volume of both testes is 37.57 cm°.
.
.
:
.
4
3
.-14.
To
Thymus. The thymus is formed by the ellipsoid
1x +
VI
(10:21+ ( the app = 72 = 40.5)° si
and has a volume of 25. 13 cm?
Thyroid. The lobes of the thyroid lie between two concentric cylinders and
.
are formed by a cutting surface. The inequalities for this organ are
: x + (y+63< (2.272
x2 + (y+6)22 (132
y + 6 So
70 sz s 75
where
26
I for
0
<
z
7
2
fy+ 6) Ixı° 22 (2? + (+0%) 12 :
:1 = 247-2) (2 - 70) + 1 for O $2•70 s .
T = 242712) 62 +70) + 2 (7-1 for < 2-10 ss.
The volume is 19.89 cm?
(11+(2*2(*psi
< 2 - 70
< 5.
Uterus. The uterus is an ellipsoid cut by a plane and is given by
1.5
.
-
- 15 -
y
= -4.5.
It has a volume of 66. 27 cm3.
A computer code has been written which takes a point (x, y, z) and applies
the tests for each organ sequentially. For points distributed uniformly in the entire
phantom, a Control Data 1604 computer using this code can classify the points as to
their organ location at an average rate of about 10,000 per minute.
II. A Monte-Carlo Method
A Monte-Carlo-type method of estimating dose was used. This method requires
that the history of a photon be mathematically determined by selecting interaction sites
and types of interactions in an unbiased manner. Through probabilistic rules, the energy
deposition of the photon at an interaction site is recorded. After a large number of such
simulated photon histəries have been calculated, the average energy deposition per photon
in a region is then estimated and the dose per photon may be calculated. This code is
similar to the one used by Ellett, Callahan, and Brownell, "") but the phantom used here
is different. The gamma-ray-attenuation coefficients for the medium were taken from
Grodstein. (11)
After specifying the location of the source region, photons are randomly selected
uniformly in that region. Then the direction of flight for each photon is selected randomly.
.: The flight distance to the first interaction site is determined randomly using the cross section
of the medium at the energy of the photon. After selecting a new flight direction emanating
from this interaction site probabilistically from the Klein-Nishina distribution, the energy
deposition at this site can be determined. The process of photon flight is now repeated
: ..::
F
.
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but with a decreased energy. Lat n-l, n, and n + 1 be consecutive interaction
sites for a photon. The marhematical photon is characterized by eight independent
quantities-, Y, and z, the coordinates of the present interaction site; a and b, the
direction cosines specifying the direction of flight to the next interaction site; L, the
length of the photon's flight path to the next interaction site; E, the energy of the
photon during its flight; and W, the weight of the photon during its flight. The weight
of a mathematical photon takes on all values from zero to one. It is set equal to one
for a photon just started from the source and is reduced after each interaction. This
fictitious quantity, the weight of a photon, is introduced to obtain better statistics
for a given number of source photons in an absorbing media. Suppose a photon, Pm-1 .
= P(xn-Jo Yn-1, 2n-10 On-ndo bm-le Lin-1, En-lo Wn-1), is in flight between points
n-1 and n. One now desires to know the energy deposition at point n and the location
of the point n + 1 which may be found if we find Pn and use it in conjunction with Pin-1-
The coordinates Xne Yn, and zmay be found by applying algebraic geometry using
Xn-10 Yn-11 2n-10 On-lo bajo and In-1. The new direction of flight, an and bene
is determined by using E-, and the Klein-Nishina gamma, photon-scattering distribution.
The new energy E, is calculated from the angle of scatter which involves On-1, boule
can, and b. Length Ln is calculated as follows:
.. 4 In N
where o (E) is the attenuation cross section of the medium, and N is a random number
chosen uniformly on OSN s I. The weight Wn is given by
W = White
www.
W
where - (E) is the cross section for the Compton process. The energy deposition at
point n is
o
..
EA
on – "n-1
= W ,
(
EJ
(E ) .
(
EJ En-1 * OE J (En-lEnt.
(E
.
may *
OE
where o (E), (E), and opplem) are the cross sections for the photoelectric, Compton,
and pair production processes, respectively, and e is the rest mass of an electron in
energy units. The total flight history of a photon' may end in one of three ways. It may
..
:.
.
.
end by escaping from the phantom, or when its energy falls below 2 kev, or when its
weight falls below 10-5.
The uncertainty due to statistical variation from a finite sample size of source
photons may be calculated. Although there may be many regions in which dose and its
star:dard deviation are to be determined, the following account will be concerned with
only one region. :
Let E. be the energy deposited in the region on the n-th interaction of the
i-ih source photon. The total energy deposited by the i-th photon or on the i-th history
to the region will be
where m; is the nuniber of interactions occurring in the i-th history before termination
of the photon. The average energy deposited per photon in the region is merely
L
.
...
71....
1."
"
."
..
.
",
EA
..
where M source photons were begun. Let o be the standard deviation of Ē. Then
for the region
M
m
Dose and its standard deviation will be proportional
û where W is the
mass of the region.
.
:
Other than the obvious inaccuracies that the shape of the phantom only roughly
approximates the shape of the human body and that the phantom remains in a fixed
standing position and is in free space from which no backscatter occurs, there is one
restriction that should be emphasized. This phantom is homogeneous throughout. There
is no low density area for the lungs, nor is there a high density and modified cross sectional
area for bone. To take these into account would irivolve a rewriting of the entire code
and the use of different cross sections for these regions. These complex regions probably
would increase the running time considerably. For gamma energies above 0.2 Mev, the
cross sections for bone are like those for tissue within several percent. Below 0.2 Mev,
bone has a much larger photoelectric cross section than that of soft tissue, and interpre-
tation of results for these low-energy x- or gamma photons must be made with care.
:
.
.
.
..
Le
-
..
*
III. Gamma Dose to Organs
a. Whole Body Source
i A source of gamma photons uniformly distributed in the phantom was
programmed for
Toim a the computer. The first objective was to estimate the fraction of the
emitted energy that would be absorbed in the phantom. Determination of dose to
individual organs will be given later. Photons were given an initial energy E and
the energy they imparted in the phantom was recorded. This procedure was followed
for seven different initial energies-0.02, 0.05, 0.2, 0.5, 1.0, 2.0, and 4.0 Mev.
There were 1000 photons generated at each energy. .
The fractional energy absorption by the total body, which is defined as the
: ratio of the energy emitted per photon to the average energy absorbed by the total body
per photon, was determined from the Monte Carlo data. These results are given in Fig. :
3. One standard deviation for our data points is less than 1.6% of the mean. An inter-
polating curve passing through the data points permits the estimation of the fractional
'energy absorption at other energies. A large number of gamma-emitting radionuclides
produce gamma photons with energies in the range 0.1 to 1 Mev, and for such photons
the total body fraction absorption is about 35%. At higher energies, the mean free path
is larger, permitting a larger percentage of such photons to escape from the phantom and
resulting in a lower fractional absorption. Toward lower photon energies, the photo-
electric cross section rises steeply, producing an increasing fractional absorption which
reaches about 90% at 0.02 Mev.
...i.
.
.
1
)
:11
:
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.
•
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-."
1:
- 20 -
Also shown in Fig. 3 are the Monte Carlo results of Ellett, Callahan,
and Brownell(12) for a source uniformly distributed in an ellipsoid. Although their
phantom was an ellipsoid, its mass was nearly, the same as the mass of the phantom used
here, and the fractional absorptions are very similar to those predicted in this paper.
The upper curve in Fig. 3 gives the fractional energy absorption predicted from the
ICRP first-collision formula. In deriving this formula, three major assumptions were :
made. First, the organ or body is assumed to be spherical. Second, the entire organ
or body burden is located at the center of the sphere. Third, a first-collision-dose
calculation is then effected to obtain the formula giving the fractional energy absorption
AF - 16-
os)!
where
is the radius of the sphere (effective radius)
He is the total gamma cross section at E.
Os is the Compton scattering cross section at E...
It is evident from Fig. 3 that the ICRP formula gives a conservative estimate
of the fractional absorption since the Monte Carlo results are seen to be about 55% of
method
those of the ICRP, at intermediate gamma energies.
With the source aga in uniformly distributed in the phantom, dose to 22 organs
was determined. To obtain estimates of dose' to individual organs with, at most, 10%
statistics required the generation of a larger number of source photons than had been
"
.
.
generated in the first case. This was done for initial photon energies of 0.05, 0.2,
...
.
:
.
:
0.5, and 1.0 Mey. The number of source photons produced at each energy was 20,000;
30,000; 30,000; and 40,000 photons, respectively.
These results are presented graphically in Figs. 4-7 to permit interpolation.
The source is distributed uniformly in the entire phantom, and the dose to various organs
in rads/photon emitted by the source is given on the ordinate. The bars on the Monte-
Carlo-data points represent one standard deviation on either side of the mean as estimated
from the Monte Carlo calculation. When no bars are given, one sigma is less than 2%.
Organs located near the center of the phantom, such as the uterus and ovaries,
receive a dose of about 1.5 times that of the total body. Most of the organs, however,
receive a dose of 1.2 to 1.4 times that of the total body. Of the phantom's organs,
the brain receives the lowest dose, 0.45 times that of the total body. This is followed
1
closely by skin with 0.55 times the body average.
Even with 40,000 initial photons, some organs do not receive a sufficient
'.
number of photon collisions to determine the dose received to within 10%. This may
be due to the small size of the organ or to its distance from many source photons. An
alternative to producing more source photons is to ircrease the volume in which dose is
.
.
estimared. This latter procedure was followed. When the standard deviation of dose
exceeded 10%, the dose in the arbitrary region(s) (Fig. 1). encompassing the organ was
taken as the best available :zstimate of dose received by that organ. When this procedure . .
was necessary, these dose estimates shown in the graphs bear the name of the organ followed
by the word "region."
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.
.
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.
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.- 22 -
The doses received by the group of organs listed in Fig. 7 varied little from
each other. Rather than give the doses to each organ individually, the doses received
by these organs will lie in the range between the dashed curves in Fig. 7.
It is possible to examine the doses received by the organs for very low-energy
photons analytically, bypassing the Monte Carlo procedure. At low photon energies,
the total cross section is composed almost entirely of that contributed by the photoelectric
effect. In addition, the numerical value of this cross section becomes very large,
resulting in a small range of the gamma photons before absorption.
If there is a home yeneous medium, infinite in extent, containing a source
uniformly distributed throughout which is emitting gamma photons isotropically of energy
E. Mev at the rate of No per unit time per unit volume, then under steady-state conditions
the energy emitted per unit time per unit volume will be equal to the energy absorbed per
unit time per unit volume. The dose rate in rads per unit time in any region is then
:
D= No B 1.6x10-6 months to = 1.6x 10-8 Ng€
where p is the density of the medium in g/cmº. Suppose now that instead of an infinite
medium, there is a finite volume of mass W, grams. Also, suppose that the mean range
of the photon is small compared to the dimensions of the volume so that the result discussed
above applies far from the surfaces in the interior with only a small error. If the source
produces photons homogeneously distributed in this medium at the rate of n photons per
unit time, then the normalized dose in rads/photon for any interior volume which is far
from the boundary of the phantom as compared with the mean free path of the photon is
..:- 23 -
MP4
D - $ - 1.04 1018 Nose 1.6* 108
=
1.6
In the case of a gamma source in the total body, the dose to interior organs should
asymptotically approach
D. (rads/photon) = 2.28 x 10-13 Ę. (Mev)
as the mean free path approaches zero. Át 0.01 Mev and below, the mean free path.
of photons in tissue is less than 1/4 cm, and this formula should yield a more reliable
result than could be obtained by Monte Carlo even with large photon sample sizes.
.. . The above does not apply to organs located near the surface. Even in this:
case, however, one may obtain information as to the surface dose by examining a special
case. Suppose that a medium, infinite in extent, is cut by a plcne and one-half of the
medium is removed. The dose rate at the newly formed surface will be one-half of the
equilibrium dose rate in the infinite media by sym netry. The normalized dose at such ::.
a surface of a large finite volume is, therefore, . .
Des = 0.8 x 1018 W
Although the phantom has no such plane surface, the radius of curvature of the elliptical
cylinder of the trunk is large compared to the mean free path of low-energy gamma
photons. An approximate surface dose for a source distributed uniformly in the total
body is, therefore,
.
Dps (rads/photor) -- !. 14 x 10-13 E. (Mev)
E. S 0.01 Mev.
►
'
'.

;
. These limiting dose rates appear consistent with the Monte Carlo calculations
at 0.02 Mev. The organs inside the rib cage of the trunk received doses within 10% of
the predicted equilibrium dose, 4.56 x 10-15 rads/photon, while the skin of the trunk
received a dose within 10% of the equilibrium surface dose.
ko. Skeletal Source
A source of gamma photons uniformly distributed in the skeletal region of the
phantom was also simulated on the computer. This program was carried out for five
gamma energies--0.2 0.5, 1.0, 2.0, and 4.0 Mev.
The fractional energy absorption by the skeleton is given in Fig. 8. The
standard deviation of the data points is less than 2.5% of the mean. Although there
is some variation of the absorbed fraction from 0.2 to 1.0 Mev, as shown in Fig. 8,
an approx inate value of 8% could be used over this energy range with little error.
The Monte Carlo estimates given here are about a factor of two lower than those given
by the first-collision, effective radius method of the ICRP..
... In the energy range under consideration, 0.2 to 4.0 Mev, the gamma cross
sections for tissue are very similar to those for bone within several percent. Therefore,
there should be little error introduced by the use of a tissue phantom, except for the fact
that bone is a denser material than tissue.
...
The photoelectric cross section for bone rises steeply with decreasing gamma
GAS
energy, and although the skeleton is not a compact organ, gamma-ray absorption will
be essentially complete at 0.01 Mev and below since the mean free path of these photons
las
2
YT
.
.
.
.
-
.
:
- 25 -
2
.
will be less than 0.05 cm. In order to obtain a rough estimate for the fractional
.
energy absorption for photons with energies between 0.01 and 0.2 Mev, the entire
phantom was considered to be bone. The material in the entire phantom was given
the cross section for bone. With the source in bone, the fractional absorption should
.
:(
be more nearly correct for the skeleton than that obtained by using the tissue phantom.
Wit
iii.
However, these results will still be lower than the ture values by an undetermined
amount for the following reasons. Photons that remain in the skeleton of the phantom
will contribute the same amount of energy that a real photon would. However, once
a photon escapes from the phantom's skeleton, it will still find itself in a strongly
::
absorbing medium and, therefore, have a smaller probability of returning to the skeleton
than a photon would have if it escaped from skeleton into tissue. A somewhat smaller
estimate of the absorbed fraction for the skeleton is obtained, therefore, with the bone
phantom at low energies than occurs in the actual situation. With the bone phantom,
the fractional energy absorption for the skeleton was 0.81 at 0.02 Mev and ou/ at
.
05 Mev.
skeletal source and
The dose rate to other organs using the tissue phantom and for energies between
.
0.2 and 4.0 Mev is given in Figs. 9-12. The notation on these graphs is the same as
that described for the total body source. As expected, the skeleton was the organ with
the highest dose. Marrow appears to receive a slightly greater dose than the skeleton
.but not significantly so. This is because the bones which receive the higher doses happen
to contain a greater portion of the marrow. There are compensating factors which would
.-.
-
.

..tones
:- 26 -
tend to lower the marrow dose, but they are not represented in the model. Marrow
radionuci ide that localizes in bone, the marrow should not contain as great a
concentration as the bone. This is not the case with the model. Consideration of
these factors as well as the Monte Carlo results leads one to believe that the average
marrow and average skeletal gamma doses are not very different. The dose estimates
to many of the organs or regions were very similar and are not shown separately. The
doses received by organs listed in the group called range I in Fig. 12 received doses
between the lower and middle curve in the graph. Similar remarks apply to the organs
of range II.
For energies below 0.01 Mev where absorption is nearly complete, the skeleton
would receive a dose in rads per photon of about 1.6x 10 E. where E. is the initial
gamma energy in Mev. An estimate of dose to the various bones of the skeleton also
was obtained from the Monte Carlo code. The part of the skeleton receiving the highest
..
i
dose was the leg bone, while that receiving the lowest was rib. For energies between
0.2 and 4.0 Mev, the ratio of the dose in rads/photon of a skeletal part to that of the
entire skeleton was formed. These ratios are approx imately as follows:
1. Lag Bones/Skeleton a 1.4 4. Arm Bones/Skeleton ~ 0.8 ...
2. Spine/Skeleton 1.2. .. 5. Skull/Skeleton - 0:6 .
3. Pelvis/Skeleton 0.8 6. Ribs/Skeleton . 0.5
a
•
......
.
..19. --------
N.
Conclusion
It appears that a Monte Carlo method of esi imating organ doses is feasible
under certain conditions. Anatomical differences such as variation of body and
.:: organ size have been neglected. Doses have been determined to fixed organ-
similar regions of a homogeneous tissue phantom. This gives results that may be
extrapolated to many real situations. This paper has examined the dose to organs
from gamma sources located in the total body and in the skeleton, although external
as well as various other internal sources may be used in conjunction with the Monte
Carlo code and phantom.
:.
.
V. Acknowledgments
Appreciation is expressed to A. M. Craig, G. G. Warner, and R. T. Boughner
of the ORNL Mathematics Division for the programming and computer operations.
..
.
:
- 28 -
.
..
References
1. P. L. Altman and D. S. Dittmer, Growth Including Reproduction and
Morphological Development, Biological Handbook, Fed. Am. Soc. Exptl. Biol.
Washington, 1962.
2. W. M. Krogman, "Growth of Man," pp. 712-15 in Tabulae Biologicae, Vol. XX,
ed. by H. Denzer et al., Den Haag, 1941.
3. Report of ICRP Task Group on the Revision of Standard Man, In preparation.
4. R. L. Hayes and M. Brucer, Intern. J. Applied Rad. Isotopes , 111 (1965).
5. H. Gray, Anatomy of the Human Body, Lea and Febriger, Philadelphia, 1942.
6. W. J. Hamilton, Textbook of Human Anatomy, Macmillan and Co., London,
1957.
7. A. C. Eycleshymer and D. M. Schoemaker, A Cross-Section Anatomy, D.
Appleton-Century Co., New York, 1911.
8. Protection Against Neutron Radiation up to 30 Million Electron Volts, NBS
Handbook 63, U. S. Dept. of Commerce, 1957.
9. N. Mechanik,"Untersuchungen uber des Gewicht des Knochenmarkes des Merschen,"
Zeit fur'anat..u. Entwicklungagesch 79(1),(1926).
10. W. H. Ellett, A. B. Callahan, and G. L. Brownell, Brit. J. Radiol. 37(433),
45 (1964).
:
:
11. G. W. Grodstein, X-Ray Attenuation coefficients for 10 kev to 100 Mev, NBS
Circular 583, 1957; and R. T. McGinnis, Supplement to NBS Circular 583, 1959...
12: W. H. Ellett, A. B. Callahan, and G. L. Brownell, Brit. J. Radiol. 38, 541-44
.
... (1965).
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