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NATIONAL BUREAU OF STANDARDS - 1963
CRNE P. 3648
Cont. 66100/- -15/
CESTO ES
MAY 1 8 1967
MASTER
conseil

HO
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DISTRIBUTION OF DOSE AND DOSE EQUIVALENT IN AN ANTHROPOMORPHIC PHANTOM
RESULTING FROM BROAD-BEAM SOURCES OF MONOENERGETIC NEUTRONS*
W. S. Snyder, J. A. Auxier, M. D. Brown, T. D. Jones,
Health Physics Division
and
Mathematics Division
Oak Ridge National Laboratory
Oak Ridge, Tennessee
LEGAL NOTICE
This report was prepared as an account of Government apcarored work. Neither the United
Su '96, por the Commission, nor any person acting on behalf of the Commission:
A. Makes may warranty or ropresentation, expressed or implied, with respect to the accu-
racy, completac., or usefulness of the information contained in this report, or that the use
pothod, or procon disclosed in this roport may not intringo
privately owned rights; or
B. Aukumos any liabilities with respect to the use of, or for damages rouwuing from the
use of any information, apparatus, method, or procesu disclosed in this report,
As used in the above, "person acting on behall of the Commission" includes way on-
ployee or contractor of the Commission, or emplo; e of such contractor, to the extent that
such employee or contractor of the Commission, or employee of such contractor prepares,
disseminates, or provides access to, any information pursuant to his employment or contract
with the Commission, or his employment with such contractor,
**Research sponsored by the U. $. Atomic Energy Commission under contract,
with Union Carbide Corporation. .
DISORIBUTION OF THIS, DOCUMENT IS UNLIMITED
ART
DISTRIBUTION OF DOSE AND DOSE EQUIVALENT IN AN ANTHROPOMORPHIC PHANTOM
RESULTING FROM BROAD-BEAM SOURCES OF MONOENERGETIC NEUTRONS
W. S. Snyder, J. A. Auxier, M. D. Brown,
T. D. Jones, and R. T. Boughner
ABSTRACT
A Monte-Carlo-type program nas been coded for a digital
computer to estimate dose in a tissue phantom from a varichy
of neutron sources with neutron energy not exceeding 14 MeV.
The program allows for elastic and inelastic scattering as
well as for some 24 absorption interactions. The cross-sec-
tion data are taken from BNL-325 or other literature as avail-
able, and remaining gaps in the cross-section data are filled
by linear interpolation.
.
.
.
In some cases, information on the energies af. secondary
particles produced by an absorption interaction was not found
in the literature and has been calculated so that both momentum
and energy have been conserved in the interaction. The phantom
consists of a right circular cylinder with a radius of 15 cm
and a height of 60 cm and is thus a reasonable approximation
of a human torso. It is considerea to he homogeneous and codi-
poscă of H, C, N, and o in the proportions indicated for
standard man. With some rewriting of the source subroutine,
the program may be used for a wide variety of sources, but
s for a monodirectional, monoenergetic, broad, lateral
beam of neutrons are reported here. Results are obtained for
a selection of energies ranging from thermal to 14 Mev. Over
the range below 10 MeV, the maximum doses do not differ greatly
from the maximum doses in slabs as given in NBS Handbook 63.
However, a greater difference is found when the results for
slabs and cylinders are compared at depths well below the irradi-
ated surface. The variation of dose along a' diameter perpendicular
to the beam is found here and may be as much as a factor of 3 in ..
some cases. In addition to giving dose in each of 150 volume
elements of the phantom,. the partition of these doses in each of
12 intervals of LET is obtained. Thus the quality of the radia-
tion and the magnitude of the dose are provided for any desired
portion of the phantom.
!
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.
k ironim matiem
o
!Liter Shimmer animali ammestu
----...-.e
...
-
2.
When the human body 1. irradiated unilaterally by neutrons, the
resulting dose within the body generally varies appreciably in magnitude
and in quality at different depths below the irradiated surface. Bilateral
or isotropic sources produce more nearly constant patterns of dose, but
dose cquivalent in different regions of the body. Only at neutroa energies
of hundreds of Mov or more will the dose pattern be approximately constant i
within the body. ' Thun for neutrons of energy not exceeding 14 Mev--and this
is the practical limit of the fission spectrum--neutron dose within the
ocay can seldom, if ever, be adequately characterized by a single number.
any interpretation of neutron dose in terms of biological effects probably
wid heed to take into account not merely a single value (for example, the
maximum dose, or the midline dose), but will more likely need to consider
tie general pattern of dose within the body. The remainder of this time
16 intended to illustrate this thesis by presenting quantitative results of
recent studies of neutron dose in an anthropomorphic phantom. These studies
have been the joint work of staff in the Health Physics Division, and have had
extensive cooperation from the staff of the Mathematics Division, and the ·
Neutron Physics Division of ORNL .
The basic program used in these studies 18 of straightforward, Monte
Carlo type which, for the most part, follows the basic physical processes
quite closely. The cross sections used for elastic and for inelastic scattere
ing have been developed largely by the Neutron Pysics Division and are in
......
.
..
-3-
general use at ORNL. In addition, cross sections for 17 nuclear interactione
have been programmed and used in the calculation. These include elestic
neutron interactions of H, C, N, and o, inelastic interactions of C, N, and
0, and n-a, nop, and n-t reactions with N and 0. \*!.
. There are many gaps in some of the measured cross sections, and these
have been filled in largely by smoothly connecting the measured values. For
example, the more important interactions with oxygen are probably those of
the n-Go interaction (ground state) which shows the peaks in the region below
8 Mev and the n-oy reaction which dominates all of these processes at 14 Mev.
In fact, the cross section of this n-ay interaction is about 12% of the total
oxygen cross section at 14 Mev. These interactions are also of special
importance because of the high let values at which the dose from these a
particles is deposited. Similar cross section data were used for the other
irteractions. . . .
The energies and cross sections zor these nuclear interactions were
worked out by M. D. Prown of the țhiversity of Tennessee Physics Department
ariv. of the ORNI Health Physics Division. Some compromises with physical
reality were necessary to keep within the capacity of the computer--an TBM-360,
Modei 75. Thus only an average energy was used for the alpha particles, .
neutrons, protons, tritons, and reccil's produced by these muclear interactions
and by the inelastic scattering processes. This average energy was computed
so that both momentum and energy were conserved for the interactions. The
formula' used for this everage energy is shown as follows:

"mismo, para
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an-
to....l--
--
-
-
.
E2 M M EL MO + E (Mg - M)
(Mo + Mo). Ma + Me
where
in = mass of incident, particle,
Me. = mass of reaction product with energy ER,
No = mass of reaction product with energy Es = E
+ Q - Es,
Q * Q value for reaction,
Ey * energy of incident particle,
En = average energy of reaction product with mass Mg.
Figure 1 shows the linear energy transfer, or LET, of the various
charged particles considered in this calculation. As you are aware, the
bioiogical effectiveness of the dose is thought to be influencer! by the
Let at which the dose has been deposited, and quality factors which
depend on LET have been recomaended by ICRP and NCRP (15) to convert dose in
ras to dose equivalent in rem. Thus it is of some interest to know not
merely the dose in rad but also what fraction of the dose was delivered in
various ranges of LET so that the dose equivalent can be obtained. . It is
easy to see that if a charged particle, say, a proton, is produced with
energy E, the energy absorbed with LET less than a value I, is given by
A E = Min(E, ,) + Max(0, E - bad
-5-
- -
.
.
.
.
R
:.
*
-
-
-----
where a, and by are the proton energies at which the proton LET equals In
That is, if we consider the line on the figure where LET = I, and if this
line crosses the proton curve at proton energies a, and bi, then the formula
gives the total energy deposited below a; and above bi, i.e., where LET is
less than I
Using this device, the fraction of dose deposited in 12 intervals of
LET was estimated for each volume element where dose was recorded. Many
of these intervals and quality factors are those directly recommended by ICRP.
and NCRP,-5) but we did add some additional intervals in order to obtain
a better idea of the distribution of dose with LET, and the quality factor
was linearly interpolated for these additional intervals from the recom-
mended values.
Figure 2 shows the subdivision of the phantom into subregions for
evaluation of dose. All cases calculated to date have been for broad beams
of monoenergetic neutrons entering along the bisector of the angle of region
27. The phantom is a right circular cylinder of dimensions nearly those of
the torso of a husky male, i.e., height 60 cm, radius 15 cm. The composi-
tion is homogeneous, consisting only of the four elements H, C, N, and o
ir. the proportions typical of soft tissue with a density of 1. The energy
carried by charged particles produced by an interaction within one of these
subregions is assumed to be absorbed in that région. Photons are produced &s
a result of inelastic scattering or as a result of some capture processes,
arou a sample of such photons are run on a separate program to estimate the
dose due to these photons.
iniwhes.*********
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vita
n
the
with
ter
los até 7 dit bet
r ding to one's withipaimarno
B
-6.
Figure 3 shows the distribution of dose with LET for neutrons of
energies 2.5 Mev, 5 Mev, and 14 Mev. These are for volume elements at .
the irradiated surface, at the center, and at the greatest depth within
the phantom. As you see, the distributions are quite different. Figure 4
shi ws the variation in LET for neutrons of energy 1 Mev at three different
depths below the irradiated surface, namely, on the irradiated surface, near
the center, and on the far side of the phantom. It is clear that the quality
of the radiation varies greatly with distance from the irradiated surface.
Many other examples of this variation in quality could be given. Since LET
may plausibly be one of the parameters influencing the biological response,
it seems clear that data of the type just shown are desirable if a close
correlation of dose within a large animal and biological effects is attempted.
One of the reasons for undertaking these studies is to provide data of this
kind.
Figure 5 shows the dosimetric pattern within the central layer of the
piantom for irradiation by neutrons of 14 Mev and 1 Mev. The quality factors'
have been used here as described earlier to obtain dose in rem. Of course,
the dose in rad also is available. Figure 6 shows the similar data for
neutrons of energies 0.5 and 2.5 Mev.
The next three figures present the unsmoothed data in depth for neutrons
of energies 2.5 Mev, 0.5 Mev and 0.1 kev. From these you can judge the general
10 000
siatistical accuracy we obtain with yoga neutron case histories as well as
the surprisingly little variation we see from one tier to another. Figure 10
shows the trend of dose down the center of the phantom for neutron energies
.
10 kov, 5 Mev, and 14 Movi The dose from capture gamma rays and the dose
from beutron interactions are shown separately. Of courro, cach polat
represents an average dose over a wedge-shapod rerion u sbown earl.x.
Hera, again, the quality of the radiation will vary with both depth and .
neutron energy and so does the magnitude of the dose.
We turn now to a very practical situation, that of the doteruinatia
of the dose pattern within the body for a practical situation. In 1958
a criticality incident occurred at one of the Oak Ridge plants, and five
men were exposed to levels above 100 rad. Doses ranged from 236 to 365 rad,
estimated by Hurst, Ritchie, and Emerson. Actually these values munt be'
considered as the maximum doses within the bodies of these individuals.
Less than a year later, & criticality incident occurred' at Vinca in
Yugoslavia, and cssentially the same group of health physicists estimated
doses to these individuals. The 81x individuals with high doses were
estimated to have received from 207 to 436 rad. The range of doses in the .
case of the Yugoslavs included the range of doses estimated for the Oak Ridge:
cases and extended upward beyond the Oak Ridge doses by about 20%, which does
not seem to be a very marked increase in dose. Yet many have felt that the
one might expect from ..
symptons exhibited by the Yugoslavs were more severe than the difference in
dose. might Andijonte Perhaps this feeling 18'in part a reflection of the
fact that one of the Yugoslave died. We cannot resolve this question at
present, but we can, perhaps, use it to illustrate something of the com-
mest 3
plexity of the problem. Theffigures show the distribution of dose with IET
in these two cuses at depths of 2.5. an, 15 on, 'and 28.5 cm.' Then distribetione
.
1
...
have been obtained by using only the noutron spoctrı from the two sources as
estimated and measured by the town of houlth physicists who "mockod up" each
of the sources. Thus dose from photons incident on the body or pharton
must be added to the doses shown in the lowost interval of LET, 1.o., 0 to 3.5
kov/u. Except for this low 3st Interval of LeT, the distribution would not
be changed due to this neglect of a part of the dose. However, our
calculations use this spectrum only us a broad-beun, nonodi noctional source
and thus do not take into account the effect of novenonts of the exposed
individuals. Thus these results sho'sld be considered us qual:Itativo evidence,
and there might be some averaging of dose in different portions of the body
due to the novonents of the individual. Nevertheless, it is apparent that
the radiation quality is markedly different in the two cases and the duta
on the dose lovels within the body indicate that in the Oak Ridge casos
Some portions of tha trunk received much less dose than the portion where
tha naxinum occurred. This naxinn would correspond to the estimated dose.
You can see too how different the dose pattern would be if the individual
had turned and had received half the exposure fror opposite sides of his
·body, or the same dose was received in terns of Na activation of the blood
but resulted from an isotropic source rather when it was an unidirectimal source.
This merely illustratos again that a single rubor doos not serve to
represent adequatoly the dose pattern within the body and that if any
close evaluation of biological offects is undertaken, more information is
needed.
The last figure gives the dose to a mouss-sized phantom and to a
rat-sized phantom exposed to a beam of noutrons with the mass of the rat
being about 8 times the mass of the mouse. The distributions oź dose with
LET in the two cases are shown for neutrons of three different energies.
The dose is estimated for the volume olement nourest the front surface, and
the LET distribution of the dose is shown us a cumulative so that the value
on the right represents the total doso. In all cases the nouso received more
-9-
than the rat, and yet, intuitively, we feel the buildup must be greater
in the rat than in the mouse. However, the computer gives the higher dose
to the mouse. The computer 18 not wrong, and neither is our intuition; in
changing the phantom size, we have also changed the dimensions of the volume
elements. Thus the dose for the rat is averaged over a depth which is about
twice as great as in the case of the mouse. At first one might feel that
this is a poor way to present data, but after some thought about the matter
we decided it was better to keep the volume elements in a l'ixed relationship
to the whole phantom. In ceparing biological effects seen in mouse, rat,
and man, it may well be a poor way of looking at dose to compare only surface
doses or only doses at & depth of 1 cm in each animal. A certain dose at one
centimeter below the irradiated surface may have quite different significance
for a mouse, a rat, and a man merely because of the different anatomical
structures one finds at such a depth in the three cases. Perhaps, as a
first approximation, one would do better to compare doses, rot at the same
depth, but at corresponding depths at which the organs of concern are Cound.
This scaling of the volume elements in proportion to the phantom is a first
crude approximation to this and is mentioned here to emphasize that in extrapolati
animal data on biological effects to infer results concerning human expos we we
must consider the dose patterns within each of the bodies--and it may very well be
quite different in magnitude and in quality in comparing a man with a mouse !
But our thesis remains that for a really adequate assessmert o exposure and
for interpretation in terms of hazard or biological effects, ɔne needs the
entire dose pattern found within the body. We hope these studies will
-10-
. illustrate this thesis and that the much more extensive body of data we are
producing will provide a more adequate basis for assessment and interpretation
in terms of the biological effects. ..
.

-
-
-
REFERENCES
1. F. Aj zenberg-Selove and T. Lauritsen, Nucl. Phys. 11, 1 (1959).
. 2.' 'F. Everling et al., 1960 Nuclear Data Tables, Parts 1 and 2, Nuclear
Data Project, NAS-NRC (Edited by K. Way) (1961).
3. D. J. Hughes and R. B. Schwartz, Neutron Cross Sections, Brookhaven
National Laboratory Report BNL-325, 2nd Edition (1958).
4. D. J. Hughes, 'B. A. Magurno, and M. K. Brussel, Neutron Cross Sections,
Brookhaven National Laboratory Report BNL-325, 2nd Edition, Supplement 1
(1960).
S. J. R. Stehn et al., Neutron Cross Sections, Brookhaven National
Laboratory Report BNL-325, 2nd Edition, Supplement 2, Volume 1 (1964).
6. J. R. Smith; Phys. Rev. 95, 730 (1954).
7. A. B. Lillie, Phys. Rev. 87, 716 (1952).
8. W. J. McDonald et al., Nucl. Phys. 75, 353 (1966). .
9. V. V. Nefedov et al., Soviet Progress in Neutron Physics (Edited by
P. A. Krupchitskii), p. 241-247 (1961). .
10. R. A. AL-Kital and R. A. Peck, Jr., Phys. Rev. 130, 1500 (1963).
V. E. Scherrer, R. B. Theus, and W. R. Faust, Phys. Rev. 21, 1476
(1953).
12. J. P. Conner, lys. Rev. 89, 712 (1953).
13. J. B. Singletary and D. E. Wood, Phys. Rev. 114, 1595 (1959).'
M. D. Goldberg, V. M. Way, and J. R./Stehn, Angular Distribution
in Neutron-Induced Reactions, Brookhaven National Laboratory
Report BNL-400, 2nd Edition, Volume 1 (1962). .
15. NBS Handbook No. 59, Permissible Dose from External Sources of
. Ionizing Radiation (September 24, 1954).
16. G. S. Hurst, R. H. Ritchie, and L. C. Emerson, Health Phys. 2,
121-133 (1959).
17. G. S. Hurst et al., Health Phys. 5, 179-202 (1961).
Figure 1. Stopping Power for Recoil Ions in Soft Tissue as a
Function of Particle Energy,
Figure 2. Cylindrical Phantom Used in Dose and Dose-Equivalent
Calculations.
Figure 3. Dose as a function of LET for Penetration Depths of
1.5 cm, 13.5 cm, 28.5 cm, and Neutron Suurce Energies
of 2.5 MeV, 5 MeV, and 14 Mev.
Figure 4. Fraction of Dose from 1 MeV Incident Neutrons as a
Function of LET.
Figures 5 and 6. Dose-Equivalent Distributions in the Middle Tier
of the Cylindrical Phantom for Neutron Source
Energies of 0.025 ev, 1 kev, 1 MeV, and 14 Mey,
Figures 7, 8, and 9. D. and D, as a function of Penetration Depth
for Source Energies of 0.1 kev, 0,5 MeV, and
2.5 MeV.
.
Figure 10. Dose as a function of Penetration Depth in a Cylindrical
Phantom.
Figures 11, 12, and 13. Percent Dose as a function of LET for
Penetration Depths of 1.5 cm, 15 cm, and
28.5 cm.
Figure 14. Dose as a function of LET in a Mouse- and Rat-Sized
Phantom for Source Energies of 0.1 MeV, 0.5 MeV, and
2.5 MeV--Volume Element 17.
ORNL DWG 66-8656
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NUMBERING (I) OF VOLUME
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LAYER I VOLUME ELEMENTS
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BEAM
LAYER 2 VOLUME ELEMENTS
NUMBERED BY 1 + 20
60 cm
NEUTRON
BEAM
LAYER 3 VOLUME ELEMENTS
NUMBERED BY i + 40
NEUIRON
BEAM
LAYER 4 VOLUME ELEMENTS
NUMBERED BY 1+ 20
LAYER 5 VOLUME ELEMENTS
NUMBERED BY
NUMBERING OF VOLUME ELEMENTS IN THE CYLINDRICAL PHANTOM
• ORNL-DWG 66-11428
DOSE AS A FUNCTION OF LET
.
.
1.5 cm PENETRATION
DEPTH
2.5 MeV
- 5 Mev
..... 14 Mev
OFF SCALE
13.5 cm PENETRATION
DEPTH
- 2.5 MeV
--- 5 MeV
. ..... 14 MeV
OFF SCALE
28.5 cm PENETRATION
DEPTH
- 2.5 MeV
-- 5 MeV
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| OFF SCALE
DOSE (rad in /cm)/(kovin)
. Fig. 3
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A FRACTION OF DOSE FROM I MEV INCIDENT
NEUTRONS AS A FUNCTION OF LET
28.5 cm
13.5 cm
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-
1.5cm
1.5 cm
28.5 cm
13.5 cm
0.001
0.0001
10
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30 40 50 60 70 80 90 100
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SOURCE
Fig. 6
ORNL DWG 66 -11386
DOSE EQUIVALENT ( 10° rem /n/cm',


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19.59
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32.54 31.49
34.58
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Fig. 9
RAD/A /cm
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15
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.
ORNL-OWG. 66-11354
ABSORBED DOSE AS A FUNCTION OF PENETRATION DEPTH IN A CYLINDRICAL
PHANTOM (30 cm x 60 cm)
10
n (14 MeV)
n (5 MeV)
DOSE (RAD/n/cm2)
y (14 MeV)
Fig.ro

y (5 MeV)
y (10 keV)
n (10 keV)
10
:
4
6
&
To
12
14
16 18
20 2² 24 26 28 30
PENETRATIO
ORNL-DWG. 66-3008
PERCENT ABSORBED DOSE AS A FUNCTION OF LET
100
90
1.5 cm
OF
.
PENETRATION DEPTH
HPRR
----- Y-12
-•- YUGOSLAV
% ABSORBED DOSE
teg.nl

2
20
30 40
50
60 80 100
70 90
200
5
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LET (ke VIN)
Website
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.
..
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ORNL- DVIG. 66-3009
PERCENT ABSORBED DOSE AS A FUNCTION OF LET.
100
901
15 cm
PENETRATION DEPTH
HPRR
.
Y-12
YUGOSLAV
805
Fig. 12

% ABSORBED DOSE
2
4T
4 16 18110
5 . 7 9
20
30 40 60 80 100
50 70 90
200
o LET (ke VIH)
ORNL-DWG. 66-3007
PERCENT ABSORBED DOSE AS A FUNCTION OF LET
100
90
:
80
TTTTT
PENETRATION DEPTH 28.5 cm
HPRR
----- Y-12
--- YUGOSLAV
Fig. 13

% ABSORBED DOSE
.
:
go
40
304
201
! 618110
5 7 9
20
30 40 60 80 100
50 70 90
200
-
LET (ke VIND
Zig 14 .
UNCLASSIFIED
ORNL OWO. 63-4822

DOSE IN MOUSE AND RAT - BOX 17 VERSUS LET
MOUSE
- RAT
4X10
2.5 MEV
2.5 MEV
DOSE (RADS/N/CM',
2 X 18
0.5 MEV
0.5 MEV
0.1 MEV
COTS
0.1 MEV
1010
3.57 75
62.5
35T
50
200
25
75
82.
51
100
LET ( KEVIN).
FIG. 3

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intis. T.2
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