The radiation dose equivalents to blood-forming organs (BFO's) of the astronauts at the Martian surface due to major solar flare events are calculated using the detailed body geometry of Langley and Billings. The solar flare spectra of February 1956, November 1960, and August 1972 events are employed instead of the idealized Webber form. The detailed geometry results are compared with those based on the 5-cm sphere model which was used often in the past to approximate BFO dose or dose equivalent. Larger discrepancies are found for the later two events possibly due to the lower numbers of highly penetrating protons. It is concluded that the 5-cm sphere model is not suitable for quantitative use in connection with future NASA deep-space, long-duration mission shield design studies

Nealy, John E.

Shinn, Judy L.

Wilson, John W.

English

NASA Technical Reports Server

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NASA Technical Memorandum 4178
Reliability of Equivalent Sphere
Model in Blood-Forming Organ
Dose Estimation
Judy L. Shinn, John W. Wilson,
and John E. Nealy
Langley Research Center
Hampton, Virginia
NJ SA
National Aeronautics and
Space Administration
Office of Management
Scientific and Technica,
Information Division
1990

Abstract
The radiation dose equivalents to blood-forming
organs (BFO's) of astronauts on the Martian sur-
face due to major solar flare events are calculated
using the detailed body geometry of Langley and
Billings. The solar flare spectra of February 1956,
November 1960, and August 1972 events are em-
ployed instead of the idealized Webber form. The
detailed geometry results are compared with those
based on the 5-cm sphere model, which has been used
often in the past to approximate BFO dose and dose
equivalent. Larger discrepancies are found for the
later two events possibly due to the lower numbers
of highly penetrating protons. It is concluded that
the 5-cm sphere model is not suitable for quantita-
tive use in connection with future NASA deep-space,
long-duration mission shield design studies.
Introduction
One of the challenges for the future NASA space
programs, which include lunar bases, a manned Mars
mission, and Space Station Freedom, is to provide
adequate radiation shielding to the astronauts. In
the past, the missions were not as complex and long-
durationed. The radiation exposure to the astronaut
was not critically high enough to warrant precise
risk analysis. However, for the future missions, the
astronauts not only will stay in space for extended
durations, but will also be exposed to galactic cosmic
rays (GCR's) and solar flare particles, for those
missions beyond the lower Earth orbit, without the
umbrella of the Earth's magnetic field.
The significance of improving the accuracy for
predicting the dose and dose equivalent that astro-
nauts will incur during future NASA missions has
been demonstrated in several studies (refs. 1 and 2).
For example, reference 1 indicates that an increase of
20 percent in predicted blood-forming organ (BFO)
dose equivalent due to GCR's equates to a tripling of
the required shield mass from 5 g/cm 2 to 16 g/cm 2
of water in order to satisfy the recommended (ref. 3)
annual BFO limit of 50 rem. There are large uncer-
tainties associated with the current state-of-the-art
dose estimate analysis (refs. 1, 2, and 4), and every
possible effort is needed to improve the accuracy in
order to accomplish these missions in the most eco-
nomical way without compromising the well-being of
the astronauts.
One of the customary estimation practices that
has been considered to be fairly reliable in the past
is the use of the equivalent sphere model to ob-
tain dose or dose equivalent to BFO's. Langley and
Billings (ref. 5) examined the feasibility of using a
set of dosimetry spheres to monitor real-time organ
doses received by astronauts under various space ra-
diation and vehicle conditions. They made compar-
isons between the doses calculated for the spheres
and the detailed body geometry under a range of so-
lar proton energy spectrum characteristics and also
under various vehicle radiation shielding thicknesses.
The spectra were characterized by an assumed form
due to Webber (ref. 6). The optimal radii of those
spheres with the corresponding correlation constants
that best represented the averaged organ doses un-
der those assumed conditions were determined. Al-
though a moderate error of 18 percent for the corre-
lation was found (ref. 5), one might question if the
accuracy will hold under less idealized particle spec-
tral conditions.
The purpose of this study is to reexamine the ac-
curacy of the equivalent sphere model in approximat-
ing the BFO doses for more realistic conditions. The
calculation made in a separate study (ref. 7) for the
radiation transport through the atmosphere of Mars
for the three largest solar flares observed in the last
half century is extended here to include detailed BFO
geometry. Comparisons are made for the dose equiv-
alent to the various distributed BFO's with the re-
ported (ref. 7) values based on the equivalent sphere
model.
Symbols
D()_) dose or dose equivalent at the point
)(, rad or rem
Dx (t) dose or dose equivalent at depth t for
normal proton incidence
E incident proton energy, MeV
fz(t) areal density distribution function,
1
glcm_
Po rigidity parameter, MV (megavolt)
R(t, E) dose response at depth t for protons of
energy E, rad or rem
proton/cm _
t depth from surface or areal density,
glcm 2
vector locating point within the body,
g/cm 2
¢(E) proton fluence spectrum,
cm -MeV
Calculational Methods
The Langley Research Center nucleon transport
code BRYNTRN (ref. 4) was used in reference 7
to obtain dose and dose equivalent on the surface
of Mars due to large solar flares. This transport
codewasbasedon the "straightahead"approxima-
tion,whichreducesconsiderationto one-dimensional
transport;themeritsofthisapproximationhavebeen
discussedelsewhere(refs.8 and9). An asymptotic
expansionfor thesolutionto thetransportequation
in two dimensions,subjectto boundaryconditions
givenfor an arbitrary convexregion,wasderived
(ref.10).Thefirst term of theexpansionwasfound
to beanaccurateapproximationofthedose(ref.11),
andfor thecaseof an isotropicprotonfluencespec-
trum isgivenby
]0D()_) = 47r ¢(E) R(t,E)fz(t) dt dE (1)
with
c¢ fx(t) dt = 1 (2)
where R(t, E) is the fluence-to-dose conversion factor
at the depth t for normal incidence protons on a slab,
and fx (t) is the areal density distribution function for
the point X. The quantity fx(t)dt is the fraction of
the solid angle for which the distance to the surface
from the point )_ lies between t and t + dr.
To simplify the computational task (that is, with-
out making any change to BRYNTRN code), equa-
tion (1) is rewritten as
_0 (X3
D(X) = 4r_ fz(t)Dz(t) dt (3)
with
//Dx(t) -- ¢(E)R(t,E) dE (4)
where Dz (t) is the dose (or dose equivalent) at depth
t for normal incidence protons on a slab of tis-
sue. With the areal density distribution function for
BFO's given by the detailed geometry work described
by Langley and Billings (ref, 12) and Billings and
Yucker (ref. 13), equation (3) can be calculated.
Results
The three solar flare spectra used for this study
are that of February 1956, November 1960, and Au-
gust 1972 events, while Langley and Billings (ref. 5)
used a Webber form (ref. 6) of integral spectra given
by the inverse exponential of proton magnetic rigid-
ity with a range of rigidity parameter Po from 50
to 200 MV. Figure 1 shows these three flare spectra
and the best fit to the earlier two events with the
Webber form. It can be seen that the actual spectra,
especially the high-energy range of the February i956
event, are very different from the analytical form of
Webber.
2
The average dose equivalents at the surface of
Mars due to these three solar flare events are shown in
figure 2 as a function of slab (water) thickness for the
low density Mars atmosphere model (16 g/cm 2 CO2
vertically) used in reference 7. These average dose
equivalent values are obtained by summing the direc-
tional (anisotropic) dose equivalent over the solid an-
gle (ref. 7) and are used as Dz (t) in this report. The
calculated results from equation (3) are presented in
table I for the five distributed organs. Also shown for
comparison are the average BFO and 5-cm (water)
depth dose equivalents.
It is customary (refs. 14 and 15) to represent
the average BFO exposure (dose or dose equivalent)
with the 5-cm depth exposure or exposure in a 5-cm
sphere based on the recommendation of the Space
Science Board (ref. 14). Conversely, the average BFO
dose was found to be approximately half the 5-cm
sphere dose in several analytical findings, such as
the one from Langley and Billings (ref. 5). For the
August 1972 event, the average BFO value for the
detailed geometry (see table I) is fairly close (within
10 percent) to half of the value for a 5-cm sphere.
However, the differences are larger for the other two
flares, with 30 and 41 percent for November 1960
and February 1956 spectra, respectively. This wide
discrepancy among these three events probably is due
to the fact that there are more penetrating high-
energy protons contained in the two earlier flares (see
fig. 2) and that the actual spectra are not conforming
to the simple analytical form as used by Langley and
Billings. We further note that the 5-cm sphere dose
is conservative for these three events.
Concluding Remarks
It has been found that the equivalent sphere
model of Billings and Langley is not accurate enough
for precise, quantitative estimates of body doses and
vehicle shielding requirements in connection with
future NASA mission studies. Furthermore, the
5-cm sphere dose recommended by the Space Science
Board is always an overestimate and could lead to
shielding penalties. This is based on the comparison
made with the detailed body geometry calculation
for BFO's (blood-forming organs) using actual solar
flare spectra. The 5-cm equivalent sphere model of
the BFO is shown to break down for more realistic
spectra than the simple mathematical forms used
in previous studies. It is recommended that future
works involving actual exposure estimates or shield
mass requirements be extended to include all the
body geometries, including other critical organs, such
as eyes, skin, and active BFO's.
qlL
References
1. Townsend, Lawrence W.; Wilson, John W.; and Nealy,
John E.: Preliminary Estimates of Galactic Cosmic
Ray Shielding Requirements for Manned Interplanetary
Missions. NASA TM-101516, 1988.
2. Nealy, John E.; Wilson, John W.; and Townsend,
Lawrence W.: Preliminary Analyses of Space Radiation
Protection for Lunar Base Surface Systems. SAE Tech.
Paper Ser. 891487, July 1989.
3. National Council on Radiation Protection and Mea-
surements: Guidance on Radiation Received in Space
Activities. NCRP Rep. No. 98, July 31, 1989.
4. Wilson, John W.; Townsend, Lawrence W.; Nealy,
John E.; Chun, Sang Y.; Hong, B. S.; Buck, Warren W.;
Lamkin, S. L.; Ganapol, Barry D.; Khan, Ferdous; and
Cucinotta, Francis A.: BRYNTRN: A Baryon Transport
Model. NASA TP-2887, 1989.
5. Langley, R. W.; and Billings, M. P.: A New Model for
Estimating Space Proton Dose to Body Organs. Nucl.
Technol., vol. 15, no. 1, July 1972, pp. 68-74.
6. Webber, W. R.: An Evaluation of the Radiation Hazard
Due to Solar Particle Events. D2-90469, Boeing Co., Dec.
1963.
7. Simonsen, Lisa C.; Nealy, John E.; Townsend,
Lawrence W.; and Wilson, John W.: Radiation Expo-
sure for Manned Mars Surface Missions. NASA TP-2979,
1990.
8. Alsmiller, R. G., Jr.; Irving, D. C.; and Moran, H. S.:
Validity of the Stralghtahead Aproximation in Space-
Vehicle Shielding Studies, Part II. Nuel. Sci. _ Eng.,
vol. 32, no. 1, Apr. 1968, pp. 56-61.
9. Alsmiller, R. G., Jr.; Irving, D. C.; Kinney, W. E.;
and Moran, H. S.: The Validity of the Straightahead
Approximation in Space Vehicle Shielding Studies. Second
Symposium on Protection Against Radiations in Space,
Arthur Reetz, Jr., ed., NASA SP-71, 1965, pp. 177-181.
10. Wilson, John W.; and Khandelwal, G. S.: Proton Dose
Approximation in Arbitrary Convex Geometry. Nucl.
Technol., vol. 23, no. 3, Sept. 1974, pp. 298-305.
11. Khandelwal, G. S.; and Wilson, John W.: Proton Tissue
Dose for the Blood Forming Organ in Human Geometry:
Isotropic Radiation. NASA TM X-3089, 1974.
12. Langley, R. W.; and Billings, M. P.: Methods of Space
Radiation Dose Analysis With Applications to Manned
Space Systems. Proceedings of the National Symposium
on Natural and Manmade Radiation in Space, E. A.
Warman, ed., NASA TM X-2440, 1972, pp. 108-116.
13. Billings, M. P.; and Yucker, W. R.: The Computerized
Anatomical Man (CAM) Model. NASA CR-134043, 1973.
14. Space Science Board: Radiation Protection Guides and
Constraints for Space-Mission and Vehicle-Design Stud-
ies Involving Nuclear Systems. National Academy of
Sciences National Research Council, 1970.
15. Beck, W. L.; Stokes, T. R.; and Lushbaugh, C. C.:
Dosimetry for Radiobiological Studies of the Human
Hematopoietic System. Proceedings of the National
Symposium on Natural and Manmade Radiation in
Space, E. A. Warman, ed., NASA TM X-2440, 1972,
pp. 974 981.
16. Foelsche, Trutz; Mendell, Rosalind B.; Wilson, John W.;
and Adams, Richard R.: Measured and Calculated Neu-
tron Spectra and Dose Equivalent Rates at High Altitudes;
Relevance to SST Operations and Space Research. NASA
TN D-7715, 1974.
TableI. BFODoseEquivalentsonMarsSurface
[Lowdensityatmospheremodel]
Solar
flareevent
Feb.1956
Nov.1960
Aug.1972
Arms
8.74
5.66
3.20
Legs
8.60
5.34
2.73
Dose equivalent, rem, for--
High trunk Low trunk Skull
8.32 7.98 8.91
4.95 4.32 5.75
2.42 .... I, 76 3.09
Average 5-cm sphere
BFO value (ref. 7)
8.45 9.94
5.21 7.31
2.56 4.61
4
1011 --
1010
9Q. 10 9
_o 10 8
U-
10 7
106
101
Actual (ref. 16)
.... Webber form, Po = 195 MV
,%
%
%.
%
I I I l I I l I I l I
10 2
%
%
%
%
I I I i i
E, MeV
, I
10 3
(a) February 1956 event.
Figure 1. Fluence spectra for three major solar particle events.
5
1011
1010
10 9
...,:.
_ 10 8
10 7
10 6
101
Actual
.... Webber form, Po = 124 MV
I 1 I I I I l I I I z l l _"'+ "1-,.I ! ]
10 2 10 3
E, MeV
(b) November 1960 event.
Figure 1. Continued.
6
1011 --
1010
E
C
O
a. 10 9
U.l
^1
i'-
10 8
8
l--
"l
IJ_
10 7
10 6
10 1 10 2
E, MeV
(c) August 1972 event.
Figure 1. Concluded.
I I I L I I I
10 3
7
12
10
• Aug. 72
• Nov. 60
• Feb. 56
E
t-
.> 6
r.D
OE3
4
2
I,, I
10 20
Depth, cm
Figure 2. Dose equivalent as a function of slab (water) thickness on Mars surface. (Low density atmosphere
model.)
8
Report DocumentationPage
National Aeronaul_s and
Space Admm_slr albOn
1. Report No. [ 2. Government Accession No. 3. Recipient's Catalog No.
NASA TM-4178
4. Title and Subtitle
Reliability of Equivalent Sphere Model in Blood-Forming Organ
Dose Estimation
7. Author(s)
Judy L. Shinn, John W. Wilson, and John E. Nealy
9. Performing Organization Name and Address
NASA Langley Research Center
Hampton, VA 23665-5225 11.
12, Sponsoring Agency Name and Address 13,
National Aeronautics and Space Administration
Washington, DC 20546-0001 14.
5, Report Date
April 1990
6, Performing Organization Code
8. Performing Organization Report No.
L-16733
10. Work Unit No.
199-04-16-11
Contract or Grant No.
Type of Report and Period Covered
Technical Memorandum
Sponsoring Agency Code
15. Supplementary Notes
16. Abstract
The radiation dose equivalents to blood-forming organs (BFO's) of astronauts on the Martian
surface due to major solar flare events are calculated using the detailed body geometry of Langley
and Billings. The solar flare spectra of February 1956, November 1960, and August 1972 events
are employed instead of the idealized Webber form. The detailed geometry results arc compared
with those based on the 5-cm sphere model, which has been used often in the past to approximate
BFO dose and dose equivalent. Larger discrepancies are found for the later two events possibly due
to the lower numbers of highly penetrating protons. It is concluded that the 5-cm sphere model
is not suitable for quantitative use in connection with future NASA deep-space, long-duration
mission shield design studies.
17. Key Words (Suggested by Authors(s))
Space radiation
Shielding
Organ dose
19. Security Classif. (of this report)
Unclassified 20. Security Classif. (of this page)Unclassified
18. Distribution Statement
Unclassified--Unlimited
Subject Category 93
21. No, of Pages ] 22. Price
9 [ A02
NASA FORM 1626 OCT 86
For sale by the National Technical Information Service, Springfield, Virginia 22161-2171
NASA-Langley, 19°o'0



Reliability of equivalent sphere model in blood-forming organ dose estimation

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