Photon specific absorbed fractions calculated in adult voxel phantoms with the EGS4 and the MCNP4 Monte Carlo codes

Abstract

Dose coefficients for intakes of radionuclides published by the International Commission on Radiological Protection (ICRP) are based on specific absorbed fractions (SAFs), which have been calculated in the mathematical MIRD phantoms. The organs of the mathematical phantoms, defined by geometrical bodies, like circular and elliptical cylinders, ellipsoids, cones, tori, etc., serve as rather simple representations of real human body organs. Tomographic or voxel phantoms are based on digital images recorded from scanning of real persons by computed tomography (CT) or magnetic resonance imaging (MRI). Compared to the mathematical MIRD phantoms, voxel phantoms are true to nature representations of the human body. The replacement of the MIRD phantoms by voxel phantoms proposed by the ICRP raises the question about the changes to be expected for the SAFs, and consequently also for the dose coefficients. In order to investigate the dosimetric consequences of this replacement, SAFs have been calculated in the recently introduced MAX (Male Adult voXel) and FAXht (Female Adult voXel) head+trunk phantoms for photon energies between 10 keV and 4 MeV. For this purpose the phantoms have been connected to the EGS4 as well as to the MCNP4 code, which at present are probably the most used general-purpose Monte Carlo codes. Thereby it was possible to assess the impact on the SAFs, if different radiation transport methods are used. The mathematical MIRD phantoms have also been connected to the EGS4 code, and their elemental compositions of body tissues were replaced by those used in the voxel phantoms. In this manner it was possible to compare the SAFs of the MIRD phantoms on the one hand and the MAX and FAX phantom on the other hand as a function of the geometrical anatomy only, i.e. the volume, the shape and the position of organs at risk.

Full text

Photon specific absorbed fractions calculated in adult voxel phantoms with the EGS4 and the
MCNP4 Monte Carlo codes
R. Kramer
1
, H. J. Khoury
1
, H. Yoriyaz
2
and F. R. A. Lima
3
1
Departamento de Energia Nuclear, UFPE, Recife, PE, Brazil.
E-mail: rkramer@uol.com.br
2
Instituto de Pesquisas Energéticas e Nucleares, CNEN, São Paulo, Brazil.
3
Centro Regional de Ciências Nucleares, CNEN, Recife, PE, Brazil.
Abstract. Dose coefficients for intakes of radionuclides published by the International Commission on
Radiological Protection (ICRP) are based on specific absorbed fractions (SAFs), which have been
calculated in the mathematical MIRD phantoms. The organs of the mathematical phantoms, defined
by geometrical bodies, like circular and elliptical cylinders, ellipsoids, cones, tori, etc., serve as rather
simple representations of real human body organs. Tomographic or voxel phantoms are based on
digital images recorded from scanning of real persons by computed tomography (CT) or magnetic
resonance imaging (MRI). Compared to the mathematical MIRD phantoms, voxel phantoms are true
to nature representations of the human body. The replacement of the MIRD phantoms by voxel
phantoms proposed by the ICRP raises the question about the changes to be expected for the SAFs,
and consequently also for the dose coefficients. In order to investigate the dosimetric consequences of
this replacement, SAFs have been calculated in the recently introduced MAX (Male Adult voXel) and
FAXht (Female Adult voXel) head+trunk phantoms for photon energies between 10 keV and 4 MeV.
For this purpose the phantoms have been connected to the EGS4 as well as to the MCNP4 code, which
at present are probably the most used general-purpose Monte Carlo codes. Thereby it was possible to
assess the impact on the SAFs, if different radiation transport methods are used. The mathematical
MIRD phantoms have also been connected to the EGS4 code, and their elemental compositions of
body tissues were replaced by those used in the voxel phantoms. In this manner it was possible to
compare the SAFs of the MIRD phantoms on the one hand and the MAX and FAX phantom on the
other hand as a function of the geometrical anatomy only, i.e. the volume, the shape and the position
of organs at risk.
1. Introduction
For more than three decades equivalent or absorbed dose estimates from incorporated radionuclides
were based on specific absorbed fractions (SAFs), which have been calculated by Monte Carlo
methods in so-called ‘MIRD phantoms’, a serie of adult and pediatric mathematical representations of
human bodies. In mathematical human phantoms size and form of the body and its organs are
described by mathematical expressions representing combinations and intersections of planes, circular
and elliptical cylinders, spheres, cones, tori, etc.
Fisher and Snyder [1, 2] introduced this type of phantom for an adult male which also contains ovaries
and a uterus. During the compilation of the Report of the Task Group on Reference Man [3] the
phantom has been further developed by Snyder et al [4, 5]. Since then it is known as “MIRD-5
phantom” (Medical Internal Radiation Dose Committee (MIRD) Pamphlet No.5).
The MIRD-5 phantom has been the basis for various derivations representing infants and children of
various ages [6], gender-specific phantoms called ADAM and EVA [7] and a pregnant female adult
phantom [8]. Body height and weight as well as the organ masses of these MIRD-type phantoms are in
accordance with the first set of Reference Man data [3]. Although being rather crude representations of
the human body, at the time of their introduction the MIRD-type phantoms represented a significant
progress for the assessment of equivalent or absorbed dose to radiosensitive organs of the human body
in the areas of radiation protection and nuclear medicine.
In the meantime progress took place in the development of clock-speed and storage capacity of
computers, and as a consequence the production and processing of images has been pushed to levels
hardly imagined before. These new image capabilities have recently been used to introduce

tomographic or voxel-based phantoms, which overcome the crude representation of the human body
by mathematical phantoms. Voxel phantoms are based on digital images recorded from scanning of
real persons by computed tomography (CT) or magnetic resonance imaging (MRI). Each image
consists of a matrix of pixels (picture elements), whose number depends on the resolution chosen
during scanning. A consecutive set of such images can be considered as a three-dimensional matrix
made of voxels (volume pixels), where each voxel belongs to a specific organ or tissue. Compared to
the mathematical phantoms, voxel phantoms are true to nature representations of the human body.
Based on data published by Zubal [9] on a website of the YALE university, Kramer et al [10]
developed the MAX (Male Adult voXel) phantom, which corresponds anatomically to the
specifications of the revised Reference Man Report [11], and in a paper presented at this congress the
FAXht (Female Adult voXel) head+trunk phantom [12] will be described, which corresponds to the
anatomical specifications for the Reference Adult Female defined in ICRP89 [11].
This paper will present SAFs for various radiosensitive organs and tissues for the mathematical
ADAM and EVA phantoms as well as for the MAX and FAXht phantoms when the liver represents
the source organ. The data have been taken from an ongoing investigation which involves many other
source and target organs and tissues,and which was motivated by the intention of the ICRP [13] to
replace the MIRD-type phantoms by voxel phantoms.
2. Materials and methods
Compared to the exposure models used 25-30 years ago to calculate SAFs, the change intended by the
ICRP would not only imply replacing the mathematical by voxel phantoms, but also updating the
tissue compositions, and substituting the ALGAM-based Monte Carlo code for photons by modern
codes which allow for secondary particle transport, Rayleigh scattering, etc.
In order to show the dosimetric consequences of these changes separately, the following exposure
models were used:
a) ADEV/EGS4: The mathematical ADAM and EVA phantoms connected to the EGS4 Monte
Carlo code with the original tissue composition from Kramer et al [7].
b) ADEV44/EGS4: The mathematical ADAM and EVA phantoms connected to the EGS4 Monte
Carlo code with new tissue compositions taken from ICRU44 [14], with a homogeneous mixture in all
skeletal voxels based on ICRP70 [15], and a homogeneous mixture of adipose and muscle in all
unspecified regions of the body.
c) MFHOM/EGS4: The MAX and the FAXht phantoms connected to the EGS4 Monte Carlo code
with ICRU44 tissue compositions, and with the same homogeneous mixture in all skeletal voxels, and
for adipose and muscle in all unspecified regions of the body used for b).
d) MAX/FAXht-EGS4: The MAX and the FAXht phantoms connected to the EGS4 Monte Carlo
code with ICRU44 tissue compositions, heterogeneous skeleton and separately segmented regions for
adipose and muscle.
e) MAX/MCNP4: The MAX phantom connected to the MCNP4 Monte Carlo code with ICRU44
tissue compositions, heterogeneous skeleton and separately segmented regions for adipose and muscle.
Detailed descriptions of the phantoms used for this study can be found in Kramer et al [7, 10, 16, 28],
and in Lima et al [17].
3. Results
3.1 Specific absorbed fractions
Figures 1 to 3 present SAFs for four organs and tissues with the greatest tissue weighting factors based
on the concept of effective dose [18], that is the gonads, the lungs, the colon, and the stomach for
photon emitters homogeneously distributed in the liver. Figures 1a, 2a, and 3a show data for reference
adult males, while Figures 1b, 2b, and 3b present the same quantities for reference adult females.

1,0E-08
1,0E-07
1,0E-06
1,0E-05
1,0E-04
1,0E-03
0,01 0 ,1 1 10
Photon Energy (M eV)
Specific absorbed fraction (1/g)
ADAM
ADAM44
MAXHOM
MAX
So urce o rgan: Liv er
Liver
Lungs
Teste s
FIG 1a. Male specific absorbed fractions
1,0E-08
1,0E-07
1,0E-06
1,0E-05
1,0E-04
1,0E-03
0,01 0 ,1 1 10
Photon Energy (MeV)
Specific absorbed fraction (1/g)
EVA
EVA44
FAXHOM
FAXht
So urce o rgan: Liver
Liver
Lungs
Ovaries
FIG 1b. Female specific absorbed fractions
FIG 2a. Male specific absorbed fractions
1,0E-08
1,0E-07
1,0E-06
1,0E-05
1,0E-04
0,01 0,1 1 10
Photon Energy (MeV)
Specific absorbed fraction (1/g)
ADAM
ADAM44
MAXHOM
MAX
Source or gan: Liver
Colon

1.0E-09
1.0E-08
1.0E-07
1.0E-06
1.0E-05
1.0E-04
0.01 0.1 1 10
Photon Energy (MeV )
Specific absorbed fraction (1/g)
EVA
EVA44
FAXHOM
FAXht
Source or gan: Liver
Colon
FIG 2b. Female specific absorbed fractions
1.0E-08
1.0E-07
1.0E-06
1.0E-05
1.0E-04
0.01 0.1 1 10
Photon Energy (MeV)
Specific absorbed fraction (1/g)
ADAM
ADAM44
MAXHOM
MAX
Source organ: Liver
Stomach
FIG 3a. Male specific absorbed fractions

1.0E-07
1.0E-06
1.0E-05
1.0E-04
0.01 0.1 1 10
Photon Energy (MeV)
Specific absorbed fraction (1/g)
EVA
EVA44
FAXHOM
FAXht
Source organ: Liver
Stomach
FIG 3b. Female specific absorbed fractions
3.1.1 Tissue composition (a – b)
According to the ratios between the mass-energy absorption coefficients of the old and new tissue
compositions shown in Figure 4, the equivalent dose to soft-tissue organs, the bones, and the skin are
expected to increase as a result of this change, while the equivalent dose to the lungs would slightly
decrease or remain unchanged. The unspecified regions in the body would see a decrease of equivalent
dose when soft-tissue is replaced by a homogeneous mixture of adipose and muscle (ADIMUS). The
data of Figure 4 were compiled for an investigation on external exposures to photons [16], but they
can also serve as an indicator for what is to be expected in the actual study for internal emitters.
0.9
0.95
1
1.05
1.1
0 20 40 60 80 100 120 140 160 180 200
Photon Energy (keV)
MEA(ADEV44) / MEA(ADEV)
SOFT
LUNGS
SKELETON
ADIMUS/SOFT-TISSUE
SKIN
FIG 4. Ratios of mass-energy absorption coefficients
Indeed, most of the SAFs for ADAM44 and EVA44 presented in Figures 1 – 3 show a small increase
compared to the SAFs for ADAM and EVA.

3.1.2 Anatomy (b – c)
The introduction of voxel phantoms based on patient data, which usually have shorter inter-organ
distances than the mathematical phantoms, leads generally to an increase of the SAFs (Figures 1 to 3),
except for the colon and the ovaries of the FAXht phantom. The colon of the FAXht phantom is in a
greater distance from the liver compared to the MAX phantom. The same argument holds for the
ovaries compared to their position in the EVA phantom. Because of poor statistics it is difficult to
identify a clear trend for the testes. Contrary to the findings for external exposures to photons [16], the
introduction of voxel phantoms of real persons often increases the exposure to radiosensitive organs
and tissues, at least to the gonads, the lungs, the colon, and the stomach as target organs when the liver
is the source organ. Future evaluation for other combinations of source and target organs will show if
this can be considered as a general aspect for internal exposures.
3.1.3 Heterogeneous skeleton and separately segmented adipose and muscle (c – d)
The introduction of a heterogeneous distribution of skeletal tissues among the bone voxels, and the
separately segmented regions for adipose and muscle leads sometimes to a small decrease of the SAFs,
or cause no change at all. This substitution actually changes to some extent the “shielding
environment” for some of the radiosensitive organs and tissues, but for the combination of source and
target organs given no dramatic changes were expected, which is confirmed by the MAX and FAXht
SAFs of Figures 1 – 3.
3.1.4 Monte Carlo code (d – e)
Figure 5 shows SAFs calculated with the MAX phantom which was connected to the EGS4 as well as
to the MCNP4 Monte Carlo codes. The average differences found between the SAFs are 3.7% for the
liver, 11.3% for the lungs, 4.4% for the red bone marrow (RBM), and 12.9% for the testes. The small
size and the relatively distant location from the source organ explain the deviation between the two
testes SAFs. The agreement between the liver and the RBM SAFs for the two Monte Carlo codes is
satisfactory. The SAFs for the lungs show relatively great differences for energies below 50 keV. The
explanation for these differences has still to be investigated.
1.00E-08
1.00E-07
1.00E-06
1.00E-05
1.00E-04
1.00E-03
0.01 0.1 1 10
Photon Energy (MeV)
Specific Absorbed Fraction (1/g)
MCNP4
EGS4
Testes
Source organ: Liver
Liver
Lungs
RBM
FIG 5. MAX specific absorbed fractions for EGS4 and MCNP4

3.2 Effective dose
Figure 6 shows effective doses for the ADAM and EVA phantoms for the old (ADEV) and the new
(ADEV44) tissue compositions, and for the MAX and the FAXht phantoms with homogeneous
skeletons and ADIMUS tissue (MHOM/FHOM), and with heterogeneously distributed skeletal tissues
and separately segmented regions for adipose and muscle (MAX/FAXht). The curves reflect the
findings which have already been discussed in the previous section for the SAFs of the radiosensitive
organs and tissues.
On the logarithmic scale of Figure 6 it is difficult to estimate the percentage difference between two
quantities. Figure 7 therefore presents effective dose ratios between ADEV44 and ADEV, which
reflects the replacement of the tissue compositions, between MHOM/FHOM and ADEV44 which
represents the change of the anatomy, and between MAX/FAXht and ADEV which quantifies the
replacement of the exposure model with all its components, except for the Monte Carlo code.
1.0E-14
1.0E-13
1.0E-12
1.0E-11
0.01 0.1 1 10
Photon Energy (MeV )
Effective dose per emitted particle (mGy)
ADEV
ADEV44
MHOM/FHOM
MAX/FAXht
So urce o rgan:
Liver
FIG 6. Effective dose for mathematical and voxel phantoms
0
0.5
1
1.5
2
0.01 0.1 1 10
Photon Energy (MeV)
Effective dose ratio
ADEV44/ADEV
MFHOM /ADEV 44
MAX-FAXht/ADEV
Source organ: Liver
FIG 7. Effective dose ratios

The change of the tissue compositions leads to a small decrease of the effective dose below 50 keV,
and to a small increase between 50 keV and 500 keV. Above 20 keV these changes never exceed 5%,
and above 500 keV they are almost undetectable. The introduction of a realistic human anatomy leads
to an increase of the effective dose by a factor of 2 below 50 keV. Above 50 keV this increase is ca.
70%.
The complete replacement of the exposure model causes a ca. 70% increase of the effective dose over
the whole range of energies. Changes caused by the replacement of the Monte Carlo code have to be
added, which would be ca. 8% for the source-target combination considered here.
Comparison with other investigations
Jones [19] compared SAFs calculated for the NORMAN voxel phantom [20] with corresponding data
for the MIRD5 phantoms [21].
The results showed sometimes significant differences between the SAFs of the two exposure models.
Jones’ calculations demonstrated that a change of the tissue composition had only little effect on the
results, and he concluded that especially different inter-organ distances in the two phantoms were the
main cause of the large discrepancies in the SAF values. Differences in organ and tissues masses could
not have been the reason, because both phantoms had organ and tissue masses which agreed fairly
well with the reference masses of ICRP23 [3].
Significant discrepancies between MIRD5 and voxel SAFs have also been reported by Petoussi-Henss
et al [22], by Smith et al [23], by Yoriyaz et al [24], by Smith et al [25], by Stabin et al [26] and by
Zankl et al [27], confirming that the voxel phantom SAFs are often significantly greater than the
MIRD5 SAFs, and also confirming that such large discrepancies typically do not appear for the source
organ itself (see liver SAF in Figures 1a and 1b), thereby also indicating that the distance between the
source and a target organ is the dominant factor.
4. Conclusions
The dosimetric consequences of the replacement of a MIRD-type by a voxel-based exposure model for
the calculation of SAFs were investigated separately with respect to changes of the tissue
compositions, the phantom anatomy, the distribution of skeletal tissues and adipose and muscle, and
the Monte Carlo code. The results presented SAFs for four important radiosensitive organs and tissues
caused by photon emitters homogeneously distributed in the liver. For these source-target
combinations the results have shown, that for the effective dose the percentage difference caused by
the change of the tissue compositions remains generally below 5% for photon energies between 50
keV and 4 MeV. The dominant dosimetric impact on the SAFs, and on the effective dose comes from
the change of the human anatomy, which, as shown for the source-target combinations considered
here, can cause an increase of the effective dose by a factor of two. The complete replacement of the
MIRD5-based by a voxel-based exposure model with all its components, including also the
replacement of the Monte Carlo code would lead to an increase of the effective dose of ca. 70-80% for
the range of energies and the source-target organ combination considered.
Similar calculations for other source organs will produce the data necessary in order to evaluate the
complete dosimetric impact to be expected on the SAFS and the effective dose when voxel phantoms
will supersede the MIRD-type phantoms in radiation protection.
5. Acknowledgement
The authors would like to thank to CNPq and FACEPE for the financial support to this study.
6. References
1. Fisher, H. L. and Snyder W. S., Distribution of dose in the body from a source of gamma rays
distributed uniformly in an organ, Report No. ORNL-4168, Oak Ridge National Laboratory, Oak
Ridge, Tenn., USA, 1967.

2. Fisher, H. L. and Snyder W.S., Distribution of dose in the body from a source of gamma rays
distributed uniformly in an organ, In: Proceedings of the First International Congress on Radiation
Protection, Pergamon Press, Oxford, pp 1473-1486, 1968.
3. ICRP - Report of the Task Group on Reference Man. ICRP Publication 23, International
Commission on Radiological Protection, Pergamon Press, Oxford, 1975.
4. Snyder W. S., Ford M. R., Warner G. G., Watson G. G., Revision of MIRD Pamphlet No. 5
Entitled “Estimates of absorbed fractions for monoenergetic photon sources uniformly distributed
in various organs of a heterogeneous phantom”. ORNL-4979, Oak Ridge National Laboratory,
Oak Ridge, Tenn., 1974.
5. Snyder W. S., Ford M. R. and Warner G. G., Estimates of absorbed fractions for monoenergetic
photon sources uniformly distributed in various organs of a heterogeneous phantom, MIRD
Pamphlet No.5, revised, Society of Nuclear Medicine, New York N. Y, 1978.
6. Cristy M., Mathematical phantoms representing children at various ages for use in estimates of
internal dose, Report ORNL/NUREG/TM-367, Oak Ridge National Laboratory, Oak Ridge,
Tenn., USA, 1980.
7. Kramer R., Zankl M., Williams G., Drexler G., The Calculation of Dose from External Photon
Exposures Using Reference Human Phantoms and Monte Carlo Methods. Part I: The Male
(ADAM) and Female (EVA) Adult Mathematical Phantoms. GSF-Report S-885.Reprint July
1999.Institut für Strahlenschutz, GSF-Forschungszentrum für Umwelt und Gesundheit,
Neuherberg-München, 1982.
8. Stabin M., Watson E., Cristy M., Ryman J., Eckerman K., Davis J., Marshall D. and Gehlen K.,
Mathematical models and specific absorbed fractions of photon energy in the nonpregnant adult
female and at the end of each trimester of pregnancy, Report No. ORNL/TM-12907, Oak Ridge
National Laboratory, Oak Ridge, Tenn., USA, 1995.
9. Zubal I. G. The YALE voxel phantoms, http://noodle.med.yale.edu/phantom, 2000.
10. Kramer R., Vieira J. W., Khoury H. J., Lima F. R. A. and Fuelle D., All About Max: A Male
Adult Voxel Phantom for Monte Carlo Calculations in Radiation Protection Dosimetry, Phys.
Med. Biol., 48, No.10, 1239-1262, 2003.
11. ICRP 89, Basic Anatomical and Physiological Data for Use in Radiological Protection: Reference
Values, International Commission on Radiological Protection, Pergamon Press, Oxford, 2003.
12. Loureiro E. C. M., Kramer R., Vieira J. W., Khoury H. J., Lima F. R. A. and Hoff G.,
Construction of the FAXht (Female Adult voXel) head+trunk phantom from CT images of
patients for applications in radiation protection, submitted to IRPA11, 2004.
13. ICRP - 2001 Annual Report of the International Commission on Radiological Protection
http://www.icrp.org, 2002.
14. ICRU - Tissue substitutes in radiation dosimetry and measurement ICRU Report 44.International
Commission on Radiation Units and Measurements, Bethesda, MD, 1989.
15. ICRP - Basic Anatomical and Physiological Data for use in Radiological Protection: The Skeleton
ICRP Publication 70.International Commission on Radiological Protection, Pergamon Press,
Oxford, 1995.
16. Kramer R., Vieira J. W., Khoury H. J. and Lima F. R. A., MAX meets ADAM: A dosimetric
comparison between a voxel-based and a mathematical model for external exposure to photons,
Phys. Med. Biol. (accepted for publication), 2004.
17. Lima F. R. A., Kramer R., Vieira J. W., Khoury H. J., Loureiro E. C. M. and Hoff G., Effective
dose conversion coefficients calculated with gender-specific, adult voxel phantoms for
radiographic examinations common in diagnostic radiology, submitted to IRPA11, 2004.
18. ICRP - 1990 Recommendations of the International Commission on Radiological Protection.
ICRP Publication 60 International Commission on Radiological Protection, Pergamon Press,
Oxford, 1991.
19. Jones D. G., A realistic Anthropomorphic Phantom for Calculating Specific Absorbed Fractions of
Energy from Internal Gamma Emitters Radiation Protection Dosimetry Vol.79, Nos.1-4, pp. 411-
414, 1998.
20. Dimbylow P. J. (1995) The development of realistic voxel phantoms for electromagnetic field
dosimetry, In: Proceedings of an International Workshop on Voxel Phantom Development held at
the National Radiological Protection Board, Chilton, UK, 6-7 July, 1995.

21. Cristy M. and Eckerman K. F., Specific Absorbed Fractions of Energy at Various Ages from
Internal Photon Sources ORNL/TM-8381 Vol. 1-7,Oak Ridge National Laboratory, Oak Ridge,
Tenn., USA, 1987.
22. Petoussi-Henss N. and Zankl M., Voxel Anthropomorphic Models as a Tool for Internal
Dosimetry Rad. Prot. Dos. Vol.79, Nos 1-4, pp. 415-418, 1998.
23. Smith T., Petoussi-Henss N. and Zankl M., Comparison of internal radiation doses estimated by
MIRD and voxel techniques for a “family” of phantoms Eur. J Nucl Med 27:1387-1398, 2000.
24. Yoriyaz H., Santos A., Stabin M. G. and Cabezas R., Absorbed fractions in a voxel-Based
phantom calculated with the MCNP-4B code Med Phys 27(7)1555-1562, 2000.
25. Smith T., Phipps A. W., Petoussi-Henss N. and Zankl M., Impact on Internal Doses of Photon
SAFs Derived with the GSF Adult Male Voxel Phantom Health Physics, Vol. 80 No.5, 2001.
26. Stabin M. G. and Yoriyaz H., Photon Specific Absorbed Fractions Calculated in the Trunk of an
Adult Male Voxel-Based Phantom Health Physics 82(1): 21-44, 2002.
27. Zankl M., Petoussi-Henss N., Fill U., Regulla D., The Application of Voxel Phantoms to the
Internal Dosimetry of Radionuclides, Rad. Prot. Dosim. Vol. 105, No 1-4, 539-548, 2003.
28. Kramer R., Vieira J. W., Khoury H. J., Loureiro E. C. M., Lima F. R. A. and Hoff G., Comparison
of effective dose between tomographic and mathematical phantoms for external exposures to
photons, submitted to IRPA 11, 2004.