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European Journal of Applied Sciences – Vol. 12, No. 1
Publication Date: February 25, 2024
DOI:10.14738/aivp.121.16228
Sardari, D., Bashiri, B., Zehtabvar, M., Hashemi, S., & Anvariazar, L. (2024). Gamma Ray Energy Absorption Buildup Factor
Computation for Human Tissues in Energy Range of Medical Radionuclides Up to 10 Mean Free Paths. European Journal of Applied
Sciences, Vol - 12(1). 77-95.
Services for Science and Education – United Kingdom
Gamma Ray Energy Absorption Buildup Factor Computation for
Human Tissues in Energy Range of Medical Radionuclides Up to
10 Mean Free Paths
Dariush Sardari
ORCID: 0000-0002-9400-8243
Department of Medical Radiation Engineering, Science and Research Branch,
Islamic Azad University, Tehran, Iran
Bashir Bashiri
Department of Chemistry and Biotechnology, Tallinn University of Technology,
Tallinn, Estonia
Mehrnaz Zehtabvar
Department of Chemistry and Biotechnology, Tallinn University of Technology,
Tallinn, Estonia
Shahnaz Hashemi
Department of Medical Radiation Engineering, Science and Research Branch,
Islamic Azad University, Tehran, Iran
Leila Anvariazar
Department of Medical Radiation Engineering, Science and Research Branch,
Islamic Azad University, Tehran, Iran
ABSTRACT
Gamma ray energy absorption buildup factors (EABF) have been meticulously
computed for a comprehensive set of 16 human tissues, encompassing breast, lung,
kidney, pancreas, liver, eye lens, thyroid, brain, ovary, heart, large intestine, blood,
skin, spleen, muscle, and cortical bone. These calculations encompass photon
energies inherent to prevalent radionuclides, spanning from 0.021 to 1.25 MeV,
while delving into penetration depths reaching up to 10 mean free paths (mfp), all
accomplished via the utilization of MCNPX2.6. The outcomes underscore the pivotal
role of chemical composition of tissue in determining EABF, shedding light on the
substantial influence this factor wields. Particularly noteworthy is the observation
that cortical bone distinctly exhibits significantly lower EABF values compared to
the other tissues under investigation. Leveraging the EABF values furnished in this
study offers a powerful means of regulating dose levels for both therapeutic and
diagnostic applications, contributing to the precise administration of radiation- based medical interventions.
Keywords: Buildup factors; Human tissues; MCNP; Gamma-ray; Photon dose
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European Journal of Applied Sciences (EJAS) Vol. 12, Issue 1, February-2024
INTRODUCTION
The interaction between photons and attenuating materials results in the division of their
energy spectrum into two primary components: uncollided and collided photons. The
uncollided category encompasses photons that have undergone no interaction with the
attenuating material. In contrast, the collided category involves photons that have experienced
single or multiple scatterings, along with secondary photons like X-rays resulting from
Bremsstrahlung radiation or gamma rays arising from electron-positron annihilation.
According to the defined terms, the buildup factor (BF) is the ratio of the total response
(combining uncollided and collided) to the uncollided response[1]
.
Given that the BF is a crucial parameter in radiation shielding tasks, numerous studies have
been conducted to estimate this parameter in various media, including soft tissue[2–4], blood,
bone, brain, breast, eye lens, lung, adipose tissue, muscle, and ovary[1,5,6]. Additionally, BF
estimation has been carried out for certain hydrocarbons acting as neutron moderators[7]and
for specific natural rocks[8,9]
.
The BF holds critical significance not only in shield design but also in dosimetry and
radiotherapy treatment plans[10]. In medical applications, photons (Gamma and X-rays)
predominantly find use in radiotherapy and diagnostic procedures, exposing various body
tissues to photon radiation. Consequently, the BF of photons becomes a pivotal parameter in
predicting the distribution and absorption of flux and dose within biological molecules, along
with other photon interaction parameters such as mass attenuation coefficients and effective
atomic numbers in biological materials[4,5,11,12]. This understanding is crucial for assessing
potential health risks and ensuring radiation doses remain within safe limits. Moreover, the
buildup of photons within tissues can lead to variations in radiation dose distribution,
emphasizing the need for accurate BF data[10,13]. Thus, the acquisition of information
concerning the interactions of these radiations with the body stands as an indispensable
dataset for radiation safety, precise dose estimation, and reliable diagnostic and therapeutic
outcomes.
Given the scarcity of prior evidence regarding the estimation of EABF for human organs and
tissues within the energy range of these medical sources, it is noteworthy to mention that
Manohara et al.[5] have undertaken the calculation of gamma ray EABF for human organs and
tissues relevant to radiotherapy and diagnostics using the GP-fitting method. However, it's
important to note that they have not provided exact numerical values, but rather presented
graphs exclusively. In the light of this context, the present article endeavors to address this
knowledge gap comprehensively. The overarching objective of this study is to meticulously
compute the gamma ray energy absorption buildup factor (EABF) within the energy spectrum
of medical radioisotopes, encompassing diverse human organs, and extending the analysis to
encompass penetration depths of up to 10 mean free paths (mfp). This effort aims to deliver
valuable quantitative insights where previous data might have been limited to graphical
representations.
Various methods have been developed and employed to calculate the BF, including Monte Carlo
simulation[6,14–16], G-P fitting approximation[5,6,17–21], experimental techniques[20,22,23], invariant
embedding[24], and the moment method[25]. Monte Carlo N-Particle (MCNP) simulations have
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Sardari, D., Bashiri, B., Zehtabvar, M., Hashemi, S., & Anvariazar, L. (2024). Gamma Ray Energy Absorption Buildup Factor Computation for Human
Tissues in Energy Range of Medical Radionuclides Up to 10 Mean Free Paths. European Journal of Applied Sciences, Vol - 12(1). 77-95.
URL: http://dx.doi.org/10.14738/aivp.121.16228
been demonstrated to possess reliable capabilities in estimating the buildup factor across a
broad energy range and different density materials (such as water[16], hydrocarbons[7]), and
high-density materials like tungsten[15]. Therefore, the calculations are conducted using the
MCNPX 2.6 code. In contrast to the extensive study conducted by Yazdani Darki et al.[26], which
focused on the estimation of mass attenuation coefficients for 16 human organs across a
spectrum of 10 medical radioisotopes, our research stands out for its targeted strength in
exploring the gamma ray EABF. While their work provided valuable insights into mass
attenuation, our study takes a focused approach to gamma ray EABF for a diverse set of 16
human tissues. This deliberate emphasis on EABF not only complements but also significantly
strengthens the existing body of knowledge, providing a more detailed and comprehensive
understanding of radiation interactions crucial for medical applications.
The structure of the paper is organized as follows: Section 2 extensively and transparently
elaborates on the materials and methods, outlining the human organs under investigation, the
energy range, and simulation geometry. Section 3 is dedicated to the validation of the
simulation, followed by the presentation and discussion of results in Section 4.
MATERIALS AND METHODS
The geometry of simulation involves concentric spheres containing the materials of interest. A
point isotropic sources is positioned at the center of the sphere. The radius of each sphere
extends up to 10 mean free paths (mfp). To determine the average surface flux, the *F2 Tally
card is employed on the surface of each sphere. The flux of uncollided particles is separated
using FT and FU cards. Both photons and electrons are transported simultaneously in particle
mode p,e. Both electron and photon modes were incorporated into this model, designated as
mode p,e. To exclude coherent (Rayleigh) scattering and focus radiation interactions solely on
Pair production, Compton (incoherent) scattering, and the photoelectric effect, the Phys:p card
was implemented. Additionally, to eliminate secondary electrons generated as a result of these
interactions, the Phys:e card was employed[27]
.
The mean free path (mfp) of photons in the corresponding medium is the reciprocal of the total
linear attenuation coefficient (μ), as defined by equation 1. The total mass attenuation
coefficients are obtained from XCOM data and then converted to total attenuation using
equation 2.
mfp =
1
μ
(1)
μ = ρ. μm (2)
BF is calculated using the following correlation:
BF =
RUncollided+RCollided
RUncollided
= 1 +
RCollided
RUncollided
(3)
The term "RCollided" denotes photons that have encountered interactions (such as Compton
scattering) prior to reaching the tallying surface, while "RUncollided" signifies photons that
successfully reached the tallying surface without any interaction. Table 1 offers details on the
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composition and density of human tissues[26,28], while Table 2 presents the mass attenuation
coefficients of human tissues at the gamma energies of interest, sourced from the NIST XCOM
database[26]
.
Table 1: Composition and density of human tissues under study[26]
Materials Density
(g/cm3
)
Weight fraction (%)
H C N O Na P S Cl K Ca Fe Mg I
Breast 1.02 0.106 0.332 0.03 0.527 0.001 0.001 0.002 0.001 - - - - -
Lung 1.05 0.103 0.105 0.031 0.749 0.002 0.002 0.003 0.003 0.002 - - - -
Kidney 1.05 0.103 0.132 0.03 0.724 0.002 0.002 0.002 0.002 0.002 0.001 - - -
Pancreas 1.04 0.106 0.169 0.022 0.694 0.002 0.002 0.001 0.002 0.002 0.001 - - -
Liver 1.06 0.102 0.139 0.03 0.716 0.002 0.003 0.003 0.002 0.003 - - - -
Eye lens 1.07 0.096 0.195 0.057 0.646 0.001 0.001 0.003 0.001 0.002 0.001 - - -
Thyroid 1.05 0.104 0.119 0.024 0.746 0.002 0.001 0.001 0.002 0.001 - - - 0.001
Brain 1.04 0.107 0.145 0.022 0.712 0.002 0.004 0.002 0.003 0.003 - - - -
Ovary 1.05 0.105 0.093 0.024 0.768 0.002 0.002 0.002 0.002 0.002 - - - -
Heart 1.06 0.103 0.121 0.032 0.734 0.001 0.001 0.002 0.003 0.002 - 0.001 - -
Large intestine 1.03 0.106 0.115 0.022 0.751 0.001 0.001 0.001 0.002 0.001 - - - -
Blood 1.06 0.102 0.110 0.033 0.745 0.001 0.001 0.002 0.003 0.002 - 0.001 - -
Skin 1.09 0.100 0.204 0.042 0.645 0.002 0.001 0.002 0.003 0.001 - - - -
Spleen 1.06 0.103 0.113 0.032 0.741 0.001 0.003 0.002 0.002 0.003 - - - -
Muscle (skeletal) 1.05 0.102 0.143 0.034 0.710 0.001 0.002 0.003 0.001 0.004 - - - -
Cortical bone 1.95 0.034 0.165 0.042 0.435 0.001 0.103 0.003 - - 0.225 - 0.002 -
Table 2: Mass attenuation coefficient of body tissues under study[26]
Radionuclide Pd-103 I-125 Cs-131 Tc-99 m Ba-133 Ir-192 Au-198 Cs-137 Ra-226 Co-60
Mean-energy
(MeV) 0.021 0.029 0.030 0.140 0.218 0.380 0.412 0.663 0.830 1.25
Breast 0.6214 0.3561 0.3403 0.1525 0.1322 0.1077 0.1043 0.0852 0.07686 0.06287
Lung 0.74430 0.40180 0.38150 0.15260 0.13200 0.10740 0.10400 0.08498 0.07667 0.06271
Kidney 0.73430 0.39820 0.37820 0.15260 0.13200 0.10740 0.10400 0.08498 0.07667 0.06271
Pancreas 0.71630 0.39180 0.37250 0.15290 0.13230 0.10770 0.10430 0.08520 0.07687 0.06287
Liver 0.73920 0.39990 0.37980 0.15250 0.13180 0.10730 0.10390 0.08490 0.07660 0.06265
Eye lens 0.70280 0.38570 0.36680 0.15150 0.13110 0.10670 0.10330 0.08443 0.07617 0.06230
Thyroid 0.73320 0.39850 0.37860 0.15330 0.13220 0.10750 0.10410 0.08505 0.07673 0.06276
Brain 0.74150 0.40130 0.38110 0.15310 0.13240 0.10780 0.10440 0.08527 0.07694 0.06293
Ovary 0.73840 0.39970 0.37960 0.15290 0.13220 0.10760 0.10420 0.08513 0.07681 0.06283
Heart 0.75000 0.40440 0.38390 0.15260 0.13200 0.10740 0.10400 0.08498 0.07667 0.06271
Large intestine 0.70570 0.38750 0.36860 0.15290 0.13230 0.10770 0.10430 0.08523 0.07690 0.06289
Blood 0.73420 0.39790 0.37790 0.15250 0.13180 0.10730 0.10390 0.08491 0.07661 0.06266
Skin 0.68950 0.38100 0.36260 0.15200 0.13150 0.10710 0.10370 0.08475 0.07646 0.06254
Spleen 0.74250 0.40100 0.38070 0.15240 0.13180 0.10730 0.10390 0.08484 0.07655 0.06261
Muscle (skeletal) 0.73480 0.39830 0.37830 0.15250 0.13180 0.10730 0.10390 0.08491 0.07660 0.06265
Cortical bone 3.46000 1.44100 1.32000 0.15280 0.12630 0.10120 0.09784 0.07965 0.07180 0.05869
VALIDATION OF SIMULATION
To assess the credibility of the simulation model in computing BF values, the BFs were initially
computed for water and soft tissue, then compared with published data[16,27]. BF values
calculated using the MCNP code up to 10 mfp for water and soft tissue are detailed in Table 3
and 4, respectively. These tables also include previously reported BF values. Overall, the
calculated BFs exhibit substantial conformity with the published data, substantiating the
precision of our simulation. Discrepancies can be ascribed to variations in Monte Carlo models
and cross-section data libraries used.
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Sardari, D., Bashiri, B., Zehtabvar, M., Hashemi, S., & Anvariazar, L. (2024). Gamma Ray Energy Absorption Buildup Factor Computation for Human
Tissues in Energy Range of Medical Radionuclides Up to 10 Mean Free Paths. European Journal of Applied Sciences, Vol - 12(1). 77-95.
URL: http://dx.doi.org/10.14738/aivp.121.16228
Table 3: Validation of buildup factor for water and comparison with previous studies
Energy
(MeV)
EABF (this
study) a
EABF[16] EABF[27] EABF[5]
Relative
difference (%)
(b-a)/b *100
Relative
difference (%)
(c-a)/c *100
Relative
difference (%)
(d-a)/d *100
1 mfp
0.2 3.30 3.53 3.30 -- 6.60 0 --
0.5 2.53 2.61 2.57 2.47 3.25 1.55 -2.42
1 2.06 2.14 2.08 2.11 3.83 0.96 2.36
2 1.71 1.73 1.73 -- -0.20 1.15 --
2 mfp
0.2 7.41 7.44 7.45 -- 0.39 0.53 --
0.5 4.99 4.95 5.09 4.84 -0.76 1.96 -3.09
1 3.54 3.6 3.60 3.59 1.76 1.66 1.39
2 2.54 2.3 2.58 -- -10.59 1.55 --
4 mfp
0.2 22.79 25 24.10 -- 8.81 5.43 --
0.5 12.71 12.5 12.82 12.40 -1.74 0.85 -2.5
1 7.35 7.21 7.61 7.54 -2.00 3.41 2.51
2 4.37 4.75 4.58 -- 7.89 4.58 --
7 mfp
0.2 74.37 66 79.21 -- -12.69 6.11 --
0.5 33.14 31 31.00 31.97 -6.92 -6.90 -3.65
1 15.34 14.5 15.53 15.68 -5.86 1.22 2.16
2 7.89 6.36 7.74 -- -24.19 -1.93 --
10 mfp
0.2 175.67 157 201.48 -- -11.89 12.81 --
0.5 66.24 60 70.3 62.57 -10.41 5.77 -5.86
1 26.92 23 27.5 26.16 -17.06 2.10 -2.90
2 11.75 9.15 11.76 -- -28.47 0.08 --
Table 4: Validation of buildup factor for soft tissue and comparison with previous
studies
Energy (MeV) EABF (this study)
a
EABF[16] EABF[27] Relative difference (%)
(b-a)/b *100
Relative difference (%)
(c-a)/c *100
1 mfp
0.2 3.27 3.24 3.32 -0.98 1.50
0.5 2.53 2.50 2.56 -1.04 1.17
1 2.06 2.04 2.08 -0.91 0.96
2 1.71 1.70 1.73 -0.79 1.15
2 mfp
0.2 7.33 7.39 7.51 0.69 2.39
0.5 5.00 4.9 5.07 -2.11 1.38
1 3.53 3.5 3.58 -1.12 1.39
2 2.54 2.5 2.57 -1.80 1.16
4 mfp
0.2 22.69 23 24.20 1.35 6.23
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0.5 12.81 12.7 12.92 0.90 0.85
1 7.37 7.2 7.34 2.39 -0.40
2 4.37 4.5 4.60 2.80 5.00
7 mfp
0.2 72.90 80 77.18 8.87 5.54
0.5 33.27 32 29.00 -3.97 -14.72
1 15.43 14.5 15.02 -6.45 -2.72
2 7.91 7.3 7.48 -8.38 -5.74
10 mfp
0.2 178.15 183 198.01 2.65 10.02
0.5 67.14 61.1 74.24 -9.89 9.56
1 27.16 23 28.82 -18.10 5.75
2 11.80 11.1 11.36 -6.39 -3.87
RESULTS AND CONCLUSION
Tables 5 to 20 present the calculated energy absorption buildup factors (EABF) for the selected
human tissues. Each table provides EABF values corresponding to specific gamma energies of
medically relevant radionuclides, considering penetration depths up to 10 mfp.
Table 5: Gamma EABF for breast tissue
Radionuclide Energy (MeV) 1 mfp 2 mfp 4 mfp 7 mfp 10 mfp
Pd-103 0.021 1.41 1.65 2.01 2.47 2.84
I-125 0.029 1.90 2.64 3.93 5.88 7.94
Cs-131 0.030 1.97 2.79 4.26 6.64 8.90
Tc-99 m 0.140 3.55 8.18 26.03 87.43 218.62
Ba-133 0.218 3.23 7.24 22.45 71.95 176.28
Ir-192 0.380 2.75 5.75 15.93 45.04 96.85
Au-198 0.412 2.69 5.53 15.04 41.80 87.37
Cs-137 0.663 2.33 4.37 10.37 24.94 47.26
Ra-226 0.830 2.18 3.91 8.62 19.34 34.92
Co-60 1.25 1.94 3.19 6.23 12.25 20.56
Table 6: Gamma EABF for lung tissue
Radionuclide Energy (MeV) 1 mfp 2 mfp 4 mfp 7 mfp 10 mfp
Pd-103 0.021 1.32 1.50 1.75 2.07 2.28
I-125 0.029 1.73 2.27 3.15 4.44 5.55
Cs-131 0.030 1.79 2.38 3.40 4.88 6.20
Tc-99 m 0.140 3.47 7.83 23.92 75.96 184.13
Ba-133 0.218 3.19 7.03 21.15 65.66 156.52
Ir-192 0.380 2.74 5.64 15.36 42.50 90.32
Au-198 0.412 2.67 5.44 14.47 39.60 81.90
Cs-137 0.663 2.32 4.32 10.12 24.11 45.52
Ra-226 0.830 2.17 3.86 8.45 18.79 33.93
Co-60 1.25 1.93 3.16 6.14 12.06 20.17
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Ir-192 0.380 2.74 5.67 15.46 43.21 91.87
Au-198 0.412 2.68 5.47 14.65 40.17 83.27
Cs-137 0.663 2.32 4.33 10.20 24.32 45.93
Ra-226 0.830 2.17 3.87 8.49 18.94 34.26
Co-60 1.25 1.93 3.17 1.93 3.17 20.25
Table 11: Gamma EABF for thyroid tissue
Radionuclide Energy (MeV) 1 mfp 2 mfp 4 mfp 7 mfp 10 mfp
Pd-103 0.021 1.32 1.51 1.77 2.10 2.30
I-125 0.029 1.74 2.29 3.19 4.49 5.69
Cs-131 0.030 2.79 2.41 3.47 4.97 6.39
Tc-99 m 0.140 3.39 7.45 21.71 65.04 152.62
Ba-133 0.218 3.15 6.80 19.64 58.43 136.84
Ir-192 0.380 2.71 5.52 14.61 39.77 83.12
Au-198 0.412 2.65 5.32 15.41 37.10 76.19
Cs-137 0.663 2.30 4.25 9.83 23.18 43.55
Ra-226 0.830 2.16 3.81 8.23 18.22 32.77
Co-60 1.25 1.92 3.13 6.04 11.86 19.80
Table 12: Gamma BF for brain tissue
Radionuclide Energy (MeV) 1 mfp 2 mfp 4 mfp 7 mfp 10 mfp
Pd-103 0.021 1.32 1.50 1.76 2.08 2.29
I-125 0.029 1.73 2.28 3.18 4.50 5.60
Cs-131 0.030 1.79 2.40 3.44 4.93 6.30
Tc-99 m 0.140 3.48 7.84 23.87 76.34 184.47
Ba-133 0.218 3.19 7.04 21.07 65.69 157.32
Ir-192 0.380 2.74 5.64 15.34 42.51 90.27
Au-198 0.412 2.67 5.44 14.47 39.52 81.73
Cs-137 0.663 2.32 4.32 10.13 24.11 45.44
Ra-226 0.830 2.17 3.86 8.45 18.78 34.28
Co-60 1.25 1.93 3.16 6.14 12.07 20.26
Table 13: Gamma EABF for ovary tissue
Radionuclide Energy (MeV) 1 mfp 2 mfp 4 mfp 7 mfp 10 mfp
Pd-103 0.021 1.32 1.51 1.76 2.09 2.28
I-125 0.029 1.74 2.28 3.18 4.46 5.63
Cs-131 0.030 1.80 2.40 3.43 4.95 6.33
Tc-99 m 0.140 3.48 7.85 23.95 76.90 186.36
Ba-133 0.218 3.19 7.05 21.16 66.03 158.26
Ir-192 0.380 2.74 5.65 15.37 42.61 90.81
Au-198 0.412 2.67 5.44 14.56 39.70 82.25
Cs-137 0.663 2.32 4.32 10.13 24.16 45.64
Ra-226 0.830 2.17 3.87 8.46 18.83 34.00
Co-60 1.25 1.93 3.16 6.15 12.08 20.18
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Sardari, D., Bashiri, B., Zehtabvar, M., Hashemi, S., & Anvariazar, L. (2024). Gamma Ray Energy Absorption Buildup Factor Computation for Human
Tissues in Energy Range of Medical Radionuclides Up to 10 Mean Free Paths. European Journal of Applied Sciences, Vol - 12(1). 77-95.
URL: http://dx.doi.org/10.14738/aivp.121.16228
Table 14: Gamma EABF for heart tissue
Radionuclide Energy (MeV) 1 mfp 2 mfp 4 mfp 7 mfp 10 mfp
Pd-103 0.021 1.31 1.49 1.74 2.05 2.25
I-125 0.029 1.72 2.25 3.12 4.39 5.43
Cs-131 0.030 1.78 2.37 3.37 4.80 6.09
Tc-99 m 0.140 3.47 7.81 23.66 75.33 181.25
Ba-133 0.218 3.19 7.01 21.00 65.12 155.02
Ir-192 0.380 2.73 5.63 15.25 42.24 89.73
Au-198 0.412 2.67 5.43 14.46 39.40 81.52
Cs-137 0.663 2.32 4.31 10.11 24.02 45.35
Ra-226 0.830 2.17 3.86 8.43 18.74 33.85
Co-60 1.25 1.93 3.16 6.14 12.05 20.15
Table 15: Gamma EABF for large intestine tissue
Radionuclide Energy (MeV) 1 mfp 2 mfp 4 mfp 7 mfp 10 mfp
Pd-103 0.021 1.34 1.54 1.81 2.17 2.39
I-125 0.029 1.77 2.36 3.33 4.77 6.07
Cs-131 0.030 1.83 2.49 3.60 5.26 6.84
Tc-99 m 0.140 3.49 7.93 24.46 79.32 192.84
Ba-133 0.218 3.20 7.09 21.54 67.41 162.75
Ir-192 0.380 2.79 5.81 16.07 45.00 92.13
Au-198 0.412 2.68 5.46 14.63 40.19 83.40
Cs-137 0.663 2.32 4.33 10.21 24.40 46.06
Ra-226 0.830 2.17 3.87 8.49 18.95 34.29
Co-60 1.25 1.93 3.17 6.17 12.11 20.27
Table 16: Gamma EABF for blood tissue
Radionuclide Energy (MeV) 1 mfp 2 mfp 4 mfp 7 mfp 10 mfp
Pd-103 0.021 1.32 1.50 1.75 2.09 2.30
I-125 0.029 1.73 2.26 3.12 4.41 5.42
Cs-131 0.030 1.79 2.38 3.37 4.84 6.09
Tc-99 m 0.140 3.47 7.79 23.56 74.67 180.71
Ba-133 0.218 3.19 7.01 20.92 64.85 155.08
Ir-192 0.380 2.73 5.63 15.29 42.24 89.45
Au-198 0.412 2.67 5.43 14.41 39.34 81.33
Cs-137 0.663 2.32 4.31 10.09 24.01 45.39
Ra-226 0.830 2.17 3.86 8.43 18.73 33.83
Co-60 1.25 1.93 3.16 6.13 12.03 20.15
Table 17: Gamma EABF for skin tissue
Radionuclide Energy (MeV) 1 mfp 2 mfp 4 mfp 7 mfp 10 mfp
Pd-103 0.021 1.35 1.55 1.84 2.21 2.43
I-125 0.029 1.79 2.40 3.42 4.89 6.35
Cs-131 0.030 1.85 2.53 3.70 5.45 7.10
Tc-99 m 0.140 3.50 7.97 24.63 80.42 196.40
Ba-133 0.218 3.21 7.12 21.63 68.02 164.28
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Ir-192 0.380 2.74 5.68 15.60 43.60 92.74
Au-198 0.412 2.68 5.48 14.73 40.40 84.23
Cs-137 0.663 2.32 4.34 10.23 24.47 46.21
Ra-226 0.830 2.17 3.88 8.51 19.01 34.34
Co-60 1.25 1.94 3.17 6.18 12.14 20.30
Table 18: Gamma EABF for spleen tissue
Radionuclide Energy (MeV) 1 mfp 2 mfp 4 mfp 7 mfp 10 mfp
Pd-103 0.021 1.32 1.50 1.75 2.07 2.27
I-125 0.029 1.73 2.27 3.16 4.46 5.58
Cs-131 0.030 1.79 2.39 3.41 4.89 6.22
Tc-99 m 0.140 3.48 7.85 24.01 76.70 185.18
Ba-133 0.218 3.19 7.05 21.13 65.81 156.54
Ir-192 0.380 2.74 5.65 15.40 42.81 90.47
Au-198 0.412 2.68 5.45 14.52 39.83 82.06
Cs-137 0.663 2.32 4.33 10.15 24.16 45.65
Ra-226 0.830 2.17 3.87 8.46 18.86 33.89
Co-60 1.25 1.93 3.17 6.16 12.12 20.10
Table 19: Gamma EABF for Muscle tissue
Radionuclide Energy (MeV) 1 mfp 2 mfp 4 mfp 7 mfp 10 mfp
Pd-103 0.021 1.32 1.51 1.76 2.09 2.30
I-125 0.029 1.74 2.29 3.19 4.52 5.64
Cs-131 0.030 1.80 2.41 3.46 5.01 6.35
Tc-99 m 0.140 3.48 7.84 23.99 76.58 185.76
Ba-133 0.218 3.19 7.05 21.17 65.95 157.74
Ir-192 0.380 2.74 5.65 15.36 42.73 90.43
Au-198 0.412 2.67 5.44 14.55 39.67 82.21
Cs-137 0.663 2.32 4.32 10.15 24.16 45.62
Ra-226 0.830 2.17 3.86 8.45 18.81 34.01
Co-60 1.25 1.93 3.16 6.15 12.08 20.20
Table 20: Gamma EABF for cortical bone tissue
Radionuclide Energy (MeV) 1 mfp 2 mfp 4 mfp 7 mfp 10 mfp
Pd-103 0.021 1.05 1.07 1.10 1.12 1.13
I-125 0.029 1.12 1.18 1.26 1.36 1.41
Cs-131 0.030 1.14 1.20 1.29 1.40 1.45
Tc-99 m 0.140 2.70 4.75 9.93 21.62 39.10
Ba-133 0.218 2.75 5.12 11.70 27.89 55.47
Ir-192 0.380 2.51 4.64 10.74 25.56 50.97
Au-198 0.412 2.47 4.54 10.43 24.55 48.72
Cs-137 0.663 2.20 3.82 8.19 18.27 33.81
Ra-226 0.830 2.07 3.49 7.13 15.09 27.22
Co-60 1.25 1.87 2.94 5.53 10.65 17.70
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Sardari, D., Bashiri, B., Zehtabvar, M., Hashemi, S., & Anvariazar, L. (2024). Gamma Ray Energy Absorption Buildup Factor Computation for Human
Tissues in Energy Range of Medical Radionuclides Up to 10 Mean Free Paths. European Journal of Applied Sciences, Vol - 12(1). 77-95.
URL: http://dx.doi.org/10.14738/aivp.121.16228
Across all examined materials except cortical bone, the highest EABF is achieved at the gamma
energy of the Tc-99m radionuclide (0.14 MeV). This phenomenon results from the prevalence
of multiple Compton scatterings, which are the dominant interactions at this energy range (0.14
MeV). Notably elevated BF values characterize the Compton scattering region[1,6]. Above this
energy threshold, the growing significance of pair production gradually reduces the EABF as
photon energy increases. Pair production leads to the removal of one photon, giving rise to the
production of an electron-positron pair.
Consequently, fewer photons persist within the medium, causing the BF to decline. Cortical
bone primarily consists of high-Z materials like calcium (Ca) and phosphorus (P), in contrast to
other tissues predominantly composed of low-Z materials such as hydrogen (H) and oxygen
(O). Consequently, the EABF for cortical bone reaches its peak at a higher energy level (0.218
MeV) compared to other tissue materials. Additionally, the maximum EABF for cortical bone
generally remains lower than the peak observed for other tissues across all thicknesses.
Figure 1 visually illustrates the trend of EABF, showcasing the highest value for breast tissue
and the lowest for cortical bone. This phenomenon is consistent with findings from other
studies as well[5,6]. This contrast can be explained by considering the equivalent atomic number
(Zeq) of the compound. Breast tissue, characterized by a low Zeq, contrasts with cortical bone
where medium-Z elements carry a higher weight fraction.
0.00
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250.00
0 0.2 0.4 0.6 0.8 1 1.2 1.4
EABF
Energy (MeV)
Breast Tissue
1 mfp 2 mfp 4 mfp 7 mfp 10 mfp
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0.00
50.00
100.00
150.00
200.00
0 0.2 0.4 0.6 0.8 1 1.2 1.4
EABF
Energy (MeV)
Lung tissue
1 mfp 2 mfp 4 mfp 7 mfp 10 mfp
0.00
50.00
100.00
150.00
200.00
0 0.2 0.4 0.6 0.8 1 1.2 1.4
EABF
Energy (meV)
Kidney tissue
1 mfp 2 mfp 4 mfp 7 mfp 10 mfp
0.00
50.00
100.00
150.00
200.00
0 0.2 0.4 0.6 0.8 1 1.2 1.4
EABF
Energy (MeV)
Pancreas tissue
1 mfp 2 mfp 4 mfp 7 mfp 10 mfp
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Sardari, D., Bashiri, B., Zehtabvar, M., Hashemi, S., & Anvariazar, L. (2024). Gamma Ray Energy Absorption Buildup Factor Computation for Human
Tissues in Energy Range of Medical Radionuclides Up to 10 Mean Free Paths. European Journal of Applied Sciences, Vol - 12(1). 77-95.
URL: http://dx.doi.org/10.14738/aivp.121.16228
0.00
50.00
100.00
150.00
200.00
0 0.2 0.4 0.6 0.8 1 1.2 1.4
EABF
Energy (MeV)
Liver tissue
1 mfp 2 mfp 4 mfp 7 mfp 10 mfp
0.00
50.00
100.00
150.00
200.00
250.00
0 0.2 0.4 0.6 0.8 1 1.2 1.4
EABF
Energy (MeV)
Eye lens tissue
1 mfp 2 mfp 4 mfp 7 mfp 10 mfp
0.00
50.00
100.00
150.00
200.00
0 0.2 0.4 0.6 0.8 1 1.2 1.4
EABF
Energy (MeV)
Thyroid tissue
1 mfp 2 mfp 4 mfp 7 mfp 10 mfp
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0.00
50.00
100.00
150.00
200.00
0 0.2 0.4 0.6 0.8 1 1.2 1.4
EABF
Energy (meV)
Brain tissue
1 mfp 2 mfp 4 mfp 7 mfp 10 mfp
0.00
50.00
100.00
150.00
200.00
0 0.2 0.4 0.6 0.8 1 1.2 1.4
EABF
Energy (meV)
Ovary tissue
1 mfp 2 mfp 4 mfp 7 mfp 10 mfp
0.00
50.00
100.00
150.00
200.00
0 0.2 0.4 0.6 0.8 1 1.2 1.4
EABF
Energy (meV)
Heart tissue
1 mfp 2 mfp 4 mfp 7 mfp 10 mfp
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Sardari, D., Bashiri, B., Zehtabvar, M., Hashemi, S., & Anvariazar, L. (2024). Gamma Ray Energy Absorption Buildup Factor Computation for Human
Tissues in Energy Range of Medical Radionuclides Up to 10 Mean Free Paths. European Journal of Applied Sciences, Vol - 12(1). 77-95.
URL: http://dx.doi.org/10.14738/aivp.121.16228
0.00
50.00
100.00
150.00
200.00
250.00
0 0.2 0.4 0.6 0.8 1 1.2 1.4
EABF
Energy (meV)
Large intestine tissue
1 mfp 2 mfp 4 mfp 7 mfp 10 mfp
0.00
50.00
100.00
150.00
200.00
0 0.2 0.4 0.6 0.8 1 1.2 1.4
EABF
Energy (meV)
Blood tissue
1 mfp 2 mfp 4 mfp 7 mfp 10 mfp
0.00
50.00
100.00
150.00
200.00
250.00
0 0.2 0.4 0.6 0.8 1 1.2 1.4
EABF
Energy (meV)
Skin tissue
1 mfp 2 mfp 4 mfp 7 mfp 10 mfp
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Figure 1: Variation of EABF with energy for investigated penetration depths
0.00
50.00
100.00
150.00
200.00
0 0.2 0.4 0.6 0.8 1 1.2 1.4
EABF
Energy (meV)
Spleen tissue
1 mfp 2 mfp 4 mfp 7 mfp 10 mfp
0.00
50.00
100.00
150.00
200.00
0 0.2 0.4 0.6 0.8 1 1.2 1.4
EABF
Energy (meV)
Muscle tissue
1 mfp 2 mfp 4 mfp 7 mfp 10 mfp
0.00
10.00
20.00
30.00
40.00
50.00
0 0.2 0.4 0.6 0.8 1 1.2 1.4
EABF
Energy (meV)
Cortical bone tissue
1 mfp 2 mfp 4 mfp 7 mfp 10 mfp
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Sardari, D., Bashiri, B., Zehtabvar, M., Hashemi, S., & Anvariazar, L. (2024). Gamma Ray Energy Absorption Buildup Factor Computation for Human
Tissues in Energy Range of Medical Radionuclides Up to 10 Mean Free Paths. European Journal of Applied Sciences, Vol - 12(1). 77-95.
URL: http://dx.doi.org/10.14738/aivp.121.16228
Figures 1 to 16 collectively demonstrate that EABF escalates with increasing penetration depth.
A larger penetration depth indicates a higher number of scattering events, thereby yielding
higher EABF values. Moreover, we successfully calculated the EABF for the human tissues,
extending our analysis across the energy spectrum of common medical radionuclides. The
validity of our values is substantiated through meticulous validation of our simulations against
existing literature data, specifically for water and soft tissues. This validation process ensures
the reliability and accuracy of our calculated EABF values, allowing for informed and confident
utilization of the results in medical applications, radiation safety considerations, and treatment
planning.
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