Studies on mass attenuation coefficients for some body tissues with different medical sources and their validation using Monte Carlo codes

Studies on mass attenuation coefficients for some body tissues with different medical sources and their validation using Monte Carlo codes 1 first-author 2 corresp Corresponding author: sajadkeshavarz7@gmail.com Corresponding author: sajadkeshavarz7@gmail.com sajadkeshavarz7@gmail.com https://orcid.org/0000-0003-1103-6810 Department of Physics, University of Yazd, Yazd, Iran Department of Physics, University of Yazd, Yazd, Iran Department of Medical Radiation Engineering, University of Science and Research Branch Tehran, Tehran, Iran Department of Medical Radiation Engineering, University of Science and Research Branch Tehran, Tehran, Iran The mass attenuation coefficients of the breasts, lungs, kidneys, pancreas, liver, eye lenses, thyroid, brain, ovary, heart, large intestines, blood, skin, spleen, muscle, and cortical bone were measured at different sources (i.e., 0.021, 0.029, 0.03, 0.14, 0.218, 0.38, 0.412, 0.663, 0.83, and 1.25 MeV) using various methods including the Monte Carlo N-particle transport code (MCNP), the Geometry and Tracking code (GEANT4), and theoretical approach described in this study. Mass attenuation coefficients were also compared with the values from the National Institute of Standards and Technology (NIST-XCOM). The values obtained were similar to those obtained using NIST-XCOM. Our results show that the theoretical method is quite convenient in comparison to GEANT4 and MCNP in the calculation of the mass attenuation coefficients of the human body samples applied when compared with the NIST values and demonstrated an acceptable difference. Mass attenuation coefficient MCNP Geant4 XCOM Human organs 1. Introduction 1 Many sources are used in medicine to diagnose and treat different abnormalities and cancers. Using these sources can be helpful for determining the rate of attenuation in each organ. In this study, sources that have more applications in various types of diagnosis and treatment have been studied. To treat prostate cancer, palladium-103 with an average photon energy of 0.021 MeV has been used [ 1 1 , 2 2 ]. In addition, Cs-137 source (mean energy = 0.030 MeV) has been applied to intracavitary brachytherapy [ 3 3 – 5 5 3–5 ]. Moreover, Ba-133 has been used in dose distribution measurements at distances that range from very close up to the brachytherapy source [ 6 6 ], and Ir-192 with a 0.380 MeV mean photon energy is used in brachytherapy with a high dose rate [ 7 7 – 9 9 7–9 ]. The intra-articular injection of Au-198 (mean photon energy = 0.412 MeV) has been used to treat repeated hemarthrosis of the elbows, knees, or ankles, which reduces the incidence of hemarthrosis and slows the rate of evolution of radiographic changes [ 10 10 , 11 11 ]. In addition, Co-60 and Cs-137 are used for the measurement and calculation of the dose at long distances when applying brachytherapy [ 12 12 – 14 14 12–14 ], and radium-226 is used for the treatment of cervical and endometrial cancer. However, radium-226 is a dangerous material, and other sources are being applied as a replacement [ 15 15 ]. In addition, technetium-99m (mean photon energy = 0.14 MeV) compounds are being used in the imaging of heart muscle perfusion [ 16 16 ]. The use of iodine 125 diagnostic kits for radioimmunoassay (RIA) measurements in conventional medical diagnostic laboratories is common. Iodine 125 emits gamma and X-rays with a mean energy of 0.029 MeV [ 17 17 ]. When a photon moves through matter, it may interact through any of the three major interactions: Compton, photoelectric, and pair production based on their energy [ 18 18 ]. When a beam of gamma rays passes through matter, the absorption and scattering of the primary photons are called attenuation [ 19 19 ]. Mass attenuation coefficients provide essential data on various fields, such as the elemental concentration or biological composition, nuclear medicine, medical applications, and radiation dosimetry. In the biological and medical contexts, the mass attenuation coefficient is a key parameter for various dosimetry material s [ 20 20 , 21 21 ]. When photons deposit their energy in tissues, the radiation dose can be estimated based on the mass attenuation coefficients, particularly in the human body [ 20 20 ]. The calculations of the mass attenuation coefficients are based on the Beer–Lambert law: <math display="block" id="M1"><mrow><mi>I</mi><mo> </mo><mo>=</mo><mo> </mo><msub><mi>I</mi><mn>0</mn></msub><mo> </mo><msup><mi>e</mi><mrow><mo>−</mo><mi>μ</mi><mi>x</mi></mrow></msup><mo>,</mo></mrow></math> where I 0 and I are the initial (before the sample) and final (after the model) photon intensities, respectively, and x is the thickness of the material. The mass attenuation coefficient μ m = μ⁄ρ is the slope of a straight-line equation [ 22 22 , 23 23 ]. There have been many articles on the mass attenuation coefficient in various tissues of the human body. In Ref. [ 23 23 ], Arslan investigated the mass attenuation coefficients, effective atomic numbers, effective electron densities, and Kerma relative to air for muscle, bone, and adipose tissues within a photon energy region of 20 keV to 50 MeV using the Geant4 simulation package and toretical calculations, and compared the values of the Auto-Zeff program with the results of other studies. The authors of Ref. [ 21 21 ] calculated the mass attenuation coefficient (μ/ρ), mass energy absorption coefficient (μ en /ρ), and effective atomic number ( Z eff ) in different tissues of human organs using a pocket formula. The new chemical formula was assigned in Ref. [ 21 21 ] for all tissues studied based on their composition. Tissue-equivalent phantoms are valuable for experimental biomedical research because they can provide a good simulation of real human tissue, and aid in the development and validation of the modalities in medical applications [ 24 24 ]. Many research groups have recently measured the mass attenuation coefficients using Monte Carlo simulation models in different materials and have obtained successful results. Ermis et al. [ 19 19 ] used various theoretical methods to determine the mass attenuation coefficient of other tissues. Their results show that calculating the mass attenuation coefficient with the FLUKA code is more appropriate than the GEANT4 code when compared with NIST values at 60, 80, and 150 keV of photon energy. The percentage difference between the mass density of each material and each organ tissue was evaluated by Alssabbagh et al. [ 25 25 ], who compared the mass attenuation coefficient and density for nine 3D printing materials as tissue-equivalent materials using the NIST-XCOM database, and the x-ray attenuation properties of nine different human organ tissues using the values listed in the International Commission on Radiation Units and Measurements (ICRU), report 44. These results showed that we can use 3D wood material to create and simulate human phantoms. El-Khayatt et al. [ 26 26 ] analyzed tissue-equivalent materials for use as human brain tissue substitutes in dosimetry for diagnostic radiology and calculated the total mass attenuation coefficients, absorbed dose, and mass energy-absorption coefficient for bolus, nylon, orange articulation wax, red articulation wax paraffin, and water. The results have shown that water is the best material for the brain among the other materials that were investigated. The study of the mass attenuation coefficient in different tissues of human organs plays a vital role in radiotherapy and medical diagnosis. It is difficult to measure the basic photon interaction parameters in the tissues of human organs because many chemical and biological reactions take place simultaneously. Thus, there is a need to estimate these parameters theoretically. Hence, in the present study, we considered the mass attenuation coefficient of many tissues of human organs (blood, brain, breasts, spleen, eye lenses, heart, liver, lungs, muscle, ovaries, pancreas, skin, thyroid, kidneys, cortical bone, and large intestines) within the mean photon energy range of 0.021–1.25 MeV. In previous studies, fewer organs and fewer sources were used. However, in this study, even more organs and more sources were used and were also prevented by receiving doses from other tissues in medicine, particularly tissues that are close to each other. This causes secondary cancers in other organs, which can be reduced by knowing the mass attenuation coefficient of each organ. Because a direct measurement of the attenuation coefficient is not easily possible using a simulation, the desired results can be achieved more quickly before conducting clinical studies. 2. Materials and Methods 1 The chemical composition, weight fractions, tissue densities, and tissue equivalents have been studied in this present study, which are listed in Table 1 Table 1 . These values are used from the ICRU Report 44 [ 27 27 ], which are referenced data providing the required mass attenuation coefficient calculations. 1 1 Materials 1 1 Density (g/cm 3 ) 13 1 Weight fraction (%) 1 1 1 1 1 1 H 1 1 C 1 1 N 1 1 O 1 1 Na 1 1 P 1 1 S 1 1 Cl 1 1 K 1 1 Ca 1 1 Fe 1 1 Mg 1 1 I 1 1 Breast 1 1 1.02 1 1 0.106 1 1 0.332 1 1 0.03 1 1 0.527 1 1 0.001 1 1 0.001 1 1 0.002 1 1 0.001 1 1 - 1 1 - 1 1 - 1 1 - 1 1 - 1 1 Lung 1 1 1.05 1 1 0.103 1 1 0.105 1 1 0.031 1 1 0.749 1 1 0.002 1 1 0.002 1 1 0.003 1 1 0.003 1 1 0.002 1 1 - 1 1 - 1 1 - 1 1 - 1 1 Kidney 1 1 1.05 1 1 0.103 1 1 0.132 1 1 0.03 1 1 0.724 1 1 0.002 1 1 0.002 1 1 0.002 1 1 0.002 1 1 0.002 1 1 0.001 1 1 - 1 1 - 1 1 - 1 1 Pancreas 1 1 1.04 1 1 0.106 1 1 0.169 1 1 0.022 1 1 0.694 1 1 0.002 1 1 0.002 1 1 0.001 1 1 0.002 1 1 0.002 1 1 0.001 1 1 - 1 1 - 1 1 - 1 1 Liver 1 1 1.06 1 1 0.102 1 1 0.139 1 1 0.03 1 1 0.716 1 1 0.002 1 1 0.003 1 1 0.003 1 1 0.002 1 1 0.003 1 1 - 1 1 - 1 1 - 1 1 - 1 1 Eye Lens 1 1 1.07 1 1 0.096 1 1 0.195 1 1 0.057 1 1 0.646 1 1 0.001 1 1 0.001 1 1 0.003 1 1 0.001 1 1 0.002 1 1 0.001 1 1 - 1 1 - 1 1 - 1 1 Thyroid 1 1 1.05 1 1 0.104 1 1 0.119 1 1 0.024 1 1 0.746 1 1 0.002 1 1 0.001 1 1 0.001 1 1 0.002 1 1 0.001 1 1 - 1 1 - 1 1 - 1 1 0.001 1 1 Brain 1 1 1.04 1 1 0.107 1 1 0.145 1 1 0.022 1 1 0.712 1 1 0.002 1 1 0.004 1 1 0.002 1 1 0.003 1 1 0.003 1 1 - 1 1 - 1 1 - 1 1 - 1 1 Ovary 1 1 1.05 1 1 0.105 1 1 0.093 1 1 0.024 1 1 0.768 1 1 0.002 1 1 0.002 1 1 0.002 1 1 0.002 1 1 0.002 1 1 - 1 1 - 1 1 - 1 1 - 1 1 Heart 1 1 1.06 1 1 0.103 1 1 0.121 1 1 0.032 1 1 0.734 1 1 0.001 1 1 0.001 1 1 0.002 1 1 0.003 1 1 0.002 1 1 - 1 1 0.001 1 1 - 1 1 - 1 1 Large intestine 1 1 1.03 1 1 0.106 1 1 0.115 1 1 0.022 1 1 0.751 1 1 0.001 1 1 0.001 1 1 0.001 1 1 0.002 1 1 0.001 1 1 - 1 1 - 1 1 - 1 1 - 1 1 Blood 1 1 1.06 1 1 0.102 1 1 0.110 1 1 0.033 1 1 0.745 1 1 0.001 1 1 0.001 1 1 0.002 1 1 0.003 1 1 0.002 1 1 - 1 1 0.001 1 1 - 1 1 - 1 1 Skin 1 1 1.09 1 1 0.100 1 1 0.204 1 1 0.042 1 1 0.645 1 1 0.002 1 1 0.001 1 1 0.002 1 1 0.003 1 1 0.001 1 1 - 1 1 - 1 1 - 1 1 - 1 1 Spleen 1 1 1.06 1 1 0.103 1 1 0.113 1 1 0.032 1 1 0.741 1 1 0.001 1 1 0.003 1 1 0.002 1 1 0.002 1 1 0.003 1 1 - 1 1 - 1 1 - 1 1 - 1 1 Muscle (Skeletal) 1 1 1.05 1 1 0.102 1 1 0.143 1 1 0.034 1 1 0.710 1 1 0.001 1 1 0.002 1 1 0.003 1 1 0.001 1 1 0.004 1 1 - 1 1 - 1 1 - 1 1 - 1 1 Cortical bone 1 1 1.92 1 1 0.034 1 1 0.165 1 1 0.042 1 1 0.435 1 1 0.001 1 1 0.103 1 1 0.003 1 1 - 1 1 - 1 1 0.225 1 1 - 1 1 0.002 1 1 - 2.1 Theoretical method 2 When a photon moves through matter, it may interact through any of the three significant interactions: Compton, photoelectric, and pair production based on their energy [ 18 18 ]. There are other interactions that are not crucial for photon interactions. The probability of the total interaction, which is called the linear attenuation coefficient ( μ ), is shown in Equation (2) [ 28 28 ]: <math display="block" id="M2"><mrow><mi>μ</mi><mrow><mo>(</mo><mrow><msup><mrow><mtext>cm</mtext></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow><mo>)</mo></mrow><mo>=</mo><msub><mi>σ</mi><mrow><mtext>Compton</mtext></mrow></msub><mo>+</mo><msub><mi>σ</mi><mrow><mtext>photo electrice</mtext></mrow></msub><mo>+</mo><msub><mi>σ</mi><mrow><mtext>pair production</mtext></mrow></msub><mo>,</mo></mrow></math> <math display="block" id="M3"><mrow><msub><mi>σ</mi><mrow><mtext>photo electrice</mtext></mrow></msub><mo>=</mo><mi>c</mi><mi>N</mi><mrow><mo>(</mo><mrow><mfrac><mrow><msup><mi>z</mi><mi>b</mi></msup></mrow><mrow><msubsup><mi>E</mi><mi>γ</mi><mi>a</mi></msubsup></mrow></mfrac></mrow><mo>)</mo></mrow><mrow><mo>[</mo><mrow><mn>1</mn><mo>−</mo><mi>f</mi><mrow><mo>(</mo><mi>Z</mi><mo>)</mo></mrow></mrow><mo>]</mo></mrow><mo>,</mo></mrow></math> <math display="block" id="M4"><mrow><msub><mi>σ</mi><mrow><mtext>Compton</mtext></mrow></msub><mo>=</mo><mi>N</mi><mi>Z</mi><mi>f</mi><mrow><mo>(</mo><mrow><msub><mi>E</mi><mi>γ</mi></msub></mrow><mo>)</mo></mrow><mo>,</mo></mrow></math> <math display="block" id="M5"><mrow><msub><mi>σ</mi><mrow><mtext>pair production</mtext></mrow></msub><mo>=</mo><mi>N</mi><msup><mi>Z</mi><mn>2</mn></msup><mi>f</mi><mrow><mo>(</mo><mrow><msub><mi>E</mi><mi>γ</mi></msub><mo>,</mo><mi>Z</mi></mrow><mo>)</mo></mrow><mo>,</mo></mrow></math> where c is a constant coefficient, independent of Z and <math id="M6"><mrow><msub><mi>E</mi><mi>γ</mi></msub></mrow></math> ., and parameters a a b are constants with values of between 3 and 5 depending on the gamma energy, N is the nuclear density, and Z is the atomic number [ 28 28 ]. As a result, <math display="block" id="M7"><mrow><msub><mi>μ</mi><mtext>m</mtext></msub><mrow><mo>(</mo><mrow><msup><mrow><mtext>cm</mtext></mrow><mn>2</mn></msup><mo>/</mo><mtext>g</mtext></mrow><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><mi>μ</mi><mrow><mo>(</mo><mrow><msup><mrow><mtext>cm</mtext></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow><mo>)</mo></mrow></mrow><mrow><mi>ρ</mi><mrow><mo>(</mo><mrow><mfrac bevelled="true"><mtext>g</mtext><mrow><msup><mrow><mtext>cm</mtext></mrow><mn>3</mn></msup></mrow></mfrac></mrow><mo>)</mo></mrow></mrow></mfrac><mo>,</mo></mrow></math> where <math id="M8"><mrow><msub><mi>μ</mi><mi>m</mi></msub></mrow></math> . is the mass attenuation coefficient and ρ is the density. Using the dinitions of the photoelectric, Compton, and pair production cross-sections, we calculated the value of the linear attenuation coefficient. There are many tables in which the mass attenuation coefficient has been calculated for all elements and at a greater photon energy, with results almost identical to those listed in the tables in Ref. [ 29 29 ]. The total mass attenuation coefficient for a compound will be calculated by cbining Equation (6) and the weight fraction (%wt) for every element in the compound, as shown in Equation (7): <math display="block" id="M9"><mrow><msub><mi>μ</mi><mtext>c</mtext></msub><mrow><mo>(</mo><mrow><msup><mrow><mtext>cm</mtext></mrow><mn>2</mn></msup><mo>/</mo><mtext>g</mtext></mrow><mo>)</mo></mrow><mo>=</mo><munder><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mi>i</mi></munder><msub><mi>w</mi><mi>i</mi></msub><mo>×</mo><msub><mi>μ</mi><mi>m</mi></msub><msub><mrow/><mi>i</mi></msub><mo>,</mo></mrow></math> wre <math id="M10"><mrow><msub><mi>μ</mi><mtext>c</mtext></msub></mrow></math> ., <math id="M11"><mrow><msub><mi>w</mi><mi>i</mi></msub></mrow></math> ., and <math id="M12"><mrow><msub><mi>μ</mi><mrow><msub><mi>m</mi><mi>i</mi></msub></mrow></msub></mrow></math> are the total mass attenuation coefficient of a compound, weight fraction, and mass attenuation coefficient for every element, respectively [ 30 30 ]. 2.2 MCNP simulation 2 A Monte Carlo simulation is a general-purpose tool for studying the ieraction of X and gamma rays, neutrons, and electrons with matter owing to the comprehensive applications of the Monte Carlo N-particle transport code (MCNPX) in medical and medical radiation investigations. This comparative study can use a unified database on the mass attenuation coefficients of the mials [ 12 12 ]. The composition and density of the samples used are presented in Table 1 Table 1 . In this study, MCNPX was used to calculate the attenuation properties of human body organs. MCNPX is a radiation transport code for modeling and calculating the interaction of radiation with materials and tracking all particles at different energies. When a photon passes through a material, it loses its energy through well-known processes such as Compton scattering, photoelectric effects, and pair production [ 31 31 ]. Blood, brain, breast, spleen, eye lens, heart, liver, lung, muscle, ovary, pancreas, skin, thyroid, kidney, cortical bone, and large intestine materials, with a radius of 3 cm and height of 1 cm, as sketched in Fig. 1 Fig. 1 , were selected to investigate the photon attenuation. MCNPX simulation parameters (cards) such as cell, surface, and material descriptions, the position of each tool, and the definitions and features of the sources are defined in the input file according to their properties [ 32 32 ]. The geometry of the sample was defined as a cylinder with a 1 cm thickness (height) and a radius of 3 cm. A schematic view of the MCNP-X simulation setup with a lead (Pb) collimator, investigated for sample organs and detection areas with defined geometries in the MCNP-X input file, is presented in Fig. 1 Fig. 1 . The geometry includes a gamma-ray source, lead collimators, samples, and detection areas that have been defined in the cell card, surface card, and data card sections of the MCNP input by considering different variables such as CEL, ERG, DIR, POS, and PAR. The geometric center of the detection area was considered for the location of the plating source. The source has been defined with mean photon energies of 0.021, 0.029, 0.03, 0.14, 0.218, 0.38, 0.412, 0.663, 0.83, and 1.25 MeV. In addition, the sample was located 10 cm away from the source, and the detector was found in a 5 cm model. A lead shield surrounded the sample and source. Tally F2 was used to obtain the MCNP simulation data. This tally calculates the flux on the detector for every energy source. The MCNP sources were simulated as a circle surface using different photon energies for every source. Simulations were conducted using 5 × 10 7 histories, and all simulation data were reported to have less than 1% error. 2.3 Geant4 simulation 2 The determination of the mass attenuation coefficient for soft tissues and tissue substitute materials given in Table 1 by the Geant4 simulation code was achieved by writing C++ types [ 33 33 ] depending on the object-oriented programming concept. The model was written using three mandatory classes: First, the geometry of the model defined in detector construction and the physics process, which were coded in the physics list, were used. Finally, the primary generator action, which is one of the few mandatory classes that need to be set up, was used to define the primary events and particles that are to be propagated through the simulation geometry. The physics of the simulation are based on a narrow beam geometry with various photon energies according to the mass attenuation coefficient. The mean ene rgy of the incident photons varied between 0.021–1.25 MeV. To calculate the mass attenuation coefficients in relevant physical processes such as the photoelectric effect, Compton scattering and pair production were used. Geant4 electromagnetic physics processes have been successfully compared with the National Institute of Standards and Technologies (NIST) reference data. The simulated geometry and source are shown in Fig. 2 Fig. 2 . This allows users to define classes for the detector geometry, primary particle generator, and physics processes to handle the interactions of particles with matter. It provides a set of electromagnetic physics processes driving the photon-tissue interactions (photoelectric effect, Compton scattering, Rayleigh scattering, and pair production) over a wide range of energy [ 23 23 ]. 2.4. XCOM program 2 The mass attenuation coefficient values of tissues and tissue-equivalent materials were calculated using the XCOM program. XCOM is a program that generates mass attenuation coefficient elements, compounds, and mixtures for desired energies of 1 keV up to 100 GeV, and this program can generate cross-sections under standard energy or a grid selected by the user [ 30 30 ]. In addition, it provides a total cross-section for processes such as incoherent and coherent scattering, photoelectric absorption, and pair production from the atomic nucleus. In this program, we used the ICRU report 44 for the components of the organs and used different photon energies of the sources for calculating the mass attenuation coefficient [ 19 19 , 20 20 ]. 3. Results and discussion 1 3.1 Total mass attenuation coefficient 2 By using Tables 2 Tables 2 , 3 3 , 4 4 , 5 5 , 6 6 , 7 7 , 8 8 , 9 9 and inserting the weight fraction of each material and human organ into the web version of XCOM software, MCNP, Geant4, and the theoretical method, the total mass attenuation coefficient and percentage difference were calculated for the mean photon energy range of 0.21 to 1.25 MeV, for which most of the medical applications fall within this energy interval and sources. The total mass attenuation coefficient decreases proportionally with the number of X-ray photon interactions with the materials for this energy range. In Figs. 3 Figs. 3 , 4 4 , 5 5 , 6 6 , 7 7 , 8 8 , 9 9 , 10 10 , the calculated mass attenuation coefficients versus the mean photon energies of each absorber material are shown. A comparison of the results from the programs can be seen in these figures and tables. 1 1 Nuclide 1 1 Mean-energy (MeV) 4 1 mass attenuation coefficient of breast 3 1 percentage difference (%) for breast 1 1 1 1 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 XCOM 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 Pd-103 1 1 0.021 1 1 0.63446 1 1 0.62547 1 1 0.62024 1 1 0.6214 1 1 2.058 1 1 0.650 1 1 0.187 1 1 I-125 1 1 0.029 1 1 0.35881 1 1 0.36692 1 1 0.34431 1 1 0.3561 1 1 0.755 1 1 2.948 1 1 3.424 1 1 Cs-131 1 1 0.030 1 1 0.35745 1 1 0.36511 1 1 0.33357 1 1 0.3403 1 1 4.797 1 1 6.795 1 1 2.017 1 1 Tc-99m 1 1 0.140 1 1 0.15242 1 1 0.16275 1 1 0.16448 1 1 0.1525 1 1 0.052 1 1 6.298 1 1 7.283 1 1 Ba-133 1 1 0.218 1 1 0.13001 1 1 0.13657 1 1 0.13517 1 1 0.1322 1 1 1.684 1 1 3.199 1 1 2.197 1 1 Ir-192 1 1 0.380 1 1 0.10093 1 1 0.10688 1 1 0.10358 1 1 0.1077 1 1 6.707 1 1 0.767 1 1 3.977 1 1 Au-198 1 1 0.412 1 1 0.09991 1 1 0.10328 1 1 0.10342 1 1 0.1043 1 1 4.393 1 1 0.987 1 1 0.850 1 1 Cs-137 1 1 0.663 1 1 0.08344 1 1 0.08692 1 1 0.08693 1 1 0.0852 1 1 2.109 1 1 1.978 1 1 1.990 1 1 Ra-226 1 1 0.830 1 1 0.07492 1 1 0.07135 1 1 0.07417 1 1 0.07686 1 1 2.589 1 1 7.722 1 1 3.626 1 1 Co-60 1 1 1.25 1 1 0.06197 1 1 0.06897 1 1 0.06409 1 1 0.06287 1 1 1.452 1 1 8.844 1 1 1.903 1 1 Nuclide 1 1 Mean-energy (MeV) 4 1 mass attenuation coefficient of blood 3 1 percentage difference (%) for blood 1 1 1 1 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 XCOM 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 Pd-103 1 1 0.74778 1 1 0.74778 1 1 0.74357 1 1 0.75083 1 1 0.73420 1 1 1.816 1 1 1.26 1 1 2.214 1 1 I-125 1 1 0.40588 1 1 0.40588 1 1 0.39172 1 1 0.41101 1 1 0.39790 1 1 1.966 1 1 1.577 1 1 3.189 1 1 Cs-131 1 1 0.38372 1 1 0.38372 1 1 0.40445 1 1 0.37009 1 1 0.37790 1 1 1.516 1 1 6.564 1 1 2.11 1 1 Tc-99m 1 1 0.15102 1 1 0.15102 1 1 0.16444 1 1 0.15082 1 1 0.15250 1 1 0.98 1 1 7.261 1 1 1.113 1 1 Ba-133 1 1 0.13025 1 1 0.13025 1 1 0.14518 1 1 0.14000 1 1 0.13180 1 1 1.19 1 1 9.216 1 1 5.857 1 1 Ir-192 1 1 0.10083 1 1 0.10083 1 1 0.11408 1 1 0.10375 1 1 0.10730 1 1 6.416 1 1 5.943 1 1 3.421 1 1 Au-198 1 1 0.09887 1 1 0.09887 1 1 0.10631 1 1 0.10358 1 1 0.10390 1 1 5.087 1 1 2.266 1 1 0.308 1 1 Cs-137 1 1 0.08293 1 1 0.08293 1 1 0.08734 1 1 0.08838 1 1 0.08491 1 1 2.387 1 1 2.782 1 1 3.926 1 1 Ra-226 1 1 0.07514 1 1 0.07514 1 1 0.07333 1 1 0.07554 1 1 0.07661 1 1 1.956 1 1 4.472 1 1 1.416 1 1 Co-60 1 1 0.06132 1 1 0.06132 1 1 0.06028 1 1 0.06637 1 1 0.06266 1 1 2.185 1 1 3.948 1 1 5.589 1 1 Nuclide 1 1 Mean-energy (MeV) 4 1 Mass attenuation coefficient of skin 3 1 Percentage difference (%) for skin 1 1 1 1 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 XCOM 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 Pd-103 1 1 0.021 1 1 0.69821 1 1 0.69851 1 1 0.68247 1 1 0.68950 1 1 1.247 1 1 1.289 1 1 1.03 1 1 I-125 1 1 0.029 1 1 0.39068 1 1 0.37823 1 1 0.39496 1 1 0.38100 1 1 2.477 1 1 0.732 1 1 3.534 1 1 Cs-131 1 1 0.030 1 1 0.37193 1 1 0.35793 1 1 0.35732 1 1 0.36260 1 1 2.508 1 1 1.304 1 1 1.477 1 1 Tc-99m 1 1 0.140 1 1 0.15450 1 1 0.16306 1 1 0.15511 1 1 0.15200 1 1 1.618 1 1 6.782 1 1 2.005 1 1 Ba-133 1 1 0.218 1 1 0.13001 1 1 0.13873 1 1 0.14368 1 1 0.13150 1 1 1.146 1 1 5.211 1 1 8.477 1 1 Ir-192 1 1 0.380 1 1 0.10045 1 1 0.10051 1 1 0.10383 1 1 0.10710 1 1 6.62 1 1 6.556 1 1 3.149 1 1 Au-198 1 1 0.412 1 1 0.09881 1 1 0.10107 1 1 0.10366 1 1 0.10370 1 1 4.948 1 1 2.602 1 1 0.038 1 1 Cs-137 1 1 0.663 1 1 0.08297 1 1 0.09377 1 1 0.08894 1 1 0.08475 1 1 2.145 1 1 9.619 1 1 4.711 1 1 Ra-226 1 1 0.830 1 1 0.07599 1 1 0.07111 1 1 0.07602 1 1 0.07646 1 1 0.618 1 1 7.523 1 1 0.578 1 1 Co-60 1 1 1.25 1 1 0.06149 1 1 0.06255 1 1 0.06212 1 1 0.06254 1 1 1.707 1 1 0.0159 1 1 0.676 1 1 Nuclide 1 1 Mean-energy (MeV) 4 1 Mass attenuation coefficient of lungs 3 1 Percentage difference (%) for lungs 1 1 1 1 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 XCOM 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 Pd-103 1 1 0.021 1 1 0.75502 1 1 0.75290 1 1 0.73259 1 1 0.74430 1 1 1.419 1 1 1.142 1 1 1.598 1 1 I-125 1 1 0.029 1 1 0.40779 1 1 0.39464 1 1 0.40241 1 1 0.40180 1 1 1.468 1 1 1.814 1 1 0.151 1 1 Cs-131 1 1 0.030 1 1 0.38470 1 1 0.39131 1 1 0.37268 1 1 0.38150 1 1 0.831 1 1 2.506 1 1 2.366 1 1 Tc-99m 1 1 0.140 1 1 0.15354 1 1 0.16427 1 1 0.16934 1 1 0.15260 1 1 0.612 1 1 7.104 1 1 9.885 1 1 Ba-133 1 1 0.218 1 1 0.12996 1 1 0.14221 1 1 0.13879 1 1 0.13200 1 1 1.569 1 1 7.179 1 1 4.892 1 1 Ir-192 1 1 0.380 1 1 0.10579 1 1 0.10108 1 1 0.10373 1 1 0.10740 1 1 1.521 1 1 6.252 1 1 3.538 1 1 Au-198 1 1 0.412 1 1 0.10001 1 1 0.10522 1 1 0.10356 1 1 0.10400 1 1 3.989 1 1 1.159 1 1 0.424 1 1 Cs-137 1 1 0.663 1 1 0.07253 1 1 0.09717 1 1 0.08195 1 1 0.08498 1 1 17.165 1 1 12.545 1 1 3.697 1 1 Ra-226 1 1 0.830 1 1 0.07502 1 1 0.08503 1 1 0.07537 1 1 0.07667 1 1 2.199 1 1 9.831 1 1 1.724 1 1 Co-60 1 1 1.25 1 1 0.06105 1 1 0.06313 1 1 0.06580 1 1 0.06271 1 1 2.719 1 1 0.665 1 1 4.696 1 1 Nuclide 1 1 Mean-energy (MeV) 4 1 Mass attenuation coefficient of kidneys 3 1 Percentage difference (%) for kidneys 1 1 1 1 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 XCOM 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 Pd-103 1 1 0.021 1 1 0.74399 1 1 0.73916 1 1 0.72274 1 1 0.73430 1 1 1.302 1 1 0.657 1 1 1.599 1 1 I-125 1 1 0.029 1 1 0.40380 1 1 0.38201 1 1 0.39871 1 1 0.39820 1 1 1.386 1 1 4.238 1 1 0.127 1 1 Cs-131 1 1 0.030 1 1 0.38147 1 1 0.39251 1 1 0.37975 1 1 0.37820 1 1 0.857 1 1 3.645 1 1 0.408 1 1 Tc-99m 1 1 0.140 1 1 0.15359 1 1 0.16914 1 1 0.16927 1 1 0.15260 1 1 0.644 1 1 9.778 1 1 9.848 1 1 Ba-133 1 1 0.218 1 1 0.13064 1 1 0.12391 1 1 0.13880 1 1 0.13200 1 1 1.041 1 1 6.528 1 1 4.899 1 1 Ir-192 1 1 0.380 1 1 0.10573 1 1 0.10363 1 1 0.10372 1 1 0.10740 1 1 1.579 1 1 3.637 1 1 3.548 1 1 Au-198 1 1 0.412 1 1 0.10999 1 1 0.10498 1 1 0.10355 1 1 0.10400 1 1 5.445 1 1 0.933 1 1 0.434 1 1 Cs-137 1 1 0.663 1 1 0.08335 1 1 0.09204 1 1 0.08119 1 1 0.08498 1 1 1.955 1 1 7.67 1 1 4.668 1 1 Ra-226 1 1 0.830 1 1 0.07507 1 1 0.07785 1 1 0.07529 1 1 0.07667 1 1 2.131 1 1 1.515 1 1 1.832 1 1 Co-60 1 1 1.25 1 1 0.06094 1 1 0.06552 1 1 0.06580 1 1 0.06271 1 1 2.904 1 1 4.288 1 1 4.696 1 1 Nuclide 1 1 Mean-energy (MeV) 4 1 Mass attenuation coefficient of pancreas 3 1 Percentage difference (%) for pancreas 1 1 1 1 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 XCOM 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 Pd-103 1 1 0.021 1 1 0.72288 1 1 0.72821 1 1 0.71861 1 1 0.71630 1 1 0.91 1 1 1.635 1 1 0.321 1 1 I-125 1 1 0.029 1 1 0.40275 1 1 0.38353 1 1 0.38870 1 1 0.39180 1 1 2.718 1 1 2.156 1 1 0.797 1 1 Cs-131 1 1 0.030 1 1 0.38035 1 1 0.38917 1 1 0.37150 1 1 0.37250 1 1 2.063 1 1 4.283 1 1 0.269 1 1 Tc-99m 1 1 0.140 1 1 0.15626 1 1 0.16129 1 1 0.16817 1 1 0.15290 1 1 2.15 1 1 5.201 1 1 9.08 1 1 Ba-133 1 1 0.218 1 1 0.13039 1 1 0.13850 1 1 0.13796 1 1 0.13230 1 1 1.464 1 1 4.476 1 1 4.102 1 1 Ir-192 1 1 0.380 1 1 0.10068 1 1 0.10827 1 1 0.10369 1 1 0.10770 1 1 6.972 1 1 0.526 1 1 3.867 1 1 Au-198 1 1 0.412 1 1 0.10994 1 1 0.10361 1 1 0.10352 1 1 0.10430 1 1 5.13 1 1 0.665 1 1 0.753 1 1 Cs-137 1 1 0.663 1 1 0.08468 1 1 0.07415 1 1 0.08785 1 1 0.08520 1 1 0.614 1 1 14.902 1 1 3.016 1 1 Ra-226 1 1 0.830 1 1 0.07781 1 1 0.07616 1 1 0.07504 1 1 0.07687 1 1 1.208 1 1 0.932 1 1 2.438 1 1 Co-60 1 1 1.25 1 1 0.06232 1 1 0.05345 1 1 0.06432 1 1 0.06287 1 1 0.882 1 1 17.623 1 1 2.254 1 1 Nuclide 1 1 Mean-energy (MeV) 4 1 Mass attenuation coefficient of liver 3 1 Percentage difference (%) for liver 1 1 1 1 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 XCOM 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 Pd-103 1 1 0.021 1 1 0.74979 1 1 0.74769 1 1 0.73256 1 1 0.73920 1 1 1.412 1 1 1.135 1 1 0.906 1 1 I-125 1 1 0.029 1 1 0.40841 1 1 0.38750 1 1 0.40450 1 1 0.39990 1 1 2.083 1 1 3.2 1 1 1.137 1 1 Cs-131 1 1 0.030 1 1 0.38627 1 1 0.39151 1 1 0.36549 1 1 0.37980 1 1 1.674 1 1 2.99 1 1 3.915 1 1 Tc-99m 1 1 0.140 1 1 0.15100 1 1 0.16853 1 1 0.15075 1 1 0.15250 1 1 0.993 1 1 9.511 1 1 1.16 1 1 Ba-133 1 1 0.218 1 1 0.13015 1 1 0.13495 1 1 0.13999 1 1 0.13180 1 1 1.267 1 1 2.334 1 1 5.85 1 1 Ir-192 1 1 0.380 1 1 0.10610 1 1 0.10275 1 1 0.10376 1 1 0.10730 1 1 1.131 1 1 4.428 1 1 3.411 1 1 Au-198 1 1 0.412 1 1 0.10999 1 1 0.10213 1 1 0.10360 1 1 0.10390 1 1 5.536 1 1 1.733 1 1 0.289 1 1 Cs-137 1 1 0.663 1 1 0.07215 1 1 0.08243 1 1 0.08469 1 1 0.08490 1 1 17.671 1 1 2.996 1 1 0.247 1 1 Ra-226 1 1 0.830 1 1 0.07511 1 1 0.07364 1 1 0.07561 1 1 0.07660 1 1 1.983 1 1 4.019 1 1 1.309 1 1 Co-60 1 1 1.25 1 1 0.06337 1 1 0.06956 1 1 0.06637 1 1 0.06265 1 1 1.136 1 1 9.933 1 1 5.604 1 1 Nuclide 1 1 Mean-energy (MeV) 4 1 Mass attenuation coefficient of thyroid 3 1 Percentage difference (%) for thyroid 1 1 1 1 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 XCOM 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 Pd-103 1 1 0.021 1 1 0.74203 1 1 0.72400 1 1 0.72088 1 1 0.73320 1 1 1.189 1 1 1.27 1 1 1.709 1 1 I-125 1 1 0.029 1 1 0.40712 1 1 0.37700 1 1 0.39875 1 1 0.39850 1 1 2.117 1 1 5.702 1 1 0.062 1 1 Cs-131 1 1 0.030 1 1 0.38462 1 1 0.39719 1 1 0.37926 1 1 0.37860 1 1 1.565 1 1 4.68 1 1 0.174 1 1 Tc-99m 1 1 0.140 1 1 0.15281 1 1 0.16145 1 1 0.15029 1 1 0.15330 1 1 0.32 1 1 5.048 1 1 2.002 1 1 Ba-133 1 1 0.218 1 1 0.13059 1 1 0.13950 1 1 0.13922 1 1 0.13220 1 1 1.232 1 1 5.232 1 1 5.042 1 1 Ir-192 1 1 0.380 1 1 0.10573 1 1 0.10894 1 1 0.10371 1 1 0.10750 1 1 1.674 1 1 1.321 1 1 3.654 1 1 Au-198 1 1 0.412 1 1 0.10024 1 1 0.10776 1 1 0.10354 1 1 0.10410 1 1 3.85 1 1 3.396 1 1 0.54 1 1 Cs-137 1 1 0.663 1 1 0.06182 1 1 0.06959 1 1 0.08014 1 1 0.08505 1 1 37.576 1 1 22.215 1 1 6.126 1 1 Ra-226 1 1 0.830 1 1 0.07625 1 1 0.08344 1 1 0.07520 1 1 0.07673 1 1 0.629 1 1 8.041 1 1 2.034 1 1 Co-60 1 1 1.25 1 1 0.06337 1 1 0.06585 1 1 0.06592 1 1 0.06276 1 1 0.962 1 1 4.692 1 1 4.793 1 1 Nuclide 1 1 Mean-energy (MeV) 4 1 Mass attenuation coefficient of brain 3 1 Percentage difference (%) for brain 1 1 1 1 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 XCOM 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 Pd-103 1 1 0.021 1 1 0.75250 1 1 0.74792 1 1 0.74305 1 1 0.74150 1 1 1.461 1 1 0.858 1 1 0.208 1 1 I-125 1 1 0.029 1 1 0.41159 1 1 0.39012 1 1 0.39857 1 1 0.40130 1 1 2.5 1 1 2.865 1 1 0.684 1 1 Cs-131 1 1 0.030 1 1 0.38829 1 1 0.39598 1 1 0.38014 1 1 0.38110 1 1 1.851 1 1 3.757 1 1 0.252 1 1 Tc-99m 1 1 0.140 1 1 0.15329 1 1 0.16265 1 1 0.15827 1 1 0.15310 1 1 0.123 1 1 5.871 1 1 3.266 1 1 Ba-133 1 1 0.218 1 1 0.13076 1 1 0.13033 1 1 0.13796 1 1 0.13240 1 1 1.254 1 1 1.588 1 1 4.03 1 1 Ir-192 1 1 0.380 1 1 0.10611 1 1 0.10221 1 1 0.10371 1 1 0.10780 1 1 1.592 1 1 5.469 1 1 3.943 1 1 Au-198 1 1 0.412 1 1 0.10032 1 1 0.11945 1 1 0.10355 1 1 0.10440 1 1 4.066 1 1 12.599 1 1 0.82 1 1 Cs-137 1 1 0.663 1 1 0.09637 1 1 0.07250 1 1 0.08073 1 1 0.08527 1 1 11.518 1 1 17.613 1 1 5.623 1 1 Ra-226 1 1 0.830 1 1 0.07673 1 1 0.08530 1 1 0.07524 1 1 0.07694 1 1 0.273 1 1 9.8 1 1 2.259 1 1 Co-60 1 1 1.25 1 1 0.06368 1 1 0.06249 1 1 0.06540 1 1 0.06293 1 1 1.177 1 1 0.704 1 1 3.776 1 1 Nuclide 1 1 Mean-energy (MeV) 4 1 Mass attenuation coefficient of eye lens 3 1 Percentage difference (%) for eye lens 1 1 1 1 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 XCOM 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 Pd-103 1 1 0.021 1 1 0.67638 1 1 0.65354 1 1 0.70630 1 1 0.70280 1 1 3.906 1 1 7.537 1 1 0.495 1 1 I-125 1 1 0.029 1 1 0.38203 1 1 0.35979 1 1 0.39420 1 1 0.38570 1 1 0.96 1 1 7.201 1 1 2.156 1 1 Cs-131 1 1 0.030 1 1 0.36090 1 1 0.37438 1 1 0.35676 1 1 0.36680 1 1 1.634 1 1 2.024 1 1 2.814 1 1 Tc-99m 1 1 0.140 1 1 0.15095 1 1 0.17993 1 1 0.15177 1 1 0.15150 1 1 0.364 1 1 15.8 1 1 0.177 1 1 Ba-133 1 1 0.218 1 1 0.12911 1 1 0.15047 1 1 0.14095 1 1 0.13110 1 1 1.541 1 1 12.873 1 1 6.988 1 1 Ir-192 1 1 0.380 1 1 0.10597 1 1 0.11360 1 1 0.10377 1 1 0.10670 1 1 0.688 1 1 6.073 1 1 2.823 1 1 Au-198 1 1 0.412 1 1 0.10997 1 1 0.10200 1 1 0.10360 1 1 0.10330 1 1 6.065 1 1 1.274 1 1 0.289 1 1 Cs-137 1 1 0.663 1 1 0.07155 1 1 0.07540 1 1 0.08477 1 1 0.08443 1 1 18.001 1 1 11.976 1 1 0.401 1 1 Ra-226 1 1 0.830 1 1 0.07586 1 1 0.07664 1 1 0.07561 1 1 0.07617 1 1 0.408 1 1 0.613 1 1 0.74 1 1 Co-60 1 1 1.25 1 1 0.06280 1 1 0.06694 1 1 0.06682 1 1 0.06230 1 1 0.796 1 1 6.931 1 1 6.764 1 1 Nuclide 1 1 Mean-energy (MeV) 4 1 Mass attenuation coefficient of heart 3 1 Percentage difference (%) for heart 1 1 1 1 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 XCOM 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 Pd-103 1 1 0.021 1 1 0.74409 1 1 0.75111 1 1 0.74671 1 1 0.75000 1 1 0.794 1 1 0.147 1 1 0.44 1 1 I-125 1 1 0.029 1 1 0.40718 1 1 0.40232 1 1 0.40954 1 1 0.40440 1 1 0.682 1 1 0.517 1 1 1.255 1 1 Cs-131 1 1 0.030 1 1 0.38481 1 1 0.39201 1 1 0.38953 1 1 0.38390 1 1 0.236 1 1 2.068 1 1 1.445 1 1 Tc-99m 1 1 0.140 1 1 0.15112 1 1 0.16892 1 1 0.15095 1 1 0.15260 1 1 0.979 1 1 9.661 1 1 1.093 1 1 Ba-133 1 1 0.218 1 1 0.13026 1 1 0.13568 1 1 0.13013 1 1 0.13200 1 1 1.335 1 1 2.712 1 1 1.437 1 1 Ir-192 1 1 0.380 1 1 0.10641 1 1 0.10696 1 1 0.10375 1 1 0.10740 1 1 0.93 1 1 0.411 1 1 3.518 1 1 Au-198 1 1 0.412 1 1 0.10999 1 1 0.10649 1 1 0.10359 1 1 0.10400 1 1 5.445 1 1 2.338 1 1 0.395 1 1 Cs-137 1 1 0.663 1 1 0.08471 1 1 0.09429 1 1 0.08839 1 1 0.08498 1 1 0.318 1 1 9.873 1 1 3.857 1 1 Ra-226 1 1 0.830 1 1 0.07546 1 1 0.08371 1 1 0.07654 1 1 0.07667 1 1 1.603 1 1 8.409 1 1 0.169 1 1 Co-60 1 1 1.25 1 1 0.06326 1 1 0.07318 1 1 0.06429 1 1 0.06271 1 1 0.869 1 1 14.307 1 1 2.457 1 1 Nuclide 1 1 Mean-energy (MeV) 4 1 Mass attenuation coefficient of large intestine 3 1 Percentage difference (%) for large intestine 1 1 1 1 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 XCOM 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 Pd-103 1 1 0.021 1 1 0.71729 1 1 0.68561 1 1 0.70400 1 1 0.70570 1 1 1.615 1 1 2.93 1 1 0.241 1 1 I-125 1 1 0.029 1 1 0.39928 1 1 0.38402 1 1 0.38168 1 1 0.38750 1 1 2.95 1 1 0.906 1 1 1.524 1 1 Cs-131 1 1 0.030 1 1 0.37632 1 1 0.38403 1 1 0.36465 1 1 0.36860 1 1 2.051 1 1 4.017 1 1 1.083 1 1 Tc-99m 1 1 0.140 1 1 0.15207 1 1 0.16131 1 1 0.15644 1 1 0.15290 1 1 0.545 1 1 5.213 1 1 2.262 1 1 Ba-133 1 1 0.218 1 1 0.13067 1 1 0.13920 1 1 0.13651 1 1 0.13230 1 1 1.247 1 1 4.956 1 1 3.084 1 1 Ir-192 1 1 0.380 1 1 0.10608 1 1 0.10731 1 1 0.10363 1 1 0.10770 1 1 1.527 1 1 0.363 1 1 3.927 1 1 Au-198 1 1 0.412 1 1 0.11912 1 1 0.10272 1 1 0.10347 1 1 0.10430 1 1 12.441 1 1 1.538 1 1 0.802 1 1 Cs-137 1 1 0.663 1 1 0.09262 1 1 0.09329 1 1 0.08744 1 1 0.08523 1 1 7.978 1 1 8.639 1 1 2.527 1 1 Ra-226 1 1 0.830 1 1 0.07573 1 1 0.08463 1 1 0.07469 1 1 0.07690 1 1 1.544 1 1 9.133 1 1 2.958 1 1 Co-60 1 1 1.25 1 1 0.06111 1 1 0.06903 1 1 0.06473 1 1 0.06289 1 1 2.912 1 1 8.894 1 1 2.842 1 1 Nuclide 1 1 Mean-energy (MeV) 4 1 Mass attenuation coefficient of ovary 3 1 Percentage difference (%) for ovary 1 1 1 1 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 XCOM 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 Pd-103 1 1 0.021 1 1 0.74828 1 1 0.73239 1 1 0.73554 1 1 0.73840 1 1 1.338 1 1 0.813 1 1 0.387 1 1 I-125 1 1 0.029 1 1 0.40850 1 1 0.38551 1 1 0.39991 1 1 0.39970 1 1 2.201 1 1 3.55 1 1 0.052 1 1 Cs-131 1 1 0.030 1 1 0.38587 1 1 0.39254 1 1 0.37075 1 1 0.37960 1 1 1.651 1 1 3.408 1 1 2.331 1 1 Tc-99m 1 1 0.140 1 1 0.15173 1 1 0.16729 1 1 0.15960 1 1 0.15290 1 1 0.765 1 1 9.411 1 1 4.381 1 1 Ba-133 1 1 0.218 1 1 0.13042 1 1 0.13253 1 1 0.13904 1 1 0.13220 1 1 1.346 1 1 0.249 1 1 5.173 1 1 Ir-192 1 1 0.380 1 1 0.10598 1 1 0.10720 1 1 0.10372 1 1 0.10760 1 1 1.505 1 1 0.371 1 1 3.605 1 1 Au-198 1 1 0.412 1 1 0.10020 1 1 0.10646 1 1 0.10355 1 1 0.10420 1 1 3.838 1 1 2.168 1 1 0.623 1 1 Cs-137 1 1 0.663 1 1 0.08502 1 1 0.09701 1 1 0.08139 1 1 0.08513 1 1 0.129 1 1 13.955 1 1 4.393 1 1 Ra-226 1 1 0.830 1 1 0.07703 1 1 0.08973 1 1 0.07532 1 1 0.07681 1 1 0.286 1 1 16.82 1 1 1.939 1 1 Co-60 1 1 1.25 1 1 0.06354 1 1 0.07183 1 1 0.06592 1 1 0.06283 1 1 1.13 1 1 14.324 1 1 4.918 1 1 Nuclide 1 1 Mean-energy (MeV) 4 1 Mass attenuation coefficient of spleen 3 1 Percentage difference (%) for spleen 1 1 1 1 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 XCOM 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 Pd-103 1 1 0.021 1 1 0.75267 1 1 0.75276 1 1 0.73715 1 1 0.74250 1 1 1.351 1 1 1.362 1 1 0.725 1 1 I-125 1 1 0.029 1 1 0.40881 1 1 0.38173 1 1 0.40537 1 1 0.40100 1 1 1.91 1 1 5.048 1 1 1.078 1 1 Cs-131 1 1 0.030 1 1 0.38711 1 1 0.39811 1 1 0.38624 1 1 0.38070 1 1 1.655 1 1 4.373 1 1 1.434 1 1 Tc-99m 1 1 0.140 1 1 0.15114 1 1 0.15819 1 1 0.15091 1 1 0.15240 1 1 0.833 1 1 3.66 1 1 0.987 1 1 Ba-133 1 1 0.218 1 1 0.13022 1 1 0.14130 1 1 0.13012 1 1 0.13180 1 1 1.213 1 1 6.723 1 1 1.291 1 1 Ir-192 1 1 0.380 1 1 0.10645 1 1 0.10806 1 1 0.10376 1 1 0.10730 1 1 0.798 1 1 0.703 1 1 3.411 1 1 Au-198 1 1 0.412 1 1 0.10003 1 1 0.10447 1 1 0.10359 1 1 0.10390 1 1 3.868 1 1 0.545 1 1 0.299 1 1 Cs-137 1 1 0.663 1 1 0.08479 1 1 0.09626 1 1 0.08454 1 1 0.08484 1 1 0.0589 1 1 11.863 1 1 0.354 1 1 Ra-226 1 1 0.830 1 1 0.07544 1 1 0.08569 1 1 0.07656 1 1 0.07655 1 1 1.471 1 1 10.666 1 1 0.013 1 1 Co-60 1 1 1.25 1 1 0.06152 1 1 0.06317 1 1 0.06643 1 1 0.06261 1 1 1.771 1 1 0.886 1 1 5.75 1 1 Nuclide 1 1 Mean-energy (MeV) 4 1 Mass attenuation coefficient of muscle 3 1 Percentage difference (%) for muscle 1 1 1 1 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 XCOM 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 Pd-103 1 1 0.021 1 1 0.75216 1 1 0.73864 1 1 0.73794 1 1 0.73480 1 1 2.308 1 1 0.519 1 1 0.425 1 1 I-125 1 1 0.029 1 1 0.41131 1 1 0.39976 1 1 0.39903 1 1 0.39830 1 1 3.163 1 1 0.365 1 1 0.182 1 1 Cs-131 1 1 0.030 1 1 0.38842 1 1 0.38517 1 1 0.36152 1 1 0.37830 1 1 2.605 1 1 1.783 1 1 4.641 1 1 Tc-99m 1 1 0.140 1 1 0.15305 1 1 0.16913 1 1 0.15910 1 1 0.15250 1 1 0.359 1 1 9.832 1 1 4.148 1 1 Ba-133 1 1 0.218 1 1 0.13101 1 1 0.13491 1 1 0.13869 1 1 0.13180 1 1 0.603 1 1 2.305 1 1 4.967 1 1 Ir-192 1 1 0.380 1 1 0.10689 1 1 0.10552 1 1 0.10372 1 1 0.10730 1 1 0.383 1 1 1.686 1 1 3.451 1 1 Au-198 1 1 0.412 1 1 0.10073 1 1 0.10759 1 1 0.10356 1 1 0.10390 1 1 3.147 1 1 3.429 1 1 0.328 1 1 Cs-137 1 1 0.663 1 1 0.08591 1 1 0.07351 1 1 0.08142 1 1 0.08491 1 1 1.164 1 1 15.508 1 1 4.286 1 1 Ra-226 1 1 0.830 1 1 0.07589 1 1 0.06854 1 1 0.07531 1 1 0.07660 1 1 0.935 1 1 11.759 1 1 1.712 1 1 Co-60 1 1 1.25 1 1 0.06268 1 1 0.06038 1 1 0.06575 1 1 0.06265 1 1 0.047 1 1 3.759 1 1 4.714 1 1 Nuclide 1 1 Mean-energy (MeV) 4 1 Mass attenuation coefficient of cortical bone 3 1 Percentage difference (%) for cortical bone 1 1 1 1 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 XCOM 1 1 MCNP 1 1 GAENT4 1 1 Theoretical 1 1 Pd-103 1 1 0.021 1 1 3.97160 1 1 3.82857 1 1 3.46192 1 1 3.46000 1 1 12.881 1 1 9.626 1 1 0.055 1 1 I-125 1 1 0.029 1 1 1.70540 1 1 1.64494 1 1 1.49289 1 1 1.44100 1 1 15.503 1 1 12.398 1 1 3.475 1 1 Cs-131 1 1 0.030 1 1 1.54922 1 1 1.49721 1 1 1.39676 1 1 1.32000 1 1 14.795 1 1 11.836 1 1 5.495 1 1 Tc-99m 1 1 0.140 1 1 0.14587 1 1 0.16152 1 1 0.16139 1 1 0.15280 1 1 4.75 1 1 5.398 1 1 5.322 1 1 Ba-133 1 1 0.218 1 1 0.12065 1 1 0.13845 1 1 0.12427 1 1 0.12630 1 1 4.682 1 1 8.775 1 1 1.633 1 1 Ir-192 1 1 0.380 1 1 0.11508 1 1 0.11009 1 1 0.10545 1 1 0.10120 1 1 12.061 1 1 8.075 1 1 4.03 1 1 Au-198 1 1 0.412 1 1 0.10691 1 1 0.10385 1 1 0.09134 1 1 0.09784 1 1 8.483 1 1 5.787 1 1 7.116 1 1 Cs-137 1 1 0.663 1 1 0.07824 1 1 0.09546 1 1 0.07190 1 1 0.07965 1 1 1.802 1 1 16.561 1 1 10.778 1 1 Ra-226 1 1 0.830 1 1 0.07082 1 1 0.08420 1 1 0.07373 1 1 0.07180 1 1 1.383 1 1 14.726 1 1 2.617 1 1 Co-60 1 1 1.25 1 1 0.05754 1 1 0.04501 1 1 0.05366 1 1 0.05869 1 1 1.998 1 1 30.393 1 1 9.373 In the low-energy region, the calculated mass attenuation coefficients were less than those of Geant4 and MCNPX when compared to the XCOM values, as can be seen in Figs. 3–10 Figs. 3–10 . The differences in attenuation values can be due to different models in the Monte Carlo codes. Fundamentally, both MC codes use the Evaluated Photon Data Library (EPDL), which is mostly related to the NIST standard reference data products [ 19 19 ]. The theoretical results are in excellent agreement with the XCOM program. However, the values of Geant4 and MCNPX show extremely little difference from both academic and XCOM costs. The discrepancy between these results could be due to the scattering of radiation around and not reaching the detector and the random process of the Monte Carlo method [ 20 20 ]. As shown in Tables 2–9 Tables 2–9 , it can be noted that the lowest standard deviation rates were obtained for the theoretical data as compared to XCOM. It was observed that the photon attenuation parameter of each sample decreased with enhanced photon energy owing to the increased penetration of the photons from the attenuator. In low-energy regions, the MCNPX and GEANT4 results are closer to each other than they are with the theoretical products. This result indicates that MCNPX may be a more suitable program for live biological media investigations in low-energy regions. In addition, MCNPX has extensive cross-sectional libraries for low-energy areas. The results also show that MCNPX and GEANT4 within the range of low, medium, and high energy can differ because these codes have been used for other physical models. The mass attenuation coefficients of human body organs are comparable with the theoretical and standard NIST results [ 32 32 ]. To analyze and compare the percentage difference among XCOM data, MCNPX, the Geant4 programs, and the theoretical approach, we calculated the deviations among these methods ( Tables 2–9 Tables 2–9 ). The percentage difference was calculated using the formula ( D = ( E a − E b )/ E b × 100%). In this formula, E a is the first result and E b is the second result in calculating the percentage difference between two values. The mass attenuation coefficient (μ/ρ) values of tissues within the mean photon energy range of 21 keV to 1.25 MeV are listed in Tables 2–9 Tables 2–9 . The μ/ρ values of the tissues vary significantly between different energy regions. Within the low-energy region, the variation is quite broad, and is merely due to a photoelectric effect, and sharply increases and decreases along with the changes in the energy levels. This is natural because the interaction between the cross section is dependent on the photon energy and atomic number. However, Compton scattering becomes a dominant incident within the medium-energy region as the interaction between the cross-section is independent of the photon energy, whereas it is largely dependent upon the atomic number. The MCNPX and Geant4 simulated mass attenuation coefficients for tissues were comparable with the theoretical XCOM values and theoretical data. It can be concluded that the mass attenuation coefficients for tissues having low and high atomic number elements for low- to high-energy photons were found to be comparable with the experiment and GEANT-4 results, as well as the MCNP simulation codes. The present study will be beneficial for developing materials with different energy levels for radiation dosimetry and medical and nuclear technologies. According to the results obtained from Tables to 2–9 Tables to 2–9 , with increasing energy, the mass attenuation coefficient decreased for all tissues. Whereas the cortical bone has the highest mass attenuation, the breast has the least mass attenuation. In other words, bone tissue has a higher attenuation coefficient than the other organs because of its higher atomic number and density, and breast tissue, owing to its lower density, has a lower mass attenuation coefficient than the other organs. The increase in mass attenuation is related to the inverse of energy and directly related to the density. The percentage differences were calculated for each simulation code separately. As observed in Tables 2–9 Tables 2–9 , the theoretical and Geant4 methods had mostly similar deviations for the investigated organs. It can be concluded that each Monte Carlo code has different capabilities in different energy regions. In the low-energy area, the standard deviation rates of theoretical and Geant4 were less than those of MCNPX. Ermis et al. [ 19 19 ] and Huseyin et al. [ 34 34 ] measured the mass attenuation coefficients of different parts of the human body using Monte Carlo methods, and the results were in good agreement with the results of their study on the calculation of the mass attenuation coefficient. 4. Conclusion 1 The Monte Carlo method is a powerful tool for simulating the interaction of photons with the material, and one of its applications is to calculate the mass attenuation coefficient. The accuracy of this method depends on the simulated geometry, composition of the material, and density and use from the corrected physical model. This study proved that the MCNPX and Geant4 code are suitable and efficient codes for mass attenuation coefficients in low- and high-energy fields and can be beneficial for future studies, where experimental conditions and data are unavailable. The mass attenuation coefficients of human body organs were calculated using MCNPX, GEANT4, XCOM, and theoretical methods for the different medical sources within a photon energy range of 0.021–1.25 MeV and have used a standard simulation geometry. In this study, the data obtained from the Monte Carlo simulation for the standard deviation of mass attenuation coefficients simulated using the theoretical method and XCOM data were found to be extremely small, indicating that the results of the present investigation were in excellent agreement with the standard database. The discrepancy between the mass attenuation coefficients simulated using the Geant4 and theoretical methods and NIST data were found to be extremely small. The disparity between some of the results could be due to differences between the cross-section libraries of the Monte Carlo programs. The results of the present investigation into the Monte Carlo method were in excellent agreement with the standard database. According to the results, the mass attenuation coefficient for cortical bone is higher due to its atomic number and higher density. Breast tissue has a lower mass attenuation coefficient than other organs because of its lower density. In addition, the results showed that, within the low photon energy range, the mass attenuation coefficient decreases with increasing energy, and within the higher energy range (1–2 MeV), the mass attenuation coefficients of the materials differ less and are almost equal. Reference A.C. Moreno , R.J. Kudchadker , J. Wang , et al ., MRI Image-Guided Low-Dose Rate Brachytherapy for Prostate Cancer . In: Mayadev J. , Benedict S ., Kamrava M. (eds) Handbook of Image-Guided Brachytherapy . Springer , Cham . ( 2017 ). https://doi.org/10.1007/978-3-319-44827-5_12 https://doi.org/10.1007/978-3-319-44827-5_12 . MRI Image-Guided Low-Dose Rate Brachytherapy for Prostate Cancer J.C. Blasko , P.D. Grimm , J.E. Sylvester , et al ., Palladium-103 brachytherapy for prostate carcinoma . Int. J. Radiation Oncology Biol. Phys 46 , 839 - 850 ( 2000 ). https://doi.org/10.1016/S0360-3016(99)00499-X https://doi.org/10.1016/S0360-3016(99)00499-X . Palladium-103 brachytherapy for prostate carcinoma T.L. Fowler , M.K. Buyyounouski , C.H. Jenkins , et al ., Clinical implementation of 3D printing for brachytherapy: techniques and emerging applications . Brachytherapy 15 , S166 ( 2016 ). https://doi.org/10.1016/j.brachy.2016.04.297 https://doi.org/10.1016/j.brachy.2016.04.297 Clinical implementation of 3D printing for brachytherapy: techniques and emerging applications E.A. Markelova , S.S. Khujaev , A. Vasidov . The calculation of barium-131 radioactivity and obtaining the cesium-131 from barium-131 at Nuclear Reactor . Uzbekiston Fizika Zhurnali 13 , 381 - 386 ( 2011 ). https://inis.iaea.org/search/search.aspx?orig_q=RN:44048651 https://inis.iaea.org/search/search.aspx?orig_q=RN:44048651 . The calculation of barium-131 radioactivity and obtaining the cesium-131 from barium-131 at Nuclear Reactor M. Fragoso , P.A. Love , F.V. erhaegen , et al ., The dose distribution of low dose rate Cs-137 in intracavitary brachytherapy: comparison of Monte Carlo simulation, treatment planning calculation and polymer gel measurement . Physics in Medicine & Biology 49 , 5459 - 5474 ( 2004 ). https://doi.org/10.1088/0031-9155/49/24/005 https://doi.org/10.1088/0031-9155/49/24/005 . The dose distribution of low dose rate Cs-137 in intracavitary brachytherapy: comparison of Monte Carlo simulation, treatment planning calculation and polymer gel measurement F. Issa , A.A. Rahman , R.P. Hugtenburg , et al ., Establishment of Ge-doped optical fibers as thermoluminescence dosimeters for brachytherapy . Appli. Radiation and Isotopes 70 , 1158 - 1161 ( 2012 ). https://doi.org/10.1016/j.apradiso.2011.12.027 https://doi.org/10.1016/j.apradiso.2011.12.027 . Establishment of Ge-doped optical fibers as thermoluminescence dosimeters for brachytherapy M.G. David , C. Salata , P.H. Rosado , et al ., Determination of the chemical yield on the Fricke dosimetry for 192Ir sources used in brachytherapy . Brazilian Congress of Metrology , ( 2015 ). https://hdl.handle.net/2050011876/943 https://hdl.handle.net/2050011876/943 . Determination of the chemical yield on the Fricke dosimetry for 192Ir sources used in brachytherapy M.E. Alden , M. Mohiuddin , The impact of radiation dose in combined external beam and intraluminal Ir-192 brachytherapy for bile duct cancer . Int. J. Radiation Oncology Biol. Phys 28 , 945 - 951 ( 1994 ). https://doi.org/10.1016/0360-3016(94)90115-5 https://doi.org/10.1016/0360-3016(94)90115-5 . The impact of radiation dose in combined external beam and intraluminal Ir-192 brachytherapy for bile duct cancer I. El. Gamal , C. Cojocaru , E. Mainegra-Hing , et al ., The Fricke dosimeter as an absorbed dose to water primary standard for Ir-192 brachytherapy . Physics in Medicine & Biology 60 , 4481 - 4495 ( 2015 ). https://doi.org/10.1088/0031-9155/60/11/4481 https://doi.org/10.1088/0031-9155/60/11/4481 . The Fricke dosimeter as an absorbed dose to water primary standard for Ir-192 brachytherapy E.C. Merchan , M. Magallon , J. Martin-Villar , et al ., Long term follows up of hemophilic arthropathy treated by Au-198 radiation synovectomy . International orthopedics 17 , 120 - 124 ( 1993 ). https://doi.org/10.1007/BF00183554 https://doi.org/10.1007/BF00183554 . Long term follows up of hemophilic arthropathy treated by Au-198 radiation synovectomy J. Dybicki , O. J. Balchum , G.R. Meneely , et al ., Treatment of pleural and peritoneal effusion with intracavitary colloidal radiogold (Au 198) . AMA Arch. Intern. Med . 104 , 802 - 815 ( 1959 ). https://doi.org/10.1001/archinte.1959.00270110122017 https://doi.org/10.1001/archinte.1959.00270110122017 . Treatment of pleural and peritoneal effusion with intracavitary colloidal radiogold (Au 198) M.I. Sayyed , F. Akman , I.H. Geçibesler , et al ., Measurement of mass attenuation coefficients, effective atomic numbers, and electron densities for different parts of medicinal aromatic plants in low-energy region . Nucl. Sci. Tech . 29 , 144 ( 2018 ). https://doi.org/10.1007/s41365-018-0475-0 https://doi.org/10.1007/s41365-018-0475-0 . Measurement of mass attenuation coefficients, effective atomic numbers, and electron densities for different parts of medicinal aromatic plants in low-energy region A. Bagulya , J.M. Brown , H. Burkhardt , et al ., Recent progress of GEANT4 electromagnetic physics for LHC and other applications . J Phys. Conference Series 898 , 042032 ( 2017 ). https://doi.org/10.1088/1742-6596/898/4/042032 https://doi.org/10.1088/1742-6596/898/4/042032 . Recent progress of GEANT4 electromagnetic physics for LHC and other applications J.L. Venselaar , P.H. Van der Giessen , W.J. Dries , Measurement and calculation of the dose at large distances from brachytherapy sources: Cs-137, Ir-192, and Co-60 . Med. Phys . 23 , 537 - 543 ( 1996 ). https://doi.org/10.1118/1.597811 https://doi.org/10.1118/1.597811 . Measurement and calculation of the dose at large distances from brachytherapy sources: Cs-137, Ir-192, and Co-60 G. Kemikiler , History of Brachytherapy . Turk J Oncol . 34 , 1 - 10 ( 2019 ). https://doi.org/10.5505/tjo.2019.1 https://doi.org/10.5505/tjo.2019.1 . History of Brachytherapy R.J. Gibbons , Myocardial perfusion imaging . Heart 83 , 355 - 360 ( 2000 ). https://doi.org/10.1136/heart.83.3.355 https://doi.org/10.1136/heart.83.3.355 . Myocardial perfusion imaging C.P. Goddard , A.H. Stead , P.A. Mason , et al ., An iodine-125 radioimmunoassay for the direct detection of benzodiazepines in blood and urine . Analyst 111 , 525 - 529 ( 1986 ). https://doi.org/10.1039/AN9861100525 https://doi.org/10.1039/AN9861100525 . An iodine-125 radioimmunoassay for the direct detection of benzodiazepines in blood and urine M.R. Ioan , V. Fugaru , S. Bercea , et al ., Co-60 Specific Gamma-Ray Constant (Γ) Determinations for Various Biological Materials Involved in Radiotherapy Procedures, by Using GEANT4 and NIST XCOM . Rom. J. Phys 63 . 701 ( 2018 ). https://www.researchgate.net/publication/319442968 https://www.researchgate.net/publication/319442968 . Co-60 Specific Gamma-Ray Constant (Γ) Determinations for Various Biological Materials Involved in Radiotherapy Procedures, by Using GEANT4 and NIST XCOM E.E. Ermis , F.B. Pilicer , E. Pilicer , et al ., A comprehensive study for mass attenuation coefficients of different parts of the human body through Monte Carlo methods . Nucl. Sci. Tech . 27 , 54 ( 2016 ). https://doi.org/10.1007/s41365-016-0053-2 https://doi.org/10.1007/s41365-016-0053-2 . A comprehensive study for mass attenuation coefficients of different parts of the human body through Monte Carlo methods M.S. Al-Buriahi , H. Arslan , B.T. Tonguç , Mass attenuation coefficients, water, and tissue equivalence properties of some tissues by Geant4, XCOM, and experimental data . IJPAP 57 , 433 - 437 ( 2019 ). https://op.niscair.res.in/index.php/IJPAP/article/view/22878/465477021 https://op.niscair.res.in/index.php/IJPAP/article/view/22878/465477021 . Mass attenuation coefficients, water, and tissue equivalence properties of some tissues by Geant4, XCOM, and experimental data H.C. Manjunatha , L. Seenappa , Pocket formula for mass attenuation coefficient, effective atomic number, and electron density of human tissues . Nucl. Sci. Tech . 30 , 1 - 8 ( 2019 ). https://doi.org/10.1007/s41365-019-0565-7 https://doi.org/10.1007/s41365-019-0565-7 . Pocket formula for mass attenuation coefficient, effective atomic number, and electron density of human tissues A.H. Taqi , H.J. Khalil , Experimental, and theoretical investigation of gamma attenuation of building materials . J. Nucl. Particle Phys . 7 , 6 - 13 ( 2017 ). https://doi.org/10.5923/j.jnpp.20170701.02 https://doi.org/10.5923/j.jnpp.20170701.02 . Experimental, and theoretical investigation of gamma attenuation of building materials H. Arslan , Photon attenuation parameters for some tissues from Geant4 simulation, theoretical calculations, and experimental data: a comparative study . Nucl. Sci. Tech . 30 , 96p1 - 10 ( 2019 ). https://doi.org/10.1007/s41365-019-0617-z https://doi.org/10.1007/s41365-019-0617-z . Photon attenuation parameters for some tissues from Geant4 simulation, theoretical calculations, and experimental data: a comparative study B. Ababneh , R. Hashim , I.L. Shuaib , Investigation of mass attenuation coefficient of almond gum bonded Rhizophora spp. particleboard as equivalent human tissue using XRF technique in the 16.6-25.3 keV photon energy . Australas Phys. Eng. Sci. Med . 39 , 871 - 876 ( 2016 ). https://doi.org/10.1007/s13246-016-0482-6 https://doi.org/10.1007/s13246-016-0482-6 . Investigation of mass attenuation coefficient of almond gum bonded Rhizophora spp. particleboard as equivalent human tissue using XRF technique in the 16.6-25.3 keV photon energy M. Alssabbagh , A.A. Tajuddin , M.B. Manap , et al ., Evaluation of nine 3D printing materials as tissue- equivalent materials in terms of mass attenuation coefficient and mass density . INTERNATIONAL J. Adv. Appl. Sci . 4 , 168 - 173 ( 2017 ). https://www.researchgate.net/publication/321823909 https://www.researchgate.net/publication/321823909 . Evaluation of nine 3D printing materials as tissue- equivalent materials in terms of mass attenuation coefficient and mass density A.M. El-Khayatt , A.M. Ali , V.P. Singh , et al ., Determination of mass attenuation coefficient of low-Z dosimetric materials . Radiation Effects Defects in Solids 169 , 1038 - 44 ( 2014 ). https://doi.org/10.1080/10420150.2014.988626 https://doi.org/10.1080/10420150.2014.988626 . Determination of mass attenuation coefficient of low-Z dosimetric materials M. Bethesda . Tissue substitutes in radiation dosimetry and measurement . International Commission on Radiation Units and Measurements (ICRU) , ( 1989 ). Tissue substitutes in radiation dosimetry and measurement Y.S. Rammah , A.S. Abouhaswa , A.H. Salama , et al ., Optical, magnetic characterization, and gamma-ray interactions for borate glasses using XCOM program . J Theor. Appl. Phys . 13 , 155 - 164 ( 2019 ). https://doi.org/10.1007/s40094-019-0331-6 https://doi.org/10.1007/s40094-019-0331-6 . Optical, magnetic characterization, and gamma-ray interactions for borate glasses using XCOM program J.H. Hubbell , Photon cross-section, attenuation coefficient, and energy absorption coefficients from 10 keV to 100 GeV. NSRDS-NBS 29 C ( 1969 ). Photon cross-section, attenuation coefficient, and energy absorption coefficients from 10 keV to 100 GeV. NSRDS-NBS 29 C G. Lakshminarayana , M.I. Sayyed , S.O. Baki , et al ., Borotellurite glasses for gamma-ray shielding: an exploration of photon attenuation coefficients and structural and thermal properties . Journal of Elec Materi . 48 , 930 - 941 ( 2019 ). https://doi.org/10.1007/s11664-018-6810-8 https://doi.org/10.1007/s11664-018-6810-8 . Borotellurite glasses for gamma-ray shielding: an exploration of photon attenuation coefficients and structural and thermal properties V.P. Singh , S.P. Shirmardi , M.E. Medhat , et al ., Determination of mass attenuation coefficient for some polymers using Monte Carlo simulation . Vacuum 119 , 284 - 288 ( 2015 ). https://doi.org/10.1016/j.vacuum.2015.06.006 https://doi.org/10.1016/j.vacuum.2015.06.006 . Determination of mass attenuation coefficient for some polymers using Monte Carlo simulation H.O. Tekin , E.E. Altunsoy , T. Manici , et al ., Mass attenuation coefficients of human body organs using MCNPX Monte Carlo code . Iranian J Med. Phys . 14 , 229 - 240 ( 2017 ). https://doi.org/10.22038/IJMP.2017.23478.1230 https://doi.org/10.22038/IJMP.2017.23478.1230 . Mass attenuation coefficients of human body organs using MCNPX Monte Carlo code A. Bagulya , J.M. Brown , H. Burkhardt , et al ., Recent progress of GEANT4 electromagnetic physics for LHC and other applications . J Phys. Conf. Series 898 , 042032 ( 2017 ). https://doi.org/10.1088/1742-6596/898/4/042032 https://doi.org/10.1088/1742-6596/898/4/042032 . Recent progress of GEANT4 electromagnetic physics for LHC and other applications K. Özge , H.O. Tekin , V.P. Singh , Determination of mass attenuation coefficients of different types of concretes using Monte Carlo method . EJOSAT 15 , 591 - 598 ( 2019 ). https://doi.org/10.31590/ejosat.535203 https://doi.org/10.31590/ejosat.535203 . Determination of mass attenuation coefficients of different types of concretes using Monte Carlo method 10.1007/s41365-020-00827-1 2020-07-26 2020-10-18 2020-10-22 2020-12-04 2020-12-01 2021-04-10 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2020 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-020-00827-1 http://dx.doi.org/10.1007/s41365-020-00827-1 . 2020 Nuclear Science and Techniques 12 31