1 Introduction

When a beam of X or gamma-rays pass through the matter, the removal of photons from the beam is called attenuation. Absorption and scattering of the primary photons cause to attenuation. The linear attenuation coefficient (µ) is defined as the fraction of photons removed from a monoenergetic beam of X- or gamma-rays per unit thickness of material. It is typically expressed in units of inverse centimeters (cm^-1). For a monoenergetic beam of photons,the relationship between the number of incident photons (N₀) and those that are transmitted (N) through a thickness x without interaction are exponential.

The numbers of atoms per volume affect the probability of interaction for a given thickness. The linear attenuation coefficient is normalized by dividing the density of the material to overcome the dependency of the material. This is calledthe mass attenuation coefficient. The units of the mass attenuation coefficient are cm²/g ^[1].

XCOM is a program which generates mass attenuation coefficients for desired energies from 1 keV up to 100 GeV and also elements, compounds, and mixtures. It does not only generate attenuation coefficients but also partial cross-sections for incoherent, coherent scattering, photoelectric absorption, and pair production from the nucleus of atom or atomic electrons ^[2].

The simulation to estimate the mass attenuation coefficient can also be done with the use of well-known simulation programs such as GEANT4 and FLUKA ^[3-6].These tools are based on the Monte Carlo (MC) methods to simulate the interaction of particles with their traversing medium. Their application areas vary from a wide range of topics including space, accelerators, medical, high energy, and particle physics ^[7-10].

Tomal et al. ^[11]experimentally determined the linear attenuation coefficient of the breast tissue. Linear attenuation coefficients of tissue were theoretically calculated by Böke^[12].Akar et al. ^[13] investigated mass attenuation coefficients of bone, muscle, fat, and water by an experimental method.

In medical imaging, such as PET, an attenuation correction for gamma photons is fulfilled to enhance the spatial resolution i.e. image quality. This correction is performed by taking into consideration the mass attenuation coefficients of the related parts of the human body. In this regard, mass attenuation coefficients of the related biological materials have great importance in this process. For this reason, another MC method (FLUKA) was utilized for the first time to determine the coefficients for blood, bone, lung, eye lenses, adipose, tissue, muscle, brain, and skin materials at different energiesin this study as an alternative method,and the obtained results were compared with GEANT4, XCOM, and NIST values.

2 Methods

GEANT4 is a C++ based MC simulation code. There are three mandatory classes for the geometry description (DetectorConstruction), physics (PhysicsList), and generated particles (PrimaryGeneratorAction), while there are additional user classes to get information from each step, event, and run (SteppingAction.cc, EventAction.cc and RunAction.cc).FLUKA is another well-known code which is based on the FORTRAN language. Even if there are built-in scoring cards to evaluate requested quantities, it also has various routines to retrieve information from different processes. In this work,userini.f, userin.f, and mgdraw.f routines and theirentries (bxdraw, endraw)were used. For both MC codes, we utilized the advantage of built-in physics lists, PENELOPE (PENetration and Energy LOss of Positrons and Electrons) physics for GEANT4 (version tag 4.10.p02) and PRECISIOn physicsfor FLUKA (version tag 2011.2c). It takes into account detailed photoelectric edge treatments, Compton scattering with inelastic factors and computed without fully taking into account binding and orbital electron motion, Rayleigh scattering, and fluorescence.PENELOPE is essential for low energies, and it includes Compton scattering, photoelectric effects, Rayleigh scattering, gamma conversion, bremsstrahlung, ionization, and positron annihilation ^[14]. More details about this physics lists can be found in the literature ^[15,16].While performing simulations for each photon energy impinging on different materials, we also took advantage of parallel job executions by using the power of PYTHON scripting language, as well as in the analysis phase of the results. The primary photons impinging on the materials are monoenergetic photons, which are defined as point like particles without any divergence.

When the photon transverses in the material, it loses its energy bywell-known processessuch as Compton scattering, photoelectric effects, and pair production.Blood, bone, lung, eye lenses, adipose, tissue, brain, muscle, and skin materials,which have the dimensions of 10 cm (width) x 10 cm (height) x 5 cm (thickness), as sketched in Fig. 1,were selected to investigate the photon attenuation.

Figure 1.Full-screen View

A sketch of simulated geometry.

All material definitions,such as stoichiometry and density,were kept the same in order to compare results amongst performed simulations. The elemental concentrations (% weight) of the materials are presented in Table 1.These concentrations were determined according tothe ICRP report ^[17].Photons with different energies were trackedfrom the surface of the material in the simulation. Afterwards, we determined the number of absorbed photons by subtracting the transferred photons from the incident onesin the material to evaluate mass attenuation coefficients from the known Eq.(1).

XCOM program (ver. 3.1) was also used to calculate the gamma-ray mass attenuation coefficients of the selected materials. This program used ICRU Report 44^[18]for material concentration. In the program, material types were first defined by their elemental fractions, which are exactly the same as in FLUKA and GEANT4, and then the gamma-ray energies were specified. The coefficients of the selected materials were finally calculated by the XCOM program.

In the MC calculation process, 10⁶ photons were sent to the used samples. They were tracked and the transmitted photons through the samples were determined. The linear attenuation coefficients were calculated according to Eq. (1) for each sample. Their mass attenuation coefficients were determined by dividing the obtained linear attenuation coefficients by the sample densities. This process was repeated for 10³ cycles for each sample. The averages of the results were found and the uncertainties were obtained by calculating their standard deviations.

Allcalculated coefficients from FLUKA, GEANT4, and XCOM programs were compared to NIST values ^[19]. The results are given in the next section.

3 Results

The calculated mass attenuation coefficients (µ_ρ) through FLUKA, GEANT4, XCOM, and NIST values(except for skin) were presented in Tables 2-10. In these tables,the calculated coefficients viathe FLUKA and GEANT4 programs were given with their standard deviations.

In Figs. 2, 3, 4, 5, 6, 7, 8, 9 and 10, calculated mass attenuation coefficients versus the photon energies of each absorber material are shown.The comparison of the results from the programs with the NIST values can be seen in these figures and tables as follows.

Figure 2.Full-screen View

Obtained mass attenuation coefficients vs. different photon energies for adipose tissue (ρ=0.92 g/cm³).

Figure 3.Full-screen View

Obtained mass attenuation coefficients vs. different photon energies for blood (ρ=1.069 g/cm³).

Figure 4.Full-screen View

Obtained mass attenuation coefficients vs. different photon energies for eye lens (ρ=1.1 g/cm³).

Figure 5.Full-screen View

Obtained mass attenuation coefficients vs. different photon energies for lung (ρ=1.05 g/cm³).

Figure 6.Full-screen View

Obtained mass attenuation coefficients vs. different photon energies for muscle (ρ=1.04 g/cm³).

Figure 7.Full-screen View

Obtained mass attenuation coefficients vs. different photon energies for tissue (ρ=1.00 g/cm³).

Figure 8.Full-screen View

Obtained mass attenuation coefficients vs. different photon energies for bone (ρ=1.85 g/cm³).

Figure 9.Full-screen View

Obtained mass attenuation coefficients vs. different photon energies for brain (ρ=1.039 g/cm³).

Figure 10.Full-screen View

Obtained mass attenuation coefficients vs. different photon energies for skin (ρ=1.1 g/cm³).

4 Discussion and Conclusion

The gamma-ray mass attenuation coefficients of blood, bone, lung, eye lenses, adipose, tissue, muscle, brain, and skin were calculated at different energies from low energy to high energy (60, 80, 150, 400, 500, 600, 1000, 1250, 1500 and 2000 keV) through FLUKA, GEANT4 MC, and XCOM programs. Calculated mass attenuation coefficients were also compared with NIST values.

In the low energy region, the calculated mass attenuation coefficients via GEANT4 were less than those of FLUKA when they were compared to NIST values, as seen in Figs. 2, 3, 4, 5, 6, 7, 8, 9 and 10 and Tables 2, 3, 4, 5, 6, 7, 8, 9 and 10. The results show that the FLUKA and GEANT4 values have differences at low energies up to 8% under the same conditions. But the difference decreases about 1%, which is reasonable for the higher energies. The difference at low energies comes from the variety of physics models used in each MC codes. Fundamentally, both MC codes use the EPDL (Evaluated Photon Data Library) library, which is mostly related to the NIST standard reference data products ^[20]. FLUKA uses the EPDL97 library for photon cross-section values, with the exception of Compton scattering, without fully considering binding and orbital electron motion ^[21] and performs detailed photoelectric edge treatments. GEANT4 also uses EPDL97 libraries for photon cross sections for various processes like the photoelectric effect, Compton scattering, the Rayleigh effect, and Bremsstrahlung; sub-shell integrated cross sections for the photoelectric effect and ionization; energy spectra of the secondary particles for electron processes; scattering functions for the Compton effect; form factors for the Rayleigh effect ^[22]. One reason for the difference between the FLUKA and GEANT4 MC codes at low energies comes from the treatment in this energy regime at which FLUKA handles a detailed photoelectric edge evaluation. On the other hand, the comparison of the MC results with the NIST values shows that calculated mass attenuation coefficients through FLUKA are closer to the NIST values than GEANT4 in the low energy region. It can be concluded that both MC codes are generally good candidates within small relative errors for medical applications.

Our results showed thatFLUKA was somewhat successful in comparison to GEANT4 in the calculation of the mass attenuation coefficients of the human body samples used here for low-energy photons (60, 80, and 150 keV) when compared to the NIST values.Additionally, Robert et al. ^[23] expressed that GEANT4 was originally developed for high energy physics applications, whereas FLUKA was developed and successfully applied both in the high and the low energy ranges. Our results have supported this expression in terms of gamma photon attenuations in the human body samples.

Medhat^[24] has calculated mass attenuation coefficients of three biological samples (blood, bone, and muscle) by GEANT4. When we compared our GEANT4 results with his results, it was seen that our results were in agreement with them, even if the used energies and material concentrations were different from each other. Further more, comparison showed that Medhat’s coefficient for muscle at 81 keV increased (0.220 cm²g^-1) unexpectedly while the coefficient was 0.200 cm²g^-1 for 59.5 keV gamma energy. However, our coefficient for muscle at 80 keV has normally decreased as the energy was increased.This showed that our result for muscle at 80 keVwas more acceptable than his result. As the incident photon energy increases, a decrease in the attenuation coefficient of a material is expected.

It is suggested from our results that similar calculations for different human body or biological samples should be repeated and the obtained results should be supported by experimental data for an accurate and satisfactory conclusion. Our analysis serves as a starting point for better understanding the discrepancies between the mass attenuation coefficient results of the GEANT4 and FLUKA programs for the human body samples, especially at low energies.

The XCOM method was also used to calculate the gamma-ray mass attenuation coefficients of the materials. The mass attenuation coefficients of brain from XCOM were foundto be higher than those of other programs,especially at low energies (Table 9, Fig. 9), although its elemental concentration (% weight) was the same as FLUKA and GEANT4.Since the NIST value and an experimental result were not available for the brain, it was impossible to compareour resultswith reference data. But this conclusion needs to be checked and repeated with further studies.

Different theoretical methods, such as Monte Carlo N-Particle Transport Code (MCNP), GEANT4,and XCOM have been used to calculate the gamma-ray mass attenuation coefficients of various elementsand compounds at various energies ^[25-27]. The FLUKA program was additionally used to determine the coefficients here, unlike these studies, as a novelty. The calculations through FLUKA, GEANT4, and XCOM, in this work, were performed for more materials and energy values than these studies also.

Consequently, the study was carried out to determine individual absorption radiation dose and interpret the criteria for radiation damage of the body in the future studies.It has been noticed that FLUKA results agreed betterin the selected energy range of gammas with NIST values than the others.It can be proposed from this conclusion that FLUKA MC program can be efficientlyused in the determination of gamma-ray mass attenuation coefficients of the samples of the human body, as well as GEANT4 and XCOM. In addition, it is believed that the FLUKA MC program can be a useful alternative tool for medical physics applications.