Abstract
Radiation that is emitted from unstable nuclei during radioactive decay is an important phenomenon to be used in large fields, and thus, radiation shielding properties are important especially for gamma rays. Thus, in the present work, the radiation shielding properties in terms of linear attenuation coefficients and some other quantities for medical interest materials of water, fat and bone have been obtained. The results simulated by Phy-X/PSD online code the energy range of 10−3–105 MeV.
1 Introduction
Some of the atomic nuclei are not stable and could be due to natural reasons or due to some nuclear reactions, which are man-made. Those nuclei must be converted to stable nuclei by emitting some particles, the so-called radiation. If this emission is the result of natural, then the emitting radiation is called natural radiation and if it is man-made (after nuclear reaction), then it is called man-made radiation. While natural radiation has existed since the formation of the universe and because of the long half-life of radionuclides. Using radiation in different fields has spread man-made radiation. Besides using radiation in different fields, its hazardous effect on human beings has led researchers to work in dosimetry and shielding topics. Many different radiation processes are used in the health sector, especially to diagnose and treat diseases. This radiation may affect both radiation workers and patients and thus they should be kept away from these radiations. Thus, medical dosimetry is developed in order to design, calculate and measure the radiation dose portals. Gamma radiation types are different from others as they are uncharged and thus it is difficult t to stop them, and also detection is more difficult than other charged particles. Therefore, simulation works are commonly used to estimate the shielding of gamma rays. The linear attenuation coefficient (LAC, µ cm−1) is generally used to express the shielding quantity of the material. The LAC is expressed as the possibility of a radiation coupling with a material per unit path length [1]. The shielding characteristics depend on densities, the atomic number of the materials and also gamma-ray energies [1,2,3,4,5].
Many different shielding materials have been tested in order to develop valuable material besides conventional material for shielding purposes [6–39].
Thus, many different research works have been performed on the development of shielding materials for gamma rays [6–39] and a number of studies were performed in the pharmaceutical sector [40–42]. There are also other works done by other methods such as ANN [43–49].
In this study, shielding capabilities of some materials of medical interest were obtained using Phy-X/PSD software.
2 Materials and methods
In this study, the shielding properties of gamma rays of human tissue-related materials are determined. The human tissue is made of water, fat, and bone tissue. Therefore, human tissue-related materials of medical interest are considered as fat, water, and bone matrix. The elemental composition of these materials is given in Table 1 [50].
Chemical contents of materials (wt%) [50]
| Code | Materials | H | C | N | O | P | Ca | Density (g cm−3) |
|---|---|---|---|---|---|---|---|---|
| S1 | Water | 0.1119 | — | — | 0.8881 | — | — | 1.00 |
| S2 | Fat | 0.1190 | 0.7720 | — | 0.1090 | — | — | 0.92 |
| S3 | Bone matrix | 0.0344 | 0.7140 | 0.1827 | 0.0689 | — | — | 1.13 |
The LACs (µ cm−1) of gamma rays of any material are a basic parameter and it is also used to obtain other parameters in medical dosimetry. The theory of the LAC (µ cm−1) is expressed by the Beer–Lambert law as in equation (1) [39]
where N o and N are the number of counts before and after in the spectrum, respectively, passing through, and x is the material’s thickness.
The LAC and LAC-based parameters were also determined by Phy-X/PSD online software program, which was developed by Sakar et al. [51,52].
3 Results and discussion
In order to investigate radiation shielding properties of related tissue materials of medical interest, the LAC, MAC, mfp, HVL, TVL, Z eff, N eff, and C eff have been determined.
The calculated results of LAC are displayed in Figure 1 as a function of gamma-ray energies. It may be clearly seen in Figure 1 that the distribution of LAC decreased when the gamma-ray energies increased. It is also clear from this that the variation of LAC with the gamma rays is energy-dependent.
The results of LAC as a function of gamma-ray energies.
At low energy, the LAC sharply decreased and slightly decreased at mid energy. At high energy, it seemed to be constant. This could be due to different absorption mechanisms for different gamma energies [4]. For the special gamma-ray energies of 0.511, 0.662, 0.835, 1.173, 1.275, and 1.332 MeV, which are interesting in medical application, the LACs are shown in Figure 2 for all materials. It may be observed from this figure that the LAC decreased linearly when the gamma-ray energies increased. A high correlation rate (R 2 > 97%) has been obtained for all materials. On comparing the LAC with the material type, the highest LAC has been obtained for the S3 material while the lowest one is for the S2 material. This may be due to the fact that the density depends on LAC [2,3,5]; thus, the LAC is plotted versus the density at 0.511, 0.662, 0.835, 1.173, 1.275, and 1.332 MeV gamma rays in Figure 3. It may be observed from this figure that the LAC increased with the increase of the density of materials. This is in agreement with the previous works [6,7,8] and a good correlation has been obtained (R 2 > 99% for all energies).
The LAC as a function of gamma-ray energies for four materials.
The calculated LAC as a function of density.
The density of a material is also used to obtain mass attenuation coefficients (MACs) by dividing the LAC by the density. This is obtained and shown in Figure 4 for all materials. It may be observed from this figure that a similar structure has been obtained with the LAC apart from the quantities. It may also be observed in this figure that in the mid energy the MAC values are comparable for all materials, while, at other energies, S3 is higher than others.
The MAC distribution as a function of gamma-ray energies.
The mfp of any material, defined as the gamma-ray penetration length, may be obtained using equation (2)
The results of mfp varying with energies is shown in Figure 5; it can be observed from the figure that the mfp has a nonlinear relation with the LAC. It can also be observed that mfp is highest for S2 and lowest for S3.
The mfp distribution with the gamma-ray energies.
Other radiological parameters of HVL and TVL are expressed as the thickness of materials to stop half (50%) and 10% of gamma rays, respectively, and they are obtained using equations (3) and (4), respectively:
The obtained HVL and TVL results are shown in Figures 6 and 7 and it can be observed that the distribution of HVL and TVL is similar to the mfp. It can also be observed that the highest values of HVL and TVL are for S2 while the lowest ones are for S3, as expected.
The HVL distribution with the gamma-ray energies.
The TVL distribution with the gamma-ray energies.
The effective atomic number (Z eff) and electron density (N eff) are other important parameters for the radiation shielding material and are obtained using equations (5) and (6), respectively [39]:
where σ a and σ el are the total atomic and electric cross sections, respectively, and they are obtained via MAC using equations (7 and 8):
In equation (7), μ/ρ is the total MAC, N is the Avogadro’s number, and A i and w i are atomic weights and fractional weights of each constituent of materials:
where f i is the atomic number of element i and Z i is the atomic number of the ith element in a mixture.
The calculated Z eff and N eff have been displayed as a function of gamma-ray energies in Figures 8 and 9, respectively. It is clearly seen from these figüres that both depend on the energy of gamma rays and the distributions are similar. As can be seen from this figure, the values decreased at gamma energies of 0.1-1 MeV.
The calculated Z eff as a function of gamma-ray energies.
The N eff distribution as a function of gamma-ray energies.
The effective conductivity (C eff) of materials was also calculated as a function of gamma-ray energies and the results are shown in Figure 10.
The calculated C eff as a function of gamma-ray energies.
4 Conclusion
The shielding properties of some human tissue-related materials against gamma rays have been determined. The energy range of gamma rays is 10−3–105 MeV and the calculations were done using Phy-X/PSD. It can be concluded that the LAC decreases with an increase of gamma-ray energies. It is also seen that the bone has a higher shielding capability than water and fat.
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Funding information: The authors declare that there is no funding to be acknowledged.
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Author contributions: M.S. has performed all work (simulation, analyses, and writing) and accepts responsibility for releasing this material.
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Conflict of interest: The author declares that she has no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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Ethical approval: The conducted research is not related to either human or animal use.
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Data availability statement: The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.
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