

TECHNICAL NOTE 



Year : 2022  Volume
: 47
 Issue : 1  Page : 105108 

Effective atomic number and electron density determination for fricke gel dosimeters using different methods
Ouiza Moussous
Departement of Medical Physics, Nuclear Research Center of Algiers, Algiers, Algeria
Date of Submission  13Jun2021 
Date of Decision  01Nov2021 
Date of Acceptance  05Nov2021 
Date of Web Publication  31Mar2022 
Correspondence Address: Dr. Ouiza Moussous 02 Boulevard Frantz Fanon B.P. 399 AlgerGare, Algiers Algeria
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/jmp.jmp_83_21
Abstract   
The effective atomic number and electron density of some Fricke gel dosimeters were calculated for photon interaction in the energy range from 10 keV to 1000 MeV using AutoZ_{eff}, direct and power law methods. The results are presented relative to those of water to allow direct comparison. It is found, that the effective atomic numbers and effective electron densities calculated with the AutoZ_{eff} and direct methods, demonstrates a good agreement in the energy interval extending from 0.1 MeV to 10 MeV. For effective atomic number relative to water, Ferrous Agarose Xylenol gel showed better water equivalence with difference up to 0.3%, while FXPVAGTA and Ferrous Xylenol Gelatin gels showed differences up to 2.26% and 2.25%, respectively.
Keywords: Effective atomic number, electron density, fricke gel dosimeter, water equivalence
How to cite this article: Moussous O. Effective atomic number and electron density determination for fricke gel dosimeters using different methods. J Med Phys 2022;47:1058 
How to cite this URL: Moussous O. Effective atomic number and electron density determination for fricke gel dosimeters using different methods. J Med Phys [serial online] 2022 [cited 2022 May 18];47:1058. Available from: https://www.jmp.org.in/text.asp?2022/47/1/105/341433 
Introduction   
Fricke and polymer gel dosimetry has emerged as a suitable tool to measure threedimensional dose distribution for complex delivery verification and quality assurance of modern radiotherapy techniques such as IMRT.^{[1],[2]} For externalbeam radiotherapy international protocol recommend calibration be carried out in terms of absorbed dose to water.^{[3]} Therefore, it is preferable to use a gel dosimeter with the composition to be very close to that of water. Effective atomic number, Z_{eff}, and electron density, N_{e}, of gels dosimeters are of the suitable constants that used as a way of identifying radiological properties of dosimeters. In literature, several studies have been made to calculate Z_{eff} and N_{e} for total photon interaction in gel dosimeters using various methods such as power law method,^{[4]} logarithmic interpolation method,^{[5]} AutoZ_{eff} software,^{[6]} cross section parameter method.^{[7]} Furthermore, there are not studies dealing with the comparison of the methods used to compute Z_{eff} and N_{e} for different formulations of Fricke gel dosimeters. In this work, our aim (i) is to compare the direct, auto Z_{eff} and power law methods used to calculate Z_{eff} and (ii) to compare Fricke gel dosimeters each other.
Materials and Methods   
The chemical composition of four Fricke gel dosimeters studied is available for Ferrous Agarose Xylenol (FAX) gel in,^{[8]} Ferrous Xylenol Gelatin (FXG) gel,^{[9]} FXG Glycin (FXGG) gel^{[10]} and Ferrous Xylenol.
Poly(vinyl alcohol) Glutaraldehyde (FXPVAGTA) gel.^{[11]} [Table 1] reports the corresponding elemental compositions, calculated as fraction by weight for all Fricke gel dosimeters used in this work.  Table 1: Chemical composition, expressed in terms of fractions by weight of the different investigated Fricke gel dosimeters
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Mass attenuation coefficient
The mass attenuation coefficients for the Fricke gel dosimeters have been calculated using WinXCom computer program.^{[12]}
Effective atomic number and electron density
In this work, the effective atomic number (Z_{eff}) was evaluated by three methods described below.
 AutoZ_{eff} computer program evaluated the Z_{eff} through the smooth correlation between atomic cross section and atomic number. The Z_{eff} of each material is calculated at discrete energy levels over the energy range of 10 kev–1 GeV^{[13]}
 Direct method, by this way the effective atomic number of the Fricke gel dosimeters can be obtained using the following formula.^{[14]}
where f_{i} is the molar fraction in the mixture/compound, μ/ρ is the mass attenuation coefficient calculated with WinXcom, A_{i} is the mass number and Z_{i} is the atomic number.
 Power law method dates back to 1930s,^{[15]} it allows us to calculate the effective atomic number for mixture by means of the next equation.^{[4]}
With the mass numbers, A_{i}, the atomic number, Z_{i}, and the percentage mass composition of the element, i, to the sample f_{i} and α as an empirical number which is taken to be 2.94.
The electron density of the Fricke gels has been calculated according to the succeeding expression.^{[14]}
where 〈A〉 is the average atomic mass of the gels, and N_{A} is the Avogadro's number.
Results   
Mass attenuation coefficient
[Figure 1] shows the variation of the mass attenuation coefficient, μ/ρ, calculated at the photon energies between 0.1 MeV and 100 MeV for four Fricke gel dosimeters and water.  Figure 1: Variations of mass attenuation coefficient of Fricke gel dosimeters and water with photon energy
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Effective atomic number and electron density
The calculated values of Z_{eff} and Ne for different Fricke gels dosimeters examined and water are presented in [Figure 2] and [Figure 3], respectively.  Figure 2: The effective atomic numbers of the Fricke gel dosimeters and water as a function of photon energy
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 Figure 3: The electron density of the Fricke gel dosimeters and water as a function of photon energy
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The effective atomic number and electron density of the Fricke gels dosimeters relative to water were also calculated to evaluate the water equivalence of each of them. The results obtained are shown in [Table 2].  Table 2: <Z_{eff}> and <N_{e}> calculated for the different Fricke gel dosimeter formulations in terms of values for water in the energy range 0.110 MeV
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Discussion   
From the data illustrated in [Figure 1], it can be seen that the mass attenuation coefficient is decreasing with the increasing photon energies.
In general, as shown in [Figure 2] and [Figure 3], Z_{eff} and Ne behavior with photon energy for all dosimeters studied are similar. The Z_{eff} and Ne data, calculated by AutoZ_{eff} and direct methods shows the variation of up to 2.5% in the energy region 0.1MeV≤ E ≤ 4MeV, 9% and 23% in the energy regions 5MeV≤ E ≤ 10MeV and 11MeV≤ E ≤ 100MeV, respectively.
A good agreement is achieved in comparison in the region 0.1MeV≤ E ≤ 10 MeV this is the energy interval of interest in Xrays external radiation therapy.
The effective atomic numbers calculated by power method are 7.45, 7.42, 7.42, 7.38, and 7.44 for FAX gel, FXG gel, FXGG gel, FXPVAGTA gel, and water, respectively. The effective electron density calculated by power method is 3.13, 3.12, 3.12, 3.14, and 3.13 for FAX gel, FXG gel, FXGG gel, FXPVAGTA gel, and water, respectively. It was found that the calculated Z_{eff} and Ne using Auto Z_{eff} and direct methods are lower than what were calculated using power law methods. This discrepancy can be assigned to the energy independence of the Mayneord formula.
From the data shown in [Table 2], the percentage difference of up to 0.3%, 0.9%, and 1.5% for FAX, FXPVAGTA, FXG, and FXGG gels, respectively, was obtained when comparing data for Z_{eff} of Fricke gel dosimeters to that of the water. Discrepancies of up to 0.2%, 2.25%, and 2.26% for FAX, FXPVAGTA, FXG, and FXGG gels, respectively, were observed when comparing data for Ne of Fricke gel dosimeters to that of the water.
Conclusion   
In this study, Z_{eff} and Ne of water and Fricke gel dosimeters were calculated for photon using theoretical methods. The direct and AutoZ_{eff}, methods show a very good agreement in the effective atomic numbers in energy region 0.1–10 MeV. Electron density is closely related to the effective atomic number and has the same quantitative energy dependence as Z_{eff.} It was found that the calculated effective atomic number and electron density of the Fricke gel dosimeters using the direct and Auto Z_{eff}, methods, were lower than that calculated using the power law method. This mismatch can be attributed to the energy independence of the method. As such, the differences in effective atomic number (0.3%–1.5%) and Ne (0.2%–2.26) between water and Fricke gels are small, consideration of the mean disparity over energy range 0.1–10 MeV shows, widely, FAX gel to be the most water equivalent gel.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
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[Figure 1], [Figure 2], [Figure 3]
[Table 1], [Table 2]
