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Year : 2022  |  Volume : 47  |  Issue : 1  |  Page : 105-108

Effective atomic number and electron density determination for fricke gel dosimeters using different methods

Departement of Medical Physics, Nuclear Research Center of Algiers, Algiers, Algeria

Date of Submission13-Jun-2021
Date of Decision01-Nov-2021
Date of Acceptance05-Nov-2021
Date of Web Publication31-Mar-2022

Correspondence Address:
Dr. Ouiza Moussous
02 Boulevard Frantz Fanon B.P. 399 Alger-Gare, Algiers
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Source of Support: None, Conflict of Interest: None

DOI: 10.4103/jmp.jmp_83_21

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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 Auto-Zeff, 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 Auto-Zeff 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 FX-PVA-GTA 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;47:105-8

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 Dec 5];47:105-8. Available from:

   Introduction Top

Fricke and polymer gel dosimetry has emerged as a suitable tool to measure three-dimensional dose distribution for complex delivery verification and quality assurance of modern radiotherapy techniques such as IMRT.[1],[2] For external-beam 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, Zeff, and electron density, Ne, 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 Zeff and Ne for total photon interaction in gel dosimeters using various methods such as power law method,[4] logarithmic interpolation method,[5] Auto-Zeff software,[6] cross section parameter method.[7] Furthermore, there are not studies dealing with the comparison of the methods used to compute Zeff and Ne for different formulations of Fricke gel dosimeters. In this work, our aim (i) is to compare the direct, auto Zeff and power law methods used to calculate Zeff and (ii) to compare Fricke gel dosimeters each other.

   Materials and Methods Top

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 (FXPVA-GTA) 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 (Zeff) was evaluated by three methods described below.

  • Auto-Zeff computer program evaluated the Zeff through the smooth correlation between atomic cross section and atomic number. The Zeff 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 fi is the molar fraction in the mixture/compound, μ/ρ is the mass attenuation coefficient calculated with WinXcom, Ai is the mass number and Zi 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, Ai, the atomic number, Zi, and the percentage mass composition of the element, i, to the sample fi 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 NA is the Avogadro's number.

   Results Top

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 Zeff 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: <Zeff> and <Ne> calculated for the different Fricke gel dosimeter formulations in terms of values for water in the energy range 0.1-10 MeV

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   Discussion Top

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], Zeff and Ne behavior with photon energy for all dosimeters studied are similar. The Zeff and Ne data, calculated by Auto-Zeff 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 X-rays 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, FXPVA-GTA 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, FXPVA-GTA gel, and water, respectively. It was found that the calculated Zeff and Ne using Auto Zeff 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, FXPVA-GTA, FXG, and FXGG gels, respectively, was obtained when comparing data for Zeff of Fricke gel dosimeters to that of the water. Discrepancies of up to 0.2%, 2.25%, and 2.26% for FAX, FXPVA-GTA, FXG, and FXGG gels, respectively, were observed when comparing data for Ne of Fricke gel dosimeters to that of the water.

   Conclusion Top

In this study, Zeff and Ne of water and Fricke gel dosimeters were calculated for photon using theoretical methods. The direct and Auto-Zeff, 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 Zeff. It was found that the calculated effective atomic number and electron density of the Fricke gel dosimeters using the direct and Auto Zeff, 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


Conflicts of interest

There are no conflicts of interest.

   References Top

Saur S, Strickert T, Wasboe E, Frengen J. Fricke gel as a tool for dose distribution verification: Optimization and characterization. Phys Med Biol 2005;50:5251-61.  Back to cited text no. 1
Wong CJ, Ackerly T, He C, Patterson W, Powell CE, Ho A, et al. High-resolution measurements of small field beams using polymer gels. Appl Radiat Isot 2007;65:1160-4.  Back to cited text no. 2
Andreo P, Burns D, Hohlfeld K, Huq M, Kanai T, Laitano F, et al. Absorbed Dose Determination in External Beam Radiotherapy: An International Code of Practice for Dosimetry Based on Standards of Absorbed Dose to Water IAEA 2000 Technical Reports Series 398 International Atomic Energy Agency. Vienna (Austria).  Back to cited text no. 3
Kron T, Metcalfe P, Pope JM. Investigation of the tissue equivalence of gels used for NMR dosimetry. Phys Med Biol 1993;38:139-50.  Back to cited text no. 4
Kurudirek M. A study of effective atomic number and electron density of gel dosimeters and human tissues for scattering of gamma rays: Momentum transfer, energy and scattering angle dependence. Radiat Environ Biophys 2016;55:501-7.  Back to cited text no. 5
Sathiyaraj P, Samuel EJ, Valeriano CC, Kurudirek M. Effective atomic number and buildup factor calculations for metal nano particle doped polymer gel. Vacuum 2017;143:138-49.  Back to cited text no. 6
Taylor ML, Franich RD, Trapp JV, Johnston PN. The effective atomic number of dosimetric gels. Australas Phys Eng Sci Med 2008;31:131-8.  Back to cited text no. 7
Gambarini G, Brusa D, Carrara M, Castellano G, Mariani M, Tomatis S, et al. Dose imaging in radiotherapy photon fields with Fricke and normoxic-polymer gels. J Phys Conf Ser 2006;41:466-74.  Back to cited text no. 8
Gohary El MI, Shabban YS, Amin EA, Abdel Gawad MH, Desouky OS. Preparation and characterization of Fricke gel dosimeter. Nat Sci 2015;13:139-43.  Back to cited text no. 9
Babu SE, Singh IR, Poornima CG, Ravindran BP. Enhancing the longevity of three-dimensional dose in a diffusion-controlled Fricke gel dosimeter. J Cancer Res Ther 2015;11:580-5.  Back to cited text no. 10
Gallo S, Artuso E, Brambilla MG, Gambarini G, Lenardi C, Monti AF, et al. Characterization of radiochromic poly(vinyl-alcohol)-glutaraldehyde Fricke gels for dosimetry in external x-ray radiation therapy. J Phys D Appl Phys 2019;52:225601.  Back to cited text no. 11
Gerward L, Guilbert N, Jensen KB, Levring H. WinXCom a program for calculating X-ray attenuation coefficients. Radiat Phys Chem 2004;71:653-4.  Back to cited text no. 12
Taylor ML, Smith RL, Dossing F, Franich RD. Robust calculation of effective atomic numbers: The Auto-Z(eff) software. Med Phys 2012;39:1769-78.  Back to cited text no. 13
Manohara SR, Hanagodimath SM, Thind KS, Gerward L. On the effective atomic number and electron density: A comprehensive set of formulas for all types of materials and energies above 1 keV. Nucl Instrum Methods B 2008;266:3906-12.  Back to cited text no. 14
Mayneord W. The significance of the Rontgen. Acta Unio Int Contra Cancrum 1937;2:271-82.  Back to cited text no. 15


  [Figure 1], [Figure 2], [Figure 3]

  [Table 1], [Table 2]


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