Effective Atomic Number and Electron Density Determination for Fricke Gel Dosimeters Using Different Methods.

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. Copyright:

INTRODUCTION

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.[12] 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

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

Element	Z atomic number	FAX	FXG	FXGG	FXVA GTA
Hydrogen	1	0.111114	0.109831	0.109847	0.109716
Carbon	6	0.004769	0.025434	0.025392	0.051273
Nitrogen	7	0.000033	0.008742	0.008720	0.000019
Oxygen	8	0.883142	0.854259	0.854372	0.838112
Sodium	11	0.000015	0.000009	0.000005	0.000015
Sulfur	16	0.000871	0.001669	0.001636	0.000838
Iron	26	0.000056	0.000056	0.000028	0.000028

FAX: Ferrous Agarose Xylenol, FXG: Ferrous Xylenol Gelatin, FXGG: Ferrous Xylenol Gelatin Glycin, FXPVA-GTA:Ferrous Xylenol Poly (vinyl alcohol) Glutaraldehide

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]

Z Σ (μ/ρ)/Σ (f / Z) (μ/ρ)     (1)

where fi is the molar fraction in the mixture/compound, μ/ρ is the mass attenuation coefficient calculated with WinXcom, A is the mass number and Z 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]

Z (Z/A)]1/α     (2)

With the mass numbers, A, the atomic number, Z, and the percentage mass composition of the element, i, to the sample f 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]

N/⟨A⟩

where 〈A〉 is the average atomic mass of the gels, and NA is the Avogadro's number.

RESULTS

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

The calculated values of Zeff and Ne for different Fricke gels dosimeters examined and water are presented in Figures 2 and 3, respectively.

Figure 2

The effective atomic numbers of the Fricke gel dosimeters and water as a function of photon energy

Figure 3

The electron density of the Fricke gel dosimeters and water as a function of photon energy

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

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

Quantity	FAX	FXG	FXGG	FXPVA-GTA
<Zeff>/<Zeff. water>	1.000a	1.012a	1.012a	1.003a
	1.003b	1.015b	1.015b	1.006b
	1.001c	0.997c	0.997c	0.991c
	1.005d
<Ne>/<Ne water>	1.002a	1.011a	1.011a	1.014a
	1.001b	1.026b	1.026b	1.025b
	1.000c	0.996c	0.996c	1.003c

aCalculated values of the present work by using Auto-Zeff, bCalculated values of the present work by using direct method, cCalculated values of the present work by using power law method, dCalculated value by using power law method from Kron et al., 1993.[4] and are the average effective atomic number and electron density, respectively. FAX: Ferrous Agarose Xylenol, FXG: Ferrous Xylenol Gelatin, FXGG: Ferrous Xylenol Gelatin Glycin, FXPVA-GTA: Ferrous Xylenol Poly(vinyl alcohol) Glutaraldehyde

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 Figures 2 and 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

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

Nil.

Conflicts of interest

There are no conflicts of interest.