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Water and tissue equivalency of some gel dosimeters for photon energy absorption
Applied Radiation and Isotopes 82 (2013) 258–263
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Water and tissue equivalency of some gel dosimeters for photon energy absorption Adem Un n Department of Physics, Faculty of Sciences and Letters, University of Ağrı İbrahim Çeçen, 04100 Ağrı, Turkey
H I G H L I G H T S
Tissue and water equivalency of gel dosimeters is investigated. Effective atomic and electron numbers for gel dosimeters are calculated, with respect to the photon energy absorption. Calculations are compared to previous work for verification.
art ic l e i nf o
a b s t r a c t
Article history: Received 3 May 2013 Received in revised form 5 September 2013 Accepted 8 September 2013 Available online 14 September 2013
The mass energy absorption coefficients, μen =ρ, effective atomic numbers for photon energy absorption, ZPEAeff, and effective electron numbers for photon-energy absorption, NPEAeff, is calculated for 14 polymer gel dosimeter, five gel dosimeter, soft tissue and water, in the energy range from 1 keV to 20 MeV. The ZPEAeff(Gel)/ZPEAeff(Tissue) and NPEAeff(Gel)/NPEAeff (Tissue) are used to evaluate the tissue equivalency. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Effective atomic number Effective electron number Polymer gel dosimeter Photon energy absorption Tissue equivalency
1. Introduction Gel dosimeters are mostly composed of water, gelatin and small amount of substance that changes under irradiation such as the transformation of the ferrous Fe þ 2 ions into ferric Fe þ 3 ions (Taylor et al., 2008). Polymer gel dosimeters are produced from radiation sensitive acrylic monomers in a water based-matrix, such as gelatin. When a polymer gel dosimeter is subjected to radiation, polymerization which is difference between polymer gel and gel dosimeters takes place. The associated chemical changes are used for measuring the radiation dose distribution in intensitymodulated radiation therapy (IMRT), stereotactic radiosurgery (SRS) and stereotactic radiotherapy (SRT) (Sellakumar et al., 2007; Baldock et al., 2010). An ideal radiation dosimeter should have the same (effective atomic number, number of electrons per gram, mass energy absorption coefficient, mass attenuation coefficient and mass density) as
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water or tissue (Sellakumar et al., 2007; Baldock et al., 2010; Khan, 2010; Gorjiara et al., 2011). Water equivalency and radiological properties of some dosimeters were investigated in previous studies (Keall and Baldock, 1999; Venning et al., 2005; Sellakumar et al., 2007; Brown et al., 2008; Gorjiara et al., 2011, 2012). The mass energy absorption coefficient, μen =ρ, is a measure of the mean fractional amount of incident photon energy transferred to the kinetic energy of charged particles and its value is readily available (Hubbell, 1982; Hubbell and Seltzer, 1995). The effective atomic number for photon energy absorption, ZPEAeff, corresponding to mass energy absorption coefficients, μen =ρ, can also be used to determine water and tissue equivalency. The ZPEAeff values are available for composite materials, such as soft tissue and some TL dosimeters (Un, 2013), and for some low-Z substances of dosimetric intereset (Shivaramu et al., 2001). A third useful parameter is the effective electron density for energy absorption, NPEAeff is introduced. The NPEAeff values were calculated for soft tissue and some TL dosimeters by Un (2013). The three parameters are utilized in this work to assay the tissue and water equivalency for a number of polymer gel and gel dosimeters, listed in Table 1 in the energy range 1 keV–20 MeV.
A. Un / Applied Radiation and Isotopes 82 (2013) 258–263
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Table 1 Elemental compositions (% weight fractions) of soft tissue, water and different gel dosimeters. Material
wH
wC
wN
wO
wNa
wP
wS
wCl
wK
wFe
wCu
wBr
Soft tissuea Water BANG-1b BANG-2c PABIGd PAGe MAGICf VIPARg ABAGICh PAGATi HEAGj MAGASk MAGATl nMAGm nPAGn NIPAMo PRESAGEp SDAq Gelatinr Frickes Genipint
10.200 0.1119 10.7685 10.6369 10.6454 10.7367 10.5473 10.7321 10.5263 10.7257 10.7641 10.5087 10.5220 10.6775 10.7107 10.8055 8.9200 11.0490 10.7630 10.7360 11.0500
14.300 – 5.6936 5.6728 6.8373 6.2009 9.2231 7.1825 0.8963 6.2174 5.7243 9.3591 9.5417 7.5066 6.5251 6.5998 60.740 0.6910 1.9590 2.0000 1.5220
3.4000 – 2.0063 1.4152 1.5649 2.1804 1.3916 2.0638 0.3105 1.9688 1.4152 1.3799 1.3660 1.3868 2.1814 1.7531 4.460 0.0014 0.6650 0.6700 0.5216
70.8000 0.8881 81.5316 81.7004 80.9524 80.882 78.8373 80.0217 77.4054 80.2166 82.0964 78.7523 77.6988 80.2527 80.1385 79.9702 21.720 88.0290 85.7570 85.7360 86.9600
0.2000 – – 0.5748 – – – – – – – – – – – – – – 0.0021 0.0021 –
0.3000 – – – – – – – – 0.4064 – – 0.4064 0.0822 0.5748 0.4064 – – – – –
0.3000 – – – – – 0.0003 – 0.0003 – – – – – – – – 0.2270 0.8470 0.8500 0.3108
0.2000 – – – – – – – – 0.4651 – – 0.4651 0.0941 0.2371 0.4651 3.3400 – 0.0033 0.0033 –
0.3000 – – – – – – – – – – – – – – – – – – – –
– – – – – – – – – – – – – – – – – 0.0027 0.0026 0.0026 –
– – – – – – 0.0005 – 0.0005 – – – – – – – – – – – –
– – – – – – – – – – – – – – – – 0.8400 – – – –
a
ICRU (1989). Maryanski et al. (1994); Michael et al. (2000). Maryanski et al. (1996a, 1996b). d Sandilos et al. (2004). e Maryanski et al. (1993); Maryanski et al. (1994); Baldock et al. (1998); Michael et al. (2000). f Fong et al. (2001). g Kipouros et al. (2001); Pappas et al. (1999). h Taylor et al. (2008). i Venning A. et al. (2005). j Gustavsson et al. (2004). k De Deene et al. (2002a, 2002b); Venning A.J. et al. (2005); Venning A. et al. (2005). l De Deene et al. (2002a, 2002b); Venning A.J. et al. (2005); Venning A. et al. (2005). m De Deene et al. (2002a, 2002b); Venning A.J. et al. (2005); Venning A. et al. (2005). n De Deene et al. (2002a, 2002b); Venning A.J. et al. (2005); Venning A. et al. (2005). o Senden et al. (2006). p Brown et al. (2008); Mostaar et al. (2011). q Kron et al. (1993). r Kron et al. (1993). s Keall and Baldock (1999). t Gorjiara et al. (2011). b c
This is the range of photons commonly used in the radiation dosimetry and radiation applications. Using these three parameters together, an “ideal” dosimeter can be identified.
2. Calculating of the effective atomic number The effective atomic number for photon energy absorption, ZPEAeff, can be calculated using the mass energy absorption coefficient, μen =ρ, determined for composite materials by the additivity law (Shivaramu et al., 2001). The ðμen =ρÞi values of the ith constituent element is tabulated in Hubbel and Seltzer (1995). The effective electronic energy absorption cross section, se;en , is as follows: 1 f A μ sa;en se;en ¼ ∑ i i en ¼ ; ð1Þ NA i Z i ρ i Z PEAef f where Z i is the atomic number of the ith constituent element, f i ¼ ni =∑ nj is the fractional abundance of the ith element and the j
effective atomic energy absorption cross section, sa;en , can be determined as sa;en ¼
sm;en : ∑ i ni
ð2Þ
The effective atomic number for photon energy absorption, ZPEAeff, can be calculated using Eq. (1) Z PEAef f ¼
sa;en : se;en
ð3Þ
The effective electron density for photon energy absorption, NPEAeff (number of electrons per unit mass) can be derived as NPEAef f ¼
NA μ =ρ Z ∑ni ¼ en : se M PEAef f
ð4Þ
More detailed information about the calculation of ZPEAeff and NPEAeff is given in Manohara and Hanagodimath (2007), Un and Sahin (2012); Un (2013).
3. Results and discussion The elemental compositions (% weight fractions) of soft tissue, water and different gel dosimeters are tabulated in Table 1. The energy dependence of the mass energy absorption coefficients, μen =ρ, are shown in Fig. 1 for the soft tissue, water and different gel dosimeters, while Figs. 2 and 3 show this dependence for ZPEAeff for the polymer gel and the gel dosimeters, respectively. In the low energy region E o0.01 MeV, the maximum values of ZPEAeff are found in the low-energy range because of the
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Fig. 1. Energy dependence of the mass energy absorption coefficient, μen =ρ, of gel dosimeters, soft tissue and water.
dominance of the photoelectric effect, as can be seen in Figs. 2 and 3. The ZPEAeff values for Presage is higher than that for other studied dosimeters in this low energy, because of the high atomic number of the elements of this material and their K-edge energies. In the intermediate energy range of 100 keV–3 MeV, the ZPEAeff values are almost constant for the dosimeters, soft tissue and water, due to the dominance of Compton scattering is this energy range. These ZPEAeff values for studied samples are smaller than those on the lower energy range, as seen in Figs. 2 and 3, because of the proportionality the Compton scattering with Z and of the photoelectric effect with Z4. In the high energy region E 43 MeV in which dominant photon interaction is the pair production, the ZPEAeff values are lower than those on the lower energy range and higher than those on the intermediate energy range, because of the proportionality pair production with Z2. In order to verify the adequacy of our method for calculating ZPEAeff, and given that is no experimental ZPEAeff values are available for soft tissue and water in the literature, the ZPEAeff values are compared with values calculated by Kumar and Reddy (1997) and Jayachandran (1971). As Fig. 2 shows, our calculated values are in agreement with those of others. As can be seen in Figs. 2 and 3, the maximum values of the ZPEAeff are 8.24 (NIPAM and PAGAT) at 10 keV for polymer gel dosimeters, 12.63 (PRESAGE) at 30 keV for gel dosimeters, 7.995 at 50 keV for water and 8.36 at 15 keV for soft tissue. The minimum values of ZPEAeff are 3.23 (ABAGIC) for polymer gel dosimeters, 3.34
Fig. 2. Comparison of the effective atomic number, ZPEAeff, of polymer gel dosimeters to soft tissue and water.
Fig. 3. Comparison of the effective atomic number, ZPEAeff, of gel dosimeters to soft tissue and water.
(SDA) for gel dosimeters, 3.33 for water and 3.43 for soft tissue at 1.25 MeV. The percentage differences between the ZPEAeff values of all gel dosimeters and the soft tissue under 5.0 except for the MAGIC and MAGAS at 35 keV, the ABAGIC at 60 keV–1.33 MeV and
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Table 2 The effective atomic number (ZPEAeff) for photon energy absorption of water, soft tissue and gel dosimeters for selected specific energies. Energy (MeV)
2.21E 02 3.50E 02 6.00E 02 8.10E 02 8.80E 02 1.22E 01 1.45E 01 2.79E 01 3.02E 01 3.56E 01 5.11E 01 5.14E 01 6.62E 01 1.12E þ00 1.17E þ03 1.33Eþ03
ZPEAeff BANG-1
BANG-2
PABIG
7.71 6.76 4.54 3.80 3.73 3.49 3.37 3.41 3.37 3.39 3.34 3.34 3.39 3.34 3.37 3.40
7.76 6.82 4.59 3.84 3.76 3.51 3.39 3.43 3.39 3.41 3.36 3.36 3.41 3.36 3.40 3.43
7.70 6.75 4.55 3.81 3.74 3.50 3.38 3.42 3.39 3.40 3.36 3.36 3.40 3.36 3.39 3.42
nMAG
nPAG
NIPAM
7.78 6.82 4.57 3.82 3.75 3.50 3.38 3.41 3.38 3.40 3.35 3.35 3.40 3.35 3.38 3.41
8.02 7.07 4.70 3.87 3.79 3.51 3.39 3.42 3.39 3.40 3.36 3.36 3.40 3.36 3.39 3.42
8.10 7.12 4.70 3.86 3.78 3.50 3.37 3.40 3.37 3.38 3.34 3.34 3.38 3.34 3.37 3.40
PAG
MAGIC
VIPAR
ABAGIC
PAGAT
HEAG
MAGAS
MAGAT
7.67 6.73 4.54 3.81 3.74 3.50 3.39 3.43 3.39 3.41 3.36 3.36 3.41 3.36 3.40 3.42
7.69 6.74 4.52 3.79 3.72 3.48 3.37 3.40 3.37 3.39 3.34 3.34 3.39 3.34 3.37 3.40
7.76 6.74 4.43 3.67 3.60 3.35 3.23 3.27 3.23 3.25 3.20 3.20 3.25 3.20 3.23 3.27
8.10 7.14 4.72 3.88 3.79 3.51 3.39 3.42 3.38 3.40 3.35 3.35 3.40 3.35 3.38 3.41
7.71 6.76 4.54 3.80 3.73 3.49 3.37 3.41 3.37 3.39 3.34 3.34 3.39 3.34 3.37 3.41
7.67 6.73 4.54 3.82 3.75 3.51 3.40 3.43 3.40 3.41 3.37 3.37 3.41 3.37 3.40 3.43
8.08 7.12 4.72 3.89 3.81 3.53 3.41 3.44 3.40 3.42 3.37 3.37 3.42 3.37 3.40 3.43
PRESAGE
SDA
Gelatin
Frice
Genipin
Water
Tissue
12.66 11.91 7.13 5.01 4.66 3.85 3.66 3.51 3.47 3.48 3.46 3.46 3.47 3.45 3.48 3.47
7.89 6.93 4.61 3.82 3.74 3.48 3.35 3.39 3.35 3.37 3.32 3.32 3.37 3.32 3.35 3.39
8.16 7.20 4.77 3.91 3.82 3.53 3.40 3.43 3.40 3.41 3.36 3.36 3.41 3.36 3.40 3.43
8.16 7.20 4.78 3.92 3.83 3.54 3.41 3.44 3.40 3.42 3.37 3.37 3.42 3.37 3.40 3.43
7.91 6.94 4.62 3.82 3.74 3.48 3.35 3.39 3.35 3.37 3.32 3.32 3.37 3.32 3.35 3.39
7.78 6.82 4.54 3.78 3.70 3.45 3.33 3.37 3.33 3.35 3.30 3.30 3.35 3.30 3.33 3.37
8.05 7.09 4.72 3.91 3.82 3.55 3.43 3.46 3.42 3.44 3.40 3.40 3.44 3.40 3.43 3.45
7.70 6.75 4.53 3.80 3.73 3.49 3.37 3.41 3.37 3.39 3.34 3.34 3.39 3.34 3.38 3.41
ZPEAeff
2.21E 02 3.50E 02 6.00E 02 8.10E 02 8.80E 02 1.22E 01 1.45E 01 2.79E 01 3.02E 01 3.56E 01 5.11E 01 5.14E 01 6.62E 01 1.12E þ00 1.17E þ03 1.33Eþ03
the PRESAGE at 22.1–145 keV. To assist in evaluating the tissue and water equivalency of gel dosimeters, the ZPEAeff values are tabulated for some specific energies in Table 2. The change in the NPEAeff values with energy for the polymer gel and the gel dosimeters is shown in Figs. 4 and 5, respectively. The tabulated values are given in Table 3. As can be seen in Figs. 4 and 5, the maximum values of the NPEAeff are 8.29E þ23 e/g (ABAGIC) at 50 keV for polymer gel dosimeters, 11.93E þ23 e/g (PRESAGE) at 30 keV for gel dosimeters, 8.02E þ23 e/g at 50 keV for water and 8.06E þ23 e/g at 15 keV for soft tissue. The minimum values are 3.32E þ23 e/g (BANG-2, PABIG, PAG, MAGIC, VIPAR, PAGAT, MAGAS, MAGAT, nMAG, and nPAG) for polymer gel dosimeters, 3.26E þ23 e/g (PRESAGE) for gel dosimeters, 3.34E þ23 e/g for water and 3.31E þ23 e/g for soft tissue at 1.25 MeV. The percentage differences between the NPEAeff values of all gel dosimeters and the soft tissue are under 5.0 except for the PRESAGE at 22.1–122 keV. To examine the tissue equivalency, the ZPEAeff and the NPEAeff values for gel dosimeters relative to the soft tissue ZPEAeff (Gel)/ZPEAeff(Tissue)and NPEAeff(Gel)/NPEAeff(Tissue) are shown in Figs. 6 and 7. Because of the elemental composition of the gel dosimeters, the tissue equivalency of the gel dosimeters with respect to ZPEAeff is somewhat different than that of the gel dosimeters with respect to NPEAeff. It can be seen in Figs. 6 and 7 that NPEAeff(Gel)/NPEAeff(Tissue) is closer to 1.0 than the values of the ZPEAeff(Gel)/ZPEAeff(Tissue). Since the PRESAGE contains Br, which has a Br high atomic number, its ZPEAeff(Gel)/ZPEAeff(Tissue) and NPEAeff(Gel)/NPEAeff(Tissue) values are higher than those of the other gel dosimeters in the low energy ranges 10–150 keV where the photoelectric interaction is dominant.
Fig. 4. Comparison of the effective electron number, NPEAeff, of polymer gel dosimeters to soft tissue and water.
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4. Conclusions The mass energy absorption coefficients,μen =ρ, the effective atomic number for photon energy absorption, ZPEAeff and the effective electron number for photon energy absorption, NPEAeff of some gel dosimeters, soft tissue and water are calculated to evaluate the tissue/water equivalency in the energy range 1 keV– 20 MeV. The energy dependence of ZPEAeff and NPEAeff for the studied gel dosimeters, except for PRESAGE in the low energy region, resembles that of the soft tissue and water. Since the ratios of NPEAeff(Gel)/NPEAeff(Tissue) for studied materials are somewhat
Fig. 5. Comparison of the effective electron number, NPEAeff, of gel dosimeters to soft tissue and water.
Fig. 6. Variation of ZPEAeff(Gel)/ZPEAeff(Tissue) with photon energy.
Table 3 The effective electronic density (NPEAeff) for photon energy absorption of water, soft tissue and gel dosimeters for selected specific energies. Energy (MeV)
2.21E 02 3.50E 02 6.00E 02 8.10E 02 8.80E 02 1.22E 01 1.45E 01 2.79E 01 3.02E 01 3.56E 01 5.11E 01 5.14E 01 6.62E 01 1.12E þ 00 1.17E þ 03 1.33Eþ 03
NPEAeff ( 1023 e/g) BANG-1
BANG-2
PABIG
7.61 6.67 4.48 3.75 3.68 3.44 3.33 3.36 3.33 3.34 3.30 3.30 3.34 3.30 3.33 3.36
7.59 6.67 4.49 3.75 3.68 3.44 3.32 3.36 3.32 3.34 3.29 3.29 3.34 3.29 3.33 3.36
7.56 6.63 4.46 3.74 3.67 3.44 3.32 3.36 3.32 3.34 3.29 3.29 3.34 3.29 3.33 3.36
PAG 7.59 6.66 4.47 3.75 3.68 3.44 3.32 3.36 3.33 3.34 3.30 3.30 3.34 3.30 3.33 3.36
MAGIC
VIPAR
ABAGIC
PAGAT
HEAG
MAGAS
MAGAT
7.51 6.59 4.44 3.73 3.67 3.43 3.32 3.35 3.32 3.34 3.29 3.29 3.34 3.29 3.32 3.35
7.59 6.65 4.47 3.75 3.68 3.44 3.32 3.36 3.33 3.34 3.30 3.30 3.34 3.30 3.33 3.36
8.06 7.01 4.60 3.81 3.74 3.48 3.36 3.39 3.36 3.38 3.32 3.32 3.38 3.32 3.36 3.39
7.97 7.02 4.65 3.82 3.73 3.45 3.33 3.36 3.33 3.34 3.30 3.30 3.34 3.30 3.33 3.36
7.61 6.67 4.48 3.75 3.68 3.44 3.33 3.36 3.33 3.34 3.30 3.30 3.34 3.30 3.33 3.36
7.49 6.58 4.44 3.73 3.66 3.43 3.32 3.35 3.32 3.34 3.29 3.29 3.34 3.29 3.32 3.35
7.89 6.95 4.61 3.80 3.72 3.44 3.33 3.35 3.32 3.34 3.29 3.29 3.34 3.29 3.32 3.35
NPEAeff ( 1023 e/g)
2.21E 02 3.50E 02 6.00E 02 8.10E 02 8.80E 02 1.22E 01 1.45E 01 2.79E 01 3.02E 01 3.56E 01 5.11E 01 5.14E 01 6.62E 01 1.12E þ 00 1.17E þ 03 1.33Eþ 03
nMAG
nPAG
NIPAM
PRESAGE
SDA
Gelatin
Frice
Genipin
Water
Tissue
7.65 6.71 4.50 3.76 3.69 3.44 3.33 3.36 3.32 3.34 3.29 3.29 3.34 3.29 3.33 3.36
7.87 6.94 4.61 3.80 3.72 3.45 3.33 3.36 3.32 3.34 3.29 3.29 3.34 3.29 3.33 3.36
8.01 7.04 4.65 3.82 3.74 3.46 3.34 3.36 3.33 3.34 3.30 3.30 3.34 3.30 3.33 3.36
11.96 11.25 6.73 4.73 4.40 3.63 3.46 3.31 3.28 3.28 3.27 3.27 3.28 3.26 3.28 3.28
7.86 6.90 4.59 3.80 3.72 3.46 3.34 3.37 3.34 3.35 3.30 3.30 3.35 3.30 3.34 3.37
8.00 7.05 4.68 3.84 3.75 3.46 3.33 3.36 3.33 3.34 3.30 3.30 3.34 3.29 3.33 3.36
7.99 7.04 4.68 3.83 3.74 3.46 3.33 3.36 3.33 3.34 3.29 3.29 3.34 3.29 3.33 3.36
7.86 6.90 4.59 3.80 3.72 3.46 3.34 3.37 3.34 3.35 3.30 3.30 3.35 3.30 3.34 3.37
7.81 6.84 4.56 3.79 3.72 3.46 3.34 3.38 3.34 3.36 3.31 3.31 3.36 3.31 3.34 3.38
7.79 6.86 4.57 3.78 3.70 3.43 3.32 3.35 3.31 3.33 3.29 3.29 3.33 3.29 3.32 3.34
A. Un / Applied Radiation and Isotopes 82 (2013) 258–263
Fig. 7. Variation of NPEAeff(Gel)/NPEAeff(Tissue) with photon energy.
different than the ratios of ZPEAeff(Gel)/ZPEAeff(Tissue), the values of NPEAeff should be considered as well as the values of ZPEAeff for determination of tissue/water equivalency.
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Applied Radiation and Isotopes 69, 1540–1545. Pappas, E., Maris, T., Angelopoulos, A., Paparigopoulou, M., Sakelliou, L., Sandilos, P., Voyiatzi, S., Vlachos, L., 1999. A new polymer gel for magnetic resonance imaging (MRI) radiation dosimetry. Physics in Medicine and Biology 44, 2677–2684. Sandilos, P., Angelopoulos, A., Baras, P., Dardoufas, K., Karaiskos, P., Kipouros, P., Kozicki, M., Rosiak, J.M., Sakelliou, L., Seimenis, I., Vlachos, L., 2004. Dose verification in clinical IMRT prostate incidents. International Journal of Radiation Oncology, Biology 59, 1540–1547. Sellakumar, P., Samuel, E.J.J., Supe, S.S., 2007. Water equivalence of polymer gel dosimeters. Radiation Physics and Chemistry 76, 1108–1115. Senden, R.J., De Jean, P., McAuley, K.B., Schreiner, L.J., 2006. Polymer gel dosimetry with reduced toxicity: a preliminary investigation of the NMR and optical dose–response using different monomers. Physics in Medicine and Biology 51, 3301–3314. 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Investigation of the PAGAT polymer gel dosimeter using magnetic resonance imaging. Physics in Medicine and Biology 50, 3875–3888.
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Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Water and tissue equivalency of some gel dosimeters for photon energy absorption Adem Un n Department of Physics, Faculty of Sciences and Letters, University of Ağrı İbrahim Çeçen, 04100 Ağrı, Turkey
H I G H L I G H T S
Tissue and water equivalency of gel dosimeters is investigated. Effective atomic and electron numbers for gel dosimeters are calculated, with respect to the photon energy absorption. Calculations are compared to previous work for verification.
art ic l e i nf o
a b s t r a c t
Article history: Received 3 May 2013 Received in revised form 5 September 2013 Accepted 8 September 2013 Available online 14 September 2013
The mass energy absorption coefficients, μen =ρ, effective atomic numbers for photon energy absorption, ZPEAeff, and effective electron numbers for photon-energy absorption, NPEAeff, is calculated for 14 polymer gel dosimeter, five gel dosimeter, soft tissue and water, in the energy range from 1 keV to 20 MeV. The ZPEAeff(Gel)/ZPEAeff(Tissue) and NPEAeff(Gel)/NPEAeff (Tissue) are used to evaluate the tissue equivalency. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Effective atomic number Effective electron number Polymer gel dosimeter Photon energy absorption Tissue equivalency
1. Introduction Gel dosimeters are mostly composed of water, gelatin and small amount of substance that changes under irradiation such as the transformation of the ferrous Fe þ 2 ions into ferric Fe þ 3 ions (Taylor et al., 2008). Polymer gel dosimeters are produced from radiation sensitive acrylic monomers in a water based-matrix, such as gelatin. When a polymer gel dosimeter is subjected to radiation, polymerization which is difference between polymer gel and gel dosimeters takes place. The associated chemical changes are used for measuring the radiation dose distribution in intensitymodulated radiation therapy (IMRT), stereotactic radiosurgery (SRS) and stereotactic radiotherapy (SRT) (Sellakumar et al., 2007; Baldock et al., 2010). An ideal radiation dosimeter should have the same (effective atomic number, number of electrons per gram, mass energy absorption coefficient, mass attenuation coefficient and mass density) as
n
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water or tissue (Sellakumar et al., 2007; Baldock et al., 2010; Khan, 2010; Gorjiara et al., 2011). Water equivalency and radiological properties of some dosimeters were investigated in previous studies (Keall and Baldock, 1999; Venning et al., 2005; Sellakumar et al., 2007; Brown et al., 2008; Gorjiara et al., 2011, 2012). The mass energy absorption coefficient, μen =ρ, is a measure of the mean fractional amount of incident photon energy transferred to the kinetic energy of charged particles and its value is readily available (Hubbell, 1982; Hubbell and Seltzer, 1995). The effective atomic number for photon energy absorption, ZPEAeff, corresponding to mass energy absorption coefficients, μen =ρ, can also be used to determine water and tissue equivalency. The ZPEAeff values are available for composite materials, such as soft tissue and some TL dosimeters (Un, 2013), and for some low-Z substances of dosimetric intereset (Shivaramu et al., 2001). A third useful parameter is the effective electron density for energy absorption, NPEAeff is introduced. The NPEAeff values were calculated for soft tissue and some TL dosimeters by Un (2013). The three parameters are utilized in this work to assay the tissue and water equivalency for a number of polymer gel and gel dosimeters, listed in Table 1 in the energy range 1 keV–20 MeV.
A. Un / Applied Radiation and Isotopes 82 (2013) 258–263
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Table 1 Elemental compositions (% weight fractions) of soft tissue, water and different gel dosimeters. Material
wH
wC
wN
wO
wNa
wP
wS
wCl
wK
wFe
wCu
wBr
Soft tissuea Water BANG-1b BANG-2c PABIGd PAGe MAGICf VIPARg ABAGICh PAGATi HEAGj MAGASk MAGATl nMAGm nPAGn NIPAMo PRESAGEp SDAq Gelatinr Frickes Genipint
10.200 0.1119 10.7685 10.6369 10.6454 10.7367 10.5473 10.7321 10.5263 10.7257 10.7641 10.5087 10.5220 10.6775 10.7107 10.8055 8.9200 11.0490 10.7630 10.7360 11.0500
14.300 – 5.6936 5.6728 6.8373 6.2009 9.2231 7.1825 0.8963 6.2174 5.7243 9.3591 9.5417 7.5066 6.5251 6.5998 60.740 0.6910 1.9590 2.0000 1.5220
3.4000 – 2.0063 1.4152 1.5649 2.1804 1.3916 2.0638 0.3105 1.9688 1.4152 1.3799 1.3660 1.3868 2.1814 1.7531 4.460 0.0014 0.6650 0.6700 0.5216
70.8000 0.8881 81.5316 81.7004 80.9524 80.882 78.8373 80.0217 77.4054 80.2166 82.0964 78.7523 77.6988 80.2527 80.1385 79.9702 21.720 88.0290 85.7570 85.7360 86.9600
0.2000 – – 0.5748 – – – – – – – – – – – – – – 0.0021 0.0021 –
0.3000 – – – – – – – – 0.4064 – – 0.4064 0.0822 0.5748 0.4064 – – – – –
0.3000 – – – – – 0.0003 – 0.0003 – – – – – – – – 0.2270 0.8470 0.8500 0.3108
0.2000 – – – – – – – – 0.4651 – – 0.4651 0.0941 0.2371 0.4651 3.3400 – 0.0033 0.0033 –
0.3000 – – – – – – – – – – – – – – – – – – – –
– – – – – – – – – – – – – – – – – 0.0027 0.0026 0.0026 –
– – – – – – 0.0005 – 0.0005 – – – – – – – – – – – –
– – – – – – – – – – – – – – – – 0.8400 – – – –
a
ICRU (1989). Maryanski et al. (1994); Michael et al. (2000). Maryanski et al. (1996a, 1996b). d Sandilos et al. (2004). e Maryanski et al. (1993); Maryanski et al. (1994); Baldock et al. (1998); Michael et al. (2000). f Fong et al. (2001). g Kipouros et al. (2001); Pappas et al. (1999). h Taylor et al. (2008). i Venning A. et al. (2005). j Gustavsson et al. (2004). k De Deene et al. (2002a, 2002b); Venning A.J. et al. (2005); Venning A. et al. (2005). l De Deene et al. (2002a, 2002b); Venning A.J. et al. (2005); Venning A. et al. (2005). m De Deene et al. (2002a, 2002b); Venning A.J. et al. (2005); Venning A. et al. (2005). n De Deene et al. (2002a, 2002b); Venning A.J. et al. (2005); Venning A. et al. (2005). o Senden et al. (2006). p Brown et al. (2008); Mostaar et al. (2011). q Kron et al. (1993). r Kron et al. (1993). s Keall and Baldock (1999). t Gorjiara et al. (2011). b c
This is the range of photons commonly used in the radiation dosimetry and radiation applications. Using these three parameters together, an “ideal” dosimeter can be identified.
2. Calculating of the effective atomic number The effective atomic number for photon energy absorption, ZPEAeff, can be calculated using the mass energy absorption coefficient, μen =ρ, determined for composite materials by the additivity law (Shivaramu et al., 2001). The ðμen =ρÞi values of the ith constituent element is tabulated in Hubbel and Seltzer (1995). The effective electronic energy absorption cross section, se;en , is as follows: 1 f A μ sa;en se;en ¼ ∑ i i en ¼ ; ð1Þ NA i Z i ρ i Z PEAef f where Z i is the atomic number of the ith constituent element, f i ¼ ni =∑ nj is the fractional abundance of the ith element and the j
effective atomic energy absorption cross section, sa;en , can be determined as sa;en ¼
sm;en : ∑ i ni
ð2Þ
The effective atomic number for photon energy absorption, ZPEAeff, can be calculated using Eq. (1) Z PEAef f ¼
sa;en : se;en
ð3Þ
The effective electron density for photon energy absorption, NPEAeff (number of electrons per unit mass) can be derived as NPEAef f ¼
NA μ =ρ Z ∑ni ¼ en : se M PEAef f
ð4Þ
More detailed information about the calculation of ZPEAeff and NPEAeff is given in Manohara and Hanagodimath (2007), Un and Sahin (2012); Un (2013).
3. Results and discussion The elemental compositions (% weight fractions) of soft tissue, water and different gel dosimeters are tabulated in Table 1. The energy dependence of the mass energy absorption coefficients, μen =ρ, are shown in Fig. 1 for the soft tissue, water and different gel dosimeters, while Figs. 2 and 3 show this dependence for ZPEAeff for the polymer gel and the gel dosimeters, respectively. In the low energy region E o0.01 MeV, the maximum values of ZPEAeff are found in the low-energy range because of the
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Fig. 1. Energy dependence of the mass energy absorption coefficient, μen =ρ, of gel dosimeters, soft tissue and water.
dominance of the photoelectric effect, as can be seen in Figs. 2 and 3. The ZPEAeff values for Presage is higher than that for other studied dosimeters in this low energy, because of the high atomic number of the elements of this material and their K-edge energies. In the intermediate energy range of 100 keV–3 MeV, the ZPEAeff values are almost constant for the dosimeters, soft tissue and water, due to the dominance of Compton scattering is this energy range. These ZPEAeff values for studied samples are smaller than those on the lower energy range, as seen in Figs. 2 and 3, because of the proportionality the Compton scattering with Z and of the photoelectric effect with Z4. In the high energy region E 43 MeV in which dominant photon interaction is the pair production, the ZPEAeff values are lower than those on the lower energy range and higher than those on the intermediate energy range, because of the proportionality pair production with Z2. In order to verify the adequacy of our method for calculating ZPEAeff, and given that is no experimental ZPEAeff values are available for soft tissue and water in the literature, the ZPEAeff values are compared with values calculated by Kumar and Reddy (1997) and Jayachandran (1971). As Fig. 2 shows, our calculated values are in agreement with those of others. As can be seen in Figs. 2 and 3, the maximum values of the ZPEAeff are 8.24 (NIPAM and PAGAT) at 10 keV for polymer gel dosimeters, 12.63 (PRESAGE) at 30 keV for gel dosimeters, 7.995 at 50 keV for water and 8.36 at 15 keV for soft tissue. The minimum values of ZPEAeff are 3.23 (ABAGIC) for polymer gel dosimeters, 3.34
Fig. 2. Comparison of the effective atomic number, ZPEAeff, of polymer gel dosimeters to soft tissue and water.
Fig. 3. Comparison of the effective atomic number, ZPEAeff, of gel dosimeters to soft tissue and water.
(SDA) for gel dosimeters, 3.33 for water and 3.43 for soft tissue at 1.25 MeV. The percentage differences between the ZPEAeff values of all gel dosimeters and the soft tissue under 5.0 except for the MAGIC and MAGAS at 35 keV, the ABAGIC at 60 keV–1.33 MeV and
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Table 2 The effective atomic number (ZPEAeff) for photon energy absorption of water, soft tissue and gel dosimeters for selected specific energies. Energy (MeV)
2.21E 02 3.50E 02 6.00E 02 8.10E 02 8.80E 02 1.22E 01 1.45E 01 2.79E 01 3.02E 01 3.56E 01 5.11E 01 5.14E 01 6.62E 01 1.12E þ00 1.17E þ03 1.33Eþ03
ZPEAeff BANG-1
BANG-2
PABIG
7.71 6.76 4.54 3.80 3.73 3.49 3.37 3.41 3.37 3.39 3.34 3.34 3.39 3.34 3.37 3.40
7.76 6.82 4.59 3.84 3.76 3.51 3.39 3.43 3.39 3.41 3.36 3.36 3.41 3.36 3.40 3.43
7.70 6.75 4.55 3.81 3.74 3.50 3.38 3.42 3.39 3.40 3.36 3.36 3.40 3.36 3.39 3.42
nMAG
nPAG
NIPAM
7.78 6.82 4.57 3.82 3.75 3.50 3.38 3.41 3.38 3.40 3.35 3.35 3.40 3.35 3.38 3.41
8.02 7.07 4.70 3.87 3.79 3.51 3.39 3.42 3.39 3.40 3.36 3.36 3.40 3.36 3.39 3.42
8.10 7.12 4.70 3.86 3.78 3.50 3.37 3.40 3.37 3.38 3.34 3.34 3.38 3.34 3.37 3.40
PAG
MAGIC
VIPAR
ABAGIC
PAGAT
HEAG
MAGAS
MAGAT
7.67 6.73 4.54 3.81 3.74 3.50 3.39 3.43 3.39 3.41 3.36 3.36 3.41 3.36 3.40 3.42
7.69 6.74 4.52 3.79 3.72 3.48 3.37 3.40 3.37 3.39 3.34 3.34 3.39 3.34 3.37 3.40
7.76 6.74 4.43 3.67 3.60 3.35 3.23 3.27 3.23 3.25 3.20 3.20 3.25 3.20 3.23 3.27
8.10 7.14 4.72 3.88 3.79 3.51 3.39 3.42 3.38 3.40 3.35 3.35 3.40 3.35 3.38 3.41
7.71 6.76 4.54 3.80 3.73 3.49 3.37 3.41 3.37 3.39 3.34 3.34 3.39 3.34 3.37 3.41
7.67 6.73 4.54 3.82 3.75 3.51 3.40 3.43 3.40 3.41 3.37 3.37 3.41 3.37 3.40 3.43
8.08 7.12 4.72 3.89 3.81 3.53 3.41 3.44 3.40 3.42 3.37 3.37 3.42 3.37 3.40 3.43
PRESAGE
SDA
Gelatin
Frice
Genipin
Water
Tissue
12.66 11.91 7.13 5.01 4.66 3.85 3.66 3.51 3.47 3.48 3.46 3.46 3.47 3.45 3.48 3.47
7.89 6.93 4.61 3.82 3.74 3.48 3.35 3.39 3.35 3.37 3.32 3.32 3.37 3.32 3.35 3.39
8.16 7.20 4.77 3.91 3.82 3.53 3.40 3.43 3.40 3.41 3.36 3.36 3.41 3.36 3.40 3.43
8.16 7.20 4.78 3.92 3.83 3.54 3.41 3.44 3.40 3.42 3.37 3.37 3.42 3.37 3.40 3.43
7.91 6.94 4.62 3.82 3.74 3.48 3.35 3.39 3.35 3.37 3.32 3.32 3.37 3.32 3.35 3.39
7.78 6.82 4.54 3.78 3.70 3.45 3.33 3.37 3.33 3.35 3.30 3.30 3.35 3.30 3.33 3.37
8.05 7.09 4.72 3.91 3.82 3.55 3.43 3.46 3.42 3.44 3.40 3.40 3.44 3.40 3.43 3.45
7.70 6.75 4.53 3.80 3.73 3.49 3.37 3.41 3.37 3.39 3.34 3.34 3.39 3.34 3.38 3.41
ZPEAeff
2.21E 02 3.50E 02 6.00E 02 8.10E 02 8.80E 02 1.22E 01 1.45E 01 2.79E 01 3.02E 01 3.56E 01 5.11E 01 5.14E 01 6.62E 01 1.12E þ00 1.17E þ03 1.33Eþ03
the PRESAGE at 22.1–145 keV. To assist in evaluating the tissue and water equivalency of gel dosimeters, the ZPEAeff values are tabulated for some specific energies in Table 2. The change in the NPEAeff values with energy for the polymer gel and the gel dosimeters is shown in Figs. 4 and 5, respectively. The tabulated values are given in Table 3. As can be seen in Figs. 4 and 5, the maximum values of the NPEAeff are 8.29E þ23 e/g (ABAGIC) at 50 keV for polymer gel dosimeters, 11.93E þ23 e/g (PRESAGE) at 30 keV for gel dosimeters, 8.02E þ23 e/g at 50 keV for water and 8.06E þ23 e/g at 15 keV for soft tissue. The minimum values are 3.32E þ23 e/g (BANG-2, PABIG, PAG, MAGIC, VIPAR, PAGAT, MAGAS, MAGAT, nMAG, and nPAG) for polymer gel dosimeters, 3.26E þ23 e/g (PRESAGE) for gel dosimeters, 3.34E þ23 e/g for water and 3.31E þ23 e/g for soft tissue at 1.25 MeV. The percentage differences between the NPEAeff values of all gel dosimeters and the soft tissue are under 5.0 except for the PRESAGE at 22.1–122 keV. To examine the tissue equivalency, the ZPEAeff and the NPEAeff values for gel dosimeters relative to the soft tissue ZPEAeff (Gel)/ZPEAeff(Tissue)and NPEAeff(Gel)/NPEAeff(Tissue) are shown in Figs. 6 and 7. Because of the elemental composition of the gel dosimeters, the tissue equivalency of the gel dosimeters with respect to ZPEAeff is somewhat different than that of the gel dosimeters with respect to NPEAeff. It can be seen in Figs. 6 and 7 that NPEAeff(Gel)/NPEAeff(Tissue) is closer to 1.0 than the values of the ZPEAeff(Gel)/ZPEAeff(Tissue). Since the PRESAGE contains Br, which has a Br high atomic number, its ZPEAeff(Gel)/ZPEAeff(Tissue) and NPEAeff(Gel)/NPEAeff(Tissue) values are higher than those of the other gel dosimeters in the low energy ranges 10–150 keV where the photoelectric interaction is dominant.
Fig. 4. Comparison of the effective electron number, NPEAeff, of polymer gel dosimeters to soft tissue and water.
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4. Conclusions The mass energy absorption coefficients,μen =ρ, the effective atomic number for photon energy absorption, ZPEAeff and the effective electron number for photon energy absorption, NPEAeff of some gel dosimeters, soft tissue and water are calculated to evaluate the tissue/water equivalency in the energy range 1 keV– 20 MeV. The energy dependence of ZPEAeff and NPEAeff for the studied gel dosimeters, except for PRESAGE in the low energy region, resembles that of the soft tissue and water. Since the ratios of NPEAeff(Gel)/NPEAeff(Tissue) for studied materials are somewhat
Fig. 5. Comparison of the effective electron number, NPEAeff, of gel dosimeters to soft tissue and water.
Fig. 6. Variation of ZPEAeff(Gel)/ZPEAeff(Tissue) with photon energy.
Table 3 The effective electronic density (NPEAeff) for photon energy absorption of water, soft tissue and gel dosimeters for selected specific energies. Energy (MeV)
2.21E 02 3.50E 02 6.00E 02 8.10E 02 8.80E 02 1.22E 01 1.45E 01 2.79E 01 3.02E 01 3.56E 01 5.11E 01 5.14E 01 6.62E 01 1.12E þ 00 1.17E þ 03 1.33Eþ 03
NPEAeff ( 1023 e/g) BANG-1
BANG-2
PABIG
7.61 6.67 4.48 3.75 3.68 3.44 3.33 3.36 3.33 3.34 3.30 3.30 3.34 3.30 3.33 3.36
7.59 6.67 4.49 3.75 3.68 3.44 3.32 3.36 3.32 3.34 3.29 3.29 3.34 3.29 3.33 3.36
7.56 6.63 4.46 3.74 3.67 3.44 3.32 3.36 3.32 3.34 3.29 3.29 3.34 3.29 3.33 3.36
PAG 7.59 6.66 4.47 3.75 3.68 3.44 3.32 3.36 3.33 3.34 3.30 3.30 3.34 3.30 3.33 3.36
MAGIC
VIPAR
ABAGIC
PAGAT
HEAG
MAGAS
MAGAT
7.51 6.59 4.44 3.73 3.67 3.43 3.32 3.35 3.32 3.34 3.29 3.29 3.34 3.29 3.32 3.35
7.59 6.65 4.47 3.75 3.68 3.44 3.32 3.36 3.33 3.34 3.30 3.30 3.34 3.30 3.33 3.36
8.06 7.01 4.60 3.81 3.74 3.48 3.36 3.39 3.36 3.38 3.32 3.32 3.38 3.32 3.36 3.39
7.97 7.02 4.65 3.82 3.73 3.45 3.33 3.36 3.33 3.34 3.30 3.30 3.34 3.30 3.33 3.36
7.61 6.67 4.48 3.75 3.68 3.44 3.33 3.36 3.33 3.34 3.30 3.30 3.34 3.30 3.33 3.36
7.49 6.58 4.44 3.73 3.66 3.43 3.32 3.35 3.32 3.34 3.29 3.29 3.34 3.29 3.32 3.35
7.89 6.95 4.61 3.80 3.72 3.44 3.33 3.35 3.32 3.34 3.29 3.29 3.34 3.29 3.32 3.35
NPEAeff ( 1023 e/g)
2.21E 02 3.50E 02 6.00E 02 8.10E 02 8.80E 02 1.22E 01 1.45E 01 2.79E 01 3.02E 01 3.56E 01 5.11E 01 5.14E 01 6.62E 01 1.12E þ 00 1.17E þ 03 1.33Eþ 03
nMAG
nPAG
NIPAM
PRESAGE
SDA
Gelatin
Frice
Genipin
Water
Tissue
7.65 6.71 4.50 3.76 3.69 3.44 3.33 3.36 3.32 3.34 3.29 3.29 3.34 3.29 3.33 3.36
7.87 6.94 4.61 3.80 3.72 3.45 3.33 3.36 3.32 3.34 3.29 3.29 3.34 3.29 3.33 3.36
8.01 7.04 4.65 3.82 3.74 3.46 3.34 3.36 3.33 3.34 3.30 3.30 3.34 3.30 3.33 3.36
11.96 11.25 6.73 4.73 4.40 3.63 3.46 3.31 3.28 3.28 3.27 3.27 3.28 3.26 3.28 3.28
7.86 6.90 4.59 3.80 3.72 3.46 3.34 3.37 3.34 3.35 3.30 3.30 3.35 3.30 3.34 3.37
8.00 7.05 4.68 3.84 3.75 3.46 3.33 3.36 3.33 3.34 3.30 3.30 3.34 3.29 3.33 3.36
7.99 7.04 4.68 3.83 3.74 3.46 3.33 3.36 3.33 3.34 3.29 3.29 3.34 3.29 3.33 3.36
7.86 6.90 4.59 3.80 3.72 3.46 3.34 3.37 3.34 3.35 3.30 3.30 3.35 3.30 3.34 3.37
7.81 6.84 4.56 3.79 3.72 3.46 3.34 3.38 3.34 3.36 3.31 3.31 3.36 3.31 3.34 3.38
7.79 6.86 4.57 3.78 3.70 3.43 3.32 3.35 3.31 3.33 3.29 3.29 3.33 3.29 3.32 3.34
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Fig. 7. Variation of NPEAeff(Gel)/NPEAeff(Tissue) with photon energy.
different than the ratios of ZPEAeff(Gel)/ZPEAeff(Tissue), the values of NPEAeff should be considered as well as the values of ZPEAeff for determination of tissue/water equivalency.
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