Studies on equivalent atomic number and photon buildup factors for some tissues and phantom materials.

Radiation Physics and Chemistry 165 (2019) 108388

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Studies on equivalent atomic number and photon buildup factors for some tissues and phantom materials.

T

H.H. Saleha,∗, J.M. Sharafb, S.B. Alkhateebc, M.S. Hamideend a

Department of Radiography, Al-Hussein Bin Talal University, P.O. Box (20), Ma'an, Jordan Department of Physics, The University of Jordan, Amman, Jordan c Department of Physics, Faculty of Science, Al-Balqa Applied University, P.O. Box 2587, Amman, 11941, Jordan d Department of Physics and Basic Sciences, Faculty of Engineering Technology, Al-Balqa Applied University, Amman, Jordan b

ARTICLE INFO

ABSTRACT

Keywords: Gamma ray build-up factor (GP) fitting formula Energy absorption buildup factor Effective atomic number Human organs and tissues

Geometric progression fitting method was used for the computation of the gamma-ray EABF of eleven tissue equivalent materials and nine human organs and tissues up to energy 3 MeV. Quantitative comparison of photon absorption and scattering properties of tissue-equivalent materials was performed with that of human organs and tissues. The variations of equivalent atomic number and the buildup factors of the tissue/equivalent materials indicate which material can be used to substitute for different human tissues in phantom construction.

1. Introduction Application of ionizing radiation in medical practice requires special materials to simulate human organs and tissues as well as water as a reference material. These tissue equivalent materials include some phantoms and test objects that could be used in diagnostic radiology, radiation protection, radiation physics, radiation dosimetry and radiobiology for dose estimations and detector calibrations. Various tissue and water equivalent materials were developed for radiation therapy last decades (Sardari, and Kurudirek, 2012; and Sahoo et al., 2010) and high accuracy in the interaction cross sections simulation was achieved for the new materials. In additions, ICRU report 44 (International Commission on Radiation Units and Measurements (ICRU), 1989) described different types of tissue substitutes for human organs and tissues. Tissue equivalence describes the ability of the material to respond to radiation in the same way as human tissue. Its photon interaction cross sections are to be as close as possible to those of respective human tissues. For a given radiation type and energy, it should absorb and scatter radiation to the same extent as irradiated biological tissue. However, the effective atomic number, Zeff, which represents a weighted average of the number of electrons per atom in a multi-element material (Manohara et al., 2008), could be used as an equivalence estimator and Zeff of each material under investigation could be compared with calculated values of respective human tissues. It is a photon interaction parameter which is considered as one of material dosimetric

∗

properties. Early calculations of Zeff were based on parameterization of the photon interaction cross section by fitting data over limited ranges of energy and atomic number. Today, accurate databases and interpolation programs, such as WinXCom (Gerward et al.,2004; and Gerward et al., 2001), have made it possible to calculate Zeff with much improved accuracy and information content over wide ranges of photon energy, for all types of materials.(Manohara et al., 2011). Many authors have made extensive Zeff studies on various materials such as dosimetric materials (Shivaramu and Ramprasath, 2000; Kiran Kumar and Venkata Reddy, 1997), gaseous mixtures (Singh and Badiger, 2012), alloys (Han et al., 2012; and Kurudirek et al.,2010), semiconductors (Çelik et al., 2008), building materials (Damla et al., 2012), soils (Kucuk et al., 2013), amino acids (Gowda et al., 2005), minerals (Han et al., 2011), glasses (Kaewkhao and Limsuwan, 2010) and biological samples (Koç and Özyol, 2000). Other significant parameter that can be used as an equivalence estimator is the buildup factor which could be investigated as a function of incident photon energy, chemical composition, Zeff, and penetration depth. It is an important parameter in predicting the distribution of photon flux in irradiated object and calculation of radiation dose received by human tissues (Sardari and Baradaran, 2010; Sardari et al., 2009). It is a multiplicative factor used to get the corrected response to uncollided photons by including the contribution of scattered photons. The buildup factor depends upon Zeff of the absorbing medium, the energy of the gamma rays, and the penetration depth, as well as the geometry of the radiation source and the medium (Manohara et al.,

Corresponding author. E-mail addresses: [email protected], [email protected] (H.H. Saleh).

https://doi.org/10.1016/j.radphyschem.2019.108388 Received 27 March 2019; Received in revised form 20 June 2019; Accepted 26 June 2019 Available online 27 June 2019 0969-806X/ © 2019 Elsevier Ltd. All rights reserved.

Radiation Physics and Chemistry 165 (2019) 108388

4.7234 14.4330 4.1990 44.6096 0.0000 0.2200 0.0000 10.4970 0.3150 0.0000 0.0000 20.9930 0.0000 0.0100 6.3984 27.8000 2.7000 41.0016 0.0000 0.2000 0.0000 7.0000 0.2000 0.0000 0.0000 14.7000 0.0000 0.0000 10.4472 23.2190 2.4880 63.0238 0.1130 0.0130 0.0000 0.1330 0.1990 0.1340 0.1990 0.0230 0.0050 0.0030 10.1278 10.2310 2.8650 75.7072 0.1840 0.0730 0.0000 0.0800 0.2250 0.2660 0.1940 0.0090 0.0370 0.0010 11.0667 12.5420 1.3280 73.7723 0.1840 0.0150 0.0000 0.3540 0.1770 0.2360 0.3100 0.0090 0.0050 0.0010 10.1997 12.3000 3.5000 72.9003 00.0800 0.0200 0.0000 0.2000 0.5000 0.0000 0.3000 0.0000 0.0000 0.0000

10.1866 10.0020 2.9640 75.9414 0.1850 0.0040 0.0030 0.0350 0.1850 0.2780 0.1630 0.0060 0.0460 0.0010

Bone, Cortical ρ = 1.85 g/cm3 Bone, Compact ρ = 1.85 g/cm3 Soft ρ = 1.00 g/cm3 Lung ρ = 1.05 g/cm3 Brain ρ = 1.03 g/cm3 Muscle ρ = 1.04 g/cm3

Blood ρ = 1.06 g/cm3

2011). On the other hand, the buildup factors can be defined in two terms: exposure in the air after penetration through the absorber or shielding material which is called the “Exposure Buildup factor” (EBF) and energy deposition in an absorbing medium which is called “Energy Absorption Buildup Factor” (EABF). Other types of buildup factors also exist, in particular dose buildup factors in absorbing media (Martin, 2006). Recognizing the importance of buildup of scattered photons, when material is exposed to radiations, the buildup factor has been evaluated by many authors for different materials including some human organs and tissues. A review on calculations and applications of buildup factors has been proposed by Harima (1993). Kurudirek and Özdemir (2011) have determined the buildup factors for some polymers and tissue equivalent materials. Singh et al (2017) have computed EABF values for 27 types of bone for photon energy 0.03–1.5 MeV. Energy absorption geometric progression (GP) fitting parameters and the corresponding buildup factors have been computed for human organs and tissues (Manohara et al., 2011). EBF and EABF of 10 human tissues and 4 equivalent materials were generated using also the geometric progression (GP) fitting parameters (Olarinoye, 2017). Other computational methods such as Iterative method (Suteau and Chiron, 2005), Invariant embedding (Shimzu, 2002), Generalised Feed Neural Network (GFFN) (Kucuk et al., 2013) and Monte Carlo N-particle (MCNP) codes (Sardari et al., 2009) were also employed to evaluate buildup factors. However, still there is a need for photon buildup factor values of low-Z materials, such as human organs and tissues, to be used for absorbed dose estimations in diagnostic, dosimetry, and radiotherapy. In the present work, the effective atomic number and the energy absorption buildup factor of eleven tissue equivalent materials of known elemental composition were generated as a function of photon energy, by using the ANSI/ANS-6.4.3-(1991) standard data and the GP fitting formula proposed by Harima et al. (1986). The calculations have been performed for irradiation in diagnostic radiology and brachytherapy within photon energy range 0.015–3 MeV up to penetration depths of 40 mean free path (mfp). The calculation procedure was also repeated to generate Zeff and EABF for nine human organs and tissues. The primary goal was to perform quantitative comparison of photon absorption and scatter properties of tissue-equivalent materials with that of respective human organs and tissues. The variations of equivalent atomic number and the buildup factors of the tissue/equivalent materials, with photon energy and penetration depth, indicates which material can be used to substitute for different human tissues in phantom construction and dose estimation. It is observed that Gelatin is an excellent tissue-equivalent material for skeletal muscle in the extended energy range. The data obtained will be useful for many applications especially in radiation brachytherapy and dosimetry as well as for the construction of phantoms using tissue-equivalent materials.

Skin ρ = 1.10 g/cm3

10.0588 22.8250 4.6420 61.9002 0.0070 0.0060 0.0000 0.0330 0.1590 0.2670 0.0850 0.0150 0.0010 0.0010

Adipose ρ = 0.92 g/cm3

11.9477 63.7240 0.7970 23.2333 0.0500 0.0020 0.0000 0.0160 0.0730 0.1190 0.0320 0.0020 0.0020 0.0020

2. Materials and methods Eleven samples of tissue equivalent materials of known chemical composition were selected and investigated in this study. Its behaviours and its photon interaction parameters were compared to that of nine different human tissues known to have measurable response to radiation. The chemical compositions (weight fraction of tissue components) of the selected human tissue samples are given in Table 1and those of tissue equivalent samples are presented in Table 2. The data of both tables have been taken from the literature (Hubbell and Seltzer, 1995; and International Commission on Radiation Units and Measurements (ICRU), 1989; ICRP, 2003; and Fuliful et al., 2017). The computational work has been carried out in three steps, as follows: 2.1. Computation of equivalent atomic number (Zeq) H C N O Na Mg Si P S Cl K Ca Fe Zn

Element

Table 1 Elemental composition (%) of adipose, skin, muscle, brain, lung, soft, bone (compact), and bone (cortical) tissues (Hubbell and Seltzer, 1995; and International Commission on Radiation Units and Measurements (ICRU), 1989).

H.H. Saleh, et al.

As a first step, the values of Compton partial mass attenuation 2

Radiation Physics and Chemistry 165 (2019) 108388

11

Paraffin2 ρ = 0.918 g/cm3

0.0068 0.7961 0.0963 0.0994 0.0014

10

Pitch ρ = 1.148 g/cm3

0.0019 0.4218 0.0042 0.5676 0.0046

H.H. Saleh, et al.

PMMA ρ = 1.178 g/cm3

0.0024 0.9496 0.0471 0.0000 0.0010

Modelling clay ρ = 1.273 g/cm3

0.0000 0.1976 0.0086 0.7583 0.0355

logR1)

(1)

0.0273 0.8200 0.0737 0.0782 0.0008

In the second step, five (GP) fitting parameters (b, c, a, Xk and d) for energy absorption buildup factors of tissues and materials of interest were computed by applying an interpolation procedure similar to that used in the above section to calculate Zeq. The interpolation formula used (Sidhu et al., 1999) was as follows:

0.0050 0.8222 0.0078 0.1641 0.0009 0.0061 0.8173 0.0074 0.1681 0.0010 0.0036 0.8017 0.1123 0.0814 0.0009 0.0187 0.7525 0.0842 0.1427 0.0019

P1 (logZ2

logZeq) + P2 (logZeq logZ2

logZ1) (2)

logZ1

where P is the (GP) fitting parameter corresponding to Zeq, and Z1 and Z2 are the atomic numbers of pure elements between which the, Zeq, of a given tissue lies, P1 and P2 are the values of (GP) fitting parameters corresponding to the pure element atomic numbers Z1 and Z2, respectively, at a given photon energy. (GP) fitting parameters for the pure elements were taken from the standard reference database ANSI/ANS-6.4.3-(1991) that was provided by the American Nuclear Society Standard Committee working group who has developed a set of gamma-ray point isotropic source buildup factors as a standard reference database for 23 elements in the range Z = 4–92, one compound(water) and two mixtures (air and concrete) in the photon energy range of 0.015–15.0 MeV and up to a penetration depth of 40 mfp — for use in radiation shielding calculations. The calculated energy absorption (GP) fitting parameters for all the selected tissues and equivalent materials are given in Tables 5–14.

0.0063 0.5949 0.0434 0.3158 0.0396

Bolus ρ = 1.112 g/cm3 Paraffin1 ρ = 0.959 g/cm3 Red articulation wax ρ = 0.911 g/cm3

2.3. Computation of the energy absorption buildup factor (EABF) In the final step, the calculated (GP) fitting parameters were used to estimate the energy absorption buildup factor, B, of the selected tissues and materials in the energy of 0.05–3 MeV and penetration depths up to 40 mfp, using the following (GP) fitting formula proposed by Harima et al. (1986):

B (E , x ) = 1 +

(b

B (E , x ) = 1 + (b

1)(K x K 1

1) x

1)

for K

1

(3) (4)

for K = 1

0.06281 0.25552 0.05706 0.62109 0.00352

where

K (E , x ) = x a + d

tanh

(

x

Xk

1

2

)

tanh( 2)

tanh( 2)

for x

40 mfp

(5)

and E is the photon energy, x is the penetration depth in mfp, a, b, c, d and Xk are the (GP) fitting parameters and b is the value of the buildup

H C N O S

Gelatin a ρ = 1.27 g/cm3

Bee wax ρ = 0.964 g/cm3

Nylon ρ = 1.160 g/cm3

Orange articulation wax ρ = 0.931 g/cm3

9

logR) + Z2 (logR logR2 logR1

where Z1 and Z2 are the atomic numbers of elements corresponding to the (μcomp/μtotal) ratios, R1 and R2, respectively; and R (μcomp/μtotal) is the ratio for the selected tissues or materials at a particular energy that lies between ratios R1 and R2. The computed values of the equivalent atomic number, Zeq, for the selected human tissues are presented in Table 3, and for the selected tissue equivalent materials are given in Table 4.

P=

4

5

Z1 (logR2

2.2. Computation of the geometric progression (GP) fitting parameters

3

6

7

8

Zeq =

2 1 Element

Table 2 Elemental composition (%) of tissue equivalent material (ICRP, 2003; Fuliful et al., 2017).

coefficient (μcomp) and total mass attenuation coefficients (μtot) in cm2/ g were obtained for elements from Z = 1 to 30 and for the selected tissues and materials in the energy of 0.05–3 MeV, using the WinXCom program. The ratio R(μcomp/μtot) was then calculated and the value of equivalent atomic number (Zeq) for the selected samples was determined by matching the ratio R (μcomp/μtot) of particular sample at a given energy with corresponding ratios of a pure element at the same energy. For the case the ratio lies in between the two ratios of known elements, the value of Zeq was interpolated by using the following formula of interpolation (Harima, 1993).

3

Adipose

6.25 6.25 6.24 6.21 6.17 6.14 6.07 6.01 5.75 6.15 6.24 6.11 5.81 5.89 6.13 5.45 4.44 5.44 5.54 5.22 5.78 5.70 5.61 5.44 5.42 5.44 5.36 5.51 5.48 5.42 5.36 5.45 5.34 5.37 5.36

Energy (MeV)

0.015 0.02 0.03 0.04 0.05 0.06 0.08 0.1 0.15 0.2 0.3 0.4 0.5 0.6 0.8 1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3

7.19 7.21 7.21 7.19 7.15 7.15 7.10 7.09 6.91 6.73 7.19 6.16 6.98 7.11 6.64 7.23 6.77 6.73 6.28 6.46 6.52 6.52 6.51 6.22 6.26 6.42 6.30 6.35 6.35 6.35 6.34 6.33 6.35 6.28 6.35

Skin 7.47 7.49 7.49 7.47 7.43 7.42 7.35 7.30 7.23 7.11 7.18 7.26 7.11 7.29 7.06 6.54 6.77 6.73 7.09 6.45 6.81 6.75 6.50 6.39 6.40 6.67 6.63 6.68 6.64 6.62 6.58 6.53 6.55 6.53 6.58

Muscle 7.47 7.49 7.49 7.47 7.44 7.41 7.37 7.31 7.21 7.08 7.16 7.23 7.09 7.09 7.04 7.20 6.75 6.70 7.06 6.41 6.77 6.48 6.47 6.35 6.51 6.50 6.59 6.63 6.59 6.47 6.45 6.48 6.50 6.48 6.47

Brain 7.48 7.50 7.50 7.48 7.45 7.44 7.37 7.37 7.23 7.11 7.18 7.26 7.25 7.11 7.36 7.23 6.77 7.36 7.09 6.45 6.81 6.75 6.50 6.58 6.56 6.67 6.63 6.68 6.65 6.71 6.50 6.60 6.62 6.60 6.59

Blood

Table 3 Equivalent atomic numbers of adipose, skin, muscle, brain, lung, soft, bone (compact), and bone (cortical) tissues.

7.50 7.52 7.53 7.51 7.48 7.47 7.40 7.38 7.23 7.11 7.18 7.26 7.12 7.29 7.36 6.54 7.46 7.37 7.09 6.45 6.82 6.75 6.69 6.58 6.56 6.55 6.64 6.68 6.65 6.62 6.59 6.60 6.62 6.60 6.65

Lung 7.23 7.25 7.25 7.23 7.20 7.18 7.13 7.11 6.90 6.90 7.17 7.25 6.97 6.87 7.05 7.22 6.31 6.72 6.25 6.44 6.50 6.51 6.31 6.20 6.24 6.40 6.28 6.32 6.33 6.33 6.24 6.31 6.25 6.33 6.33

Soft 11.40 11.57 11.71 11.77 11.79 11.78 11.71 11.63 11.36 11.10 11.10 11.01 10.53 10.38 10.73 10.50 9.78 9.73 9.63 9.49 9.49 9.22 9.24 9.04 9.05 9.06 8.93 8.82 8.86 8.87 8.87 8.89 8.81 8.89 8.84

Bone, Compact 12.69 12.86 13.01 13.09 13.14 13.12 13.09 13.03 12.79 12.63 12.34 12.24 12.13 12.09 12.14 12.06 11.62 11.58 11.25 10.72 10.57 10.71 10.64 10.58 10.39 10.54 10.51 10.38 10.32 10.38 10.32 10.27 10.30 10.23 10.24

Bone, Cortical

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Radiation Physics and Chemistry 165 (2019) 108388

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Gelatin

7.26 7.27 7.27 7.25 7.22 7.22 7.19 7.18 7.03 7.02 6.82 7.41 7.09 7.21 7.16 7.32 6.85 6.82 6.53 6.65 6.69 6.69 6.68 6.61 6.62 6.76 6.62 6.81 6.68 6.77 6.66 6.68 6.65 6.71 6.71

Energy (MeV)

0.015 0.02 0.03 0.04 0.05 0.06 0.08 0.1 0.15 0.2 0.3 0.4 0.5 0.6 0.8 1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3

6.46 6.45 6.44 6.42 6.41 6.40 6.37 6.33 6.23 6.36 6.45 6.19 6.33 6.59 6.44 5.90 6.46 6.45 5.92 5.87 6.25 6.41 6.31 6.09 6.23 6.32 6.27 6.26 6.22 6.18 6.15 6.20 6.19 6.17 6.22

Bee wax 6.37 6.36 6.35 6.34 6.32 6.32 6.29 6.27 6.13 6.39 6.49 6.24 6.39 6.32 5.99 5.99 6.49 6.49 5.98 5.97 6.43 6.23 6.18 5.98 6.15 6.27 6.23 6.23 6.31 6.28 6.16 6.21 6.21 6.26 6.25

Red articulation wax

Table 4 Equivalent atomic numbers of the selected tissue equivalent materials.

6.47 6.46 6.44 6.43 6.42 6.41 6.41 6.37 6.27 6.39 6.49 6.23 6.38 6.64 6.57 6.97 5.99 6.49 5.97 5.95 6.30 6.47 6.37 6.16 6.30 6.25 6.34 6.33 6.29 6.36 6.23 6.27 6.27 6.32 6.30

Paraffin1 6.46 6.45 6.43 6.42 6.41 6.41 6.41 6.43 6.41 6.39 6.49 6.23 6.38 6.31 5.98 6.98 6.49 6.49 5.98 6.47 6.31 6.48 6.18 6.17 6.30 6.40 6.35 6.34 6.30 6.27 6.24 6.28 6.28 6.32 6.30

Bolus 7.79 7.81 7.83 7.82 7.80 7.79 7.71 7.66 7.53 7.22 7.48 7.42 7.27 7.38 7.32 7.48 6.99 7.96 6.95 6.96 6.97 6.97 6.97 6.96 6.96 7.12 6.96 7.06 7.06 7.05 7.04 7.04 7.03 7.02 7.02

Nylon 6.22 6.21 6.20 6.19 6.18 6.16 6.14 6.09 6.06 6.14 5.84 6.04 6.11 6.23 5.91 6.87 6.33 6.43 5.89 6.36 5.84 6.13 6.08 5.86 6.02 6.14 5.98 5.96 5.95 5.94 5.93 6.00 5.91 5.98 5.97

Orange articulation wax 8.36 8.38 8.38 8.37 8.36 8.35 8.32 8.29 8.19 8.19 8.00 8.17 8.00 8.24 8.00 8.00 8.00 8.00 8.00 8.00 7.67 7.75 7.75 8.00 7.67 8.00 8.00 7.74 8.00 7.91 7.92 7.92 7.86 7.87 7.88

Modelling clay 6.09 6.08 6.08 6.08 6.07 6.07 6.05 6.05 5.99 6.19 6.50 5.99 5.99 6.32 6.49 5.99 6.00 6.49 5.37 5.99 5.99 6.24 6.19 5.99 5.99 6.13 6.11 5.99 6.10 6.09 5.99 6.06 5.98 5.98 6.05

PMMA

7.40 7.40 7.39 7.38 7.36 7.36 7.33 7.36 7.21 6.99 6.99 7.22 7.28 7.39 6.99 6.99 6.99 6.99 6.99 6.99 6.99 7.24 6.99 6.99 7.15 7.32 7.27 7.19 7.18 7.26 7.15 7.15 7.13 7.19 7.17

Pitch

6.40 6.39 6.38 6.37 6.36 6.35 6.35 6.31 6.26 6.38 6.48 6.10 6.18 6.31 6.48 5.96 6.09 6.98 5.97 5.95 6.30 6.47 6.17 6.16 6.13 6.25 6.21 6.21 6.29 6.26 6.14 6.27 6.26 6.17 6.29

Paraffin2

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0.015 0.02 0.03 0.04 0.05 0.0595 0.06 0.08 0.1 0.15 0.2 0.3 0.356 0.4 0.5 0.6 0.662 0.8 1 1.173 1.2 1.274 1.3 1.333 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3

Energy (MeV)

0.156 0.092 −0.007 −0.110 −0.154 −0.173 −0.181 −0.203 −0.209 −0.201 −0.193 −0.173 −0.168 −0.153 −0.146 −0.120 −0.120 −0.108 −0.095 −0.080 −0.079 −0.071 −0.073 −0.073 −0.067 −0.062 −0.055 −0.051 −0.047 −0.043 −0.040 −0.036 −0.032 −0.029 −0.026 −0.023 −0.021 −0.018 −0.016 −0.014 −0.012

1.356 1.808 3.471 4.831 5.468 5.334 5.382 4.866 4.310 3.552 3.203 2.808 2.688 2.628 2.451 2.395 2.326 2.199 2.086 1.990 1.980 2.003 1.950 1.926 1.928 1.936 1.890 1.867 1.848 1.833 1.837 1.813 1.807 1.796 1.790 1.788 1.786 1.778 1.781 1.776 1.715

0.515 0.696 1.075 1.634 1.988 2.137 2.232 2.469 2.544 2.477 2.338 2.111 2.056 1.922 1.812 1.669 1.653 1.560 1.468 1.399 1.387 1.299 1.305 1.303 1.269 1.283 1.213 1.197 1.182 1.169 1.176 1.146 1.136 1.129 1.122 1.115 1.109 1.106 1.100 1.097 1.052

−0.078 −0.044 −0.003 0.047 0.065 0.073 0.077 0.083 0.083 0.074 0.076 0.069 0.065 0.063 0.062 0.046 0.051 0.046 0.041 0.038 0.037 0.029 0.031 0.031 0.028 0.028 0.023 0.021 0.019 0.018 0.017 0.015 0.014 0.012 0.011 0.010 0.009 0.008 0.007 0.006 0.004

d 14.459 16.041 13.443 14.034 14.386 14.600 14.526 14.709 14.874 15.477 14.775 14.772 14.751 14.769 15.778 14.954 14.754 14.105 14.072 13.905 13.902 14.418 14.219 14.188 14.250 14.336 14.334 14.330 14.320 14.283 14.307 14.293 14.266 14.319 14.300 14.260 14.200 14.191 14.014 13.862 13.517

Xk 0.170 0.140 0.066 −0.039 −0.102 −0.124 −0.143 −0.182 −0.182 −0.190 −0.183 −0.166 −0.157 −0.153 −0.138 −0.124 −0.120 −0.106 −0.086 −0.075 −0.075 −0.069 −0.069 −0.067 −0.064 −0.060 −0.054 −0.049 −0.045 −0.042 −0.038 −0.035 −0.032 −0.029 −0.026 −0.023 −0.021 −0.019 −0.016 −0.014 −0.012

a

c

a

b

Skin Tissue

Adipose Tissue

Table 5 Energy absorption (GP) fitting parameters for adipose tissue and skin tissue in the energy range (0.015–3)MeV.

1.220 1.516 2.594 3.832 4.776 5.074 5.080 4.916 4.658 3.730 3.316 2.853 2.694 2.627 2.462 2.363 2.306 2.201 2.107 2.045 2.034 2.010 1.999 1.987 1.958 1.936 1.907 1.884 1.862 1.838 1.841 1.808 1.794 1.781 1.770 1.760 1.751 1.743 1.735 1.730 1.712

b 0.473 0.562 0.802 1.216 1.578 1.761 1.865 2.193 2.233 2.315 2.239 2.040 1.971 1.920 1.785 1.677 1.648 1.551 1.429 1.343 1.331 1.307 1.295 1.284 1.258 1.276 1.214 1.196 1.180 1.165 1.169 1.145 1.137 1.130 1.125 1.120 1.116 1.112 1.109 1.107 1.053

c −0.083 −0.070 −0.039 0.011 0.043 0.056 0.065 0.081 0.077 0.077 0.076 0.066 0.064 0.063 0.056 0.050 0.050 0.044 0.035 0.030 0.031 0.028 0.028 0.028 0.026 0.026 0.022 0.020 0.018 0.016 0.015 0.013 0.012 0.011 0.010 0.009 0.008 0.007 0.006 0.005 0.003

d

14.289 14.807 15.064 13.687 13.870 13.812 13.754 13.458 14.410 14.457 14.792 14.188 14.197 14.732 14.149 14.248 14.379 14.162 14.595 14.410 14.527 14.490 14.473 14.450 14.369 14.333 14.344 14.308 14.272 14.348 14.371 14.192 14.240 14.167 14.123 14.076 14.037 14.012 13.924 13.987 13.777

Xk

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0.015 0.02 0.03 0.04 0.05 0.0595 0.06 0.08 0.1 0.15 0.2 0.3 0.356 0.4 0.5 0.6 0.662 0.8 1 1.173 1.2 1.274 1.3 1.333 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3

Energy (MeV)

0.180 0.149 0.084 −0.021 −0.087 −0.111 −0.130 −0.173 −0.179 −0.184 −0.178 −0.166 −0.157 −0.149 −0.137 −0.123 −0.119 −0.105 −0.089 −0.075 −0.075 −0.069 −0.069 −0.067 −0.062 −0.060 −0.053 −0.049 −0.045 −0.042 −0.038 −0.034 −0.031 −0.029 −0.026 −0.024 −0.021 −0.019 −0.017 −0.015 −0.012

1.196 1.460 2.441 3.615 4.569 4.860 4.968 4.924 4.651 3.790 3.365 2.852 2.694 2.628 2.464 2.364 2.300 2.203 2.099 2.045 2.034 2.010 1.999 1.987 1.971 1.936 1.913 1.888 1.862 1.841 1.840 1.810 1.795 1.781 1.769 1.758 1.748 1.740 1.731 1.724 1.711

0.456 0.540 0.750 1.136 1.488 1.680 1.770 2.109 2.196 2.255 2.187 2.040 1.972 1.884 1.780 1.673 1.642 1.542 1.443 1.343 1.331 1.307 1.295 1.284 1.269 1.276 1.218 1.198 1.180 1.166 1.171 1.145 1.136 1.128 1.122 1.117 1.113 1.110 1.106 1.103 1.054

−0.091 −0.075 −0.042 0.002 0.035 0.050 0.058 0.077 0.077 0.075 0.076 0.066 0.064 0.059 0.055 0.049 0.048 0.043 0.038 0.030 0.031 0.028 0.028 0.028 0.026 0.026 0.022 0.020 0.018 0.016 0.016 0.014 0.012 0.011 0.010 0.009 0.008 0.007 0.007 0.006 0.004

d 13.885 14.684 13.786 13.525 13.714 13.753 13.727 13.534 14.238 14.408 14.704 14.189 14.199 14.177 14.139 14.261 14.209 14.211 14.491 14.413 14.526 14.491 14.472 14.449 14.454 14.332 14.324 14.270 14.274 14.277 14.286 14.034 13.987 13.873 13.822 13.766 13.717 13.708 13.586 13.516 13.302

Xk 0.180 0.149 0.084 −0.020 −0.087 −0.110 −0.130 −0.172 −0.179 −0.185 −0.179 −0.166 −0.157 −0.149 −0.137 −0.124 −0.123 −0.105 −0.086 −0.075 −0.075 −0.069 −0.069 −0.067 −0.062 −0.060 −0.053 −0.049 −0.045 −0.042 −0.039 −0.035 −0.031 −0.029 −0.026 −0.023 −0.021 −0.019 −0.017 −0.015 −0.012

a

c

a

b

Brain Tissue

Muscle Tissue

Table 6 Energy absorption (GP) fitting parameters for muscle tissue and brain tissue in the energy range (0.015–3)MeV.

1.196 1.459 2.439 3.611 4.564 4.856 4.969 4.925 4.650 3.786 3.365 2.851 2.693 2.627 2.464 2.363 2.298 2.202 2.107 2.045 2.034 2.010 1.998 1.986 1.971 1.937 1.912 1.883 1.861 1.840 1.839 1.809 1.795 1.781 1.769 1.759 1.750 1.741 1.732 1.725 1.712

b 0.456 0.540 0.749 1.135 1.486 1.678 1.771 2.103 2.193 2.260 2.189 2.043 1.973 1.885 1.781 1.678 1.647 1.543 1.429 1.343 1.331 1.307 1.295 1.283 1.269 1.276 1.217 1.196 1.180 1.166 1.172 1.145 1.136 1.129 1.123 1.118 1.114 1.110 1.107 1.104 1.053

c −0.091 −0.075 −0.042 0.002 0.035 0.050 0.058 0.077 0.077 0.075 0.076 0.066 0.064 0.059 0.055 0.050 0.049 0.043 0.035 0.030 0.031 0.028 0.028 0.028 0.026 0.026 0.022 0.020 0.018 0.016 0.016 0.014 0.012 0.011 0.010 0.009 0.008 0.007 0.006 0.006 0.003

d

13.884 14.682 13.762 13.522 13.710 13.752 13.727 13.539 14.227 14.408 14.729 14.192 14.216 14.181 14.136 14.246 14.230 14.207 14.608 14.425 14.521 14.496 14.467 14.444 14.457 14.329 14.326 14.315 14.285 14.296 14.223 14.143 14.022 13.918 13.873 13.931 13.895 13.778 13.670 13.608 13.526

Xk

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0.015 0.02 0.03 0.04 0.05 0.0595 0.06 0.08 0.1 0.15 0.2 0.3 0.356 0.4 0.5 0.6 0.662 0.8 1 1.173 1.2 1.274 1.3 1.333 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3

Energy (MeV)

0.180 0.150 0.085 −0.019 −0.086 −0.109 −0.129 −0.172 −0.178 −0.184 −0.178 −0.166 −0.157 −0.149 −0.136 −0.124 −0.120 −0.103 −0.086 −0.081 −0.075 −0.069 −0.067 −0.067 −0.062 −0.060 −0.053 −0.049 −0.045 −0.041 −0.039 −0.034 −0.031 −0.029 −0.026 −0.024 −0.021 −0.019 −0.017 −0.015 −0.012

1.195 1.456 2.432 3.601 4.552 4.838 4.960 4.925 4.648 3.790 3.365 2.853 2.694 2.628 2.466 2.363 2.297 2.207 2.107 1.999 2.034 2.010 2.001 1.981 1.971 1.936 1.913 1.888 1.862 1.843 1.838 1.810 1.795 1.781 1.769 1.757 1.749 1.739 1.730 1.723 1.711

0.455 0.539 0.746 1.131 1.481 1.671 1.763 2.103 2.183 2.255 2.187 2.040 1.972 1.884 1.775 1.677 1.647 1.535 1.429 1.350 1.331 1.307 1.298 1.278 1.269 1.276 1.218 1.198 1.180 1.167 1.172 1.145 1.136 1.128 1.122 1.116 1.114 1.109 1.105 1.102 1.054

−0.091 −0.076 −0.042 0.002 0.035 0.049 0.057 0.077 0.077 0.075 0.076 0.066 0.064 0.059 0.055 0.050 0.049 0.042 0.035 0.034 0.031 0.028 0.027 0.028 0.026 0.026 0.022 0.020 0.018 0.016 0.016 0.014 0.012 0.011 0.010 0.009 0.008 0.007 0.007 0.006 0.004

d 13.863 14.677 13.705 13.514 13.701 13.747 13.725 13.539 14.180 14.408 14.704 14.189 14.199 14.177 14.161 14.248 14.213 14.268 14.596 14.207 14.526 14.491 14.450 14.385 14.453 14.332 14.323 14.270 14.274 14.205 14.197 14.034 13.986 13.872 13.820 13.660 13.826 13.603 13.468 13.394 13.299

Xk 0.181 0.150 0.087 −0.018 −0.085 −0.108 −0.128 −0.171 −0.178 −0.184 −0.178 −0.166 −0.157 −0.149 −0.137 −0.123 −0.119 −0.103 −0.089 −0.075 −0.073 −0.069 −0.067 −0.067 −0.062 −0.060 −0.053 −0.049 −0.045 −0.041 −0.039 −0.034 −0.031 −0.029 −0.026 −0.024 −0.021 −0.019 −0.017 −0.015 −0.012

a

c

a

b

Lung Tissue

Blood Tissue

Table 7 Energy absorption (GP) fitting parameters for blood tissue and lung tissue in the energy range (0.015–3)MeV.

1.193 1.452 2.419 3.585 4.535 4.823 4.948 4.925 4.648 3.791 3.365 2.853 2.694 2.628 2.464 2.364 2.300 2.207 2.099 2.045 2.035 2.010 2.001 1.987 1.971 1.936 1.913 1.888 1.865 1.843 1.838 1.809 1.795 1.781 1.769 1.758 1.748 1.739 1.730 1.723 1.710

b 0.454 0.537 0.742 1.125 1.473 1.666 1.753 2.096 2.183 2.255 2.187 2.040 1.972 1.884 1.780 1.673 1.642 1.534 1.443 1.343 1.333 1.307 1.298 1.284 1.269 1.276 1.218 1.198 1.181 1.167 1.172 1.145 1.136 1.128 1.122 1.117 1.113 1.109 1.105 1.102 1.055

c −0.091 −0.076 −0.042 0.001 0.034 0.049 0.057 0.076 0.077 0.075 0.076 0.066 0.064 0.059 0.055 0.049 0.048 0.042 0.038 0.030 0.030 0.028 0.027 0.028 0.026 0.026 0.022 0.020 0.018 0.016 0.016 0.014 0.012 0.011 0.010 0.009 0.008 0.007 0.007 0.006 0.004

d

13.833 14.668 13.598 13.502 13.688 13.743 13.722 13.546 14.178 14.408 14.701 14.189 14.199 14.177 14.140 14.261 14.209 14.268 14.493 14.411 14.441 14.491 14.449 14.450 14.453 14.333 14.323 14.269 14.222 14.203 14.195 14.112 13.984 13.869 13.817 13.760 13.711 13.598 13.462 13.388 13.172

Xk

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0.015 0.02 0.03 0.04 0.05 0.0595 0.06 0.08 0.1 0.15 0.2 0.3 0.356 0.4 0.5 0.6 0.662 0.8 1 1.173 1.2 1.274 1.3 1.333 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3

Energy (MeV)

0.171 0.142 0.069 −0.036 −0.100 −0.122 −0.142 −0.181 −0.181 −0.191 −0.181 −0.166 −0.160 −0.149 −0.138 −0.123 −0.120 −0.105 −0.086 −0.081 −0.075 −0.069 −0.069 −0.068 −0.064 −0.060 −0.054 −0.049 −0.046 −0.042 −0.038 −0.035 −0.032 −0.029 −0.026 −0.023 −0.021 −0.018 −0.016 −0.014 −0.012

1.216 1.507 2.570 3.800 4.740 5.037 5.068 4.917 4.657 3.727 3.347 2.852 2.671 2.628 2.462 2.368 2.307 2.203 2.107 1.998 2.028 2.010 1.998 1.978 1.957 1.936 1.907 1.883 1.859 1.838 1.841 1.808 1.793 1.781 1.770 1.760 1.752 1.743 1.737 1.729 1.713

0.471 0.558 0.794 1.204 1.563 1.747 1.855 2.183 2.228 2.318 2.211 2.041 2.017 1.884 1.785 1.678 1.648 1.543 1.429 1.351 1.323 1.307 1.295 1.276 1.257 1.276 1.214 1.196 1.179 1.165 1.169 1.145 1.138 1.131 1.125 1.120 1.117 1.113 1.110 1.107 1.052

−0.084 −0.071 −0.040 0.010 0.042 0.055 0.064 0.080 0.077 0.077 0.076 0.066 0.066 0.059 0.056 0.049 0.050 0.043 0.035 0.034 0.031 0.028 0.028 0.028 0.026 0.026 0.022 0.020 0.018 0.016 0.015 0.013 0.012 0.011 0.010 0.009 0.008 0.007 0.006 0.005 0.003

d 14.227 14.787 14.858 13.663 13.843 13.802 13.751 13.467 14.388 14.464 14.797 14.190 14.639 14.178 14.175 14.333 14.386 14.210 14.600 14.206 14.375 14.492 14.471 14.356 14.365 14.331 14.345 14.310 14.329 14.356 14.383 14.204 14.256 14.188 14.147 14.104 14.182 14.044 14.083 13.905 13.823

Xk 0.203 0.192 0.188 0.136 0.121 0.059 0.068 −0.011 −0.060 −0.116 −0.129 −0.129 −0.129 −0.122 −0.117 −0.108 −0.104 −0.091 −0.078 −0.072 −0.069 −0.065 −0.067 −0.064 −0.058 −0.055 −0.049 −0.045 −0.040 −0.035 −0.036 −0.033 −0.026 −0.026 −0.024 −0.022 −0.016 −0.018 −0.012 −0.009 −0.008

a

c

a

b

Compact Bone Tissue

Soft Tissue

Table 8 Energy absorption (GP) fitting parameters for soft tissue and compact bone tissue in the energy range (0.015–3)MeV.

1.045 1.101 1.324 1.689 2.281 2.823 2.861 3.889 4.350 4.065 3.618 3.027 2.849 2.721 2.527 2.393 2.317 2.226 2.112 2.042 2.036 2.011 2.009 1.983 1.973 1.936 1.900 1.873 1.841 1.862 1.841 1.808 1.794 1.781 1.770 1.760 1.749 1.740 1.735 1.729 1.711

b 0.406 0.419 0.453 0.573 0.646 0.861 0.810 1.104 1.343 1.679 1.774 1.762 1.724 1.701 1.653 1.592 1.555 1.473 1.393 1.345 1.334 1.311 1.311 1.300 1.273 1.259 1.224 1.196 1.179 1.164 1.159 1.135 1.118 1.111 1.100 1.090 1.083 1.081 1.071 1.066 1.049

c −0.109 −0.101 −0.099 −0.071 −0.068 −0.040 −0.048 −0.009 0.015 0.044 0.049 0.047 0.046 0.044 0.046 0.043 0.042 0.034 0.031 0.028 0.026 0.025 0.027 0.025 0.022 0.022 0.018 0.016 0.014 0.012 0.014 0.008 0.011 0.008 0.004 0.009 0.007 0.006 0.006 −0.000 0.002

d

12.225 14.521 14.380 15.497 13.882 13.270 13.404 13.588 12.888 13.438 13.771 13.901 14.022 14.155 14.293 14.488 14.550 14.784 14.774 14.517 14.309 14.329 14.400 14.454 14.447 14.143 14.704 14.826 14.910 15.000 15.077 15.135 15.047 14.905 14.790 14.558 14.327 13.845 13.289 12.296 10.627

Xk

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0.015 0.02 0.03 0.04 0.05 0.0595 0.06 0.08 0.1 0.15 0.2 0.3 0.356 0.4 0.5 0.6 0.662 0.8 1 1.173 1.2 1.274 1.3 1.333 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3

Energy (MeV)

0.231 0.233 0.196 0.174 0.144 0.098 0.113 0.036 −0.019 −0.081 −0.106 −0.116 −0.114 −0.111 −0.105 −0.100 −0.094 −0.086 −0.075 −0.066 −0.066 −0.063 −0.062 −0.060 −0.057 −0.054 −0.049 −0.044 −0.040 −0.036 −0.035 −0.032 −0.026 −0.026 −0.023 −0.021 −0.015 −0.017 −0.011 −0.008 −0.007

1.031 1.074 1.243 1.495 1.899 2.496 2.404 3.367 3.982 4.133 3.675 3.072 2.919 2.761 2.560 2.417 2.337 2.238 2.115 2.041 2.031 2.009 2.001 1.989 1.975 1.936 1.914 1.894 1.867 1.860 1.844 1.816 1.800 1.785 1.772 1.760 1.748 1.738 1.729 1.723 1.709

0.375 0.360 0.453 0.489 0.575 0.734 0.673 0.916 1.144 1.471 1.620 1.680 1.657 1.635 1.587 1.542 1.508 1.447 1.377 1.326 1.325 1.304 1.297 1.285 1.274 1.254 1.227 1.204 1.185 1.168 1.154 1.137 1.121 1.110 1.097 1.087 1.077 1.074 1.061 1.056 1.048

−0.159 −0.123 −0.112 −0.096 −0.085 −0.065 −0.078 −0.034 −0.009 0.022 0.035 0.040 0.038 0.036 0.035 0.034 0.033 0.030 0.027 0.024 0.024 0.023 0.023 0.022 0.021 0.021 0.018 0.016 0.014 0.012 0.013 0.008 0.010 0.007 0.003 0.007 0.006 0.005 0.005 −0.002 0.001

d 13.880 14.284 14.478 14.810 14.949 14.588 14.592 14.099 13.538 14.047 13.992 14.202 14.418 14.571 14.582 14.599 14.649 14.799 15.117 15.146 14.806 14.761 14.749 14.810 14.695 14.243 14.712 14.742 14.777 14.828 14.950 14.837 14.798 14.737 14.615 14.344 14.045 13.404 12.518 11.087 8.534

Xk 0.173 0.143 0.070 −0.034 −0.098 −0.120 −0.140 −0.179 −0.180 −0.188 −0.179 −0.169 −0.156 −0.148 −0.137 −0.123 −0.120 −0.104 −0.086 −0.080 −0.075 −0.069 −0.068 −0.067 −0.063 −0.060 −0.053 −0.049 −0.045 −0.041 −0.039 −0.034 −0.031 −0.028 −0.026 −0.024 −0.021 −0.019 −0.017 −0.016 −0.012

a

c

a

b

Gelatin

Cortical Bone Tissue

Table 9 Energy absorption (GP) fitting parameters for cortical bone tissue and gelatin in the energy range (0.015–3)MeV.

1.213 1.502 2.560 3.782 4.722 5.009 5.050 4.919 4.655 3.755 3.365 2.834 2.698 2.633 2.464 2.364 2.303 2.204 2.107 2.012 2.035 2.010 2.000 1.989 1.963 1.934 1.911 1.887 1.865 1.844 1.838 1.811 1.795 1.781 1.769 1.757 1.747 1.738 1.729 1.720 1.710

b 0.468 0.556 0.791 1.198 1.555 1.736 1.839 2.163 2.216 2.293 2.194 2.068 1.963 1.876 1.781 1.675 1.648 1.540 1.428 1.342 1.333 1.307 1.297 1.286 1.262 1.276 1.216 1.197 1.181 1.167 1.173 1.145 1.136 1.128 1.122 1.116 1.112 1.108 1.104 1.101 1.055

c −0.085 −0.071 −0.040 0.009 0.041 0.054 0.063 0.079 0.077 0.076 0.076 0.067 0.063 0.059 0.055 0.049 0.049 0.043 0.035 0.034 0.031 0.028 0.028 0.028 0.026 0.026 0.022 0.020 0.018 0.016 0.016 0.014 0.012 0.011 0.010 0.009 0.008 0.008 0.007 0.006 0.004

d

14.175 14.777 14.781 13.650 13.830 13.794 13.747 13.485 14.332 14.410 14.787 14.333 14.169 14.159 14.136 14.256 14.308 14.230 14.543 14.225 14.552 14.466 14.494 14.471 14.403 14.350 14.332 14.279 14.224 14.191 14.161 13.982 13.998 13.760 13.783 13.592 13.618 13.485 13.421 13.192 13.063

Xk

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0.015 0.02 0.03 0.04 0.05 0.0595 0.06 0.08 0.1 0.15 0.2 0.3 0.356 0.4 0.5 0.6 0.662 0.8 1 1.173 1.2 1.274 1.3 1.333 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3

Energy (MeV)

0.158 0.103 0.009 −0.094 −0.141 −0.160 −0.171 −0.197 −0.200 −0.201 −0.190 −0.172 −0.165 −0.153 −0.138 −0.122 −0.120 −0.107 −0.093 −0.078 −0.075 −0.071 −0.069 −0.069 −0.065 −0.060 −0.054 −0.049 −0.046 −0.042 −0.038 −0.035 −0.032 −0.029 −0.026 −0.023 −0.021 −0.018 −0.016 −0.014 −0.011

1.320 1.739 3.263 4.592 5.295 5.285 5.305 4.882 4.430 3.578 3.245 2.818 2.673 2.627 2.458 2.377 2.318 2.200 2.087 2.027 2.030 2.003 1.994 1.966 1.948 1.940 1.902 1.882 1.859 1.836 1.841 1.807 1.793 1.781 1.771 1.761 1.753 1.745 1.738 1.733 1.713

0.506 0.663 1.012 1.532 1.880 2.031 2.131 2.385 2.443 2.445 2.301 2.094 2.048 1.920 1.795 1.673 1.650 1.554 1.462 1.331 1.325 1.299 1.290 1.277 1.256 1.276 1.211 1.195 1.179 1.165 1.169 1.145 1.138 1.131 1.126 1.121 1.118 1.114 1.111 1.109 1.052

−0.078 −0.050 −0.012 0.039 0.060 0.069 0.075 0.083 0.081 0.079 0.076 0.068 0.066 0.063 0.060 0.048 0.051 0.045 0.041 0.033 0.031 0.029 0.029 0.029 0.027 0.027 0.022 0.020 0.018 0.016 0.015 0.013 0.012 0.011 0.010 0.008 0.007 0.007 0.006 0.005 0.003

d 14.492 15.723 14.156 13.968 14.258 14.361 14.283 14.270 14.740 14.827 14.781 14.605 14.808 14.715 15.371 14.531 14.593 14.140 14.179 14.247 14.426 14.416 14.410 14.290 14.316 14.297 14.362 14.327 14.329 14.400 14.390 14.255 14.266 14.252 14.267 14.283 14.301 14.210 14.198 14.209 14.057

Xk 0.157 0.098 0.002 −0.100 −0.146 −0.164 −0.174 −0.198 −0.202 −0.203 −0.189 −0.171 −0.161 −0.152 −0.138 −0.121 −0.120 −0.109 −0.093 −0.086 −0.075 −0.072 −0.069 −0.068 −0.065 −0.060 −0.054 −0.050 −0.046 −0.043 −0.037 −0.035 −0.032 −0.029 −0.026 −0.023 −0.021 −0.018 −0.016 −0.014 −0.012

a

c

a

b

Red Articulation Wax

Bee Wax

Table 10 Energy absorption (GP) fitting parameters for bee wax and red articulation wax in the energy range (0.015–3)MeV.

1.335 1.772 3.357 4.683 5.357 5.300 5.330 4.878 4.406 3.555 3.252 2.819 2.662 2.627 2.458 2.387 2.316 2.198 2.087 1.976 2.030 1.994 1.994 1.973 1.951 1.941 1.906 1.878 1.856 1.835 1.842 1.807 1.793 1.781 1.770 1.760 1.753 1.745 1.738 1.730 1.713

b 0.510 0.678 1.040 1.571 1.919 2.065 2.164 2.406 2.463 2.464 2.295 2.092 2.036 1.918 1.795 1.669 1.650 1.563 1.461 1.390 1.326 1.291 1.291 1.273 1.254 1.275 1.213 1.193 1.178 1.165 1.168 1.145 1.138 1.131 1.125 1.120 1.118 1.114 1.111 1.108 1.052

c −0.078 −0.048 −0.008 0.042 0.062 0.070 0.076 0.083 0.082 0.079 0.076 0.068 0.066 0.062 0.059 0.047 0.050 0.046 0.041 0.037 0.031 0.030 0.029 0.028 0.027 0.027 0.022 0.020 0.018 0.016 0.015 0.013 0.012 0.011 0.010 0.009 0.007 0.007 0.006 0.005 0.003

d

14.478 15.873 13.834 13.994 14.304 14.437 14.362 14.382 14.767 14.883 14.782 14.577 14.813 14.681 15.267 14.731 14.564 14.091 14.197 14.009 14.436 14.289 14.418 14.306 14.325 14.291 14.349 14.359 14.367 14.052 14.439 14.291 14.297 14.278 14.166 14.167 14.296 14.194 14.165 14.024 13.995

Xk

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0.015 0.02 0.03 0.04 0.05 0.0595 0.06 0.08 0.1 0.15 0.2 0.3 0.356 0.4 0.5 0.6 0.662 0.8 1 1.173 1.2 1.274 1.3 1.333 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3

Energy (MeV)

0.158 0.104 0.009 −0.093 −0.141 −0.159 −0.171 −0.196 −0.199 −0.200 −0.189 −0.171 −0.159 −0.153 −0.138 −0.122 −0.120 −0.107 −0.086 −0.078 −0.076 −0.070 −0.069 −0.067 −0.065 −0.060 −0.054 −0.049 −0.045 −0.042 −0.038 −0.035 −0.032 −0.029 −0.026 −0.023 −0.021 −0.018 −0.016 −0.014 −0.012

1.319 1.738 3.260 4.577 5.284 5.281 5.304 4.884 4.444 3.587 3.251 2.819 2.680 2.627 2.458 2.375 2.317 2.200 2.107 2.032 2.022 2.011 1.994 1.983 1.951 1.941 1.903 1.883 1.860 1.838 1.840 1.807 1.794 1.781 1.770 1.760 1.752 1.744 1.737 1.729 1.713

0.506 0.662 1.011 1.525 1.873 2.024 2.130 2.376 2.431 2.437 2.296 2.092 1.999 1.918 1.795 1.674 1.650 1.552 1.430 1.328 1.317 1.308 1.291 1.280 1.254 1.275 1.212 1.195 1.179 1.165 1.170 1.145 1.137 1.131 1.125 1.120 1.117 1.113 1.110 1.107 1.052

−0.078 −0.050 −0.013 0.038 0.060 0.069 0.075 0.083 0.081 0.079 0.076 0.068 0.065 0.062 0.059 0.048 0.050 0.045 0.036 0.033 0.032 0.029 0.029 0.028 0.027 0.027 0.022 0.020 0.018 0.016 0.015 0.013 0.012 0.011 0.010 0.009 0.008 0.007 0.006 0.005 0.003

d

Xk 14.493 15.717 14.168 13.964 14.250 14.344 14.279 14.220 14.724 14.805 14.782 14.581 14.466 14.687 15.285 14.493 14.569 14.155 14.706 14.253 14.265 14.543 14.417 14.410 14.325 14.292 14.358 14.317 14.312 14.370 14.347 14.301 14.210 14.179 14.183 14.067 14.191 14.097 14.060 13.920 13.891

0.158 0.103 0.009 −0.094 −0.141 −0.160 −0.171 −0.196 −0.197 −0.198 −0.189 −0.171 −0.159 −0.153 −0.138 −0.121 −0.120 −0.109 −0.086 −0.078 −0.075 −0.072 −0.069 −0.067 −0.065 −0.060 −0.054 −0.049 −0.046 −0.042 −0.038 −0.035 −0.032 −0.029 −0.026 −0.023 −0.021 −0.018 −0.016 −0.014 −0.012

a

c

a

b

Bolus

Paraffin1

Table 11 Energy absorption (GP) fitting parameters for paraffin1and bolus in the energy range (0.015–3)MeV.

1.320 1.741 3.269 4.595 5.295 5.286 5.303 4.884 4.465 3.621 3.251 2.819 2.680 2.627 2.458 2.387 2.316 2.198 2.108 2.032 2.030 1.994 1.994 1.983 1.951 1.936 1.903 1.883 1.856 1.838 1.840 1.808 1.794 1.781 1.770 1.761 1.752 1.744 1.737 1.729 1.713

b 0.506 0.664 1.013 1.533 1.880 2.034 2.128 2.375 2.413 2.408 2.296 2.092 1.999 1.918 1.795 1.669 1.650 1.563 1.430 1.328 1.326 1.291 1.291 1.281 1.254 1.276 1.212 1.196 1.178 1.165 1.170 1.145 1.137 1.131 1.125 1.121 1.117 1.113 1.110 1.107 1.052

c −0.078 −0.050 −0.012 0.039 0.060 0.069 0.075 0.083 0.081 0.078 0.076 0.068 0.065 0.062 0.059 0.047 0.050 0.046 0.036 0.033 0.031 0.030 0.029 0.028 0.027 0.026 0.022 0.020 0.018 0.016 0.015 0.013 0.012 0.011 0.010 0.009 0.008 0.007 0.006 0.005 0.003

d

14.492 15.730 14.137 13.969 14.258 14.366 14.277 14.215 14.700 14.722 14.782 14.579 14.464 14.684 15.277 14.736 14.566 14.091 14.708 14.254 14.435 14.288 14.418 14.411 14.326 14.334 14.358 14.316 14.369 14.367 14.343 14.205 14.206 14.173 14.176 14.179 14.182 14.088 14.047 13.906 13.875

Xk

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0.015 0.02 0.03 0.04 0.05 0.0595 0.06 0.08 0.1 0.15 0.2 0.3 0.356 0.4 0.5 0.6 0.662 0.8 1 1.173 1.2 1.274 1.3 1.333 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3

Energy (MeV)

0.191 0.159 0.105 0.001 −0.068 −0.093 −0.113 −0.160 −0.174 −0.179 −0.178 −0.163 −0.155 −0.148 −0.136 −0.122 −0.118 −0.103 −0.086 −0.076 −0.074 −0.068 −0.065 −0.066 −0.063 −0.060 −0.052 −0.048 −0.044 −0.040 −0.040 −0.033 −0.031 −0.028 −0.026 −0.024 −0.022 −0.020 −0.018 −0.017 −0.013

1.170 1.396 2.262 3.348 4.306 4.576 4.820 4.935 4.639 3.844 3.365 2.871 2.704 2.633 2.467 2.365 2.301 2.206 2.106 2.047 2.037 2.009 1.997 1.992 1.971 1.931 1.916 1.891 1.869 1.848 1.835 1.812 1.796 1.781 1.768 1.755 1.743 1.732 1.723 1.714 1.708

0.437 0.516 0.688 1.038 1.373 1.572 1.645 1.999 2.137 2.199 2.179 2.015 1.949 1.875 1.774 1.670 1.640 1.536 1.428 1.345 1.335 1.306 1.296 1.289 1.268 1.277 1.219 1.200 1.183 1.168 1.176 1.143 1.135 1.126 1.119 1.113 1.108 1.103 1.099 1.096 1.057

−0.099 −0.081 −0.045 −0.008 0.025 0.041 0.049 0.072 0.077 0.072 0.075 0.065 0.063 0.059 0.055 0.049 0.048 0.042 0.035 0.031 0.031 0.028 0.026 0.027 0.026 0.026 0.022 0.020 0.018 0.017 0.017 0.014 0.013 0.012 0.011 0.010 0.009 0.008 0.007 0.007 0.004

d 13.433 14.547 12.284 13.326 13.514 13.676 13.690 13.632 13.963 14.404 14.606 14.155 14.159 14.158 14.165 14.268 14.217 14.260 14.460 14.607 14.593 14.427 14.323 14.506 14.457 14.377 14.314 14.233 14.148 14.059 13.972 13.949 13.754 13.552 13.419 13.284 13.140 12.982 12.822 12.646 12.459

Xk 0.155 0.089 −0.010 −0.112 −0.154 −0.172 −0.180 −0.201 −0.206 −0.204 −0.193 −0.176 −0.165 −0.153 −0.138 −0.120 −0.121 −0.109 −0.087 −0.082 −0.075 −0.070 −0.069 −0.069 −0.065 −0.060 −0.055 −0.050 −0.046 −0.043 −0.037 −0.035 −0.032 −0.029 −0.026 −0.023 −0.020 −0.018 −0.015 −0.013 −0.011

1.361 1.823 3.511 4.848 5.463 5.329 5.376 4.870 4.340 3.538 3.202 2.786 2.675 2.629 2.457 2.390 2.322 2.197 2.105 1.981 2.028 2.009 1.993 1.963 1.946 1.937 1.892 1.876 1.855 1.835 1.843 1.806 1.793 1.782 1.773 1.765 1.758 1.748 1.747 1.738 1.715

b

a

c

a

b

Orange Articulation Wax

Nylon

Table 12 Energy absorption (GP) fitting parameters for nylon and orange articulation wax in the energy range (0.015–3)MeV.

0.517 0.703 1.087 1.641 1.984 2.127 2.224 2.448 2.519 2.478 2.339 2.142 2.048 1.924 1.799 1.667 1.657 1.565 1.433 1.393 1.323 1.305 1.290 1.279 1.257 1.276 1.212 1.192 1.177 1.166 1.167 1.146 1.139 1.132 1.127 1.123 1.119 1.117 1.112 1.112 1.050

c −0.078 −0.043 −0.001 0.048 0.065 0.073 0.077 0.083 0.083 0.079 0.076 0.070 0.066 0.063 0.061 0.047 0.051 0.046 0.036 0.037 0.031 0.029 0.029 0.029 0.027 0.026 0.022 0.020 0.018 0.017 0.014 0.013 0.012 0.011 0.009 0.008 0.007 0.006 0.006 0.005 0.003

d

14.454 16.107 13.307 14.039 14.383 14.576 14.507 14.600 14.841 14.922 14.775 14.989 14.803 14.815 15.821 14.801 14.730 14.095 14.657 13.970 14.380 14.507 14.405 14.281 14.310 14.324 14.347 14.378 14.398 14.401 14.519 14.377 14.473 14.480 14.484 14.488 14.488 14.524 14.466 14.515 14.474

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0.015 0.02 0.03 0.04 0.05 0.0595 0.06 0.08 0.1 0.15 0.2 0.3 0.356 0.4 0.5 0.6 0.662 0.8 1 1.173 1.2 1.274 1.3 1.333 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3

Energy (MeV)

0.190 0.163 0.129 0.029 −0.037 −0.072 −0.087 −0.139 −0.161 −0.167 −0.171 −0.158 −0.150 −0.143 −0.132 −0.119 −0.116 −0.100 −0.086 −0.073 −0.071 −0.067 −0.065 −0.063 −0.060 −0.056 −0.051 −0.046 −0.042 −0.038 −0.038 −0.031 −0.029 −0.027 −0.024 −0.022 −0.020 −0.018 −0.016 −0.015 −0.011

1.132 1.312 2.019 2.977 3.941 4.274 4.557 4.889 4.610 3.937 3.391 2.901 2.733 2.653 2.479 2.370 2.314 2.214 2.104 2.044 2.033 2.006 1.996 1.985 1.964 1.943 1.910 1.885 1.864 1.842 1.838 1.809 1.794 1.781 1.769 1.759 1.749 1.740 1.732 1.725 1.710

0.411 0.491 0.617 0.923 1.224 1.428 1.482 1.826 2.011 2.093 2.100 1.974 1.895 1.838 1.746 1.650 1.627 1.519 1.427 1.340 1.330 1.304 1.296 1.285 1.265 1.261 1.217 1.197 1.179 1.162 1.170 1.137 1.126 1.120 1.109 1.103 1.097 1.092 1.088 1.084 1.053

−0.099 −0.089 −0.062 −0.026 0.010 0.029 0.036 0.060 0.069 0.069 0.070 0.062 0.059 0.056 0.053 0.048 0.047 0.040 0.035 0.029 0.028 0.026 0.026 0.025 0.023 0.022 0.020 0.018 0.016 0.014 0.015 0.011 0.010 0.010 0.008 0.007 0.006 0.006 0.005 0.004 0.002

d 12.566 14.573 10.840 13.479 13.808 13.803 13.847 13.125 13.718 14.392 14.023 14.100 14.089 14.066 14.280 14.331 14.294 14.380 14.201 14.255 14.268 14.303 14.315 14.330 14.358 14.310 14.397 14.415 14.419 14.540 14.406 14.735 14.704 14.412 14.647 14.511 14.485 14.450 14.321 14.297 14.144

Xk 0.154 0.081 −0.020 −0.121 −0.160 −0.178 −0.184 −0.203 −0.208 −0.205 −0.192 −0.171 −0.160 −0.153 −0.138 −0.121 −0.120 −0.107 −0.093 −0.075 −0.076 −0.070 −0.069 −0.068 −0.068 −0.060 −0.055 −0.050 −0.046 −0.043 −0.037 −0.035 −0.032 −0.029 −0.026 −0.023 −0.020 −0.018 −0.015 −0.013 −0.011

a

c

a

b

PMMA

Modelling Clay

Table 13 Energy absorption (GP) fitting parameters for modelling clay and PMMA in the energy range (0.015–3)MeV.

1.383 1.870 3.639 4.977 5.540 5.349 5.404 4.865 4.324 3.524 3.213 2.820 2.651 2.628 2.456 2.387 2.327 2.200 2.087 2.039 2.023 2.012 1.995 1.974 1.918 1.941 1.896 1.878 1.857 1.835 1.843 1.806 1.793 1.782 1.771 1.762 1.755 1.747 1.743 1.738 1.715

b 0.522 0.725 1.127 1.696 2.032 2.171 2.261 2.473 2.532 2.490 2.330 2.091 2.036 1.926 1.802 1.669 1.652 1.553 1.461 1.350 1.317 1.308 1.291 1.272 1.276 1.275 1.209 1.193 1.178 1.165 1.167 1.146 1.138 1.133 1.127 1.122 1.120 1.116 1.114 1.112 1.050

c −0.078 −0.039 0.005 0.052 0.068 0.075 0.078 0.083 0.083 0.079 0.076 0.068 0.066 0.063 0.062 0.047 0.051 0.045 0.041 0.031 0.032 0.029 0.029 0.028 0.029 0.027 0.022 0.020 0.018 0.016 0.014 0.013 0.012 0.010 0.009 0.008 0.007 0.006 0.005 0.005 0.003

d

14.434 16.321 12.866 14.075 14.440 14.676 14.598 14.729 14.859 14.979 14.776 14.574 14.708 14.836 16.037 14.727 14.758 14.146 14.198 14.409 14.265 14.547 14.419 14.309 14.219 14.291 14.378 14.358 14.365 14.436 14.525 14.381 14.390 14.488 14.396 14.404 14.513 14.423 14.522 14.524 14.406

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0.015 0.02 0.03 0.04 0.05 0.0595 0.06 0.08 0.1 0.15 0.2 0.3 0.356 0.4 0.5 0.6 0.662 0.8 1 1.173 1.2 1.274 1.3 1.333 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3

Energy (MeV)

0.178 0.146 0.078 −0.026 −0.091 −0.113 −0.133 −0.174 −0.178 −0.185 −0.179 −0.168 −0.155 −0.149 −0.136 −0.122 −0.118 −0.105 −0.086 −0.073 −0.074 −0.070 −0.068 −0.066 −0.062 −0.060 −0.052 −0.047 −0.044 −0.040 −0.040 −0.033 −0.030 −0.028 −0.026 −0.023 −0.021 −0.020 −0.018 −0.016 −0.013

1.202 1.477 2.494 3.684 4.621 4.892 4.993 4.923 4.649 3.788 3.364 2.841 2.702 2.627 2.467 2.365 2.302 2.202 2.108 2.044 2.037 2.012 2.003 1.992 1.972 1.931 1.916 1.890 1.869 1.849 1.836 1.811 1.796 1.781 1.768 1.756 1.745 1.734 1.725 1.717 1.708

0.460 0.546 0.768 1.161 1.511 1.692 1.791 2.117 2.186 2.258 2.196 2.056 1.953 1.886 1.774 1.670 1.640 1.544 1.429 1.345 1.335 1.308 1.299 1.289 1.269 1.277 1.220 1.199 1.183 1.168 1.175 1.142 1.133 1.125 1.118 1.110 1.106 1.102 1.098 1.093 1.056

−0.089 −0.074 −0.041 0.005 0.037 0.051 0.059 0.077 0.077 0.075 0.076 0.067 0.063 0.059 0.055 0.049 0.048 0.043 0.036 0.029 0.031 0.029 0.028 0.027 0.026 0.026 0.022 0.019 0.018 0.017 0.017 0.013 0.012 0.011 0.010 0.009 0.008 0.008 0.007 0.006 0.004

d

Xk 13.973 14.721 14.227 13.576 13.753 13.762 13.733 13.526 14.195 14.408 14.800 14.214 14.162 14.183 14.167 14.269 14.219 14.199 14.714 14.258 14.595 14.548 14.531 14.507 14.462 14.379 14.312 14.290 14.142 14.050 14.058 14.135 13.999 13.812 13.700 13.683 13.413 13.276 13.094 13.052 12.843

0.157 0.100 0.004 −0.097 −0.144 −0.163 −0.173 −0.197 −0.200 −0.201 −0.189 −0.171 −0.164 −0.153 −0.138 −0.121 −0.120 −0.107 −0.093 −0.078 −0.076 −0.072 −0.068 −0.067 −0.065 −0.060 −0.054 −0.049 −0.046 −0.042 −0.037 −0.035 −0.032 −0.029 −0.026 −0.023 −0.021 −0.018 −0.016 −0.014 −0.012

a

c

a

b

Paraffin2

Pitch

Table 14 Energy absorption (GP) fitting parameters for pitch and paraffin2 in the energy range (0.015–3)MeV.

1.330 1.760 3.326 4.647 5.333 5.294 5.321 4.881 4.423 3.586 3.250 2.819 2.671 2.628 2.457 2.387 2.317 2.200 2.087 2.032 2.024 1.993 2.003 1.983 1.951 1.941 1.903 1.883 1.856 1.837 1.842 1.807 1.793 1.781 1.770 1.761 1.753 1.744 1.737 1.733 1.713

b 0.509 0.673 1.031 1.555 1.903 2.052 2.151 2.392 2.449 2.437 2.297 2.092 2.047 1.922 1.798 1.668 1.650 1.554 1.461 1.329 1.318 1.292 1.299 1.280 1.254 1.275 1.212 1.195 1.178 1.165 1.168 1.145 1.138 1.131 1.125 1.121 1.118 1.113 1.110 1.109 1.052

c −0.078 −0.049 −0.010 0.040 0.061 0.070 0.075 0.083 0.081 0.079 0.076 0.068 0.066 0.063 0.061 0.047 0.050 0.045 0.041 0.033 0.032 0.030 0.028 0.028 0.027 0.027 0.022 0.020 0.018 0.016 0.015 0.013 0.012 0.011 0.010 0.009 0.007 0.007 0.006 0.005 0.003

d

14.483 15.821 13.941 13.984 14.286 14.407 14.331 14.307 14.748 14.806 14.782 14.583 14.815 14.771 15.686 14.741 14.570 14.145 14.192 14.253 14.296 14.287 14.528 14.410 14.325 14.293 14.359 14.317 14.371 14.372 14.450 14.304 14.310 14.297 14.188 14.193 14.324 14.102 14.066 14.204 13.899

Xk

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Fig. 1. The equivalent atomic number fractional difference as a function of photon energy.

factor at 1 mfp. The parameter K represents photon dose multiplication and its variation with penetration depth represents the change in the shape of the spectrum.

behave in the same manner, regarding absorption and scattering of ionizing radiation, as that of the human organ/tissues to be substituted. To facilitate the investigation and comparison of the samples, the Zeq values of the selected tissue equivalent materials given in Table 4 were compared to those of human organ/tissue, presented in Table 3, separately. The procedure involves the calculation of the fractional differences in their Zeq values and then investigate the variation of these differences with photon energy. The results obtained are shown in Fig. 1, which shows that Gelatin simulates muscle and brain tissue in a

3. Results and discussion 3.1. Tissue equivalence and the equivalent atomic number (Zeq) Tissue equivalent materials having good tissue equivalence should

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Fig. 2. The energy absorption buildup factor for; adipose, skin, muscle, brain, blood, lung, soft, bone (compact), and bone (cortical) tissues in the energy region 0.015–3 MeV at 1, 10, 30 and 40 mfp.

Fig. 3. Variation of EABF with equivalent atomic number of; adipose, skin, muscle, brain, blood, lung, soft, bone (compact), and bone (cortical) tissues for different penetration depths, at photon energies of 59.5 keV and 2 MeV.

wide energy range from 0.1 to 3.0 MeV and it is particularly useful for simulating lung tissue and blood at energies from 1.5 to 3.0 MeV as well as skin tissue in the energy range from 0.5 to 3.0 MeV. The fractional differences, in all cases, were about or less than 5%. The figure suggests that Nylon and Pitch could be useful as substitute materials for muscle, brain, blood and lung tissues within the

diagnostic energy range up to 1.0 MeV while Gelatin could be used to simulate soft tissue at this energy range. Among all the investigated tissue equivalent materials no material was found useful to simulate bone tissues, compact or cortical, as well as adipose tissue for a wide energy rang. The fundamental advantage of having materials with good tissue

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Fig. 4. Variation of EABF with photon energy for the eleven tissue equivalent materials at four different penetration depths.

30, and 40 mfp. It can be seen from the figure that EABF is smallest for cortical bone and largest for adipose tissue in the low energy region 0.01–0.1 MeV, at all the considered penetration depths. This can be explained by the dominance of photoelectric absorption in the low energy region and the high Zeq value of cortical bone with respect to that of adipose tissue. EABF increases with the decrease in the material Zeq value which means that it depends on material chemical composition. As the photon energy increases close to 0.1 MeV, the EABF reaches its maximum value for a given penetration depth due to the increase in Compton scattering cross section and the multiple scattering of photons. Their energies degrade but continue to exist in the material for some time that leads to an increase in the buildup factor value to reach its maximum. Fig. 2 also shows that for photon energies higher than 1 MeV, where pair production starts to dominate, the EABF is almost

equivalence, with respect to interaction with ionizing radiation, is that they allow the patient absorbed dose to be estimated correctly. The Zeq values generated for all the investigated samples, suggested that tissue equivalent material can be compared to real tissues and good substitutes for human tissues can be found. 3.2. Tissue equivalence and the energy absorption buildup factor (EABF) The energy absorption buildup factor is a function of photon energy, chemical composition/effective atomic number and penetration depth. When tissue equivalent samples are compared with human tissues/organs, the above factors should be taken in considerations. Fig. 2 shows the variation of EABF with photon energy for the selected human tissues and organs, as generated at four different penetration depths 1, 10,

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Fig. 5. Variation of EABF with penetration depth, at several photon energies used in brachytherapy for the selected human tissues.

the same for all the considered tissues and its values are minimum. This indicates that EABF of a given material is independent of its chemical composition for all penetration depths at that high energy range. Nevertheless, the complexities given in the above discussion are illustrated in Fig. 3 which shows variation of EABF for adipose, skin, muscle, brain, blood, lung, soft, bone (compact), and bone (cortical) tissues as a function of Zeq for different penetration depths, at two different photon energies. At low energy of 59.5 keV (Fig. 3(a)) the EABF is decreased with increasing Zeq for all penetration depths. This is due to the fact that photoelectric absorption is the dominating interaction at low energies and its cross section is highly dependent on Zeq value that results in lowering the value of EABF with increasing Zeq. On the other hand, at energies greater than 1 MeV the buildup factor is small and seen to be independent of Zeq due to the dominance of pair production process in this energy range. Fig. 3(b) shows how EABF got constant values, for all values of Zeq and the curves were straight lines for all penetration depths at photon energy of 2 MeV. This indicates that

the chemical composition of materials does not affect their absorption and scattering properties at high photon energies. However, similar behavior is observed when tissue equivalent materials have been studied. Fig. 4 shows the variation of EABF with photon energy for the eleven materials under investigation. On the other hand, variation of EABF with penetration depth, at several photon energies used in brachytherapy, is presented in Fig. 5, for the nine human tissues/organs under consideration and in Fig. 6, for the selected tissue equivalent materials. Both groups showed similar behavior with the variation of penetration depth. Generally, the buildup factors grow rapidly as the penetration depth increases. This growth slows down as the penetration depth continues to increase beyond about 20 mfp. As the penetration depth increases, photons suffer more collisions (scatterings) and their energies degrade to the level of photoelectric absorption, which makes them to completely disappear. This ensures that the buildup factors do not rise indefinitely as the penetration depth increases.

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Fig. 6. Variation of EABF with penetration depth, at several photon energies used in brachytherapy for the selected tissue equivalent materials.

The changes in EABF value depend on photon energy, penetration depth and material chemical composition (Zeq) for photon energy less than 1 MeV. However, this dependence vanish at energies higher than 1.0 MeV and EABF has about same value for all the investigated materials. This means that EABF is becoming independent of the chemical composition due to the dominance of pair production absorption as discussed above. Hence, EABF can be used as a good tissue equivalence indicator to compare different materials, but at photon energy lower than 1 MeV as shown in Figs. 7–15. The figures show how the selected tissue equivalent materials are compared to human soft tissue and how the spectrum was divided into two parts. The first part to the left is useful for comparison process and the difference between material buildup factors can

be observed clearly while in the second part to the right EABF for all materials got constant values and the curves are straight lines close together. 4. Conclusions Tissue-equivalent materials to be used as substitutes for human tissues in dosimetry for brachytherapy and diagnostic radiology have been investigated in terms of computed equivalent atomic number (Zeq) and energy absorption buildup factor (EABF). The generated (Zeq) values for the selected materials at different photon energies allowed good substitute materials to be chosen for specified photon energy regions.

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Fig. 7. The selected tissue equivalent materials are compared to human adipose tissue at different penetration depths.

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Fig. 8. The selected tissue equivalent materials are compared to human skin tissue at different penetration depths.

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Fig. 9. The selected tissue equivalent materials are compared to human muscle tissue at different penetration depths.

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Fig. 10. The selected tissue equivalent materials are compared to human brain tissue at different penetration depths.

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Fig. 11. The selected tissue equivalent materials are compared to human blood tissue at different penetration depths.

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Fig. 12. The selected tissue equivalent materials are compared to human lung tissue at different penetration depths.

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Fig. 13. The selected tissue equivalent materials are compared to human soft tissue at different penetration depths.

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Fig. 14. The selected tissue equivalent materials are compared to human compact bone tissue at different penetration depths.

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Fig. 15. The selected tissue equivalent materials are compared to human cortical bone tissue at different penetration depths.

The EABF value depends on photon energy, penetration depth and Zeq of the material. However, at energy larger than 1 MeV, its variations for all materials are almost constant, independent of elemental composition or penetration depth.

densities of CuGaSe2 semiconductor in the energy range 6-511 keV. X Ray Spectrom. 37 (5), 490–494. Damla, N., Baltas, H., Celik, A., Kiris, E., Cevik, U., 2012. Calculation of radiation attenuation coefficients, effective atomic numbers and electron densities for some building materials. Rad. Protect. Dosim. 150 (4), 541–549. Fuliful, F., Hashim, A., Madlool, R., 2017. Calculating the X-ray attenuation coefficients of gelatin as human tissue substitute. Aust. J. Bas. App. Sc. 11 (11), 21–29. Gerward, L., Guilbert, N., Jensen, K.B., Levring, H., 2001. X-ray absorption in matter reengineering XCOM. Radiat. Phys. Chem. 60 (1–2), 23–24. Gerward, L., Guilbert, N., Jensen, K.B., Levring, H., 2004. WinXCom – a program for calculating X-ray attenuation coefficients. Radiat. Phys. Chem. 71 (3–4), 653–654. Gowda, S., Krishnaveni, S., Gowda, R., 2005. Studies on effective atomic numbers and electron densities in amino acids and sugars in the energy range 30–1333keV. Nucl.

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