Studies on the effective atomic numbers of some human tissues in the energy region 15–100 keV

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Copyright © 1994 Elsevier Scie Phys. Chem. Vol. 44, No 6, PP. 573-5 Printed in Great Britain. All rights I

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STUDIES ON THE EFFECTIVE ATOMIC NUMBERS OF SOME HUMAN TISSUES IN THE ENERGY REGION 15-100 keV H. OZYOL University of Uludag, Faculty of Art and Science, 16059 Bursa, Turkey (Received 3 August 1993; accepted 17 December 1993)

Absfract—The effective atomic numbers for total photon interaction in muscle, bone, brain, heart, kidney, liver, lungs, ovaries, pancreas, spleen and tongue are evaluated using three different methods, for practical use in the energy region 15—100 keV. Muscle, brain, heart, kidney, lungs, ovaries, pancreas, spleen, tongue and water; bone and silicon; liver and oxygen are found to behave in an approximately similar manner in this energy region.

INTRODUCTION

are readily available in some biological and ch

The effective atomic number (Zeff) is a useful parameter for the interpretation of attenuation of ~ or gamma radiations by a complex medium such as biological material, plastic, alloy etc. Many authors (Jayachandran, 1971; Thirumala et a!., 1985; Yang et a!., 1987; Perumallu et al., 1984, 1985; Mudahar and Sahota, 1988; El-Kateb and Abdul-Hamid, 1991; Mudahar and Singh, 1991) have published studies of effective atomic number of human tissues and some multi-element materials. It may be concluded from these studies that the accuracy of the Zeff depends on the accuracy of cross-sections of the individual elements, weight factors of elements of the composite materials and the method of interpolation. In view of these observations, it is felt that the deduction of the effective atomic numbers can be done by choosing suitable power series and fitting a suitable number of parameters to values of atomic numbers vs mass attenuation coefficients of individual elements, then using this equation, calculating the equivalent atomic number corresponding to the known mass attenuation coefficient of the complex medium, in this region of interest at each energy. Since the data on the mass attenuation coefficients are available for each element, this method provides an easy and rapid solution to yield effective atomic numbers. Moreover, it is known that in build-up and dose calculations muscle, commonly used to represent various human tissues, is not actually representative of all human tissues and that several tissues differ significantly in chemical composition. Chemical compositions of human tissues are usually given in

handbooks. Kim (1974a, b) has calculated the atomic compositions of human tissues using data. Therefore, a study of effective atomic numb biological materials can provide valuable mation. In this work, based on ch compositions of human tissues given by Kim b) and attenuation coefficients of elements COl by Hubbell (1969, 1982), Z~studies of 11 bio materials have been conducted for photon ei between 15 to 100 keY. M}~THODS

A. Statistical analysis

An approximate way for finding the element represents the complex medium, is to m statistical analysis of the value of hz/p (tota: attenuation coefficient) of the mixture and the sponding p/p values for individual elements I energy region of interest. Calculated photon mass attenuation coefi for our tissue samples by means of the mixtu are given in Table 1. The values of p/p for mdi elements were taken from the compiled d~ Hubbell (1982). Using the above data, the den multi-element materials which provide the m~ tissue samples can be determined. The accur this match was analyzed with the help of the

/

~ [(~/~) (~ /p )]2 —

__________________

S

—

=‘

n —2

574

H. OZYOL 2/g) Table I. Total and scattering mass attenuation coefficients of human tissues (cm Muscle Bone Brain Heart p/p p,jp p!p p,/p p/p p,/p pip p,/p

E (MeV) 0.015 0.020 0.030 0.040 0.050 0.060 0.080 0.100

1.683 0.8161 0.3773 0.2684 0.2264 0.2050 0.1826 0.1696

0.3062 0.2674 0.2298 0.2109 0.1988 0.1898 0.1767 0.1671

E (MeV)

p/p

p,/p

0.015 0.020 0.030 0.040 0.050 0.060 0.080 0.100

1.636 0.7935 0.3676 0.2620 0.2213 0.2006 0.1787 0.1661

0.3009 0.2625 0.2254 0.2067 0.1947 0.1860 0.1731 0.1636

E (MeV)

p/p

0.015 0.020 0.030 0.040 0.050 0.060 0.080 0.100

1.594 0.7776 0.3665 0.2645 0,2250 0.2047 0.1821 0.1704

10.82 4.782 1.570 0.7692 0.4789 0.3480 0.2388 0.1952

0.4431 0.3542 0.2706 0.2326 0.2111 0.1965 0.1775 0.1651

1.593 0.7787 0.3662 0.2653 0.2237 0.2033 0.1817 0.1690

0.3020 0.2645 0.2282 0.2098 0.1980 0.1898 0.1761 0.1666

1.536 0.7535 0.3591 0.2610 0.2228 0.2032 0.1821 0.1696

pp

p,/p

p/p

p,~p

p/p

1.783 0.8584 0.3903 0.2744 0.2299 0.2075 0.1841 0.1708

0.3104 0.2704 0.2318 0.2124 0.2001 0.1911 0.1717 0.1680

1.638 0.7962 0.3713 0.2659 0.2252 0.2044 0.1824 0.1696

0.3058 0.2671 0.2298 0.2109 0.1989 0.1899 0.1768 0.1672

1.590 0.7754 0.3655 0.2639 0.2245 0.2043 0.1828 0.1701

P/P

p,/p

P/P

1.594 0.7622 0.2613 0.2618 0.2231 0.2032 0.1819 0.1694

0.3039 0.2660 0.2292 0.2106 0.1986 0.1898 0.1767 0.1671

1.512 0.7441 0.3564 0.2598 0.2221 0.2027 0.1818 0.1693

Kidney

Liver

Lungs

0.3033 0.2657 0.2292 0.2108 0.1988 0.1900 0.1769 0.1674

Ovaries p 5/p

Pancreas

Spleen PS~p

0.3068 0.2682 0.2308 0.2120 0.1999 0.1909 0.1777 0.1681

Tongue

B. Calculation ofZ~~from the (p/p) mass attenuation coefficients for total photon interaction A four parameter power series, (2)

Ze~= P1 + P2 (p/p) + P3 (ti/p )P4

was used to obtain the Z~values with the help of calculated total mass attenuation coefficients of tissue samples based on chemical composition by Kim (1974a, b) and attenuation coefficients by Hubbell (1982). The parameters were determined by fitting to a table of atomic numbers (Z = 4—15) vs total mass attenuation coefficients of elements. C. Calculation of

Ze~form

the I1/l~ratio

One criterion applying to the choice of Z~is the

0.3067 0.2680 0.2306 0.2116 0.1996 0.1906 0.1774 0.1678 Water

0.3009 0.2641 0.2283 0.2102 0.1984 0.1897 0.1767 0.1671

p/p

p,ip

1.639 0.7958 0.3718 0.2668 0.2262 0.2055 0.1835 0.1707

0.309 0.270 0.232 0.213 0.200 0.191 0.178 0.168

variation with energy of the ratio of the total section (p) to the scattering cross-section (p5) I mixture (Broder, 1970). From this standpoint choosing the suitable tion of ~ vs p /p~ratios of elements and intro calculated values of p/ps ratios of tissue sami this equation, Z,ff values were obtained. Para] of the function have been determined by fitt table of atomic numbers vs p/p5 ratios of dci Yalues of p~for tissue samples have been con from the element data given by Hubbell (l96~ using fraction by weight given by Kim (l974a, t photon mass attenuation coefficients for the si ing interaction, p5/p, thus obtained, are gi’~ Table 1.

Table 2. Standard deviations and chi-square values between the total mass attenuation coefficients of tissue samples and elements 2 S S S Muscle Bone Brain Heart S Water 1.99—02 1.80x—03 2.01 —02 1.81 —03 4.58—02 9.38 N 2.16—01 2.95—01 1.76—01 2.00—01 1.50—01 1.49 O 5.05—02 1.40—02 8.91 —02 3.35—02 1.15—01 5.36 Al 1.36+00 2.03+00 Si 3.09—01 1.05—01 p 6.09—01 2.17—01 Ca 8.38+00 1.95+01 Kidney Water N O

Liver

S

x2

4.95 —. 03 1.94—01 7.06—02

6.18 — 04 2.35 —01 2.09—02

S 6.46 — 02 2.60—01 1.83—02

Lungs 1.88 — 02 4.26—01 8.36—03

S

x2

1.07 — 03 1.95—01 6.99—02

2.85 — 05 2.44—01 2.24—02

Ovaries S 2.19 — 02 2. 15 1.74—01 1.97 9.10—02 3.54

Studies on the effective atomic numbers of some human tissues Table 3. Values of fitted parameters for effective atomic numbers, formulation (2) E (MeV)

P

1

P2

P3

P4

0.015 0.020 0.030 0.040 0.050 0.060 0.080 0.100

—6.4945+00 —3.5492 + 02 — 9.9223 + 02 — 1.4067 + 03 —1.3990+03 —1.3856+03 —2.5161+02 —2.9795+02

+0.1214+00 0.4020+00 — 0.5467 + 00 —6.9083 +00 —2.5800+01 —6.2248+01 —1.7701+02 +2.1296+02

+1.2936+01 +3.6308 + 02 + 1.0053 + 03 + 1.4292 + 03 +1.4387+03 +1.4521 +03 +4.0569+02 +2.7605+02

+0.1734+00 +7.69l9 —03 + 5.0842—03 +6.6491 —03 +1.1939—02 +1.9705—02 +0.1889+00 +5.1437—03

Table 4. Effective atomic numbers of various human tissues for total mass attenuation coefficients E (MeV)

Muscle

Bone

Brain

Heart

Kidney

Liver

Lungs

Ovaries

Pancreas

Spleen

Tongue

0.015 0.020 0.030 0.040 0.050 0.060 0.080 0.100

7.87 7.91 7.92 8.13 8.54 9.10 10.31 11.71

14.37 14.47 14.55 14.62 14.72 14.95 15.66 17.36

7.72 7.77 7.78 8.04 8.41 8.97 10.19 11.57

7.63 7.66 7.68 7.92 8.36 8.96 10.24 11.71

7.79 7.82 7.80 7.95 8.29 8.77 9.80 10.93

8.02 8.07 8.09 8.29 8.71 9.28 10.50 11.97

7.80 7.84 7.84 8.06 8.48 9.05 10.28 11.71

7.72 7.55 7.77 8.00 8.45 9.05 10.33 11.82

7.72 7.76 7.78 8.02 8.47 9.07 10.24 11.88

7.72 7.70 7.71 7.94 8.38 8.97 10.22 ll.66

7.59 7.63 7.64 7.88 8.33 8.93 10.20 11.64

RESULTS AND DISCUSSION

Using the data which are given (Hubbell, 2 invalues have 1982) been and in Table theresults SD and calculated and1, the arex given in Table 2. Choosing the minimum values of S and x2~ the elements or compounds, which provide the best match to the tissue samples, have been determined. The fit parameters of equation (2) and the Ze~ values of tissue samples, obtained by fitting of mass attenuation coefficients of samples, are given in Table 3 and Table 4. The results for muscle, also, have been plotted in Fig. I for different photon energies. The behavior of Z5~with respect to energy is interesting, From the plots, it is seen that with the increase in energy from 15 to 40 keV there is only a small

increase in Zeg and that it is nearly constant. is a sharp increase between the energy region fr to 100 keY. It is energies possible by to choosing characterize Z different photon a su power series and fitting a suitable number o ameters. Using evaluated effective atomic flu the following equation is expressed, .7

eff

—

.

1+

2

3

I

11

10 •1)

N

9 I

8

•....,.‘‘“~

2

E +

~

.

I~3

~

The values of the parameters for tissue sampl summarized in Table 5. Utilizing a suitable power series and introc the computed data of p/p, ratios of tissue samr this equation, ~ values have been determine fitting computer program and the results are gi’ Table 6. From the table, it is seen that Zeff ~5 I

12 Fitted function

.

E+D

576

H. OZYOL Table 5. Power series coefficients for use in equation (3) to obtained Z~.at energies from IS to 100 keV

Muscle Bone Brain Heart Kidney Liver Lungs Ovaries Pancreas Spleen Tongue Water

D

D

+8.3881 + 00 + 1.3915 + 01 +8.1579 + 00 +8.1713+00 +8.2720 + 00 + 8.4968 + 00 +8.3758+00 + 8.2700 + 00 +8.1912+00 + 8.2664 + 00 +8.1164+00 +8.3104+00

—5.1306 + 01 +4.2762 + 01 —4,4795 + 01 —5.4694+01 —4.7027 + 01 —4.7419 + 01 —5.6146+01 — 5.5292 + 01 —4.7585+01 — 5.6646 + 01 —5.3544+01 —5.1953+01

2

D4 + 1.3387 + 03 —9.7025 + 02 + 1,2255 + 02 +1.4473+03 + 1.1735 + 03 + 1.2563 + 03 +1.4410+03 + 1.4540 + 03 +1.2762+03 + 1,4526 + 03 +1.4327+03 +1.3762+03

—4,9369 + 03 + 8.8733 + 03 —4.3582 + 03 —5.4688+03 —4.3633 + 03 —4.3499 + 03 —5.4693+03 — 5.4668 + 03 —4.3453+03 — 5.4671 + 03 —5.4490+03 —4.9306+03

Table 6. Effective atomic numbers of various human tissues for p/p, ratios E (MeV)

Muscle

Bone

Brain

Heart

Kidney

Liver

Lungs

Ovaries

Pancreas

Spleen

Tongue

0.015 0.020 0.030 0.040 0.050 0.060 0.080 0.100

7.82 7.80 7.75 7.71 7.73 7.63 7.71 7.56

15.09 14.97 14.89 14.79 14.71 14.64 l4.59 14.58

7.67 7.66 7.62 7.65 7.59 7.48 7.56 7.4l

7.53 7.52 7.49 7.45 7.44 7.30 7.38 7.20

7.78 7.76 7.71 7.67 7.69 7.58 7.61 7.49

7.97 7.94 7.89 7.84 7.87 7.79 7.83 7.73

7.72 7.71 7.66 7.62 7.63 7.52 7.60 7.44

7.61 7.60 7.57 7.52 7.51 7.38 7.46 7.25

7.62 7.60 7.57 7.52 7.52 7.40 7.47 7.29

7.57 7.56 7.52 7.48 7.48 7.35 7.42 7.24

7.50 7.50 7.47 7.43 7.42 7.28 7.36 7.19

Average ±a

7.71 0.09

14.78 0.19

7.58 0.09

7.41 0.11

7.66 0.10

7.88 0.06

7.61 0.09

7.49 0.l2

7.50 0.11

7.45 0.11

7.39 0.11

constant between 15 and 100 keV photon energies. Mean values of Zeff and their standard deviations, are also given in Table 6.

attenuation coefficient for water (Z5ff = 7.60) used to represent mass attenuation coefficie muscle, brain, heart, kidney, lungs, ovaries, pai spleen and tongue. Moreover silicon (Z = 14)

CONCLUSIONS

nearly equivalent to bone. Also, oxygen (Z: suitable to represent liver. The effective atomic numbers, determined method B (using p/p’s) increases by 50% samples, except for bone, as the energy increase 15 to 100 keY. The significant variation in Z5 increasing photon energy is the result of the r domination of the partial photon inter

We have shown that several methods can be used to define an effective atomic number for different tissues. It is concluded from Table 2 that in photon energy absorption calculations, such as build-up and dose calculations, especially below 100 keY, the total mass

Table 7. Comparison of the atomic numbers of elements determined by the methods B and C E (MeV)

Z5

Z~.

Z5

Z~

ZB

Z~.

Z8

Z~.

Z5

Z(

0.015 0.020 0.030 0.040 0.050 0.060 0.080 0.100

4.05 4.07 4.23 4.20 4.03 3.79 3.45 3.53

4.00 4.0l 4.0l 4.00 4.06 4.02 4.67 3.93

4.91 4.90 4.92 4.93 4.90 4.84 4.84 4.93

5.00 4.97 4.99 5.07 4.97 5.00 4.51 5.2!

6.01 6.00 5.98 6.10 6.32 6.59 7.20 7.65

6.02 6.02 5.95 5.85 5.85 5.94 5.78 5.97

7.01 7.0] 6.86 6.86 6.98 7.18 7.66 8.00

6.99 7.03 7.08 7.12 7.11 6.99 6.92 6.80

8.05 8.04 7.87 7.79 7.83 7.95 8.25 8.49

7.98 7.97 8.00 8.02 8.08 8.07 8. 18 8.10

3,92 0.30 Z=ll Z5 10.93 10.94 10.97 10.87 l0.70 lO 48

4.09 0.24

4.90 4.97 0.04 0.20 Z=l2 Z5 Z1 12.04 l2.0l 12.05 12.01 12.16 12.02 12.20 11.98 12.16 ll.96 12.09 II .95

Average

±a E (MeV) 0.015 0.020 0.030 0.040 0.050 (I fl(~fl

Z=4

Z=5

Z~ 10.98 10.96 10.89 10.87 10.86 1098

Z=6

Z=7

6.49 5.92 0.62 0.09 Z=l3 Z5 Z~ l2.94 13.07 12.94 13.05 13.04 13.07 13.01 13.09 13.06 13.11 I2.96 13.03

Z=8

7.20 7.01 0.42 0.11 Z=l4 Z5 Z~. 14.09 13.99 l4.09 14.01 14.11 14.03 14.17 14.07 14.22 14.06 14. l8 14.04

8.03 8.05 0.24 0.07 Z=15 ZB Z~ 14.96 14.96 14.96 14.98 14.83 14.95 14.79 14.93 14.81 14.91 14.94 14.98

Studies on the effective atomic numbers of some human tissues

processes (coherent, incoherent scattering and photoelectric effect). This variation also depends upon the range of the atomic number of the constituent elements, which vary from H(Z = 1) to K(Z = 19), and number of elements in the tissue samples. The results, given in Table 4, show that if the total mass attenuation coefficients (pip) are used to determine Zeff’5, a single effective atomic number can not be used to characterize the interactions in this energy region. Table 6 indicates that one can determine a Z~ which is not dependent to the photon energy, for the tissue samples considered here, in the energy region of interest. Therefore, the mean values of Zeff, given in this table, may be used to represent these samples. The comparison of the known atomic numbers of elements and that determined by the two methods described above is given in Table 7. It can be seen from this table that the values determined by the method based on the (p/p 5) ratio are in good agreement with the real values and Zeff remains, more or less the same in the range 15—lOOkeY. As a summary, it can be concluded that the method based on the (p/p5) ratio seems more appropriate to

define an effective atomic number for the interaction of composite materials. REFERENCES

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