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Effective atomic numbers for photon energy absorption and photon attenuation of tissues from human organs
Medical Dosimetry, Vol. 27, No. 1, pp. 1–9, 2002 Copyright © 2002 American Association of Medical Dosimetrists Printed in the USA. All rights reserved 0958-3947/02/$–see front matter
PII: S0958-3947(01)00078-4
EFFECTIVE ATOMIC NUMBERS FOR PHOTON ENERGY ABSORPTION AND PHOTON ATTENUATION OF TISSUES FROM HUMAN ORGANS SHIVARAMU Health and Safety Division, SHINE Group, Indira Gandhi Centre for Atomic Research, Tamilnadu, India (Accepted 8 March 2001)
Abstract—Effective atomic numbers for photon energy- absorption (ZPEAeff) and photon interaction (ZPIeff) of human organs and tissues such as cortical bone, ovary, eye lens, testis, breast tissue, adipose tissue, lung tissue, soft tissue, soft tissue, (4-component), blood (whole), brain (grey/white matter), and skeletal muscle have been calculated by a direct method in the energy region of 1 keV to 20 MeV. The ZPEAeff and ZPIeff values steadily increase, up to 8 –50 keV, and steadily decrease up to 1.25–2.0 MeV for all of the substances studied. From 2.0 MeV, the values rise with the increase in energy, up to 20 MeV. Significant differences exist between the ZPIeff and ZPEAeff in the energy region of 20 – 400 keV and 3–20 MeV for cortical bone; 15–150 keV for soft tissue, ovary, testis, blood, brain, lung, and skeletal muscle; 15–100 keV for breast tissue, eye lens, and soft tissue (4-component); and 10 –100 keV for adipose tissue. A maximum difference of 28.37% is observed at 100 keV for cortical bone, and 30.43% at 40 keV for adipose tissue. For ovary, eye lens, testis, breast tissue, lung tissue, soft tissue, soft tissue (4-component), blood (whole), brain (grey/white matter), and skeletal muscle, a maximum difference of 31.74%, 29.60%, 31.87%, 30.61%, 31.47%, 31.52%, 29.95%, 31.63%, 32.36%, and 31.42%, respectively, is seen at 50 keV. The energy positions at which the maximum of ZPEAeff and ZPIeff occurs differ. The single effective atomic number directly obtained using the program XMuDat (ZXMUDATeff) are found to be higher compared to those of ZPEAeff and ZPIeff values. The effect of absorption edge on effective atomic numbers, and its variation with photon energy and the possibility of defining 2 set values of effective atomic numbers below the absorption edges of elements present in the organs and tissues, are discussed. 娀 2001 American Association of Medical Dosimetrists. © 2002 American Association of Medical Dosimetrists Key Words: Effective atomic numbers, Absorbed dose, Radiation therapy, Medical imaging
INTRODUCTION
sectional anatomy is generated by computer-assisted tomography (CAT) scans.2 The theoretical expressions for effective atomic number of composite materials are not accurate at all energies.2,3 Hence, a direct method of deriving the effective atomic numbers in composite materials without using any theoretical expressions from the / is reported in this work.4 The effective atomic number for photon interactions, which is more commonly used and is denoted here by ZPIeff and obtained using /, is a convenient parameter for representing the photon interaction. This method has been previously applied4 to thermoluminescent materials by the author. Similarly, a more useful effective atomic number is the effective atomic number for photon-energy absorption in a composite medium, denoted by ZPEAeff, can be obtained5 using en/ and is a convenient parameter for representing the photon-energy absorption (absorbed dose) in a complex medium. The present work focuses on the accurate calculation of ZPEAeff values by a direct method for some tissues from human organs such as cortical bone, ovary, eye lens, testis, breast tissue, adipose tissue, lung tissue, soft tissue, soft tissue (4-component), blood (whole), brain (grey/white matter), and skeletal muscle in the energy region of 1 keV to 20 MeV, using en/ values from the latest improved compilation of Hubbell and Seltzer.6 In this compilation, all edge energies are included and iden-
The mass attenuation coefficient / is a measure of the average number of interactions between incident photons and matter that occur in a given mass-per-unit area thickness of the material encountered. The mass energy-absorption coefficient en/, on the other hand, is a measure of the average fractional amount of incident photon energy transferred to kinetic energy of charged particles as a result of these interactions. This imparted, chargedparticles kinetic energy is, in turn, a more or less valid approximation to the amount of photon energy made available for the production of chemical, biological, and other effects associated with exposure to ionizing radiation. The en/ has thus assumed an essential role in estimating absorbed dose in medical and health physics.1 In composite materials, for photon interactions, a single number cannot represent the atomic number uniquely across the entire energy region, as in the case of pure elements. This number in composite materials is called the “effective atomic number,” and it varies with energy. The effective atomic numbers are useful in medical radiation dosimetry for the calculation of dose in radiation therapy and medical imaging, where the crossReprint requests to: Dr. Shivaramu, Health and Safety Division, SHINE Group, Indira Gandhi Centre for Atomic Research, Kalpakkam-603 102, Tamilnadu, India. E-mail: [email protected] 1
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Medical Dosimetry
Volume 27, Number 1, 2002
Table 1. Elemental composition of tissues from human organs as per ICRU– 446 Tissues from Human Organs
Composition (Z: Fraction by Weight)
Cortical bone Ovary Eye lens Testis Breast tissue Adipose tissue Lung tissue Soft tissue Soft Tissue (4-component) Blood (whole) Brain (grey/white matter) Skeletal muscle
1:0.034 6:0.155 7:0.042 8:0.435 11:0.001 12:0.002 1:0.105 6:0.093 7:0.024 8:0.768 11:0.002 15:0.002 1:0.096 6:0.195 7:0.057 8:0.646 11:0.001 15:0.001 1:0.106 6:0.099 7:0.020 8:0.766 11:0.002 15:0.001 1:0.106 6:0.332 7:0.030 8:0.527 11:0.001 15:0.001 1:0.114 6:0.598 7:0.007 8:0.278 11:0.001 16:0.001 1:0.103 6:0.105 7:0.031 8:0.749 11:0.002 15:0.002 1:0.102 6:0.143 7:0.034 8:0.708 11:0.002 15:0.003 1:0.101174 6:0.111000 7:0.026000 8:0.761826 1:0.102 6:0.110 7:0.033 8:0.745 11:0.001 15:0.001 1:0.107 6:0.145 7:0.022 8:0.712 11:0.002 15:0.004 1:0.102 6:0.143 7:0.034 8:0.710 11:0.001 15:0.002
tified, and values of en/ are given just above and below each edge to facilitate accurate interpolation. The data were based on unrenormalized Scofield7 theoretical val-
15:0.103 16:0.002 16:0.003 16:0.002 16:0.002 17:0.001 16:0.003 16:0.003
16:0.003 20:0.225 17:0.002 19:0.002 17:0.001 17:0.002 19:0.002 17:0.001 17:0.003 19:0.002 17:0.002 19:0.003
16:0.002 17:0.003 19:0.002 26:0.001 16:0.002 17:0.003 19:0.003 16:0.003 17:0.001 19:0.004
ues of photoeffect cross-sections. The earlier compilation by Hubbell1 was based on the application of renormalization factors given by Scofield. An evaluation by Salo-
Table 2. Zeff values for total photon-energy absorption and photon interaction for cortical bone, ovary, and eye lens Cortical Bone
Ovary
Eye Lens
Energy (McV)
ZPEAeff
ZPIeff
ZPEAeff
ZPIeff
ZPEAeff
ZPIeff
0.10000E-02 0.10721E-02 0.10721E-02 0.15000E-02 0.20000E-02 0.21455E-02 0.21455E-02 0.24720E-02 0.24720E-02 0.28224E-02 0.28224E-02 0.30000E-02 0.40000E-02 0.40381E-02 0.40381E-02 0.50000E-02 0.60000E-02 0.80000E-02 0.10000E-01 0.15000E-01 0.20000E-01 0.30000E-01 0.40000E-01 0.50000E-01 0.60000E-01 0.80000E-01 0.10000E⫹00 0.15000E⫹00 0.20000E⫹00 0.30000E⫹00 0.40000E⫹00 0.50000E⫹00 0.60000E⫹00 0.80000E⫹00 0.10000E⫹01 0.12500E⫹01 0.15000E⫹01 0.20000E⫹01 0.30000E⫹01 0.40000E⫹01 0.50000E⫹01 0.60000E⫹01 0.80000E⫹01 0.10000E⫹02 0.15000E⫹02 0.20000E⫹02
6.8986 6.8515 6.8480 6.9870 7.0387 7.7807 7.0617 8.4366 8.4243 — — 7.9532 8.0546 10.0139 8.0536 10.2440 10.3889 10.6034 10.7452 10.9600 11.0897 11.2382 11.2985 11.3187 11.1951 10.7271 9.8286 7.4453 6.5604 6.1354 6.1374 6.0449 6.0135 5.9992 5.9872 5.9830 5.9757 5.9738 5.9982 6.0831 6.1949 6.3076 6.4131 6.5928 6.7312 6.9463
6.9007 6.9191 6.9156 — 7.0381 7.8060 7.0526 7.8961 7.8741 — — 7.9804 8.0808 10.2659 8.0804 10.4362 10.5471 10.7046 10.7990 10.9332 10.9576 10.7951 10.3829 9.7510 9.0716 7.7691 7.0402 6.3663 6.1869 6.0541 6.0410 6.0069 5.9963 6.0042 5.9000 5.9947 5.9942 6.0242 6.1045 6.1992 6.2977 6.3926 6.5604 6.7040 6.9631 7.1329
5.8312 5.8594 5.8541 5.9191 5.9812 6.0047 5.9922 6.0477 6.0297 6.0923 6.0720 6.1031 6.1786 — — 6.2147 6.2442 — 6.3170 6.4574 6.3848 6.3540 6.1877 5.8508 5.3207 4.2923 3.8100 3.4955 3.4385 3.4126 3.4082 3.4059 3.4049 3.4034 3.4029 3.4029 3.4010 3.4109 3.4454 3.4941 3.5457 3.5938 3.6921 3.7750 3.9289 4.0297
5.8333 5.8078 5.8046 — 5.9824 6.0126 5.9990 6.0460 6.0443 6.0862 6.0672 6.1061 6.1786 — — 6.2113 6.2331 6.2514 6.2497 6.1454 5.9213 5.1591 4.4240 3.9936 3.7862 3.5838 3.5030 3.4545 3.4275 3.4135 3.4112 3.4068 3.4098 3.4058 3.4084 3.4067 3.4084 3.4187 3.4512 3.4918 3.5374 3.5797 3.6649 3.7496 3.8979 4.0034
5.7922 5.7676 5.7652 5.8848 5.9336 5.9570 5.9510 6.0403 6.0377 6.0182 6.0084 6.0344 6.0785 — — 6.1092 6.1343 6.1700 6.1959 6.3327 6.2508 6.2115 5.7759 5.7248 5.2143 4.2852 3.8608 3.5871 3.5325 3.5110 3.5061 3.5049 3.5037 3.5025 3.5009 3.5010 3.5013 3.5083 3.5436 3.5874 3.6377 3.6853 3.7731 3.8553 3.9962 4.0917
5.7942 5.8171 5.8143 — 5.9343 5.9504 5.9441 5.9920 5.9692 6.0243 6.0138 6.0858 6.0747 — — 6.1028 6.1209 6.1336 6.1284 6.0196 5.8122 5.0814 4.4161 4.0301 3.8468 3.6649 3.5390 3.5478 3.5274 3.5077 3.5084 3.5036 3.5091 3.5050 3.5065 3.5056 3.5072 3.5175 3.5471 3.5868 3.6307 3.6693 3.7498 3.8282 3.9693 4.0660
Effective atomic numbers for photon energy absorption ● SHIVARAMU
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Table 3. Zeff values for total photon-energy absorption and photon interaction for breast tissue, soft tissue, (4 component), and adipose tissue Breast Tissue
Soft Tissue (4-component)
Adipose Tissue
Energy (MeV)
ZPEAeff
ZPIeff
ZPEAeff
ZPIeff
ZPEAeff
ZPIeff
0.10000E-02 0.10721E-02 0.10721E-02 0.15000E-02 0.20000E-02 0.28224E-02 0.28224E-02 0.30000E-02 0.40000E-02 0.50000E-02 0.60000E-02 0.80000E-02 0.10000E-01 0.15000E-01 0.20000E-01 0.30000E-01 0.40000E-01 0.50000E-01 0.60000E-01 0.80000E-01 0.10000E⫹00 0.15000E⫹00 0.20000E⫹00 0.30000E⫹00 0.40000E⫹00 0.50000E⫹00 0.60000E⫹00 0.80000E⫹00 0.10000E⫹01 0.12500E⫹01 0.15000E⫹01 0.20000E⫹01 0.30000E⫹01 0.40000E⫹01 0.50000E⫹01 0.60000E⫹01 0.80000E⫹01 0.10000E⫹02 0.15000E⫹02 0.20000E⫹02
5.5422 — — 5.6426 5.6965 — — 5.7965 5.8360 5.8632 5.8848 5.9144 5.9348 6.0419 5.9732 5.9359 5.7649 5.3709 4.8184 3.9412 3.5775 3.3513 3.3082 3.2900 3.2867 3.2855 3.2838 3.2825 3.2823 3.2823 3.2806 3.2879 3.3193 3.3603 3.4029 3.4488 3.5312 3.6045 3.7376 3.8283
5.5425 — — — 5.6968 — — 5.7970 5.8313 5.8553 5.8708 5.8801 5.8715 5.7539 5.4907 4.7001 4.0701 3.7269 3.5700 3.4211 3.3568 3.3233 3.3055 3.2916 3.2858 3.2866 3.2879 3.2843 3.2870 3.2856 3.2869 3.2956 3.3232 3.3585 3.3977 3.4335 3.5075 3.5797 3.7125 3.8040
5.8551 — — 5.9464 5.9942 — — 6.0603 6.0998 6.1269 6.1486 6.1801 6.2030 6.3327 6.2472 6.2012 6.0249 5.6967 5.1713 4.2324 3.8072 3.5366 3.4818 3.4607 3.4584 3.4547 3.4537 3.4529 3.4522 3.4525 3.4515 3.4595 3.4954 3.5399 3.5928 3.6409 3.7358 3.8184 3.9658 4.0630
5.8580 — — 5.9465 5.9943 — — 6.0579 6.0942 6.1171 6.1324 6.1422 6.1327 6.0175 5.8035 5.0481 4.3704 3.9905 3.7958 3.6202 3.5533 3.4957 3.4745 3.4636 3.4614 3.4584 3.4581 3.4572 3.4564 3.4569 3.4583 3.4688 3.5008 3.5398 3.5816 3.6263 3.7094 3.7853 3.9369 4.0458
5.1235 5.1034 5.0996 5.2146 5.2649 5.3373 5.3248 5.3513 5.3928 5.4228 5.4465 5.4807 5.5049 5.5638 5.5470 5.4731 5.2181 4.7695 4.2207 3.5256 3.2711 3.1188 3.0889 3.0769 3.0755 3.0739 3.0731 3.0717 3.0711 3.0714 3.0706 3.0763 3.1021 3.1351 3.1721 3.2081 3.2764 3.3385 3.4556 3.5344
5.1259 5.1474 5.1473 5.2152 5.2647 5.3395 5.3252 5.3405 5.3865 5.4100 5.4266 5.4289 5.4057 5.2358 4.9285 4.1441 3.6300 3.3913 3.2722 3.1716 3.1301 3.0966 3.0856 3.0792 3.0764 3.0760 3.0743 3.0736 3.0735 3.0735 3.0749 3.0819 3.1048 3.1332 3.1649 3.1970 3.2581 3.3136 3.4309 3.5167
man et al.8 compared the theoretical values with the measured-value database, and concluded that overall agreement was better without this renormalization. The ZPEAeff values are compared with calculated ZPIeff data and the single ZXMUDATeff value directly obtained from the program XmuDat.9 The effect of absorption edge on effective atomic numbers, and its variation with photon energy and the possibility of defining 2 set values of effective atomic numbers below the absorption edges of elements present in some tissues from human organs are discussed. The reasons for using ZPEAeff rather than the commonly used ZPIeff in medical radiation dosimetry for the calculation of absorbed dose in radiation therapy are discussed. EFFECTIVE ATOMIC NUMBER CALCULATIONS The procedure of calculating the ZPEAeff by direct method involves finding the atomic number that corresponds to
the en/ in the composite material on a plot of atomic number vs. the en/ for the elements. The en/ of the elements does not consistently vary with the atomic number. For smoother interpolation, the cross-section of the elements vs. the atomic number is preferred. The en/ values are then converted in to atomic energyabsorption cross-section (en) by dividing its en/ with the number of atoms present in one gram of that material: en ⫽
en/ N A⌺w i/A i
(1)
where wi is the fraction by weight, Ai is the atomic weight of the ith atomic constituent, and Na is Avogadro’s number. The ZPEAeff can then be obtained from an energy absorption cross-section plot as a function of the atomic number of the element by interpolating the number that corresponds to the cross-section per atom of the composite substance. In this work, the en/ values of the tissues from human organs are taken from compila-
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Medical Dosimetry
Volume 27, Number 1, 2002
Table 4. Zeff values for total photon-energy absorption and photon interaction for lung tissue, testis, and soft tissue Lung Tissue
Testis
Soft Tissue
Energy (MeV)
ZPEAeff
ZPIeff
ZPEAeff
ZPIeff
ZPEAeff
ZPIeff
0.10000E-02 0.10721E-02 0.10721E-02 0.15000E-02 0.20000E-02 0.21455E-02 0.21455E-02 0.2472E-02 0.2472E-02 0.28224E-02 0.28224E-02 0.30000E-02 0.36074E-02 0.36074E-02 0.40000E-02 0.50000E-02 0.60000E-02 0.80000E-02 0.10000E-01 0.15000E-01 0.20000E-01 0.30000E-01 0.40000E-01 0.50000E-01 0.60000E-01 0.80000E-01 0.10000E⫹00 0.15000E⫹00 0.20000E⫹00 0.30000E⫹00 0.40000E⫹00 0.50000E⫹00 0.60000E⫹00 0.80000E⫹00 0.10000E⫹01 0.12500E⫹01 0.15000E⫹01 0.20000E⫹01 0.30000E⫹01 0.40000E⫹01 0.50000E⫹01 0.60000E⫹01 0.80000E⫹01 0.10000E⫹02 0.15000E⫹02 0.20000E⫹02
5.8335 5.8119 5.8065 5.9333 5.9823 6.0056 5.9926 6.0547 6.0304 6.1133 6.0824 6.1241 6.1866 6.1559 6.2013 6.2391 6.2703 6.3137 6.3459 6.4869 6.4178 6.3894 6.2290 5.8943 5.3751 4.3420 3.8509 3.5304 3.4690 3.4408 3.4370 3.4334 3.4323 3.4300 3.4307 3.4299 3.4290 3.4378 3.4749 3.5206 3.5737 3.6226 3.7201 3.8019 3.9571 4.0563
5.8369 5.8614 5.8560 5.9336 5.9825 6.0135 5.9996 6.0470 6.0440 6.1058 6.0776 6.1270 6.1876 6.1609 6.2030 6.2351 6.2577 6.2807 6.2789 6.1801 5.9566 5.2026 4.4659 4.0394 3.8163 3.6183 3.5394 3.4755 3.4549 3.4439 3.4393 3.4373 3.4357 3.4351 3.4347 3.4347 3.4357 3.4465 3.4790 3.5202 3.5630 3.6084 3.6932 3.7693 3.9256 4.0373
5.8175 5.7964 5.7915 5.9191 5.9694 5.9926 5.9870 6.0437 6.0421 6.0637 6.0446 6.0744 6.1415 6.1159 6.1552 6.1911 6.2202 6.2613 6.2921 6.4330 6.3591 6.3264 6.1573 5.8196 5.2842 4.2596 3.7860 3.4785 3.4181 3.3937 3.3898 3.3866 3.3856 3.3847 3.3846 3.3837 3.3833 3.3904 3.4264 3.4731 3.5266 3.5755 3.6704 3.7543 3.9071 4.0075
5.8195 5.8463 5.8409 — 5.9703 5.9860 5.9802 6.0251 6.0071 6.0698 6.0494 6.0826 6.1391 6.1095 6.1548 6.1868 6.2088 6.2253 6.2239 6.1178 5.8941 5.1242 4.3923 3.9650 3.7602 3.5616 3.4829 3.4345 3.4104 3.3941 3.3893 3.3883 3.3906 3.3870 3.3890 3.3882 3.3892 3.4005 3.4319 3.4720 3.5177 3.5594 3.6432 3.7276 3.8767 3.9831
5.7998 5.7783 5.7732 5.8995 5.9497 5.9845 5.9673 6.0437 6.0412 6.0649 6.0455 6.0826 — — 6.1742 6.2783 6.2448 6.2906 6.3237 6.4670 6.3994 6.3728 6.2130 5.8800 5.3605 4.3349 3.8467 3.5292 3.4668 3.4419 3.4368 3.4342 3.4324 3.4305 3.4298 3.4300 3.4293 3.4365 3.4732 3.5198 3.5700 3.6195 3.7139 3.7977 3.9485 4.0475
5.8018 5.8278 5.8212 — 5.9506 5.9786 5.9602 6.0261 5.9986 6.0727 6.0512 6.0858 — — 6.1766 6.2116 6.2355 6.2571 6.2580 6.1585 5.9379 5.1889 4.4568 4.0269 3.8157 3.6133 3.5310 3.4834 3.4592 3.4385 3.4363 3.4349 3.4375 3.4339 3.4358 3.4347 3.4357 3.4465 3.4790 3.5183 3.5638 3.6048 3.6878 3.7716 3.9174 4.0230
tion of Hubbell and Seltzer.6 The weight fractions of the organs and tissues are given in Table 1 and as per ICRU44. Similarly, we have obtained the ZPIeff using / and total photon interaction cross-sections following the procedure given elsewhere.4 Because of the small uncertainties in constructing the plots and in the interpolation, the error in the derived ZPEAeff and ZPIeff is found to be negligibly small. The effective atomic numbers, based on the program XMuDat (ZXMUDATeff), are directly obtained. XMuDat9 is a program for the presentation and calculation of various photon interaction coefficients. RESULTS AND DISCUSSION The calculated results of ZPEAeff and ZPIeff at various photon energies are given in Tables 2– 4, and their vari-
ation with energy is shown in Figs.1– 6. The variation of ZPEAeff and ZPIeff with energy is approximately similar for all of the substances studied, except for the abrupt changes near the absorption edges. The ZPEAeff and ZPIeff values steadily increase up to 8 –50 keV, and then steadily decrease up to 1.25–2.0 MeV for all tissues studied. From 2.0 MeV, the values rise with increase in energy, up to 20 MeV. Significant differences exist between ZPIeff and the ZPEAeff in the energy region of 20 – 400 keV and 3–20 MeV for cortical bone; 15–150 keV for soft tissue, ovary, testis, blood, brain, lung, and skeletal muscle; 15–100 keV for breast tissue, eye lens, and soft tissue (4-component); and 10 –100 keV for adipose tissue. A maximum difference of 28.37% at 100 keV for cortical bone, and 30.43% at 40 keV for adipose
Effective atomic numbers for photon energy absorption ● SHIVARAMU
5
Table 5. Zeff values for total photon-energy absorption and photon interaction for blood (whole), brain (grey/white matter), and skeletal muscle Blood, Whole
Brain, Grey/White Matter
Skeletal Muscle
Energy (MeV)
ZPEAeff
ZPIeff
ZPEAeff
ZPIeff
ZPEAeff
ZPIeff
0.10000E-02 0.10721E-02 0.10721E-02 0.15000E-02 0.20000E-02 0.24720E-02 0.24720E-02 0.28224E-02 0.28224E-02 0.30000E-02 0.36074E-02 0.36074E-02 0.40000E-02 0.50000E-02 0.60000E-02 0.80000E-02 0.10000E-01 0.15000E-01 0.20000E-01 0.30000E-01 0.40000E-01 0.50000E-01 0.60000E-01 0.80000E-01 0.10000E⫹00 0.15000E⫹00 0.20000E⫹00 0.30000E⫹00 0.40000E⫹00 0.50000E⫹00 0.60000E⫹00 0.80000E⫹00 0.10000E⫹01 0.12500E⫹01 0.15000E⫹01 0.20000E⫹01 0.30000E⫹01 0.40000E⫹01 0.50000E⫹01 0.60000E⫹01 0.80000E⫹01 0.10000E⫹02 0.15000E⫹02 0.20000E⫹02
5.8419 5.8175 5.8148 5.9374 5.9863 6.0458 6.0441 6.0937 6.0652 6.1112 — — 6.1871 6.2233 6.2534 6.3251 6.3616 6.5091 6.4480 6.4294 6.2772 5.9456 5.4363 4.3899 3.8819 3.5489 3.4827 3.4555 3.4500 3.4473 3.4457 3.4451 3.4438 3.4435 3.4423 3.4519 3.4879 3.5343 3.5874 3.6378 3.7336 3.8162 3.9680 4.0674
5.8440 5.8671 5.8644 — 5.9830 6.0459 6.0277 6.1006 6.0694 6.1142 — — 6.1877 6.2207 6.2427 6.3009 6.3047 6.2120 5.9895 5.0237 4.5077 4.0648 3.8468 3.6366 3.5490 3.4967 3.4714 3.4551 3.4520 3.4482 3.4514 3.4475 3.4499 3.4479 3.4496 3.4607 3.4933 3.5340 3.5791 3.6204 3.7067 3.7892 3.9385 4.0440
5.7531 5.7327 5.7276 5.8571 5.9090 6.0373 6.0389 6.0251 5.9973 6.0428 6.1206 6.0807 6.1364 6.1766 6.2096 6.2569 6.2912 6.4380 6.3690 6.3417 6.1764 5.8361 5.2955 4.2496 3.7619 3.4477 3.3843 3.3602 3.3563 3.3526 3.3519 3.3508 3.3510 3.3499 3.3488 3.3583 3.3928 3.4368 3.4903 3.5383 3.6330 3.7150 3.8653 3.9651
5.7565 5.7819 5.7763 5.8575 5.9093 5.9663 5.9810 6.0326 6.0014 6.0471 6.1223 6.0772 6.1394 6.1740 6.1983 6.2217 6.2219 6.1213 5.8970 5.1137 4.3704 3.9478 3.7272 3.5341 3.4577 3.3949 3.3767 3.3619 3.3573 3.3569 3.3558 3.3547 3.3543 3.3548 3.3555 3.3667 3.3973 3.4291 3.4797 3.5235 3.6053 3.6813 3.8359 3.9454
5.8024 5.8279 5.8251 5.8985 5.9485 6.0168 5.9916 6.0522 6.0414 6.0620 6.1528 6.0912 6.1644 6.2055 6.2368 6.2834 6.3165 6.4613 6.3924 6.3662 6.2064 5.8742 5.3540 4.3307 3.8439 3.5291 3.4648 3.4398 3.4359 3.4324 3.4313 3.4300 3.4285 3.4299 3.4290 3.4398 3.4719 3.5173 3.5702 3.6190 3.7122 3.7957 3.9462 4.0431
5.8056 5.7784 5.7756 5.8998 5.9491 6.0429 6.0404 6.0458 6.0364 6.0645 6.1507 6.0972 6.1702 6.2036 6.2270 6.2507 6.2498 6.1519 5.9326 5.1778 4.4487 4.0284 3.8095 3.6145 3.5374 3.4755 3.4549 3.4439 3.4393 3.4363 3.4349 3.4343 3.4337 3.4336 3.4351 3.4465 3.4781 3.5173 3.5597 3.6036 3.6865 3.7619 3.9158 4.0255
tissue, is observed. For ovary, eye lens, testis, breast tissue, lung tissue, soft tissue, soft tissue (4-component), blood (whole), brain (grey/white matter), and skeletal muscle, a maximum difference of 31.74%, 29.60%, 31.87%, 30.61%, 31.47%, 31.52%, 29.95%, 31.63%, 32.36%, and 31.42%, respectively, is seen at 50 keV. The energy positions at which the maximum of ZPEAeff and ZPIeff occurs differ, and are shown in Figs. 1– 6 and Tables 2– 4. The single ZXMUDATeff values are found to be significantly higher compared to those of ZPEAeff and ZPIeff values in the energy region of interest for all tissues and organs studied, as shown in Figs. 1– 6. The variation of ZPEAeff with energy may be attributed to the relative domination of the partial processes, viz., photoelectric effect, coherent scattering, incoherent scattering, and pair production. At low energies, the
photoelectric effect is dominant and hence the ZPEAeff for the energy- absorption is mainly described by the ZPEAeff for this partial process. Similarly, at higher energies, the contribution due to scattering and pair-production process will be more in comparison with photoelectric effect, and this will have its effect on the ZPEAeff for photon-energy absorption. Hence, at low energies, where photoelectric effect dominates, the ZPEAeff value is more; and at higher energies, where the scattering and pair production process dominates, the ZPEAeff value is less. Therefore, the ZPEAeff for photon-energy absorption varies from a higher value at lower energies to a lower value at higher energies, with a peak, due to photoelectric effect, around the absorption edge of the constituent element of the composite substance studied, depending on the relative domination of one gamma-ray process
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Volume 27, Number 1, 2002
Fig. 1. Variation of effective atomic numbers for photon-energy absorption ZPEAeff and photon interaction ZPIeff with photon energy for cortical bone and soft tissue. The effective atomic number ZXMUDATeff, obtained from the XmuDat program, is also plotted.
Fig. 2. Variation of effective atomic numbers for photon-energy absorption ZPEAeff and photon interaction ZPIeff with photon energy for blood and adipose tissue. The effective atomic number ZXMUDATeff, obtained from the XMuDat program, is also plotted.
Effective atomic numbers for photon energy absorption ● SHIVARAMU
Fig. 3. Variation of effective atomic numbers for photon-energy absorption ZPEAeff and photon interaction ZPIeff with photon energy for ovary and breast tissue. The effective atomic number ZXMUDATeff, obtained from the XMuDat program, is also plotted.
Fig. 4. Variation of effective atomic numbers for photon-energy absorption ZPEAeff and photon interaction ZPIeff with photon energy for testis and eye lens. The effective atomic number ZXMUDATeff, obtained from the XMuDat program, is also plotted.
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Fig. 5. Variation of effective atomic numbers for photon-energy absorption ZPEAeff and photon interaction ZPIeff with photon energy for brain and soft tissue (4- component). The effective atomic number ZXMUDATeff, obtained from the XMuDat program, is also plotted.
Fig. 6. Variation of effective atomic numbers for photon-energy absorption ZPEAeff and photon interaction ZPIeff with photon energy for lung and skeletal muscle. The effective atomic number ZXMUDATeff, obtained from the XMuDat program, is also plotted.
Effective atomic numbers for photon energy absorption ● SHIVARAMU
over the other. The variation of ZPIeff as a function of energy can be explained in the same manner. In Fig. 1, it is shown that the variation of ZPEAeff and ZPIeff with energy below the absorption edge of the calcium element present in the cortical bone tissue is not uniform. Because of the nonuniform variation of crosssection with atomic number at a particular energy, it is possible to get more than one ZPEAeff and ZPIeff value for a given substance. We have calculated the ZPEAeff and ZPIeff values at the absorption-edge energies of the constituent elements of the tissues from human organs, and generated two ZPEAeff and ZPIeff values at each absorption edge, one corresponding to the cross-section on the lower side and the other to the higher side (Figs. 1– 6, Tables 2–5). The oscillations seen in Fig. 1 are due to the 2 ZPEAeff and ZPIeff values, one low and one high (corresponding to the lower and higher cross sections) for the same energy. CONCLUSIONS This work reported new data on ZPEAeff and ZPIeff, calculated by direct method in the energy region of 1 keV to 20 MeV, for selected human tissues from organs and of dosimetric interest, such as cortical bone, breast tissue, ovary, eye lens, testis, and soft tissue. The ZPEAeff and ZPIeff values vary from a higher value at lower energies to a lower value at higher energies, with a peak due to photoelectric effect, around the absorption edge of the constituent of the substance. Because of the nonuniform variation of cross-section with atomic number at a particular energy, it was possible to generate more than one ZPEAeff and ZPIeff value for a given substance. The energy positions at which the maximum of ZPEAeff and ZPIeff occurs differ. Significant differences up to 32.36% exist between ZPIeff and the ZPEAeff in the energy region around 50 keV. The single ZXMUDATeff values obtained
9
from the program XMuDat are found to be higher compared to those of ZPEAeff and ZPIeff values in the energy region of interest, for all tissues from human organs studied. Because significant differences exist between ZPEAeff and ZPIeff, and the former represents the absorbed dose, it is preferable to use ZPEAeff instead of the commonly used ZPIeff for the calculation of absorbed dose in radiation therapy. It is expected that the new data on ZPEAeff and ZPIeff presented here will be useful, particularly in the energy region of interest, in view of their importance in medical dosimetry. Also, to the best knowledge of the author, these data are the first of their kind at these energies. REFERENCES 1. Hubbell, J.H. Photon mass attenuation and energy- absorption coefficients from 1 keV to 20 MeV. Int. J. Appl. Radiat. Isot. 33:1269 –90; 1982. 2. Jackson, D.F.; Hawkes, D. J. X-ray attenuation coefficients of elements and mixtures. Phys. Reports 70:169; 1981. 3. White, D.R. An analysis of the Z-dependence of photon and electron interactions. Phys. Med. Biol. 22:219; 1977. 4. Shivaramu; Amutha, R.; Ramprasath, V. Effective atomic numbers and mass attenuation coefficients of some thermoluminescent dosimetric compounds for total photon interaction. Nucl. Sci. Eng. 132:148 –53; 1999. 5. Shivaramu; Ramprasath, V. Effective atomic numbers for photonenergy absorption and energy dependence of some thermoluminescent dosimetric compounds. Nucl. Inst. Meth. B168:294 –304; 2000. 6. Hubbell, J.H.; Seltzer, S.M. Tables of X-ray mass attenuation coefficients and mass energy-absorption coefficients 1 keV to 20 MeV for elements Z ⫽ 1 to 92 and 48 additional selected substances of dosimetric interest. NISTIR–5632; 1995. 7. Scofield, J.H. Theoretical photoionization cross sections from 1 to 1500 keV. Lawrence Livermore Laboratory Report UCRL–51326; 1973. 8. Saloman, E.B.; Hubbell, J.H.; Scofield, J.H. X-ray attenuation cross sections for energies 100 eV to 100 keV and elements Z ⫽ 1 to Z ⫽ 92. Atomic Data and Nuclear Data Tables 38:1–197; 1988. 9. Nowotny, R. XMuDat: Photon attenuation data on PC. IAEA– NDS–195; 1998.
PII: S0958-3947(01)00078-4
EFFECTIVE ATOMIC NUMBERS FOR PHOTON ENERGY ABSORPTION AND PHOTON ATTENUATION OF TISSUES FROM HUMAN ORGANS SHIVARAMU Health and Safety Division, SHINE Group, Indira Gandhi Centre for Atomic Research, Tamilnadu, India (Accepted 8 March 2001)
Abstract—Effective atomic numbers for photon energy- absorption (ZPEAeff) and photon interaction (ZPIeff) of human organs and tissues such as cortical bone, ovary, eye lens, testis, breast tissue, adipose tissue, lung tissue, soft tissue, soft tissue, (4-component), blood (whole), brain (grey/white matter), and skeletal muscle have been calculated by a direct method in the energy region of 1 keV to 20 MeV. The ZPEAeff and ZPIeff values steadily increase, up to 8 –50 keV, and steadily decrease up to 1.25–2.0 MeV for all of the substances studied. From 2.0 MeV, the values rise with the increase in energy, up to 20 MeV. Significant differences exist between the ZPIeff and ZPEAeff in the energy region of 20 – 400 keV and 3–20 MeV for cortical bone; 15–150 keV for soft tissue, ovary, testis, blood, brain, lung, and skeletal muscle; 15–100 keV for breast tissue, eye lens, and soft tissue (4-component); and 10 –100 keV for adipose tissue. A maximum difference of 28.37% is observed at 100 keV for cortical bone, and 30.43% at 40 keV for adipose tissue. For ovary, eye lens, testis, breast tissue, lung tissue, soft tissue, soft tissue (4-component), blood (whole), brain (grey/white matter), and skeletal muscle, a maximum difference of 31.74%, 29.60%, 31.87%, 30.61%, 31.47%, 31.52%, 29.95%, 31.63%, 32.36%, and 31.42%, respectively, is seen at 50 keV. The energy positions at which the maximum of ZPEAeff and ZPIeff occurs differ. The single effective atomic number directly obtained using the program XMuDat (ZXMUDATeff) are found to be higher compared to those of ZPEAeff and ZPIeff values. The effect of absorption edge on effective atomic numbers, and its variation with photon energy and the possibility of defining 2 set values of effective atomic numbers below the absorption edges of elements present in the organs and tissues, are discussed. 娀 2001 American Association of Medical Dosimetrists. © 2002 American Association of Medical Dosimetrists Key Words: Effective atomic numbers, Absorbed dose, Radiation therapy, Medical imaging
INTRODUCTION
sectional anatomy is generated by computer-assisted tomography (CAT) scans.2 The theoretical expressions for effective atomic number of composite materials are not accurate at all energies.2,3 Hence, a direct method of deriving the effective atomic numbers in composite materials without using any theoretical expressions from the / is reported in this work.4 The effective atomic number for photon interactions, which is more commonly used and is denoted here by ZPIeff and obtained using /, is a convenient parameter for representing the photon interaction. This method has been previously applied4 to thermoluminescent materials by the author. Similarly, a more useful effective atomic number is the effective atomic number for photon-energy absorption in a composite medium, denoted by ZPEAeff, can be obtained5 using en/ and is a convenient parameter for representing the photon-energy absorption (absorbed dose) in a complex medium. The present work focuses on the accurate calculation of ZPEAeff values by a direct method for some tissues from human organs such as cortical bone, ovary, eye lens, testis, breast tissue, adipose tissue, lung tissue, soft tissue, soft tissue (4-component), blood (whole), brain (grey/white matter), and skeletal muscle in the energy region of 1 keV to 20 MeV, using en/ values from the latest improved compilation of Hubbell and Seltzer.6 In this compilation, all edge energies are included and iden-
The mass attenuation coefficient / is a measure of the average number of interactions between incident photons and matter that occur in a given mass-per-unit area thickness of the material encountered. The mass energy-absorption coefficient en/, on the other hand, is a measure of the average fractional amount of incident photon energy transferred to kinetic energy of charged particles as a result of these interactions. This imparted, chargedparticles kinetic energy is, in turn, a more or less valid approximation to the amount of photon energy made available for the production of chemical, biological, and other effects associated with exposure to ionizing radiation. The en/ has thus assumed an essential role in estimating absorbed dose in medical and health physics.1 In composite materials, for photon interactions, a single number cannot represent the atomic number uniquely across the entire energy region, as in the case of pure elements. This number in composite materials is called the “effective atomic number,” and it varies with energy. The effective atomic numbers are useful in medical radiation dosimetry for the calculation of dose in radiation therapy and medical imaging, where the crossReprint requests to: Dr. Shivaramu, Health and Safety Division, SHINE Group, Indira Gandhi Centre for Atomic Research, Kalpakkam-603 102, Tamilnadu, India. E-mail: [email protected] 1
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Volume 27, Number 1, 2002
Table 1. Elemental composition of tissues from human organs as per ICRU– 446 Tissues from Human Organs
Composition (Z: Fraction by Weight)
Cortical bone Ovary Eye lens Testis Breast tissue Adipose tissue Lung tissue Soft tissue Soft Tissue (4-component) Blood (whole) Brain (grey/white matter) Skeletal muscle
1:0.034 6:0.155 7:0.042 8:0.435 11:0.001 12:0.002 1:0.105 6:0.093 7:0.024 8:0.768 11:0.002 15:0.002 1:0.096 6:0.195 7:0.057 8:0.646 11:0.001 15:0.001 1:0.106 6:0.099 7:0.020 8:0.766 11:0.002 15:0.001 1:0.106 6:0.332 7:0.030 8:0.527 11:0.001 15:0.001 1:0.114 6:0.598 7:0.007 8:0.278 11:0.001 16:0.001 1:0.103 6:0.105 7:0.031 8:0.749 11:0.002 15:0.002 1:0.102 6:0.143 7:0.034 8:0.708 11:0.002 15:0.003 1:0.101174 6:0.111000 7:0.026000 8:0.761826 1:0.102 6:0.110 7:0.033 8:0.745 11:0.001 15:0.001 1:0.107 6:0.145 7:0.022 8:0.712 11:0.002 15:0.004 1:0.102 6:0.143 7:0.034 8:0.710 11:0.001 15:0.002
tified, and values of en/ are given just above and below each edge to facilitate accurate interpolation. The data were based on unrenormalized Scofield7 theoretical val-
15:0.103 16:0.002 16:0.003 16:0.002 16:0.002 17:0.001 16:0.003 16:0.003
16:0.003 20:0.225 17:0.002 19:0.002 17:0.001 17:0.002 19:0.002 17:0.001 17:0.003 19:0.002 17:0.002 19:0.003
16:0.002 17:0.003 19:0.002 26:0.001 16:0.002 17:0.003 19:0.003 16:0.003 17:0.001 19:0.004
ues of photoeffect cross-sections. The earlier compilation by Hubbell1 was based on the application of renormalization factors given by Scofield. An evaluation by Salo-
Table 2. Zeff values for total photon-energy absorption and photon interaction for cortical bone, ovary, and eye lens Cortical Bone
Ovary
Eye Lens
Energy (McV)
ZPEAeff
ZPIeff
ZPEAeff
ZPIeff
ZPEAeff
ZPIeff
0.10000E-02 0.10721E-02 0.10721E-02 0.15000E-02 0.20000E-02 0.21455E-02 0.21455E-02 0.24720E-02 0.24720E-02 0.28224E-02 0.28224E-02 0.30000E-02 0.40000E-02 0.40381E-02 0.40381E-02 0.50000E-02 0.60000E-02 0.80000E-02 0.10000E-01 0.15000E-01 0.20000E-01 0.30000E-01 0.40000E-01 0.50000E-01 0.60000E-01 0.80000E-01 0.10000E⫹00 0.15000E⫹00 0.20000E⫹00 0.30000E⫹00 0.40000E⫹00 0.50000E⫹00 0.60000E⫹00 0.80000E⫹00 0.10000E⫹01 0.12500E⫹01 0.15000E⫹01 0.20000E⫹01 0.30000E⫹01 0.40000E⫹01 0.50000E⫹01 0.60000E⫹01 0.80000E⫹01 0.10000E⫹02 0.15000E⫹02 0.20000E⫹02
6.8986 6.8515 6.8480 6.9870 7.0387 7.7807 7.0617 8.4366 8.4243 — — 7.9532 8.0546 10.0139 8.0536 10.2440 10.3889 10.6034 10.7452 10.9600 11.0897 11.2382 11.2985 11.3187 11.1951 10.7271 9.8286 7.4453 6.5604 6.1354 6.1374 6.0449 6.0135 5.9992 5.9872 5.9830 5.9757 5.9738 5.9982 6.0831 6.1949 6.3076 6.4131 6.5928 6.7312 6.9463
6.9007 6.9191 6.9156 — 7.0381 7.8060 7.0526 7.8961 7.8741 — — 7.9804 8.0808 10.2659 8.0804 10.4362 10.5471 10.7046 10.7990 10.9332 10.9576 10.7951 10.3829 9.7510 9.0716 7.7691 7.0402 6.3663 6.1869 6.0541 6.0410 6.0069 5.9963 6.0042 5.9000 5.9947 5.9942 6.0242 6.1045 6.1992 6.2977 6.3926 6.5604 6.7040 6.9631 7.1329
5.8312 5.8594 5.8541 5.9191 5.9812 6.0047 5.9922 6.0477 6.0297 6.0923 6.0720 6.1031 6.1786 — — 6.2147 6.2442 — 6.3170 6.4574 6.3848 6.3540 6.1877 5.8508 5.3207 4.2923 3.8100 3.4955 3.4385 3.4126 3.4082 3.4059 3.4049 3.4034 3.4029 3.4029 3.4010 3.4109 3.4454 3.4941 3.5457 3.5938 3.6921 3.7750 3.9289 4.0297
5.8333 5.8078 5.8046 — 5.9824 6.0126 5.9990 6.0460 6.0443 6.0862 6.0672 6.1061 6.1786 — — 6.2113 6.2331 6.2514 6.2497 6.1454 5.9213 5.1591 4.4240 3.9936 3.7862 3.5838 3.5030 3.4545 3.4275 3.4135 3.4112 3.4068 3.4098 3.4058 3.4084 3.4067 3.4084 3.4187 3.4512 3.4918 3.5374 3.5797 3.6649 3.7496 3.8979 4.0034
5.7922 5.7676 5.7652 5.8848 5.9336 5.9570 5.9510 6.0403 6.0377 6.0182 6.0084 6.0344 6.0785 — — 6.1092 6.1343 6.1700 6.1959 6.3327 6.2508 6.2115 5.7759 5.7248 5.2143 4.2852 3.8608 3.5871 3.5325 3.5110 3.5061 3.5049 3.5037 3.5025 3.5009 3.5010 3.5013 3.5083 3.5436 3.5874 3.6377 3.6853 3.7731 3.8553 3.9962 4.0917
5.7942 5.8171 5.8143 — 5.9343 5.9504 5.9441 5.9920 5.9692 6.0243 6.0138 6.0858 6.0747 — — 6.1028 6.1209 6.1336 6.1284 6.0196 5.8122 5.0814 4.4161 4.0301 3.8468 3.6649 3.5390 3.5478 3.5274 3.5077 3.5084 3.5036 3.5091 3.5050 3.5065 3.5056 3.5072 3.5175 3.5471 3.5868 3.6307 3.6693 3.7498 3.8282 3.9693 4.0660
Effective atomic numbers for photon energy absorption ● SHIVARAMU
3
Table 3. Zeff values for total photon-energy absorption and photon interaction for breast tissue, soft tissue, (4 component), and adipose tissue Breast Tissue
Soft Tissue (4-component)
Adipose Tissue
Energy (MeV)
ZPEAeff
ZPIeff
ZPEAeff
ZPIeff
ZPEAeff
ZPIeff
0.10000E-02 0.10721E-02 0.10721E-02 0.15000E-02 0.20000E-02 0.28224E-02 0.28224E-02 0.30000E-02 0.40000E-02 0.50000E-02 0.60000E-02 0.80000E-02 0.10000E-01 0.15000E-01 0.20000E-01 0.30000E-01 0.40000E-01 0.50000E-01 0.60000E-01 0.80000E-01 0.10000E⫹00 0.15000E⫹00 0.20000E⫹00 0.30000E⫹00 0.40000E⫹00 0.50000E⫹00 0.60000E⫹00 0.80000E⫹00 0.10000E⫹01 0.12500E⫹01 0.15000E⫹01 0.20000E⫹01 0.30000E⫹01 0.40000E⫹01 0.50000E⫹01 0.60000E⫹01 0.80000E⫹01 0.10000E⫹02 0.15000E⫹02 0.20000E⫹02
5.5422 — — 5.6426 5.6965 — — 5.7965 5.8360 5.8632 5.8848 5.9144 5.9348 6.0419 5.9732 5.9359 5.7649 5.3709 4.8184 3.9412 3.5775 3.3513 3.3082 3.2900 3.2867 3.2855 3.2838 3.2825 3.2823 3.2823 3.2806 3.2879 3.3193 3.3603 3.4029 3.4488 3.5312 3.6045 3.7376 3.8283
5.5425 — — — 5.6968 — — 5.7970 5.8313 5.8553 5.8708 5.8801 5.8715 5.7539 5.4907 4.7001 4.0701 3.7269 3.5700 3.4211 3.3568 3.3233 3.3055 3.2916 3.2858 3.2866 3.2879 3.2843 3.2870 3.2856 3.2869 3.2956 3.3232 3.3585 3.3977 3.4335 3.5075 3.5797 3.7125 3.8040
5.8551 — — 5.9464 5.9942 — — 6.0603 6.0998 6.1269 6.1486 6.1801 6.2030 6.3327 6.2472 6.2012 6.0249 5.6967 5.1713 4.2324 3.8072 3.5366 3.4818 3.4607 3.4584 3.4547 3.4537 3.4529 3.4522 3.4525 3.4515 3.4595 3.4954 3.5399 3.5928 3.6409 3.7358 3.8184 3.9658 4.0630
5.8580 — — 5.9465 5.9943 — — 6.0579 6.0942 6.1171 6.1324 6.1422 6.1327 6.0175 5.8035 5.0481 4.3704 3.9905 3.7958 3.6202 3.5533 3.4957 3.4745 3.4636 3.4614 3.4584 3.4581 3.4572 3.4564 3.4569 3.4583 3.4688 3.5008 3.5398 3.5816 3.6263 3.7094 3.7853 3.9369 4.0458
5.1235 5.1034 5.0996 5.2146 5.2649 5.3373 5.3248 5.3513 5.3928 5.4228 5.4465 5.4807 5.5049 5.5638 5.5470 5.4731 5.2181 4.7695 4.2207 3.5256 3.2711 3.1188 3.0889 3.0769 3.0755 3.0739 3.0731 3.0717 3.0711 3.0714 3.0706 3.0763 3.1021 3.1351 3.1721 3.2081 3.2764 3.3385 3.4556 3.5344
5.1259 5.1474 5.1473 5.2152 5.2647 5.3395 5.3252 5.3405 5.3865 5.4100 5.4266 5.4289 5.4057 5.2358 4.9285 4.1441 3.6300 3.3913 3.2722 3.1716 3.1301 3.0966 3.0856 3.0792 3.0764 3.0760 3.0743 3.0736 3.0735 3.0735 3.0749 3.0819 3.1048 3.1332 3.1649 3.1970 3.2581 3.3136 3.4309 3.5167
man et al.8 compared the theoretical values with the measured-value database, and concluded that overall agreement was better without this renormalization. The ZPEAeff values are compared with calculated ZPIeff data and the single ZXMUDATeff value directly obtained from the program XmuDat.9 The effect of absorption edge on effective atomic numbers, and its variation with photon energy and the possibility of defining 2 set values of effective atomic numbers below the absorption edges of elements present in some tissues from human organs are discussed. The reasons for using ZPEAeff rather than the commonly used ZPIeff in medical radiation dosimetry for the calculation of absorbed dose in radiation therapy are discussed. EFFECTIVE ATOMIC NUMBER CALCULATIONS The procedure of calculating the ZPEAeff by direct method involves finding the atomic number that corresponds to
the en/ in the composite material on a plot of atomic number vs. the en/ for the elements. The en/ of the elements does not consistently vary with the atomic number. For smoother interpolation, the cross-section of the elements vs. the atomic number is preferred. The en/ values are then converted in to atomic energyabsorption cross-section (en) by dividing its en/ with the number of atoms present in one gram of that material: en ⫽
en/ N A⌺w i/A i
(1)
where wi is the fraction by weight, Ai is the atomic weight of the ith atomic constituent, and Na is Avogadro’s number. The ZPEAeff can then be obtained from an energy absorption cross-section plot as a function of the atomic number of the element by interpolating the number that corresponds to the cross-section per atom of the composite substance. In this work, the en/ values of the tissues from human organs are taken from compila-
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Volume 27, Number 1, 2002
Table 4. Zeff values for total photon-energy absorption and photon interaction for lung tissue, testis, and soft tissue Lung Tissue
Testis
Soft Tissue
Energy (MeV)
ZPEAeff
ZPIeff
ZPEAeff
ZPIeff
ZPEAeff
ZPIeff
0.10000E-02 0.10721E-02 0.10721E-02 0.15000E-02 0.20000E-02 0.21455E-02 0.21455E-02 0.2472E-02 0.2472E-02 0.28224E-02 0.28224E-02 0.30000E-02 0.36074E-02 0.36074E-02 0.40000E-02 0.50000E-02 0.60000E-02 0.80000E-02 0.10000E-01 0.15000E-01 0.20000E-01 0.30000E-01 0.40000E-01 0.50000E-01 0.60000E-01 0.80000E-01 0.10000E⫹00 0.15000E⫹00 0.20000E⫹00 0.30000E⫹00 0.40000E⫹00 0.50000E⫹00 0.60000E⫹00 0.80000E⫹00 0.10000E⫹01 0.12500E⫹01 0.15000E⫹01 0.20000E⫹01 0.30000E⫹01 0.40000E⫹01 0.50000E⫹01 0.60000E⫹01 0.80000E⫹01 0.10000E⫹02 0.15000E⫹02 0.20000E⫹02
5.8335 5.8119 5.8065 5.9333 5.9823 6.0056 5.9926 6.0547 6.0304 6.1133 6.0824 6.1241 6.1866 6.1559 6.2013 6.2391 6.2703 6.3137 6.3459 6.4869 6.4178 6.3894 6.2290 5.8943 5.3751 4.3420 3.8509 3.5304 3.4690 3.4408 3.4370 3.4334 3.4323 3.4300 3.4307 3.4299 3.4290 3.4378 3.4749 3.5206 3.5737 3.6226 3.7201 3.8019 3.9571 4.0563
5.8369 5.8614 5.8560 5.9336 5.9825 6.0135 5.9996 6.0470 6.0440 6.1058 6.0776 6.1270 6.1876 6.1609 6.2030 6.2351 6.2577 6.2807 6.2789 6.1801 5.9566 5.2026 4.4659 4.0394 3.8163 3.6183 3.5394 3.4755 3.4549 3.4439 3.4393 3.4373 3.4357 3.4351 3.4347 3.4347 3.4357 3.4465 3.4790 3.5202 3.5630 3.6084 3.6932 3.7693 3.9256 4.0373
5.8175 5.7964 5.7915 5.9191 5.9694 5.9926 5.9870 6.0437 6.0421 6.0637 6.0446 6.0744 6.1415 6.1159 6.1552 6.1911 6.2202 6.2613 6.2921 6.4330 6.3591 6.3264 6.1573 5.8196 5.2842 4.2596 3.7860 3.4785 3.4181 3.3937 3.3898 3.3866 3.3856 3.3847 3.3846 3.3837 3.3833 3.3904 3.4264 3.4731 3.5266 3.5755 3.6704 3.7543 3.9071 4.0075
5.8195 5.8463 5.8409 — 5.9703 5.9860 5.9802 6.0251 6.0071 6.0698 6.0494 6.0826 6.1391 6.1095 6.1548 6.1868 6.2088 6.2253 6.2239 6.1178 5.8941 5.1242 4.3923 3.9650 3.7602 3.5616 3.4829 3.4345 3.4104 3.3941 3.3893 3.3883 3.3906 3.3870 3.3890 3.3882 3.3892 3.4005 3.4319 3.4720 3.5177 3.5594 3.6432 3.7276 3.8767 3.9831
5.7998 5.7783 5.7732 5.8995 5.9497 5.9845 5.9673 6.0437 6.0412 6.0649 6.0455 6.0826 — — 6.1742 6.2783 6.2448 6.2906 6.3237 6.4670 6.3994 6.3728 6.2130 5.8800 5.3605 4.3349 3.8467 3.5292 3.4668 3.4419 3.4368 3.4342 3.4324 3.4305 3.4298 3.4300 3.4293 3.4365 3.4732 3.5198 3.5700 3.6195 3.7139 3.7977 3.9485 4.0475
5.8018 5.8278 5.8212 — 5.9506 5.9786 5.9602 6.0261 5.9986 6.0727 6.0512 6.0858 — — 6.1766 6.2116 6.2355 6.2571 6.2580 6.1585 5.9379 5.1889 4.4568 4.0269 3.8157 3.6133 3.5310 3.4834 3.4592 3.4385 3.4363 3.4349 3.4375 3.4339 3.4358 3.4347 3.4357 3.4465 3.4790 3.5183 3.5638 3.6048 3.6878 3.7716 3.9174 4.0230
tion of Hubbell and Seltzer.6 The weight fractions of the organs and tissues are given in Table 1 and as per ICRU44. Similarly, we have obtained the ZPIeff using / and total photon interaction cross-sections following the procedure given elsewhere.4 Because of the small uncertainties in constructing the plots and in the interpolation, the error in the derived ZPEAeff and ZPIeff is found to be negligibly small. The effective atomic numbers, based on the program XMuDat (ZXMUDATeff), are directly obtained. XMuDat9 is a program for the presentation and calculation of various photon interaction coefficients. RESULTS AND DISCUSSION The calculated results of ZPEAeff and ZPIeff at various photon energies are given in Tables 2– 4, and their vari-
ation with energy is shown in Figs.1– 6. The variation of ZPEAeff and ZPIeff with energy is approximately similar for all of the substances studied, except for the abrupt changes near the absorption edges. The ZPEAeff and ZPIeff values steadily increase up to 8 –50 keV, and then steadily decrease up to 1.25–2.0 MeV for all tissues studied. From 2.0 MeV, the values rise with increase in energy, up to 20 MeV. Significant differences exist between ZPIeff and the ZPEAeff in the energy region of 20 – 400 keV and 3–20 MeV for cortical bone; 15–150 keV for soft tissue, ovary, testis, blood, brain, lung, and skeletal muscle; 15–100 keV for breast tissue, eye lens, and soft tissue (4-component); and 10 –100 keV for adipose tissue. A maximum difference of 28.37% at 100 keV for cortical bone, and 30.43% at 40 keV for adipose
Effective atomic numbers for photon energy absorption ● SHIVARAMU
5
Table 5. Zeff values for total photon-energy absorption and photon interaction for blood (whole), brain (grey/white matter), and skeletal muscle Blood, Whole
Brain, Grey/White Matter
Skeletal Muscle
Energy (MeV)
ZPEAeff
ZPIeff
ZPEAeff
ZPIeff
ZPEAeff
ZPIeff
0.10000E-02 0.10721E-02 0.10721E-02 0.15000E-02 0.20000E-02 0.24720E-02 0.24720E-02 0.28224E-02 0.28224E-02 0.30000E-02 0.36074E-02 0.36074E-02 0.40000E-02 0.50000E-02 0.60000E-02 0.80000E-02 0.10000E-01 0.15000E-01 0.20000E-01 0.30000E-01 0.40000E-01 0.50000E-01 0.60000E-01 0.80000E-01 0.10000E⫹00 0.15000E⫹00 0.20000E⫹00 0.30000E⫹00 0.40000E⫹00 0.50000E⫹00 0.60000E⫹00 0.80000E⫹00 0.10000E⫹01 0.12500E⫹01 0.15000E⫹01 0.20000E⫹01 0.30000E⫹01 0.40000E⫹01 0.50000E⫹01 0.60000E⫹01 0.80000E⫹01 0.10000E⫹02 0.15000E⫹02 0.20000E⫹02
5.8419 5.8175 5.8148 5.9374 5.9863 6.0458 6.0441 6.0937 6.0652 6.1112 — — 6.1871 6.2233 6.2534 6.3251 6.3616 6.5091 6.4480 6.4294 6.2772 5.9456 5.4363 4.3899 3.8819 3.5489 3.4827 3.4555 3.4500 3.4473 3.4457 3.4451 3.4438 3.4435 3.4423 3.4519 3.4879 3.5343 3.5874 3.6378 3.7336 3.8162 3.9680 4.0674
5.8440 5.8671 5.8644 — 5.9830 6.0459 6.0277 6.1006 6.0694 6.1142 — — 6.1877 6.2207 6.2427 6.3009 6.3047 6.2120 5.9895 5.0237 4.5077 4.0648 3.8468 3.6366 3.5490 3.4967 3.4714 3.4551 3.4520 3.4482 3.4514 3.4475 3.4499 3.4479 3.4496 3.4607 3.4933 3.5340 3.5791 3.6204 3.7067 3.7892 3.9385 4.0440
5.7531 5.7327 5.7276 5.8571 5.9090 6.0373 6.0389 6.0251 5.9973 6.0428 6.1206 6.0807 6.1364 6.1766 6.2096 6.2569 6.2912 6.4380 6.3690 6.3417 6.1764 5.8361 5.2955 4.2496 3.7619 3.4477 3.3843 3.3602 3.3563 3.3526 3.3519 3.3508 3.3510 3.3499 3.3488 3.3583 3.3928 3.4368 3.4903 3.5383 3.6330 3.7150 3.8653 3.9651
5.7565 5.7819 5.7763 5.8575 5.9093 5.9663 5.9810 6.0326 6.0014 6.0471 6.1223 6.0772 6.1394 6.1740 6.1983 6.2217 6.2219 6.1213 5.8970 5.1137 4.3704 3.9478 3.7272 3.5341 3.4577 3.3949 3.3767 3.3619 3.3573 3.3569 3.3558 3.3547 3.3543 3.3548 3.3555 3.3667 3.3973 3.4291 3.4797 3.5235 3.6053 3.6813 3.8359 3.9454
5.8024 5.8279 5.8251 5.8985 5.9485 6.0168 5.9916 6.0522 6.0414 6.0620 6.1528 6.0912 6.1644 6.2055 6.2368 6.2834 6.3165 6.4613 6.3924 6.3662 6.2064 5.8742 5.3540 4.3307 3.8439 3.5291 3.4648 3.4398 3.4359 3.4324 3.4313 3.4300 3.4285 3.4299 3.4290 3.4398 3.4719 3.5173 3.5702 3.6190 3.7122 3.7957 3.9462 4.0431
5.8056 5.7784 5.7756 5.8998 5.9491 6.0429 6.0404 6.0458 6.0364 6.0645 6.1507 6.0972 6.1702 6.2036 6.2270 6.2507 6.2498 6.1519 5.9326 5.1778 4.4487 4.0284 3.8095 3.6145 3.5374 3.4755 3.4549 3.4439 3.4393 3.4363 3.4349 3.4343 3.4337 3.4336 3.4351 3.4465 3.4781 3.5173 3.5597 3.6036 3.6865 3.7619 3.9158 4.0255
tissue, is observed. For ovary, eye lens, testis, breast tissue, lung tissue, soft tissue, soft tissue (4-component), blood (whole), brain (grey/white matter), and skeletal muscle, a maximum difference of 31.74%, 29.60%, 31.87%, 30.61%, 31.47%, 31.52%, 29.95%, 31.63%, 32.36%, and 31.42%, respectively, is seen at 50 keV. The energy positions at which the maximum of ZPEAeff and ZPIeff occurs differ, and are shown in Figs. 1– 6 and Tables 2– 4. The single ZXMUDATeff values are found to be significantly higher compared to those of ZPEAeff and ZPIeff values in the energy region of interest for all tissues and organs studied, as shown in Figs. 1– 6. The variation of ZPEAeff with energy may be attributed to the relative domination of the partial processes, viz., photoelectric effect, coherent scattering, incoherent scattering, and pair production. At low energies, the
photoelectric effect is dominant and hence the ZPEAeff for the energy- absorption is mainly described by the ZPEAeff for this partial process. Similarly, at higher energies, the contribution due to scattering and pair-production process will be more in comparison with photoelectric effect, and this will have its effect on the ZPEAeff for photon-energy absorption. Hence, at low energies, where photoelectric effect dominates, the ZPEAeff value is more; and at higher energies, where the scattering and pair production process dominates, the ZPEAeff value is less. Therefore, the ZPEAeff for photon-energy absorption varies from a higher value at lower energies to a lower value at higher energies, with a peak, due to photoelectric effect, around the absorption edge of the constituent element of the composite substance studied, depending on the relative domination of one gamma-ray process
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Medical Dosimetry
Volume 27, Number 1, 2002
Fig. 1. Variation of effective atomic numbers for photon-energy absorption ZPEAeff and photon interaction ZPIeff with photon energy for cortical bone and soft tissue. The effective atomic number ZXMUDATeff, obtained from the XmuDat program, is also plotted.
Fig. 2. Variation of effective atomic numbers for photon-energy absorption ZPEAeff and photon interaction ZPIeff with photon energy for blood and adipose tissue. The effective atomic number ZXMUDATeff, obtained from the XMuDat program, is also plotted.
Effective atomic numbers for photon energy absorption ● SHIVARAMU
Fig. 3. Variation of effective atomic numbers for photon-energy absorption ZPEAeff and photon interaction ZPIeff with photon energy for ovary and breast tissue. The effective atomic number ZXMUDATeff, obtained from the XMuDat program, is also plotted.
Fig. 4. Variation of effective atomic numbers for photon-energy absorption ZPEAeff and photon interaction ZPIeff with photon energy for testis and eye lens. The effective atomic number ZXMUDATeff, obtained from the XMuDat program, is also plotted.
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Medical Dosimetry
Volume 27, Number 1, 2002
Fig. 5. Variation of effective atomic numbers for photon-energy absorption ZPEAeff and photon interaction ZPIeff with photon energy for brain and soft tissue (4- component). The effective atomic number ZXMUDATeff, obtained from the XMuDat program, is also plotted.
Fig. 6. Variation of effective atomic numbers for photon-energy absorption ZPEAeff and photon interaction ZPIeff with photon energy for lung and skeletal muscle. The effective atomic number ZXMUDATeff, obtained from the XMuDat program, is also plotted.
Effective atomic numbers for photon energy absorption ● SHIVARAMU
over the other. The variation of ZPIeff as a function of energy can be explained in the same manner. In Fig. 1, it is shown that the variation of ZPEAeff and ZPIeff with energy below the absorption edge of the calcium element present in the cortical bone tissue is not uniform. Because of the nonuniform variation of crosssection with atomic number at a particular energy, it is possible to get more than one ZPEAeff and ZPIeff value for a given substance. We have calculated the ZPEAeff and ZPIeff values at the absorption-edge energies of the constituent elements of the tissues from human organs, and generated two ZPEAeff and ZPIeff values at each absorption edge, one corresponding to the cross-section on the lower side and the other to the higher side (Figs. 1– 6, Tables 2–5). The oscillations seen in Fig. 1 are due to the 2 ZPEAeff and ZPIeff values, one low and one high (corresponding to the lower and higher cross sections) for the same energy. CONCLUSIONS This work reported new data on ZPEAeff and ZPIeff, calculated by direct method in the energy region of 1 keV to 20 MeV, for selected human tissues from organs and of dosimetric interest, such as cortical bone, breast tissue, ovary, eye lens, testis, and soft tissue. The ZPEAeff and ZPIeff values vary from a higher value at lower energies to a lower value at higher energies, with a peak due to photoelectric effect, around the absorption edge of the constituent of the substance. Because of the nonuniform variation of cross-section with atomic number at a particular energy, it was possible to generate more than one ZPEAeff and ZPIeff value for a given substance. The energy positions at which the maximum of ZPEAeff and ZPIeff occurs differ. Significant differences up to 32.36% exist between ZPIeff and the ZPEAeff in the energy region around 50 keV. The single ZXMUDATeff values obtained
9
from the program XMuDat are found to be higher compared to those of ZPEAeff and ZPIeff values in the energy region of interest, for all tissues from human organs studied. Because significant differences exist between ZPEAeff and ZPIeff, and the former represents the absorbed dose, it is preferable to use ZPEAeff instead of the commonly used ZPIeff for the calculation of absorbed dose in radiation therapy. It is expected that the new data on ZPEAeff and ZPIeff presented here will be useful, particularly in the energy region of interest, in view of their importance in medical dosimetry. Also, to the best knowledge of the author, these data are the first of their kind at these energies. REFERENCES 1. Hubbell, J.H. Photon mass attenuation and energy- absorption coefficients from 1 keV to 20 MeV. Int. J. Appl. Radiat. Isot. 33:1269 –90; 1982. 2. Jackson, D.F.; Hawkes, D. J. X-ray attenuation coefficients of elements and mixtures. Phys. Reports 70:169; 1981. 3. White, D.R. An analysis of the Z-dependence of photon and electron interactions. Phys. Med. Biol. 22:219; 1977. 4. Shivaramu; Amutha, R.; Ramprasath, V. Effective atomic numbers and mass attenuation coefficients of some thermoluminescent dosimetric compounds for total photon interaction. Nucl. Sci. Eng. 132:148 –53; 1999. 5. Shivaramu; Ramprasath, V. Effective atomic numbers for photonenergy absorption and energy dependence of some thermoluminescent dosimetric compounds. Nucl. Inst. Meth. B168:294 –304; 2000. 6. Hubbell, J.H.; Seltzer, S.M. Tables of X-ray mass attenuation coefficients and mass energy-absorption coefficients 1 keV to 20 MeV for elements Z ⫽ 1 to 92 and 48 additional selected substances of dosimetric interest. NISTIR–5632; 1995. 7. Scofield, J.H. Theoretical photoionization cross sections from 1 to 1500 keV. Lawrence Livermore Laboratory Report UCRL–51326; 1973. 8. Saloman, E.B.; Hubbell, J.H.; Scofield, J.H. X-ray attenuation cross sections for energies 100 eV to 100 keV and elements Z ⫽ 1 to Z ⫽ 92. Atomic Data and Nuclear Data Tables 38:1–197; 1988. 9. Nowotny, R. XMuDat: Photon attenuation data on PC. IAEA– NDS–195; 1998.