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Absorbed dose estimates at the cellular level for 131I
ARTICLE IN PRESS
Applied Radiation and Isotopes 62 (2005) 861–869 www.elsevier.com/locate/apradiso
Absorbed dose estimates at the cellular level for
131
I
Perihan Unaka,, Berkan Cetinkayab a
Department of Nuclear Applications, Institute of Nuclear Sciences, Ege University, Bornova, Izmir 35100, Turkey b Abdus Salam ICTP, Strada Costiera 11, 34014 Trieste, Italy Received 31 March 2004; received in revised form 2 June 2004; accepted 1 July 2004
Abstract Microdosimetric calculations of 131I have been evaluated for a single cell and for cell clusters. A VsBasic program has been used to calculate stopping power, linear energy transfer, range values and deposited energies per decay for beta particles, Auger and conversion electrons of 131I. The chemical composition of the cell has been taken into account in this model; results were compared with water medium. Besides, total absorbed doses have been calculated for the radionuclides distributed randomly within the cell and clusters. Cross-fire irradiation has been considered for clusters of cells. In this case, absorbed doses per cell within a cluster were found to be significantly higher than absorbed doses per single cell, depending on the cluster size. Results showed that 131I is a promising radionuclide for therapy of tumors from millimeter to centimeter dimensions. r 2004 Published by Elsevier Ltd. Keywords: Microdosimetry;
131
I; Cell; Beta particles; Internal conversion electrons; Auger electrons
1. Introduction To optimize the efficacy of targeted radiotherapy, one should use ideal carrier molecule and radionuclide combinations to deliver the highest tumor doses and lowest normal-tissue doses. Radionuclides with particulate emissions such as alpha, beta, Auger and Coster Kronig electrons have therapeutic potentials in cellular ranges. The type of emitted particle required for a particular application will depend on the distribution of the radiopharmaceutical relative to the target sites. It was demonstrated that, while beta-emitting radionuclides can be effectively curative within a membrane surface of cells by antibodies, Auger electron emitters should be incorporated into DNA for efficient ther-
Corresponding author.
E-mail address: [email protected] (P. Unak). 0969-8043/$ - see front matter r 2004 Published by Elsevier Ltd. doi:10.1016/j.apradiso.2004.07.013
apeutic effect (Hofer et al., 1975; Humn et al., 1994). However, some reports indicated treatment of Auger nuclides independent of receptor density, heterogeneity and location next to the cytoplasm of the cell (Thakur et al., 2003). A number of experimental reports evaluated the therapeutic effects of Auger nuclides on cancer cells (Chen et al., 2003; Kassis, 2003; Thakur et al., 2003; Zweit, 1996). There are also several reports maintaining the cross-fire phenomena, i.e. a cell in the vicinity of the cell irradiated not only by beta particles but also by Auger electrons will be influenced by the radiation. It was suggested that Auger nuclides may be most valuable for the treatment of small-volume metastatic tumors (Chen et al., 2003; Kassis, 2003). 131 I, which has 8-day physical half-life, is clinically used as a beta-emitting therapeutic radionuclide of iodine. Govindan et al. reported that beta-particle emitters had considerably higher levels of non-specific toxicity than the Auger electron emitters. On the other
ARTICLE IN PRESS 862
P. Unak, B. Cetinkaya / Applied Radiation and Isotopes 62 (2005) 861–869
hand, 131I had higher levels of specificity than other high-energy beta-particle emitters. They demonstrated that Auger electron emitters were much less toxic than beta-particle emitters, on mice. Although it seemed that Auger electron emitters had advantages for cancer therapy, in particular 131I should not be eliminated for clinical use in antibodies called LL1 conjugates according to Govindan, since 131I is more potent than most of the Auger emitters and its specificity index is comparable with some other Auger electron emitters like 111In (Govindan et al., 2000). A microdosimetric approach in cellular dimensions has been considered for 131I in this study. Generally, microdosimetric approaches assume the cell to be composed of water, whereas the electron stopping power properties of a cell are different from those of water. For this reason, the microscopic energy deposition within the cell from beta particles, Auger and conversion electrons released by 131I have been calculated with the consideration of the estimated elemental composition of the cell. This model has been previously applied as a QBASIC program to other Auger emitters, alpha-emitting and beta-emitting radionuclides such as 125I, 201Tl, 204Tl, 51 Cr, 211At, and results obtained have agreed with those in the literature (Unak and Unak, 1988, 1995; Unak and Selvi, 1995; Unak et al., 1995; Unak et al., 1997; Unak, 1997; Unak et al., 2005). According to this method, the stopping power and the linear energy transfer (LET) value of a chemical mixture or chemical compound largely depend on the percentage atomic weights of the medium. Ranges, total deposited energies and dose values were computed after calculations of stopping powers and LET values of medium atoms.
2. Calculational method VsBasic program has been used in calculations because it is a friendly programming language which can be used under Windows. The program has been used earlier for dose calculations of 186Re and 188Re earlier (Unak et al., 2005). Total emitted energy per decay, absorbed energy fragments per cell, stopping powers, LET values and ranges were calculated. On the other hand, absorbed energy values have been calculated for random decays per cell proportional with decay constants. Results were compared with other studies. Radionuclide decay data were obtained from NUDAT (http://www-nds.iaea.org/nudat/radform.html). A cell was assumed as a sphere of 5000 nm radius filled with chemical composition mathematically. Cell volume and weight were supposed to be 5.23 10 10 cm3 and 5.23 10 10 g, respectively (Hofer et al., 1975). The cell includes many organic molecules including oxygen, nitrogen and phosphorous atoms that incorporated proteins, fats and sugar molecules as well as water
molecules. Although the cell and water molecule consist of atoms of low atomic weights, for example a water molecule contains hydrogen and oxygen and the cell additionally includes some other atoms like carbon, nitrogen and phosphorous. Therefore, a chemical composition of each cell was considered in this model. Data for chemical composition of the cell were taken from the International Commission on Radiation Units and Measurement (ICRU) Report 44 (ICRU Report 44, 1989). Radionuclides were supposed to be distributed randomly inside the cell. It was assumed that one decomposition occurs in 1 h within the cell. This is the activity of 0.00028 Bq/cell. Starting from single-radionuclide decay, a Monte Carlo calculation program has been applied for cumulative calculations of the dose absorption by a cell as functions of decay times and radioactivities of 131I. The basic principle of these calculations is random distribution of the radionuclides within the cell, and random determination of those radionuclides that decay within the decay period considered. For these calculations, the Monte Carlo program has randomly determined the position of each radionuclide within the nucleus. The program has randomly chosen the decaying radionuclides; it has found the emission direction of each particle and the distance covered by each particle within the nucleus. So, the partial energy absorption per decay and the total absorption corresponding to the number of decayed radionuclides in the cell during the decay time period have been calculated. Cross-fire irradiation has been considered for clusters of cells. The same cluster model and sizes used by Hartman et al. were used for our calculations (Hartman et al., 2000), except that 131I was suggested to be homogenously spread over the whole cell in our study. On the other hand, we used 131I electron spectra of Nudat.
3. Results and discussion Table 1 presents electron energy spectra, radiation intensity, cell doses, calculated and NUDAT’s Di (gGy/ MBq-h) values of 131I. The total emitted-electron numbers and the emitted electron energies of 131I are given in Table 2. The total emitted energy is 192.546 keV. Beta particles, Auger electrons and conversion electrons emit 182.737, 0.323 and 9.485 keV, respectively. Table 3 compares total emitted electron numbers and emitted electron energies per decomposition with other Auger nuclides and b-decay radionuclides like 201Tl, 204 Tl, 55Fe, 51Cr, and 99mTc. Although 131I has fewer emitted electrons, it emits higher electron energies compared to Auger nuclides.
ARTICLE IN PRESS P. Unak, B. Cetinkaya / Applied Radiation and Isotopes 62 (2005) 861–869 Table 1 Electron energy spectra, radiation intensity, cell doses and Di (gGy/MBq-h) values of Rad. type
Energy (E) (eV)
Radiation intensity (W)
E W (eV)
1b 2b 3b 4b 5b 6b 7 AU 8 AU 9 CE 10 CE 11 CE 12 CE 13 CE 14 CE 15 CE 16 CE 17 CE 18 CE 19 CE 20 CE 21 CE 22 CE 23 CE 24 CE 25 CE 26 CE 27 CE 28 CE 29 CE 30 CE 31 CE 32 CE 33 CE 34 CE 35 CE 36 CE 37 CE 38 CE 39 CE 40 CE 41 CE 42 CE 43 CE 44 CE 45 CE 46 CE 47 CE 48 CE 49 CE 50 CE 51 CE 52 CE 53 CE 54 CE 55 CE
69,360 86,940 96,620 19,1580 20,0220 28,3240 3430 24600 45623.6 51340 74732.2 79043 79977 80450 84760 85690 142652.6 171761.2 176072 177006 197620 226730 231040 231970 237937 249744 261240 267045 267840 271356 272290 278852 283163 283527 284097 290090 290350 291228 294660 296950 301260 312635 316946 317880 319200 320336 323510 323840 324440 324647 325581 329928 352950 357260 358190
0.021 0.00651 0.0727 0.899 0.0005 0.0048 0.051 0.00604 0.0354 0.0000013 0.00464 0.00094 0.000239 0.0000004 0.00000011 0.00000003 0.000507 0.000114 0.0000237 0.00000574 0.0000025 0.00000048 0.0000001 0.000000025 0.0000264 0.00252 0.00000017 0.00000358 0.00000042 0.00000072 0.000000179 0.000439 0.00009 0.0000236 0.0000221 0.000006 0.00000002 0.000078 0.000000004 0.000000053 0.00000001 0.00000303 0.00000061 0.000000155 0.00000085 0.0000101 0.00000017 0.0000034 0.000000042 0.00000203 0.00000052 0.0155 0.0000005 0.0000001 0.000000025
1456.56 244.4264 565.9794 63.28434 7024.274 657.0315 172230.42 5119.859 100.11 2.772812 1359.552 22.22464 174.93 170.1176 148.584 90.57717 1615.07544 575.3266 0.066742 0.019349 346.757408 50.70833 74.30042 9.864628 19.114503 2.484795 0.03218 0.004136 0.0093236 0.001091 0.0025707 0.000295 72.3248682 3.457152 19.5807768 0.692256 4.1729064 0.141606 1.01601444 0.034315 0.49405 0.01396 0.1088304 0.002483 0.023104 0.00051 0.00579925 0.000128 6.2815368 0.131913 629.35488 12.36391 0.0444108 0.000821 0.9560211 0.01698 0.1124928 0.001991 0.19537632 0.003399 0.04873991 0.000838 122.416028 2.046346 25.48467 0.41561 6.6912372 0.108484 6.2785437 0.101402 1.74054 0.027325 0.005807 9.1E-05 22.715784 0.356961 0.00117864 1.82E-05 0.01573835 0.000239 0.0030126 4.49E-05 0.94728405 0.013362 0.19333706 0.00268 0.0492714 0.000678 0.27132 0.003707 3.2353936 0.044089 0.0549967 0.000737 1.101056 0.01479 0.01362648 0.000183 0.65903341 0.0089 0.16930212 0.002242 5113.884 67.01181 0.176475 0.002082 0.035726 0.000415 0.00895475 0.000104
Given energy to cell (eV)
863
131
I
Di (cell) (gGy/ MBq h)
Di (water) (gGy/MBq h)
NUDAT Di (gGy/MBq h)
0.000142815 3.69763E 05 0.000383896 0.002991472 1.62012E 06 1.29856E 05 9.93977E 05 5.29232E 05 0.000336156 1.13051E 08 2.96283E 05 5.76378E 06 1.45184E 06 2.4169E 09 6.37294E 10 1.72575E 10 2.01997E 06 4.04477E 07 8.27387E 08 2.00499 08 8.15654E 09 1.45069E 09 2.98202E 10 7.45128E 11 7.7075E 08 7.22408E 06 4.79581E 10 9.92114E 09 1.16332E 09 1.98589E 09 4.89555E 10 1.19566E 06 2.42836E 07 6.33862E 08 5.92478E 08 1.59657E 08 5.3194E 11 2.08568E 07 1.06249E 11 1.39485E 10 2.62093E 11 7.80714E 09 1.566E 09 3.96369E 10 2.16596E 09 2.57609E 08 4.30396E 10 8.64141E 09 1.07061E 10 5.20023E 09 1.3098E 09 3.91542E 05 1.21632E 09 2.4252E 10 6.0573E 11
0.0008511 0.0003307 0.0041042 0.1006322 5.849E 05 0.0007944 0.0001022 8.682E 05 0.0009437 3.9E 08 0.0002026 4.341E 05 1.117E 05 1.88E 08 5.448E 09 1.502E 09 4.226E 05 1.144E 05 2.438E 06 5.936E 07 2.887E 07 6.359E 08 1.35E 08 3.388E 09 3.67E 06 0.0003677 2.595E 08 5.586E 07 6.573E 08 1.142E 07 2.848E 08 7.153E 05 1.489E 05 3.91E 06 3.668E 06 1.017E 06 3.393E 09 1.327E 05 6.887E 10 9.196E 09 1.76E 09 5.535E 07 1.13E 07 2.879E 08 1.585E 07 1.89E 06 3.213E 08 6.433E 07 7.962E 09 3.851E 07 9.892E 08 0.002988 1.031E 07 2.087E 08 5.232E 09
0.000837838 0.000324324 0.004054054 0.099189189 5.40541E-05 0.000783784 0.000108108 8.10811E 05 0.000918919 0 0.000189189 5.40541E 05 0 0 0 0 5.40541E 05 0 0 0 0 0 0 0 0 0.000351351 0 0 0 0 0 8.10811E 05 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.002945946 0 0 0
ARTICLE IN PRESS P. Unak, B. Cetinkaya / Applied Radiation and Isotopes 62 (2005) 861–869
864 Table 1 (continued ) Rad. type
Energy (E) (eV)
Radiation intensity (W)
E W (eV)
56 CE 57 CE 58 CE 59 CE 60 CE 61 CE 62 CE 63 CE 64 CE 65 CE 66 CE 67 CE 68 CE 69 CE 70 CE Total
359036 363347 364281 370253 399361 403672 404606 468443 497551 602428 608158 631536 637266 688350 717458
0.00246 0.000507 0.000123 0.0000083 0.00000115 0.00000024 0.00000006 0.0000269 0.00000389 0.000288 0.0000085 0.0000395 0.00000117 0.00007 0.0000087 1.125702583
883.22856 10.23361 184.216929 2.089591 44.806563 0.511337 3.0730999 0.034008 0.45926515 0.004594 0.09688128 0.000954 0.02427636 0.000237 12.6011167 0.101066 1.93547339 0.014385 173.499264 1.003691 5.169343 0.029717 24.945672 0.136823 0.74560122 0.004035 48.1845 0.237391 6.2418846 0.029413 192545.8685 7110.158
Given energy to cell (eV)
Table 2 Total emitted electron numbers and emitted electron energies for
131
I
Di (cell) (gGy/ MBq h)
Di (water) (gGy/MBq h)
NUDAT Di (gGy/MBq h)
5.97937E 06 1.22092E 06 2.98768E 07 1.98706E 08 2.68402E 09 5.57371E 10 1.3872E 10 5.90519E 08 8.40481E 09 5.86445E 07 1.73634E 08 7.99442E 08 2.35759E 09 1.38705E 07 1.71856E 08 0.00415438
0.0005161 0.0001076 2.618E 05 1.796E 06 2.683E 07 5.661E 08 1.418E 08 7.363E 06 1.131E 06 0.0001014 3.02E 06 1.458E 05 4.356E 07 2.815E 05 3.647E 06 0.1125022
0.000513514 0.000108108 0 0 0 0 0 0 0 0.000108108 0 0 0 2.7027E 05 0 0.110783784
131
I
Total b-
Total Eb Wb (keV)
Tot. Auger
Total EAuger WAuger (keV)
Total conversion
Total EconWcon (keV)
Total electron
Total EW (keV)
1.00451 89.23%
182.737 94.91%
0.05704 5.07%
0.323 0.17%
0.06415 5.70%
9.485 4.93%
1.12570
192.546
Table 4 shows the percentages of absorbed electron energies within the cell and water medium from beta particles, conversion electrons and Auger electrons of 131 I. The absorbed energy per decay of 131I is 7.110 keV/ cell (3.69% of the total released energy). On the other hand, if the cell composition is assumed to be water, the absorbed energy is 1.521 keV/water (0.79% of the total released energy). The deposited energy is 4.68 times higher in the cell compared to water composition. For example, 85.93% (6.109 keV) of absorbed energy comes from beta particles, 3.67% (0.261 keV) of absorbed energy comes from Auger electrons and 10.41% (0.740 keV) of absorbed energy comes from conversion electrons within a cell. If the cell volume is assumed to be water 77.97% (1.186 keV) of absorbed energy comes from beta particles, 12.46% (0.190 keV) of absorbed energy comes from Auger electrons and 9.57% (0.146 keV) of absorbed energy comes from conversion electrons. Consequently, cells deposit higher energy than water according to our model. Figs. 1–3 represent energies versus distance for beta particles, conversion electrons and Auger electrons of 131 I. Beta particles deposit only 3.34% and 0.65%, conversion electrons gives 7.80% and 1.53%, while
Auger electrons deposit 80.58% and 58.62% of energies in cellular dimensions and water in the same volume of the cell, respectively. Results show that the cellular dose is lower than the total emitted electron energies for 131I. Whereas dose distribution is not homogenous at the cellular dimension, Auger electrons deposit most of their energies within the cell. Conversion electrons and beta particles deposit a lesser amount of their energies compared to Auger electrons. On the other hand, there is heterogeneity of dose distribution since Auger electrons give a considerable dose in cellular dimension. Consequently, 3.69% and 0.79% of the total emitted energy of 131I is absorbed within a single cell and within water of the same volume as the cell, respectively. On the other hand, in water medium, mean ranges are longer than in the cell medium (Figs. 1–3). Calculated mean ranges and stopping power values were compared with Berger’s ESTAR program and data were well fitted for water (Berger, 1992; Berger, http://physics.nist.gov/ PhysRefData/Star/Text/contents.html). However, calculated stopping power and range data were found to be elevated in cell medium (Fig. 4). According to Table 5, 7.110 keV/cell (3.69% of emitted energy), 5.898 keV/cell (1.76% of emitted
ARTICLE IN PRESS P. Unak, B. Cetinkaya / Applied Radiation and Isotopes 62 (2005) 861–869
Table 3 Total emitted-electron numbers and emitted-electron energies per decay
I Re
186
188
Re
201
Tl
204
Tl
55
Fe
51
Cr
99m
Tc
1.125703 (this study) 1.17 (Unak et al., 2005)
1.19 (Unak et al., 2005)
20.68 (Unak et al, 1997) 20 (Rao et al., 1985)
1.10 (Unak et al., 1997)
5.341 (Unak et al., 1997) 4.75 (Humn et al., 1994) 5.420 (Unak et al., 1997) 5.42 (Kassis et al., 1985) 5.15 (Unak et al., 1997) 5.13(Makrigiorgos et al., 1989)
keV/decay
100000
10000 1.00E+00
192.546 (this study) 335.739 (Unak et al., 2005) 326.1 (Bardies and Chatal, 1994) 777.878 (Unak et al., 2005) 777.0 (Bardies and Chatal, 1994) 768 (Nahum, 1996) 44.748 (Unak et al., 1997) 43.3 (Kassis et al., 1983) 43.5 (Ftacnikova and Bohm, 2000) 245.219 (Unak et al., 1997) 243 (Kassis et al., 1983) 5.803 (Unak et al., 1997) 4.0471.66 (Humn et al., 1994) 3.652 (Unak et al., 1997) 3.65 (Vezza et al., 1987) 17.286 (Unak et al., 1997) 17.28 (Makrigiorgos et al., 1989) 16.2 (Ftacnikova and Bohm, 2000)
1.00E-01
1.00E-02
Beta Cell
Beta Water
Fig. 1. Beta-particle energies as a function of distance from decay center for beta particles of 131I. I-131 Auger
100000
Cell 10000 Nucleus 1000 1.00E-02
1.00E-03
1.00E-04
1.00E-05
1.00E-06
Distance from Decay Center (cm) AU Cell
AU Water
Fig. 2. Auger electron energies as a function of distance from decay center for Auger electrons of 131I. I-131 CE
1000000
100000
10000 1.00E+00
1.00E-01
1.00E-02
1.00E-03
1.00E-04
Distance from Decay Center (cm) CE Cell
CE Water
Fig. 3. Conversion electron energies as a function of distance from decay center for CE electrons of 131I.
Table 4 Absorbed electron energies and percent ratios of absorbed energies within cell and water medium of Cell
Absorbed energy (keV) %
1.00E-03
Distance from Decay Center (cm)
Energy (eV)
131
Total electron numbers
I-131 Beta
1000000
Energy (eV)
Radionuclides
Such results show that if the aim is to irradiate selectively very small volumes, Auger nuclides should be preferred. On the other hand, absorbed energies decrease if the water composition is used in place of cell composition. While 7.110 keV/decay is accumulated by a
Energy (eV)
energy), and 4.874 kev/cell (0.63 of emitted energy) are deposited from 131I, 186Re and 188Re, respectively. 201Tl gives 19.040 keV per cell (42.52% of the emitted energy). On the other hand, 204Tl gives only 7.170 keV to a cell, which is 2.92% of the total energy. As a result, while 201 Tl can irradiate only a volume of a few cell diameters, 131 204 I, Tl, 186Re and 188Re can irradiate larger volumes.
865
131
I
Water
Beta
Auger
CE
Total
Beta
Auger
CE
Total
6.109 85.93
0.261 3.67
0.740 10.41
7.110 100
1.186 77.97
0.190 12.46
0.146 9.57
1.521 100
ARTICLE IN PRESS P. Unak, B. Cetinkaya / Applied Radiation and Isotopes 62 (2005) 861–869 1000000
1000
Energy (eV)
2
Stopping Power (MeVcm /g)
866
100
10
1 1000
10000
100000
1000000
100000
10000
1000 1.00E+00
1.00E-01
ESTAR
Our water model
1.00E-02
1.00E-03
1.00E-04
1.00E-05
1.00E-06
Range (cm)
Energy (eV) Our Cell Model
ESTAR
Our Water Model
Our Cell Model
Fig. 4. Calculated stopping powers versus energy and energy versus range for cell and water.
Table 5 Deposited energy per cell per decay Radionuclides
keV/decay/cell
keV/decay/cell keV/cell (accepted as water)
131
7.110 (this study)a 5.898 (Unak et al., 1997)a 4.874 (Unak et al., 1997)a 19.040 (Unak et al., 1997)a
1.521 (this study)b
I
186
Re
188
Re
201
Tl
204
Tl
7.170 (Unak et al., 1997)a
55
Fe
5.517 (Unak et al., 1997)a
51
3.529 (Unak et al., 1997)a
Cr
99m
Tc
3.560 (Unak et al., 1997)a
1.578 (Unak et al., 1997)b 1.219 (Unak et al., 1997)b 13.031 (Unak et al., 1997)b 14 (Kassis et al., 1983) 13.8 (Ftacnikova and Bohm, 2000) 1.752 (Unak et al., 1997)b 1.5 (Rao et al., 1983) 4.860 (Unak et al., 1997)b 3.99 (Rao et al., 1985) 3.207 (Unak et al., 1997)b 3.43 (Kassis et al., 1985) 2.656 (Unak et al., 1997)b 2.6 (Ftacnikova and Bohm, 2000)
a
Deposited energy was calculated according to chemical composition (16). b Deposited energy was calculated for water with the same volume as the cell.
cell, 1.521 keV/decay is given to the same volume of water from 131I. We found that 5.898 and 1.578 keV/ decay are deposited in the cell and water from 186Re, respectively, while, 4.874 keV/decay and 1.219 keV/ decay is given to the cell and to water in cellular volume from 188Re, respectively.
Table 6 compares the dose rates to the cell per unit cumulated activity in gGy/MBq-h. 131I has a similar dose rate to that of 204Tl. The dose rates of the cell per unit cumulated activity of some other radionuclides like 201 Tl are higher than those for 131I, 186Re and 188Re. These calculated values have been found to be significantly smaller in water medium. The total accumulated dose rates per unit cumulated activity were calculated with the supposition of the medium as water and without considering cell dimension. Similar results with NUDAT and Van Dieren were found for 186Re (NUDAT (http://www-nds.iaea.org/nudat/radform. html); ICRU Report 44, 1989; Hartman et al., 2000; Van Dieren et al., 1996). In the case of 131I, we found 0.004154 gGy/MBq h that is slightly higher total accumulated dose rates per unit cumulated activity within the cell for 186Re and 188Re (0.003446 for 186Re and 0.002848 for 188Re). Fig. 5 shows the variations of doses absorbed from beta particles, Auger and conversion electrons in a cell for 131I activity of 0.000278 Bq (one decomposition occurs in 1 h). The total and partial dose absorptions increase as a function of decay time. Most of the absorbed doses come from beta particles; however, conversion and Auger electrons deposit significant amounts of absorbed dose over time. Edmont reported that to treat cancer successfully with 131 I-labeled antibodies, a total of 20–90 Gy must be delivered to the tumor (Edmont et al., 1992). We computed 0.0021 Gy/h absorbed dose rate for 0.00028 Bq/cell activity, and then calculated the crucial activities to achieve 20 or 90 Gy, which is the necessary activity to treat the tumor over time. Fig. 6 represents the decreasing activity of Bq to achieve 20–90 Gy total doses over time. In 1 h, 2.5 and 12 times more activity is needed to achieve 20 and 90 Gy doses, according to our supposed activity. However, if the effective half-life of the 131I-labeled compound in a cell is accepted as 24 h, 0.13 and 0.6 times, less activity is able to achieve 20–90 Gy according to our suggested activity (0.000278 Bq/cell).
ARTICLE IN PRESS P. Unak, B. Cetinkaya / Applied Radiation and Isotopes 62 (2005) 861–869
867
Table 6 Dose rates into the cell per unit cumulated activities for cell and water Radionuclide
gGy/MBq-h (cell volume)
gGy/MBq-h (cell volume, accepted as water)
Total gGy/MBq-h (water)
131
0.004154 (this study)
0.000889 (this study)
0.1125022 (this study) 0.110783784 (NUDAT) 0.1164 (Van Dieren, et al.,1996)
186
0.003446 (Unak)
0.000922 (Unak et al., 2005)
0.196169 (Unak et al., 2005) 0.193135 (NUDAT) 0.1979 (Van Dieren, et al., 1996)
188
0.0028480 (Unak)
0.0007125 (Unak et al., 2005)
0.4545048 (Unak et al., 2005) 0.4485946 (NUDAT)
201
0. 0111 (Unak, 1997)
0.007613 (Unak et al., 1997)
0.02614 (Unak et al., 1997) 0.02135 (Nass, 1977; Rao et al., 1983)
204
Tl
0.00419 (Unak, 1997)
0.001023 (Unak et al., 1997)
55
Fe
0.00322 (Unak, 1997)
0.002840 (Unak et al., 1997)
0.1433 (Unak et al., 1997) 0.1370 (Rao et al., 1983) 0.00339 (Unak et al., 1997) 0.00332 (Robertson et al., 1983)
51
0.002062 (Unak, 1997)
0.001874 (Unak et al., 1997)
0.0021 (Unak et al., 1997) 0.0027 (Vezza et al., 1987) 0.00308 (Kassis et al., 1985)
0.002083 (Unak, 1997)
0.001552 (Unak et al., 1997)
0.0101 (Unak et al., 1997)
I
Re
Re Tl
Cr
99m
Tc
I-131 14
0.60
12
0.50 0.40
Total
0.30
Beta
0.20
Auger
Activity (Bq)
Absorbed Dose (Gy)
I-131 0.70
20 Gy
8
90 Gy
6 4 2
CE
0.10
10
0 0
10
0.00 100
200
300
400
500
600
700
800
900
Time (h)
Fig. 5. Partial-dose absorptions from beta particles, Auger and conversion electrons of 131I in the cell.
Cross-fire effect provides considerable doses to adjacent cells in radionuclide therapy. It follows that the radiation dose received by any individual cell is a resultant of cross-fire radiation emitted from radionuclide targeted to adjacent cells as well as radiation from radionuclide taken up by the cell itself. Hartman et al. investigated dose distributions of subcellular 131I and influence of the cell size and cross-fire irradiation in clusters of cells. They reported that cross-fire irradiation can be a major contributor to the nuclear dose in clusters of more than six cells (Hartman et al., 2000). We applied Hartman’s cluster size and cell numbers to our model. The absorbed dose increased 6–12 times for beta particles and 7–17 times for internal conversion
20
30
40
50
Time (h)
1000
Fig. 6. Decreasing activities of Bq to achieve 20–90 Gy total doses over time.
20 15 Rate
0
10 CE
5 0
Beta 51 cell
173 cell
Auger 800 cell
Fig. 7. Cross-fire irradiation effect for several cluster sizes for Auger, beta, and conversion electrons of 131I.
ARTICLE IN PRESS P. Unak, B. Cetinkaya / Applied Radiation and Isotopes 62 (2005) 861–869
868
40 µm radius cluster (Cell medium)
60
40 µm radius cluster (Water medium)
70
(51 cells)
50 40
Total
30
Beta Auger
20
CE
10 0
Absorbed Dose (Gy)
Absorbed Dose (Gy)
70
60
(51 cells)
50 40
Total
30
Beta Auger
20
CE
10 0
0
20
40
60
80
100
120
0
20
Time (h)
40
60
80
100
120
Time (h)
Fig. 8. Cross-fire irradiation effect for 51 cell numbered cluster sizes for Auger, beta, and conversion electrons of 131I for cell and water medium.
electrons, while the absorbed dose did not change for Auger electrons, when cluster size increased from 51 to –800 cells in our work (Fig. 7). According to Hartman, total doses increase from 6 to 13 times for with the expanding size of clusters from 51 to 800 cells for beta particles. However, for internal conversion electrons, total doses increase from 8 to 20 times for the same size of clusters. Although random distributions of radionuclides were proposed in clusters in our study, point sources were taken by Hartman (Hartman et al., 2000). The dimension of the tumor is very important in cross-fire effect. For very small tumors (micrometastases) whose diameter is less than particle range, absorption of radiation energy is inefficient, a proportion of this energy being deposited outside the tumor. This indicates that very small microtumors may be underdosed (and hence less easily cured) than slightly larger ones (Wheldon, 2000). O’Donoghue et al. have shown that the optimal tumor size (diameter) is slightly greater than the mean particle range for each radionuclide (O’Donoghue et al., 1995). According to this consideration, medium-range beta emitters like 131I (mean range is 0.70 mm) would be ideal for treatment of small tumors (from millimeter to centimeter dimensions) as for larger macroscopic tumors, but would be (relatively) less effective in the treatment of very small micrometastases. Total absorbed doses were similar when the medium was accepted as water, like Hartman’s, for 24 h (0.0087 Gy/decay in Hartman’s work and 0.01 Gy/decay in our work). However, the total absorbed dose has been found to be significantly higher than Hartman’s cell composition (0.05 Gy/decay). Fig. 8 shows cross-fire irradiation effect for 51 cell numbered cluster sizes for Auger, beta, and conversion electrons of 131I in cell clusters and in water of the same volume as the cell cluster. Total absorbed doses are ~4.5 times higher in cell clusters than in water. Although most of the absorbed doses are generated by beta particles in both media, Auger electron doses are higher in cell clusters than in water medium.
4. Conclusion Conversion and Auger electrons contribute considerable doses to total absorbed doses especially in cellular range for 131I, although it has fewer Auger electrons than most of the Auger nuclides. Significant differences were found between water and cell compositions in cell dimensions. Therefore, real or equivalent atomic compositions should be taken into consideration in microdosimetric considerations. On the other hand, cross-fire irradiation supplied doses of significant amounts for clusters. Consequently, 131I has a good potential for radionuclide tumor therapy. Because the particular ranges of the internal conversion electrons and beta particles are much higher than cellular dimension, it is better for therapy of tumors which are millimeter to centimeter dimension rather than micrometastases. Although the contributions of Auger electron and conversion electrons to total doses are minor, they should be considered especially in cellular dimensions.
Acknowledgment The authors have received a grants from the Abdus Salam ICTP as a regular associate (P. Unak) and a young collaborate (B. Cetinkaya) during a part of the work. The authors thank the Abdus Salam ICTP for the support given.
References Bardies, M., Chatal, J.F., 1994. Absorbed doses for internal radiotherapy from 22 beta-emitting radionuclides: beta dosimetry of small spheres. Phys. Med. Biol. 39, 961–981. Berger, M.J., ESTAR: stopping powers and ranges for electrons http://physics.nist.gov/PhysRefData/Star/Text/contents.html.
ARTICLE IN PRESS P. Unak, B. Cetinkaya / Applied Radiation and Isotopes 62 (2005) 861–869 Berger, M.J., 1992. ESTAR, PSTAR and ASTAR: Computer codes for calculating stopping power and range tables for electrons, protons and helium ions, National Institute of standards and Technology Report NISTIR 4999. Chen, P., Cameron, R., Wang, J., Vallis, K., Reilly, R.M., 2003. Antitumor effects and normal tissue toxicity of 111Inlabeled epidermal growth factor administered to athymic mice bearing epidermal growth factor receptor positive human breast cancer xenografts. J. Nucl. Med. 44 (9), 1469–1478. Edmont, T.H., Fisher, D.R., Press, O.W., Eary, J.F., Weinstein, J.N., Badger, C.C., Bernstein, I.D., 1992. Localized beta dosimetry of 131I-labeled antibodies in follicular lymphoma. Med. Phys. 19 (1), 97–104. Ftacnikova, S., Bohm, R., 2000. Monte Carlo calculations of energy deposition on cellular, multicellular and organ level for Auger emitters. Radiat. Protect. Dosim. 92 (4), 279–288. Govindan, S.V., Goldenberg, D.M., Elsamra, S.E., Griffins, G.L., Ong, G.L., Brechbirl, M.W., Burton, J., Sgiuoros, G., Mattes, M.L., 2000. Radionuclides linked to a CD74 antibody as therapeutic agents for B-cell lymphoma: comparison of Auger electron emitters with b-particle emitters. J. Nucl. Med. 41 (12), 2012–2089. Hartman, T., Lundqvist, H., Westlin, J.E., Carlsson, J., 2000. Radiation doses to the cell nucleus in single cells and cells in microtetastases in targeted therapy with 131I labeled ligands or antibodies. Int. J. Radiat. Oncol. Biol. Phys. 46 (4), 1025–1036. Hofer, K.G., Harris, C.R., Smith, J.M., 1975. Radiotoxicity of intracellular Ga-67, I-125, and H-3: nuclear versus cytoplasmic effects in murine leukemia. Int. J. Radiat. Biol. 28, 225–241. Humn, J.L., Howell, R. W., Rao, D.V., 1994. Dosimetry of Auger electrons-emitting radionuclides, Report No 3 of AAPM N Nuclear Medicine Task Group No. 6. Med. Phys. 21(12), 1901–1915. International Commission on Radiation Units and Measurements, 1989. Tissue substitutes in radiation dosimetry and measurement, ICRU Report 44, 22pp. Kassis, A.I., 2003. Cancer therapy with Auger electrons: are we almost there? J. Nucl. Med. 44 (9), 1479–1481. Kassis, A.I., Adelstein, S.J., Haydock, C., Sastry, K.S.R., 1983. Thalium 201: an experimental and a theoretical radiobiological approach to dosimetry. J. Nucl. Med. 24, 1164–1175. Kassis, A.I., Sastry, K.S.R., Adelstein, S.J., 1985. Intracellular distribution and radiotoxicity of chromium-51 in mammalian cells: Auger electron dosimetry. J. Nucl. Med. 26, 59–67. Makrigiorgos, G., Adelstein, S.J., Kassis, A.I., 1989. Limitations of conventional internal dosimetry at the cellular level. J. Nucl. Med. 30, 1856–1864. Nahum, A.E., 1996. Microdosimetry and radiocurability: modeling targeted therapy with b-emitters. Phys. Med. Biol. 41, 1957–1972. Nass, H.W., 1977. New T1-201 nuclear decay data. J. Nucl. Med. 18, 1047–1048.
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NUDAT. http://www-nds.iaea.org/nudat/radform.html. O’Donoghue, J.A., Bardies, M., Wheldon, T.E., 1995. Relationship between tumor size and curability for targeted radionuclide therapy. J. Nucl. Med. 36, 1902–1909. Rao, D.V., Govelitz, G.F., Sastry, K.S.R., 1983. Radiotoxity of Thalium-201 in mouse testis: Inadequacy of conventional dosimetry. J. Nucl. Med. 24, 145–153. Rao, D.V., Sastry, K.S.R., Govelitz, G.F., Grimmond, H.E., 1985. In vivo effects of Iron-55 and Iron-59 on mouse testes: biophysical dosimetry of Auger electrons. J. Nucl. Med. 26, 1456–1465. Robertson, J.S., Price, R.R., Budinger, T.F., Fairbanks, V.F., Pollycove, M., 1983. Radiation absorbed doses from iron52, iron-55 and iron-59 used to study ferrokinetics. J. Nucl. Med. 24, 339–348. Thakur, M.L., Coss, R., Howell, R., Vassileva-Belnikoloska, D., Liu, J., Rao, S., Spana, G., Wachsberger, P., Leeper, D.L., 2003. Role of lipid soluble complexes in targeted tumor therapy. J. Nucl. Med. 44, 1293–1300. Unak, P., Unak, T., 1988. Microscopic energy absorption of the DNA molecules from Auger electrons of Iodine-125. Appl. Radiat. Isot. 39 (10), 1037–1040. Unak, P., Cetinkaya, B., Unak, I., 2005. Absorbed dose estimates at the cellular level for 186Re and 188Re. Radiat. Phys. Chem., in press. Unak, P., Ipek, I., Unak, T., 1997. Microdosimetry of Auger and conversion electrons of 201Tl, 51Cr, 55Fe, 99mTc and beta-rays of 204Tl at the cellular level. Phys. Med. 13 (Suppl. 1), 166–168. Unak, T., 1997. Calculations of microscopic energy deposition from Auger electrons, within the cell nucleus. Radiat. Prot. Dosim. 74 (3), 183–188. Unak, T., Selvi, S., 1995. Microdosimetry of tritium and C-14 in different materials. Appl. Radiat. Isot. 46 (6-7), 559–560. Unak, T., Unak, P., 1995. Monte-Carlo simulation method for microscopic dose calculations within the cell nucleus, third International Symposium on Biophysical Aspects of Auger Processes. August 24–25, 1995, University of Lund, Sweden. Unak, T., Ongun, B., Unak, P., Kumru, M.N., 1995. Comparison of the calculated and measured stopping powers of low-energy Auger electrons in different metals. Appl. Radiat. Isot. 46 (6/7), 561–562. Van Dieren, E.B., Plaizier, M.A.B.D., Van lingen, A., Roos, J.C., Barendsen, G.W., Teule, G.J.J., 1996. Absorbed-dose distribution of the Auger emitters 67Ga and 125I and the bemitters, 67Cu, 90Y and 186Re as a function of tumor size, uptake, and intracellular distribution. Int. J. Radiat. Oncol. Biol. Phys. 36 (1), 197–204. Vezza, M., Giuliani, D., Rao, D.V., Morse, B.S., 1987. Chromium-51 dosimetry of lymphocytes labeled incidentally during nuclear medicine procedures. Nucl. Med. Biol. 14, 75–77. Wheldon, T.E., 2000. Radiation physics and genetic targeting: new directions for radiotherapy. Phys. Med. Biol. 45, R77–R95. Zweit, J., 1996. Radionuclide and carrier molecules for therapy. Phys. Med. Biol. 41, 1905–1914.
Applied Radiation and Isotopes 62 (2005) 861–869 www.elsevier.com/locate/apradiso
Absorbed dose estimates at the cellular level for
131
I
Perihan Unaka,, Berkan Cetinkayab a
Department of Nuclear Applications, Institute of Nuclear Sciences, Ege University, Bornova, Izmir 35100, Turkey b Abdus Salam ICTP, Strada Costiera 11, 34014 Trieste, Italy Received 31 March 2004; received in revised form 2 June 2004; accepted 1 July 2004
Abstract Microdosimetric calculations of 131I have been evaluated for a single cell and for cell clusters. A VsBasic program has been used to calculate stopping power, linear energy transfer, range values and deposited energies per decay for beta particles, Auger and conversion electrons of 131I. The chemical composition of the cell has been taken into account in this model; results were compared with water medium. Besides, total absorbed doses have been calculated for the radionuclides distributed randomly within the cell and clusters. Cross-fire irradiation has been considered for clusters of cells. In this case, absorbed doses per cell within a cluster were found to be significantly higher than absorbed doses per single cell, depending on the cluster size. Results showed that 131I is a promising radionuclide for therapy of tumors from millimeter to centimeter dimensions. r 2004 Published by Elsevier Ltd. Keywords: Microdosimetry;
131
I; Cell; Beta particles; Internal conversion electrons; Auger electrons
1. Introduction To optimize the efficacy of targeted radiotherapy, one should use ideal carrier molecule and radionuclide combinations to deliver the highest tumor doses and lowest normal-tissue doses. Radionuclides with particulate emissions such as alpha, beta, Auger and Coster Kronig electrons have therapeutic potentials in cellular ranges. The type of emitted particle required for a particular application will depend on the distribution of the radiopharmaceutical relative to the target sites. It was demonstrated that, while beta-emitting radionuclides can be effectively curative within a membrane surface of cells by antibodies, Auger electron emitters should be incorporated into DNA for efficient ther-
Corresponding author.
E-mail address: [email protected] (P. Unak). 0969-8043/$ - see front matter r 2004 Published by Elsevier Ltd. doi:10.1016/j.apradiso.2004.07.013
apeutic effect (Hofer et al., 1975; Humn et al., 1994). However, some reports indicated treatment of Auger nuclides independent of receptor density, heterogeneity and location next to the cytoplasm of the cell (Thakur et al., 2003). A number of experimental reports evaluated the therapeutic effects of Auger nuclides on cancer cells (Chen et al., 2003; Kassis, 2003; Thakur et al., 2003; Zweit, 1996). There are also several reports maintaining the cross-fire phenomena, i.e. a cell in the vicinity of the cell irradiated not only by beta particles but also by Auger electrons will be influenced by the radiation. It was suggested that Auger nuclides may be most valuable for the treatment of small-volume metastatic tumors (Chen et al., 2003; Kassis, 2003). 131 I, which has 8-day physical half-life, is clinically used as a beta-emitting therapeutic radionuclide of iodine. Govindan et al. reported that beta-particle emitters had considerably higher levels of non-specific toxicity than the Auger electron emitters. On the other
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hand, 131I had higher levels of specificity than other high-energy beta-particle emitters. They demonstrated that Auger electron emitters were much less toxic than beta-particle emitters, on mice. Although it seemed that Auger electron emitters had advantages for cancer therapy, in particular 131I should not be eliminated for clinical use in antibodies called LL1 conjugates according to Govindan, since 131I is more potent than most of the Auger emitters and its specificity index is comparable with some other Auger electron emitters like 111In (Govindan et al., 2000). A microdosimetric approach in cellular dimensions has been considered for 131I in this study. Generally, microdosimetric approaches assume the cell to be composed of water, whereas the electron stopping power properties of a cell are different from those of water. For this reason, the microscopic energy deposition within the cell from beta particles, Auger and conversion electrons released by 131I have been calculated with the consideration of the estimated elemental composition of the cell. This model has been previously applied as a QBASIC program to other Auger emitters, alpha-emitting and beta-emitting radionuclides such as 125I, 201Tl, 204Tl, 51 Cr, 211At, and results obtained have agreed with those in the literature (Unak and Unak, 1988, 1995; Unak and Selvi, 1995; Unak et al., 1995; Unak et al., 1997; Unak, 1997; Unak et al., 2005). According to this method, the stopping power and the linear energy transfer (LET) value of a chemical mixture or chemical compound largely depend on the percentage atomic weights of the medium. Ranges, total deposited energies and dose values were computed after calculations of stopping powers and LET values of medium atoms.
2. Calculational method VsBasic program has been used in calculations because it is a friendly programming language which can be used under Windows. The program has been used earlier for dose calculations of 186Re and 188Re earlier (Unak et al., 2005). Total emitted energy per decay, absorbed energy fragments per cell, stopping powers, LET values and ranges were calculated. On the other hand, absorbed energy values have been calculated for random decays per cell proportional with decay constants. Results were compared with other studies. Radionuclide decay data were obtained from NUDAT (http://www-nds.iaea.org/nudat/radform.html). A cell was assumed as a sphere of 5000 nm radius filled with chemical composition mathematically. Cell volume and weight were supposed to be 5.23 10 10 cm3 and 5.23 10 10 g, respectively (Hofer et al., 1975). The cell includes many organic molecules including oxygen, nitrogen and phosphorous atoms that incorporated proteins, fats and sugar molecules as well as water
molecules. Although the cell and water molecule consist of atoms of low atomic weights, for example a water molecule contains hydrogen and oxygen and the cell additionally includes some other atoms like carbon, nitrogen and phosphorous. Therefore, a chemical composition of each cell was considered in this model. Data for chemical composition of the cell were taken from the International Commission on Radiation Units and Measurement (ICRU) Report 44 (ICRU Report 44, 1989). Radionuclides were supposed to be distributed randomly inside the cell. It was assumed that one decomposition occurs in 1 h within the cell. This is the activity of 0.00028 Bq/cell. Starting from single-radionuclide decay, a Monte Carlo calculation program has been applied for cumulative calculations of the dose absorption by a cell as functions of decay times and radioactivities of 131I. The basic principle of these calculations is random distribution of the radionuclides within the cell, and random determination of those radionuclides that decay within the decay period considered. For these calculations, the Monte Carlo program has randomly determined the position of each radionuclide within the nucleus. The program has randomly chosen the decaying radionuclides; it has found the emission direction of each particle and the distance covered by each particle within the nucleus. So, the partial energy absorption per decay and the total absorption corresponding to the number of decayed radionuclides in the cell during the decay time period have been calculated. Cross-fire irradiation has been considered for clusters of cells. The same cluster model and sizes used by Hartman et al. were used for our calculations (Hartman et al., 2000), except that 131I was suggested to be homogenously spread over the whole cell in our study. On the other hand, we used 131I electron spectra of Nudat.
3. Results and discussion Table 1 presents electron energy spectra, radiation intensity, cell doses, calculated and NUDAT’s Di (gGy/ MBq-h) values of 131I. The total emitted-electron numbers and the emitted electron energies of 131I are given in Table 2. The total emitted energy is 192.546 keV. Beta particles, Auger electrons and conversion electrons emit 182.737, 0.323 and 9.485 keV, respectively. Table 3 compares total emitted electron numbers and emitted electron energies per decomposition with other Auger nuclides and b-decay radionuclides like 201Tl, 204 Tl, 55Fe, 51Cr, and 99mTc. Although 131I has fewer emitted electrons, it emits higher electron energies compared to Auger nuclides.
ARTICLE IN PRESS P. Unak, B. Cetinkaya / Applied Radiation and Isotopes 62 (2005) 861–869 Table 1 Electron energy spectra, radiation intensity, cell doses and Di (gGy/MBq-h) values of Rad. type
Energy (E) (eV)
Radiation intensity (W)
E W (eV)
1b 2b 3b 4b 5b 6b 7 AU 8 AU 9 CE 10 CE 11 CE 12 CE 13 CE 14 CE 15 CE 16 CE 17 CE 18 CE 19 CE 20 CE 21 CE 22 CE 23 CE 24 CE 25 CE 26 CE 27 CE 28 CE 29 CE 30 CE 31 CE 32 CE 33 CE 34 CE 35 CE 36 CE 37 CE 38 CE 39 CE 40 CE 41 CE 42 CE 43 CE 44 CE 45 CE 46 CE 47 CE 48 CE 49 CE 50 CE 51 CE 52 CE 53 CE 54 CE 55 CE
69,360 86,940 96,620 19,1580 20,0220 28,3240 3430 24600 45623.6 51340 74732.2 79043 79977 80450 84760 85690 142652.6 171761.2 176072 177006 197620 226730 231040 231970 237937 249744 261240 267045 267840 271356 272290 278852 283163 283527 284097 290090 290350 291228 294660 296950 301260 312635 316946 317880 319200 320336 323510 323840 324440 324647 325581 329928 352950 357260 358190
0.021 0.00651 0.0727 0.899 0.0005 0.0048 0.051 0.00604 0.0354 0.0000013 0.00464 0.00094 0.000239 0.0000004 0.00000011 0.00000003 0.000507 0.000114 0.0000237 0.00000574 0.0000025 0.00000048 0.0000001 0.000000025 0.0000264 0.00252 0.00000017 0.00000358 0.00000042 0.00000072 0.000000179 0.000439 0.00009 0.0000236 0.0000221 0.000006 0.00000002 0.000078 0.000000004 0.000000053 0.00000001 0.00000303 0.00000061 0.000000155 0.00000085 0.0000101 0.00000017 0.0000034 0.000000042 0.00000203 0.00000052 0.0155 0.0000005 0.0000001 0.000000025
1456.56 244.4264 565.9794 63.28434 7024.274 657.0315 172230.42 5119.859 100.11 2.772812 1359.552 22.22464 174.93 170.1176 148.584 90.57717 1615.07544 575.3266 0.066742 0.019349 346.757408 50.70833 74.30042 9.864628 19.114503 2.484795 0.03218 0.004136 0.0093236 0.001091 0.0025707 0.000295 72.3248682 3.457152 19.5807768 0.692256 4.1729064 0.141606 1.01601444 0.034315 0.49405 0.01396 0.1088304 0.002483 0.023104 0.00051 0.00579925 0.000128 6.2815368 0.131913 629.35488 12.36391 0.0444108 0.000821 0.9560211 0.01698 0.1124928 0.001991 0.19537632 0.003399 0.04873991 0.000838 122.416028 2.046346 25.48467 0.41561 6.6912372 0.108484 6.2785437 0.101402 1.74054 0.027325 0.005807 9.1E-05 22.715784 0.356961 0.00117864 1.82E-05 0.01573835 0.000239 0.0030126 4.49E-05 0.94728405 0.013362 0.19333706 0.00268 0.0492714 0.000678 0.27132 0.003707 3.2353936 0.044089 0.0549967 0.000737 1.101056 0.01479 0.01362648 0.000183 0.65903341 0.0089 0.16930212 0.002242 5113.884 67.01181 0.176475 0.002082 0.035726 0.000415 0.00895475 0.000104
Given energy to cell (eV)
863
131
I
Di (cell) (gGy/ MBq h)
Di (water) (gGy/MBq h)
NUDAT Di (gGy/MBq h)
0.000142815 3.69763E 05 0.000383896 0.002991472 1.62012E 06 1.29856E 05 9.93977E 05 5.29232E 05 0.000336156 1.13051E 08 2.96283E 05 5.76378E 06 1.45184E 06 2.4169E 09 6.37294E 10 1.72575E 10 2.01997E 06 4.04477E 07 8.27387E 08 2.00499 08 8.15654E 09 1.45069E 09 2.98202E 10 7.45128E 11 7.7075E 08 7.22408E 06 4.79581E 10 9.92114E 09 1.16332E 09 1.98589E 09 4.89555E 10 1.19566E 06 2.42836E 07 6.33862E 08 5.92478E 08 1.59657E 08 5.3194E 11 2.08568E 07 1.06249E 11 1.39485E 10 2.62093E 11 7.80714E 09 1.566E 09 3.96369E 10 2.16596E 09 2.57609E 08 4.30396E 10 8.64141E 09 1.07061E 10 5.20023E 09 1.3098E 09 3.91542E 05 1.21632E 09 2.4252E 10 6.0573E 11
0.0008511 0.0003307 0.0041042 0.1006322 5.849E 05 0.0007944 0.0001022 8.682E 05 0.0009437 3.9E 08 0.0002026 4.341E 05 1.117E 05 1.88E 08 5.448E 09 1.502E 09 4.226E 05 1.144E 05 2.438E 06 5.936E 07 2.887E 07 6.359E 08 1.35E 08 3.388E 09 3.67E 06 0.0003677 2.595E 08 5.586E 07 6.573E 08 1.142E 07 2.848E 08 7.153E 05 1.489E 05 3.91E 06 3.668E 06 1.017E 06 3.393E 09 1.327E 05 6.887E 10 9.196E 09 1.76E 09 5.535E 07 1.13E 07 2.879E 08 1.585E 07 1.89E 06 3.213E 08 6.433E 07 7.962E 09 3.851E 07 9.892E 08 0.002988 1.031E 07 2.087E 08 5.232E 09
0.000837838 0.000324324 0.004054054 0.099189189 5.40541E-05 0.000783784 0.000108108 8.10811E 05 0.000918919 0 0.000189189 5.40541E 05 0 0 0 0 5.40541E 05 0 0 0 0 0 0 0 0 0.000351351 0 0 0 0 0 8.10811E 05 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.002945946 0 0 0
ARTICLE IN PRESS P. Unak, B. Cetinkaya / Applied Radiation and Isotopes 62 (2005) 861–869
864 Table 1 (continued ) Rad. type
Energy (E) (eV)
Radiation intensity (W)
E W (eV)
56 CE 57 CE 58 CE 59 CE 60 CE 61 CE 62 CE 63 CE 64 CE 65 CE 66 CE 67 CE 68 CE 69 CE 70 CE Total
359036 363347 364281 370253 399361 403672 404606 468443 497551 602428 608158 631536 637266 688350 717458
0.00246 0.000507 0.000123 0.0000083 0.00000115 0.00000024 0.00000006 0.0000269 0.00000389 0.000288 0.0000085 0.0000395 0.00000117 0.00007 0.0000087 1.125702583
883.22856 10.23361 184.216929 2.089591 44.806563 0.511337 3.0730999 0.034008 0.45926515 0.004594 0.09688128 0.000954 0.02427636 0.000237 12.6011167 0.101066 1.93547339 0.014385 173.499264 1.003691 5.169343 0.029717 24.945672 0.136823 0.74560122 0.004035 48.1845 0.237391 6.2418846 0.029413 192545.8685 7110.158
Given energy to cell (eV)
Table 2 Total emitted electron numbers and emitted electron energies for
131
I
Di (cell) (gGy/ MBq h)
Di (water) (gGy/MBq h)
NUDAT Di (gGy/MBq h)
5.97937E 06 1.22092E 06 2.98768E 07 1.98706E 08 2.68402E 09 5.57371E 10 1.3872E 10 5.90519E 08 8.40481E 09 5.86445E 07 1.73634E 08 7.99442E 08 2.35759E 09 1.38705E 07 1.71856E 08 0.00415438
0.0005161 0.0001076 2.618E 05 1.796E 06 2.683E 07 5.661E 08 1.418E 08 7.363E 06 1.131E 06 0.0001014 3.02E 06 1.458E 05 4.356E 07 2.815E 05 3.647E 06 0.1125022
0.000513514 0.000108108 0 0 0 0 0 0 0 0.000108108 0 0 0 2.7027E 05 0 0.110783784
131
I
Total b-
Total Eb Wb (keV)
Tot. Auger
Total EAuger WAuger (keV)
Total conversion
Total EconWcon (keV)
Total electron
Total EW (keV)
1.00451 89.23%
182.737 94.91%
0.05704 5.07%
0.323 0.17%
0.06415 5.70%
9.485 4.93%
1.12570
192.546
Table 4 shows the percentages of absorbed electron energies within the cell and water medium from beta particles, conversion electrons and Auger electrons of 131 I. The absorbed energy per decay of 131I is 7.110 keV/ cell (3.69% of the total released energy). On the other hand, if the cell composition is assumed to be water, the absorbed energy is 1.521 keV/water (0.79% of the total released energy). The deposited energy is 4.68 times higher in the cell compared to water composition. For example, 85.93% (6.109 keV) of absorbed energy comes from beta particles, 3.67% (0.261 keV) of absorbed energy comes from Auger electrons and 10.41% (0.740 keV) of absorbed energy comes from conversion electrons within a cell. If the cell volume is assumed to be water 77.97% (1.186 keV) of absorbed energy comes from beta particles, 12.46% (0.190 keV) of absorbed energy comes from Auger electrons and 9.57% (0.146 keV) of absorbed energy comes from conversion electrons. Consequently, cells deposit higher energy than water according to our model. Figs. 1–3 represent energies versus distance for beta particles, conversion electrons and Auger electrons of 131 I. Beta particles deposit only 3.34% and 0.65%, conversion electrons gives 7.80% and 1.53%, while
Auger electrons deposit 80.58% and 58.62% of energies in cellular dimensions and water in the same volume of the cell, respectively. Results show that the cellular dose is lower than the total emitted electron energies for 131I. Whereas dose distribution is not homogenous at the cellular dimension, Auger electrons deposit most of their energies within the cell. Conversion electrons and beta particles deposit a lesser amount of their energies compared to Auger electrons. On the other hand, there is heterogeneity of dose distribution since Auger electrons give a considerable dose in cellular dimension. Consequently, 3.69% and 0.79% of the total emitted energy of 131I is absorbed within a single cell and within water of the same volume as the cell, respectively. On the other hand, in water medium, mean ranges are longer than in the cell medium (Figs. 1–3). Calculated mean ranges and stopping power values were compared with Berger’s ESTAR program and data were well fitted for water (Berger, 1992; Berger, http://physics.nist.gov/ PhysRefData/Star/Text/contents.html). However, calculated stopping power and range data were found to be elevated in cell medium (Fig. 4). According to Table 5, 7.110 keV/cell (3.69% of emitted energy), 5.898 keV/cell (1.76% of emitted
ARTICLE IN PRESS P. Unak, B. Cetinkaya / Applied Radiation and Isotopes 62 (2005) 861–869
Table 3 Total emitted-electron numbers and emitted-electron energies per decay
I Re
186
188
Re
201
Tl
204
Tl
55
Fe
51
Cr
99m
Tc
1.125703 (this study) 1.17 (Unak et al., 2005)
1.19 (Unak et al., 2005)
20.68 (Unak et al, 1997) 20 (Rao et al., 1985)
1.10 (Unak et al., 1997)
5.341 (Unak et al., 1997) 4.75 (Humn et al., 1994) 5.420 (Unak et al., 1997) 5.42 (Kassis et al., 1985) 5.15 (Unak et al., 1997) 5.13(Makrigiorgos et al., 1989)
keV/decay
100000
10000 1.00E+00
192.546 (this study) 335.739 (Unak et al., 2005) 326.1 (Bardies and Chatal, 1994) 777.878 (Unak et al., 2005) 777.0 (Bardies and Chatal, 1994) 768 (Nahum, 1996) 44.748 (Unak et al., 1997) 43.3 (Kassis et al., 1983) 43.5 (Ftacnikova and Bohm, 2000) 245.219 (Unak et al., 1997) 243 (Kassis et al., 1983) 5.803 (Unak et al., 1997) 4.0471.66 (Humn et al., 1994) 3.652 (Unak et al., 1997) 3.65 (Vezza et al., 1987) 17.286 (Unak et al., 1997) 17.28 (Makrigiorgos et al., 1989) 16.2 (Ftacnikova and Bohm, 2000)
1.00E-01
1.00E-02
Beta Cell
Beta Water
Fig. 1. Beta-particle energies as a function of distance from decay center for beta particles of 131I. I-131 Auger
100000
Cell 10000 Nucleus 1000 1.00E-02
1.00E-03
1.00E-04
1.00E-05
1.00E-06
Distance from Decay Center (cm) AU Cell
AU Water
Fig. 2. Auger electron energies as a function of distance from decay center for Auger electrons of 131I. I-131 CE
1000000
100000
10000 1.00E+00
1.00E-01
1.00E-02
1.00E-03
1.00E-04
Distance from Decay Center (cm) CE Cell
CE Water
Fig. 3. Conversion electron energies as a function of distance from decay center for CE electrons of 131I.
Table 4 Absorbed electron energies and percent ratios of absorbed energies within cell and water medium of Cell
Absorbed energy (keV) %
1.00E-03
Distance from Decay Center (cm)
Energy (eV)
131
Total electron numbers
I-131 Beta
1000000
Energy (eV)
Radionuclides
Such results show that if the aim is to irradiate selectively very small volumes, Auger nuclides should be preferred. On the other hand, absorbed energies decrease if the water composition is used in place of cell composition. While 7.110 keV/decay is accumulated by a
Energy (eV)
energy), and 4.874 kev/cell (0.63 of emitted energy) are deposited from 131I, 186Re and 188Re, respectively. 201Tl gives 19.040 keV per cell (42.52% of the emitted energy). On the other hand, 204Tl gives only 7.170 keV to a cell, which is 2.92% of the total energy. As a result, while 201 Tl can irradiate only a volume of a few cell diameters, 131 204 I, Tl, 186Re and 188Re can irradiate larger volumes.
865
131
I
Water
Beta
Auger
CE
Total
Beta
Auger
CE
Total
6.109 85.93
0.261 3.67
0.740 10.41
7.110 100
1.186 77.97
0.190 12.46
0.146 9.57
1.521 100
ARTICLE IN PRESS P. Unak, B. Cetinkaya / Applied Radiation and Isotopes 62 (2005) 861–869 1000000
1000
Energy (eV)
2
Stopping Power (MeVcm /g)
866
100
10
1 1000
10000
100000
1000000
100000
10000
1000 1.00E+00
1.00E-01
ESTAR
Our water model
1.00E-02
1.00E-03
1.00E-04
1.00E-05
1.00E-06
Range (cm)
Energy (eV) Our Cell Model
ESTAR
Our Water Model
Our Cell Model
Fig. 4. Calculated stopping powers versus energy and energy versus range for cell and water.
Table 5 Deposited energy per cell per decay Radionuclides
keV/decay/cell
keV/decay/cell keV/cell (accepted as water)
131
7.110 (this study)a 5.898 (Unak et al., 1997)a 4.874 (Unak et al., 1997)a 19.040 (Unak et al., 1997)a
1.521 (this study)b
I
186
Re
188
Re
201
Tl
204
Tl
7.170 (Unak et al., 1997)a
55
Fe
5.517 (Unak et al., 1997)a
51
3.529 (Unak et al., 1997)a
Cr
99m
Tc
3.560 (Unak et al., 1997)a
1.578 (Unak et al., 1997)b 1.219 (Unak et al., 1997)b 13.031 (Unak et al., 1997)b 14 (Kassis et al., 1983) 13.8 (Ftacnikova and Bohm, 2000) 1.752 (Unak et al., 1997)b 1.5 (Rao et al., 1983) 4.860 (Unak et al., 1997)b 3.99 (Rao et al., 1985) 3.207 (Unak et al., 1997)b 3.43 (Kassis et al., 1985) 2.656 (Unak et al., 1997)b 2.6 (Ftacnikova and Bohm, 2000)
a
Deposited energy was calculated according to chemical composition (16). b Deposited energy was calculated for water with the same volume as the cell.
cell, 1.521 keV/decay is given to the same volume of water from 131I. We found that 5.898 and 1.578 keV/ decay are deposited in the cell and water from 186Re, respectively, while, 4.874 keV/decay and 1.219 keV/ decay is given to the cell and to water in cellular volume from 188Re, respectively.
Table 6 compares the dose rates to the cell per unit cumulated activity in gGy/MBq-h. 131I has a similar dose rate to that of 204Tl. The dose rates of the cell per unit cumulated activity of some other radionuclides like 201 Tl are higher than those for 131I, 186Re and 188Re. These calculated values have been found to be significantly smaller in water medium. The total accumulated dose rates per unit cumulated activity were calculated with the supposition of the medium as water and without considering cell dimension. Similar results with NUDAT and Van Dieren were found for 186Re (NUDAT (http://www-nds.iaea.org/nudat/radform. html); ICRU Report 44, 1989; Hartman et al., 2000; Van Dieren et al., 1996). In the case of 131I, we found 0.004154 gGy/MBq h that is slightly higher total accumulated dose rates per unit cumulated activity within the cell for 186Re and 188Re (0.003446 for 186Re and 0.002848 for 188Re). Fig. 5 shows the variations of doses absorbed from beta particles, Auger and conversion electrons in a cell for 131I activity of 0.000278 Bq (one decomposition occurs in 1 h). The total and partial dose absorptions increase as a function of decay time. Most of the absorbed doses come from beta particles; however, conversion and Auger electrons deposit significant amounts of absorbed dose over time. Edmont reported that to treat cancer successfully with 131 I-labeled antibodies, a total of 20–90 Gy must be delivered to the tumor (Edmont et al., 1992). We computed 0.0021 Gy/h absorbed dose rate for 0.00028 Bq/cell activity, and then calculated the crucial activities to achieve 20 or 90 Gy, which is the necessary activity to treat the tumor over time. Fig. 6 represents the decreasing activity of Bq to achieve 20–90 Gy total doses over time. In 1 h, 2.5 and 12 times more activity is needed to achieve 20 and 90 Gy doses, according to our supposed activity. However, if the effective half-life of the 131I-labeled compound in a cell is accepted as 24 h, 0.13 and 0.6 times, less activity is able to achieve 20–90 Gy according to our suggested activity (0.000278 Bq/cell).
ARTICLE IN PRESS P. Unak, B. Cetinkaya / Applied Radiation and Isotopes 62 (2005) 861–869
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Table 6 Dose rates into the cell per unit cumulated activities for cell and water Radionuclide
gGy/MBq-h (cell volume)
gGy/MBq-h (cell volume, accepted as water)
Total gGy/MBq-h (water)
131
0.004154 (this study)
0.000889 (this study)
0.1125022 (this study) 0.110783784 (NUDAT) 0.1164 (Van Dieren, et al.,1996)
186
0.003446 (Unak)
0.000922 (Unak et al., 2005)
0.196169 (Unak et al., 2005) 0.193135 (NUDAT) 0.1979 (Van Dieren, et al., 1996)
188
0.0028480 (Unak)
0.0007125 (Unak et al., 2005)
0.4545048 (Unak et al., 2005) 0.4485946 (NUDAT)
201
0. 0111 (Unak, 1997)
0.007613 (Unak et al., 1997)
0.02614 (Unak et al., 1997) 0.02135 (Nass, 1977; Rao et al., 1983)
204
Tl
0.00419 (Unak, 1997)
0.001023 (Unak et al., 1997)
55
Fe
0.00322 (Unak, 1997)
0.002840 (Unak et al., 1997)
0.1433 (Unak et al., 1997) 0.1370 (Rao et al., 1983) 0.00339 (Unak et al., 1997) 0.00332 (Robertson et al., 1983)
51
0.002062 (Unak, 1997)
0.001874 (Unak et al., 1997)
0.0021 (Unak et al., 1997) 0.0027 (Vezza et al., 1987) 0.00308 (Kassis et al., 1985)
0.002083 (Unak, 1997)
0.001552 (Unak et al., 1997)
0.0101 (Unak et al., 1997)
I
Re
Re Tl
Cr
99m
Tc
I-131 14
0.60
12
0.50 0.40
Total
0.30
Beta
0.20
Auger
Activity (Bq)
Absorbed Dose (Gy)
I-131 0.70
20 Gy
8
90 Gy
6 4 2
CE
0.10
10
0 0
10
0.00 100
200
300
400
500
600
700
800
900
Time (h)
Fig. 5. Partial-dose absorptions from beta particles, Auger and conversion electrons of 131I in the cell.
Cross-fire effect provides considerable doses to adjacent cells in radionuclide therapy. It follows that the radiation dose received by any individual cell is a resultant of cross-fire radiation emitted from radionuclide targeted to adjacent cells as well as radiation from radionuclide taken up by the cell itself. Hartman et al. investigated dose distributions of subcellular 131I and influence of the cell size and cross-fire irradiation in clusters of cells. They reported that cross-fire irradiation can be a major contributor to the nuclear dose in clusters of more than six cells (Hartman et al., 2000). We applied Hartman’s cluster size and cell numbers to our model. The absorbed dose increased 6–12 times for beta particles and 7–17 times for internal conversion
20
30
40
50
Time (h)
1000
Fig. 6. Decreasing activities of Bq to achieve 20–90 Gy total doses over time.
20 15 Rate
0
10 CE
5 0
Beta 51 cell
173 cell
Auger 800 cell
Fig. 7. Cross-fire irradiation effect for several cluster sizes for Auger, beta, and conversion electrons of 131I.
ARTICLE IN PRESS P. Unak, B. Cetinkaya / Applied Radiation and Isotopes 62 (2005) 861–869
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40 µm radius cluster (Cell medium)
60
40 µm radius cluster (Water medium)
70
(51 cells)
50 40
Total
30
Beta Auger
20
CE
10 0
Absorbed Dose (Gy)
Absorbed Dose (Gy)
70
60
(51 cells)
50 40
Total
30
Beta Auger
20
CE
10 0
0
20
40
60
80
100
120
0
20
Time (h)
40
60
80
100
120
Time (h)
Fig. 8. Cross-fire irradiation effect for 51 cell numbered cluster sizes for Auger, beta, and conversion electrons of 131I for cell and water medium.
electrons, while the absorbed dose did not change for Auger electrons, when cluster size increased from 51 to –800 cells in our work (Fig. 7). According to Hartman, total doses increase from 6 to 13 times for with the expanding size of clusters from 51 to 800 cells for beta particles. However, for internal conversion electrons, total doses increase from 8 to 20 times for the same size of clusters. Although random distributions of radionuclides were proposed in clusters in our study, point sources were taken by Hartman (Hartman et al., 2000). The dimension of the tumor is very important in cross-fire effect. For very small tumors (micrometastases) whose diameter is less than particle range, absorption of radiation energy is inefficient, a proportion of this energy being deposited outside the tumor. This indicates that very small microtumors may be underdosed (and hence less easily cured) than slightly larger ones (Wheldon, 2000). O’Donoghue et al. have shown that the optimal tumor size (diameter) is slightly greater than the mean particle range for each radionuclide (O’Donoghue et al., 1995). According to this consideration, medium-range beta emitters like 131I (mean range is 0.70 mm) would be ideal for treatment of small tumors (from millimeter to centimeter dimensions) as for larger macroscopic tumors, but would be (relatively) less effective in the treatment of very small micrometastases. Total absorbed doses were similar when the medium was accepted as water, like Hartman’s, for 24 h (0.0087 Gy/decay in Hartman’s work and 0.01 Gy/decay in our work). However, the total absorbed dose has been found to be significantly higher than Hartman’s cell composition (0.05 Gy/decay). Fig. 8 shows cross-fire irradiation effect for 51 cell numbered cluster sizes for Auger, beta, and conversion electrons of 131I in cell clusters and in water of the same volume as the cell cluster. Total absorbed doses are ~4.5 times higher in cell clusters than in water. Although most of the absorbed doses are generated by beta particles in both media, Auger electron doses are higher in cell clusters than in water medium.
4. Conclusion Conversion and Auger electrons contribute considerable doses to total absorbed doses especially in cellular range for 131I, although it has fewer Auger electrons than most of the Auger nuclides. Significant differences were found between water and cell compositions in cell dimensions. Therefore, real or equivalent atomic compositions should be taken into consideration in microdosimetric considerations. On the other hand, cross-fire irradiation supplied doses of significant amounts for clusters. Consequently, 131I has a good potential for radionuclide tumor therapy. Because the particular ranges of the internal conversion electrons and beta particles are much higher than cellular dimension, it is better for therapy of tumors which are millimeter to centimeter dimension rather than micrometastases. Although the contributions of Auger electron and conversion electrons to total doses are minor, they should be considered especially in cellular dimensions.
Acknowledgment The authors have received a grants from the Abdus Salam ICTP as a regular associate (P. Unak) and a young collaborate (B. Cetinkaya) during a part of the work. The authors thank the Abdus Salam ICTP for the support given.
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