{"id":2657,"date":"2015-04-28T10:05:26","date_gmt":"2015-04-28T10:05:26","guid":{"rendered":"http:\/\/biomedpharmajournal.org\/?p=2657"},"modified":"2020-04-26T07:07:45","modified_gmt":"2020-04-26T07:07:45","slug":"calculation-of-dose-distribution-around-a-clinical-252cf-source-for-neutron-therapy-based-on-aapm-tg-43-protocol","status":"publish","type":"post","link":"https:\/\/biomedpharmajournal.org\/staging\/vol6no2\/calculation-of-dose-distribution-around-a-clinical-252cf-source-for-neutron-therapy-based-on-aapm-tg-43-protocol\/","title":{"rendered":"Calculation of Dose Distribution Around a Clinical 252Cf Source for Neutron Therapy Based on AAPM, TG-43 Protocol"},"content":{"rendered":"

Introduction<\/strong><\/p>\n

Compared with photon and electron beams, fast neutrons have high therapeutic ratio for tumor cells treatment. This can be attributed to the relative high biological effect, high radiation weighting factor, low oxygen enhancement ratio and high linear energy transfer of neutrons and fission fragments (1, 2). Delivering maximum and minimum dose respectively to the tumor and healthy surrounding tissues is possible through Boron Neutron Capture Therapy (BNCT) by adjusting fast neutrons before the depth of the tumor and also targeting tumor with boron element (due to the high cross section, 3837 Barn, in the reaction with thermal neutrons) (3). Despite the potential and high accuracy of BNCT method in treating various tumors, especially hypoxic tumors and advanced cancers (particularly brain tumors), high costs and the need for reactors to produce a neutron beam, has limited the widespread use of this technique (4).<\/p>\n

Accordingly, the use of radioisotopecalifornium-252 (252<\/sup>CF) as neutron emitter is proposed recently in radiation treatment, based on Neutron Brachytherapy (NBT) as a cost effective treatment method (5). Using 252<\/sup>CF in radiation therapy was introduced for the first time by Schlea and Stoddard (6). The half-life of 252<\/sup>CF is approximately 2.645 years and in 96.6% cases decays with alpha particles irradiation and 3.1% of the disintegration will lead to nuclear fission. In each fission, on average, 3.768 neutrons are released; 1 gram 252<\/sup>CF, irradiates 2.314\u00d7106<\/sup> neutrons per second, with a most probable energy in 0.7 MeV (The neutron energy spectrum follows the Watt function, from 1eV to 20MeV) (7) which provide appropriate flux for brachytherapy (4, 8).<\/p>\n

Performing neutron brachytherapy accurately and achieving the maximum tumor dose and the minimum dose of normal tissues require appropriate determination of dose distribution around the 252<\/sup>CF source; the results will be subsequently used in the treatment designing software. In the present study, dosimetry parameters of 252<\/sup>CF source is calculated using Monte Carlo calculations and based on the proposed protocol AAPM-TG \u200b\u200b43 (9).<\/p>\n

Materials and Methods<\/strong><\/p>\n

Simulation code MCNPX (2.6.0) (8) was used for the simulation calculations. The energy of neutron cutoff was considered equal to 0.1 eV. No method was applied to reduce the error of neutron transport in the programs. The neutron scattering cross sections in the solid state, S (a, b), named lwtr.01t, was used in order to precisely calculate the transport of slow neutrons from the cross sections of thermal neutrons. In the simulation programs of this study, the number of transported neutron from neutron source was considered equal to 108<\/sup> resulting in less than 5% error in the farthest distance from the source (11 cm).<\/p>\n

CF Neutron Source<\/strong><\/p>\n

The dimensions and materials of 252<\/sup>CF neutron source utilized in this study are shown in Figure 1. The active element of cylindrical source is made \u200b\u200bof californium oxide, Cf2<\/sub>O3<\/sub>, with 12 gr\/cm3 <\/sup>density. The cylinder height and radius is 1.5 and 0.615 cm respectively, which is located in a platinum – iridium 10% capsule (Pt\/Ir-10%), with following characteristics: density= 21.55 gr\/cm3<\/sup>, the inner diameter= 0.135 cm, the external diameter= 0.175 cm, internal length= 1.55 cm and the external length= 1.77 cm. The internal and external diameter and the internal and external length of the outer capsule is 0.18, 0.28, 1.782 and 2.314 cm, respectively. As a part of the design, a spherical eye let with the diameter of 0.0635 cm is embedded at the end of the source. 252<\/sup>CF fission energy spectrum is considered as a function of W (4, 8), with the following equation:<\/p>\n

\"Vol-6No2_Calc_Ali_f1\"<\/p>\n

 <\/p>\n\n\n\n
\"Figure<\/td>\nFigure 1: The dimensions and materials of 252<\/sup>CF neutron source<\/strong><\/p>\n

 <\/p>\n

Click here to View figure<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Protocols AAPM-TG.43 and Neutron Source Dosimetry of 252<\/sup>CF<\/strong><\/p>\n

Based on the proposed protocol AAPM-TG \u200b\u200b43 (9), the absorbed dose rate of 252<\/sup>CF neutron source is calculated anywhere around the source. This computing is performed in the water phantom, , in terms of the radial distance from the central source, r, and the angle from the central axis of the source, q, \u00a0and with the following equation:<\/p>\n

 <\/p>\n

\"Vol-6No2_Calc_Ali_f2\"<\/p>\n

Where,SKN<\/sub><\/em> , the air kerma strength in a vacuum environment is the product of air kerma rate and the square of the distance from the source center:<\/p>\n

\"Vol-6No2_Calc_Ali_f3\"<\/p>\n

\u039bN<\/sub><\/em>, the constant of neutron dose rate is calculated by dividing the source neutron dose rate (in terms of cGy\/\u03bcgh in the perpendicular axis reference point on the central axis of the source),0\u00b0\u00a0<\/sub><\/em>=90\u00b0, r0\u00a0= cm,\u00a0<\/sup><\/sub><\/em>in a homogeneous water phantom by air kerma strength,SKN<\/sub><\/em> :<\/p>\n

\"Vol-6No2_Calc_Ali_f4\"<\/p>\n

Neutron absorbed dose is calculated positioning the source in the center of the water phantom with the dimensions 30\u00d730\u00d730cm3<\/sup> (using *f8 tally on perpendicular-axis to the central axis, 1 cm, and the sphere voxel with the radius of 0.5 cm) and is divided by the air kerma strength. The calculated simulation outputs are converted to Gy absorbed dose unit applying relevant coefficients.<\/p>\n

The radial dose function, gN<\/sub>(r), considers the dependence of neutron absorption and photons scattering along the transverse axis in the medium and is expressed as follows:<\/p>\n

\"Vol-6No2_Calc_Ali_f5\"<\/p>\n

According to the practical calculations, the best equation to express the radial dose function is the fifth grade function:<\/p>\n

\"Vol-6No2_Calc_Ali_f6\"<\/p>\n

The radial dose function, gN<\/sub>(r), is calculated by *f8 tally in the cylindrical shell around the central axis of the source, with 0.4cm thickness, at a distance of 0.2cm to 11cm from the source center and is converted to dose rate applying appropriate coefficients.<\/p>\n

G (r, \u03b8) is a geometric factor that considers the reduction of the neutrons flow, at any distance from the source and based on the geometry of the source; this is dependent on the distribution of radioactive material in the source. Considering the point source, G (r, \u03b8) = 1\/r2<\/sup> applies and for a line source with uniform distribution of geometric factor the equation is:<\/p>\n

\"Vol-6No2_Calc_Ali_f7\"<\/p>\n

Where L is the length of the source active element. For example, for \u03b8 = 90, the geometric factor to calculate the radial dose function is expressed as follows:<\/p>\n

\"Vol-6No2_Calc_Ali_f8\"<\/p>\n

In this study, the more stringent assumption of source linearity has been used and these coefficients were calculated separately for the studied points in the radial distances and at different angles.<\/p>\n

Anisotropy function, FN<\/sub>(r, \u03b8), takes into account non-homogeneity , angular dependence of neutron absorption and scattering within the source capsule and is expressed in the Eq. (8) as follows: (10):<\/p>\n

\"Vol-6No2_Calc_Ali_f9\"<\/p>\n

Anisotropy function, FN<\/sub>(r, \u03b8), was calculated using Eq. 8 at intervals of 2, 3, 5, 8, 10 cm and at angles of 0, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90 degrees in a water phantom.<\/p>\n

Results<\/strong><\/p>\n

Air Kerma Rate and Dose Rate Constants<\/strong><\/p>\n

Air kerma strength of neutrons, , is calculated and with a 3% error is equal to 0.345 (cGy cm2\/\u03bcgh) or 0.345 U\/\u03bcg. Dose absorbed rate in water at a distance of 1cm from the source center,DN<\/sub>(r0<\/sub>,00<\/sub>)<\/em> , is 2.075 cGy\/\u03bcgh; the constant of neutron dose rate, \u039bN<\/sub>, was estimated 6.014 cGy\/Uh, dividing dose absorbed rate by the air kerma strength of the neutrons in the air.<\/p>\n

Radial Dose Function<\/strong><\/p>\n

The calculated values \u200b\u200bfor the radial dose function, gN<\/sub>(r), are presented in Table 1. The resulted coefficients from 5 fitted variables on the values of radial dose function based on the radial distance, r, is obtained as follows:<\/p>\n

A0<\/sub>=1.17545, a1<\/sub>=-0.2298, a2<\/sub>=0.061, a3<\/sub>=-0.1090, a4<\/sub>=0.9000, a5<\/sub>=-3\u00d710-5<\/sup><\/p>\n

Table 1. The calculated values \u200b\u200bof the radial dose function, gN <\/sub>(r), based on the radial distance, r, from the source center of 252<\/sup>CF.<\/strong><\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
radial dose function, gN<\/sub>(r)<\/strong><\/td>\nDistance from the source center (4)<\/strong><\/td>\nradial dose function, gN<\/sub>(r)<\/strong><\/td>\nDistance from the source center (4)<\/strong><\/td>\nradial dose function, gN<\/sub>(r)<\/strong><\/td>\nDistance from the source center (4)<\/strong><\/td>\n<\/tr>\n
0.548<\/td>\n7<\/td>\n0.755<\/td>\n3.8<\/td>\n1.050<\/td>\n0.6<\/td>\n<\/tr>\n
0.536<\/td>\n7.2<\/td>\n0.742<\/td>\n4<\/td>\n1.030<\/td>\n0.8<\/td>\n<\/tr>\n
0.524<\/td>\n7.4<\/td>\n0.728<\/td>\n4.2<\/td>\n1.000<\/td>\n1<\/td>\n<\/tr>\n
0.513<\/td>\n7.6<\/td>\n0.716<\/td>\n4.4<\/td>\n0.975<\/td>\n1.2<\/td>\n<\/tr>\n
0.501<\/td>\n7.8<\/td>\n0.712<\/td>\n4.6<\/td>\n0.449<\/td>\n1.4<\/td>\n<\/tr>\n
0.490<\/td>\n8<\/td>\n0.689<\/td>\n4.8<\/td>\n0.920<\/td>\n1.6<\/td>\n<\/tr>\n
0.478<\/td>\n8.2<\/td>\n0.764<\/td>\n5<\/td>\n0.900<\/td>\n1.8<\/td>\n<\/tr>\n
0.467<\/td>\n8.4<\/td>\n0.662<\/td>\n5.2<\/td>\n0.882<\/td>\n2<\/td>\n<\/tr>\n
0.457<\/td>\n8.6<\/td>\n0.648<\/td>\n5.4<\/td>\n0.867<\/td>\n2.2<\/td>\n<\/tr>\n
0.447<\/td>\n8.8<\/td>\n0.634<\/td>\n5.6<\/td>\n0.852<\/td>\n2.4<\/td>\n<\/tr>\n
0.438<\/td>\n9<\/td>\n0.622<\/td>\n5.8<\/td>\n0.837<\/td>\n2.6<\/td>\n<\/tr>\n
0.427<\/td>\n9.2<\/td>\n0.610<\/td>\n6<\/td>\n0.824<\/td>\n2.8<\/td>\n<\/tr>\n
0.418<\/td>\n9.4<\/td>\n0.597<\/td>\n6.2<\/td>\n0.810<\/td>\n3<\/td>\n<\/tr>\n
0.409<\/td>\n9.6<\/td>\n0.584<\/td>\n6.4<\/td>\n0.796<\/td>\n3.2<\/td>\n<\/tr>\n
0.399<\/td>\n9.8<\/td>\n0.571<\/td>\n6.6<\/td>\n0.782<\/td>\n3.4<\/td>\n<\/tr>\n
0.389<\/td>\n10<\/td>\n0.560<\/td>\n6.8<\/td>\n0.769<\/td>\n3.6<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Anisotropy Dose Function, FN<\/sub>(r, \u03b8)<\/strong><\/p>\n

The obtained values for dose anisotropy function, FN<\/sub>(r, \u03b8) are shown in Table 2. As expected,\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 increasing the radial distance and angle to the source central axis leads to enhancing the calculated values \u200b\u200bfor the anisotropy dose.<\/p>\n

Table 2. The calculated values for dose anisotropy function, FN<\/sub>(r, \u03b8)<\/strong><\/p>\n\n\n\n\n\n\n\n\n\n\n
Angle to the central axis of the 252<\/sup>CF (degree)<\/strong><\/td>\nRadial distance (4)<\/strong><\/td>\n<\/tr>\n
90<\/strong><\/td>\n80<\/strong><\/td>\n70<\/strong><\/td>\n60<\/strong><\/td>\n50<\/strong><\/td>\n40<\/strong><\/td>\n30<\/strong><\/td>\n20<\/strong><\/td>\n10<\/strong><\/td>\n2<\/strong><\/td>\n0<\/strong><\/td>\n<\/tr>\n
1.001<\/td>\n1.010<\/td>\n0.999<\/td>\n0.999<\/td>\n0.989<\/td>\n0.987<\/td>\n0.974<\/td>\n0.960<\/td>\n0.960<\/td>\n0.943<\/td>\n0.92<\/td>\n2<\/td>\n<\/tr>\n
1.008<\/td>\n1.101<\/td>\n0.998<\/td>\n0.999<\/td>\n0.989<\/td>\n0.988<\/td>\n0.977<\/td>\n0.970<\/td>\n0.97<\/td>\n0.954<\/td>\n0.93<\/td>\n3<\/td>\n<\/tr>\n
1.007<\/td>\n0.988<\/td>\n1.023<\/td>\n1.004<\/td>\n0.994<\/td>\n0.989<\/td>\n0.983<\/td>\n0.987<\/td>\n0.95<\/td>\n0.97<\/td>\n0.95<\/td>\n4<\/td>\n<\/tr>\n
1.008<\/td>\n0.998<\/td>\n1.020<\/td>\n1.01<\/td>\n0.995<\/td>\n0.995<\/td>\n0.985<\/td>\n0.988<\/td>\n0.94<\/td>\n0.987<\/td>\n0.967<\/td>\n5<\/td>\n<\/tr>\n
1.001<\/td>\n0.989<\/td>\n1.004<\/td>\n1.008<\/td>\n0.996<\/td>\n0.997<\/td>\n0.984<\/td>\n0.991<\/td>\n0.96<\/td>\n0.989<\/td>\n0.998<\/td>\n8<\/td>\n<\/tr>\n
0.999<\/td>\n1.001<\/td>\n1.008<\/td>\n1.070<\/td>\n0.998<\/td>\n0.999<\/td>\n0.988<\/td>\n0.999<\/td>\n0.986<\/td>\n0.99<\/td>\n1.01<\/td>\n10<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Discussion<\/strong><\/p>\n

In all discussed studies at following, dose calculations and measurements were reported based on protocols AAPM, TG-43 (7) and the length of source’s active element was equal to 1.5 cm. The computed air kerma strength for 252<\/sup>CF,DN<\/sub>(r0<\/sub>,00<\/sub>)<\/em> , is equal to 0.3450 (cGy cm2\/\u03bcgh) or 0.3450 U\/\u03bcg which is consent with other reported results, 0.3348, 0.3350, 0.3300 cm2\/ \u03bcgh, respectively by Ghassoun et al. (11), Paredes et al. (12) and Rivard et al. (4). The calculated absorbed dose rate in the water phantom, at a distance of 1cm from the source center on the central axis and perpendicular to the central axis of 252<\/sup>CF,DN<\/sub>(r0<\/sub>,00<\/sub>)<\/em> , are compared to other results (Table 3) (3, 4, 11-15). The minimum calculated difference of DN<\/sub>(r0<\/sub>,00<\/sub>)<\/em>\u00a0 is -0.86% with the measured data of Colvett et al. (14) and the greatest difference was found to be +11.81% with Ghassoun et al. (11).<\/p>\n

Table 3. The calculated absorbed dose in water phantom, , at distance of 1cm from the source center on the central axis and perpendicular to the central axis of the 252<\/sup>CF source.<\/strong><\/p>\n\n\n\n\n\n\n\n\n\n\n\n
Absorbed dose rate (cGy \/ \u03bcgh) in water, , at a distance of 1cm from the source center<\/strong><\/td>\n<\/tr>\n
1.929<\/td>\nKrishnaswamy (13)<\/td>\n<\/tr>\n
2.093<\/td>\nColvett et al. (14)<\/td>\n<\/tr>\n
1.900<\/td>\nYanch and Zamenhof (3)<\/td>\n<\/tr>\n
1.880<\/td>\nWierzbicki et al. (15)<\/td>\n<\/tr>\n
1.873<\/td>\nRivard et al. (4)<\/td>\n<\/tr>\n
1.916<\/td>\nParedes et al. (12)<\/td>\n<\/tr>\n
1.868<\/td>\nGhassoun (11)<\/td>\n<\/tr>\n
2.075<\/td>\nCurrent Research<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

The constant of dose rate in 252<\/sup>CF source, \u039bN<\/sub>, are compared in Table 4 with the previous results. The calculated constant of dose rate in 252<\/sup>CF source, \u039bN<\/sub>, is equal to 6.014 cGy\/Uh and was consistent (+5.95%) with 5.676 cGy\/Uh, reported by Rivard et al. (4). Since the constant of neutron dose rate depends on the geometry of the source and the adsorbent environment, the constant of dose rate might change due to the geometrical characteristics, the source capsule material, phantom material, or on the clinical basis the tissue material the source has been planted in (4, 11, 12).<\/p>\n

Table 4. The constant of dose rate in 252<\/sup>CF source, \u039bN<\/sub>, in comparison with other results reported.<\/strong><\/p>\n\n\n\n\n\n\n\n
The constant of dose rate, \u039bN,<\/sub> 252<\/sup>CF source (cGy\/Uh)<\/strong><\/td>\n<\/tr>\n
5.676<\/td>\nRivard et al. (4)<\/td>\n<\/tr>\n
5.579<\/td>\nGhassoun (11)<\/td>\n<\/tr>\n
5.719<\/td>\nParedes et al. (12)<\/td>\n<\/tr>\n
6.014<\/td>\nCurrent Research<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Among the reviewed studies only Colvett et al. (14) is based on the measurement; Colvett\u2019s dose radial function is reported to a depth of 6 cm and is in good agreement with the results of the present study (14). The cross section of the neutrons interaction with material highly depends on the weights of the elements (especially hydrogen content), the density of the target material and also the neutron spectrum used.<\/p>\n

The unacceptable differences between the constant of dose rate and anisotropy functions reported in Wierzbicki et al. (15) compared to the present and other studies is mainly due to the difference in the source radiation neutron spectrum, hydrogen content and water density as the corresponding tissue. For example, Krishnaswamy (13) considered the watt energy spectrum for the 252<\/sup>CF source, a=0.9756 and b=2.926, which is 0.88 and 2 in this study. On the other hand, for example in the Colvett et al. (14) and Krishnaswamy (13) studies absorbed dose is considered in tissue-equivalent material instead of water in which densities are 1.06 and 1.00 g\/cm3<\/sup> respectively, containing 10.3% and 10.5% hydrogen. Wierzbicki et al. (15) and Yanch and Zamenhof (3) used water phantom with density of 1.00g\/cm3<\/sup>, containing 11.2% hydrogen.<\/p>\n

Another reason for these discrepancies is probably taking into account different values for the neutron source flux. For example, the neutron flux considered in this study is equal to 2.314\u00d7106<\/sup> n\/\u03bcgs, while Colvett et al. (14) used the flux of 2.339\u00d7106<\/sup> n\/\u03bcgs. Based on these results appropriate correction factors must be applied to make different factors equivalent such as the energy spectrum, different materials in report environment, absorbed dose and neutron flux.<\/p>\n\n\n\n
\"Figure<\/td>\nFigure 2: Anisotropy functions in 252<\/sup>CF source compared with other result.<\/strong><\/p>\n

 <\/p>\n

Click here to View figure<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Conclusion<\/strong><\/p>\n

The present study calculated dosimetry parameters of 252<\/sup>CF source as recommended by AAPM, TG-43 (9) for implementing Monte Carlo simulation ( MCNPX) (16). Air kerma strength computed for 252<\/sup>CF source, , is equal to 0.3450 U\/\u03bcg, absorbed dose rate in water at a distance of 1cm from the source center, \u00a0is 2.075 cGy\/\u03bcgh and the constant of dose rate, \u039bN<\/sub>, is 6.014 cGy\/Uh; these calculated data are in good agreement with simulation studies and measurements have been reported . The calculated values are operative\u200b\u200b with a high confidence in brachytherapy software designing and numerical calculations in brachytherapy units with a 252<\/sup>CF source.<\/p>\n

Acknowledgment<\/strong><\/p>\n

This study was performed as a part of a Master thesis at the Department of Medical Physics, Ahvaz Jundishahpur University of Medical Sciences and was financially supported by the research project No. u=92043u.<\/p>\n

\u00a0<\/strong>References<\/strong><\/p>\n

    \n
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  16. Walter LS. (Ed.). LANL (Los Alamos National Laboratory) Monte Carlo N-Particle transport code system for multiparticle and high energy applications. Version 240, LA-CP-02-408, Los Alamos National Laboratory. 2002.<\/li>\n<\/ol>\n

     <\/p>\n

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