174 Toossi MTB et al. / GZP6-TG43 TABLE 3. Dose rate constant (Λ) values for GZP6 60Co (number 3), Ralstron (type 2) 60Co (Ref. 4) and microSelectron 192Ir (Ref. 16) sources Source Type Λ (cGyh-1U-1) GZP6 (This Study) 1.1040.03 Ralstron (type 2) (Papagiannis et al.4) 1.1010.005 microSelectron (Karaiskos et al. 16) 1.1160.006 tally (in MeV/photon). Toroid tally cells of 0.05 cm in thickness were used to score the tally values. The numbers of photon histories simulated were 1.6×107, 1.6×107 and 1.45×108 respectively to obtain dose rate constant, radial dose function, and 2D anisotropy function. The corresponding statistical errors were respectively equal to 1.58, 0.5 and 0.88 percent for the Monte Carlo calculations in the used tally cells. Dose values at different radial distances and angles from the source (required for calculation of radial dose function and anisotropy function) were ob- tained through Monte Carlo simulations for a water phantom. The data for radial dose function and ani- sotropy function then were calculated respectively using equations [6] and [7]. Dose rate constant, radi- al dose function and 2D anisotropy function values for GZP6 source number 3 were compared with cor- responding data for Ralstron (type 2) 60Co source, reported by Papagiannis et al.4, and microSelectron 192Ir source, reported by Karaiskos et al..16 To obtain 2D dose rate table, a cylindrical grid of 14 cm14 cm in y-z plane, with resolution of 0.05 cm in both longitudinal and radial directions was overlaid on the geometry. The thin grid was used to reduce the Monte Carlo computation time. 3.5108 photon histories were followed, result- ing an average error of 0.44% over the mesh cells. MCNPX tally type 1 with the option of depth for photons was used to determine energy deposition per volume per photon in terms of per photon. The tally value then was converted to the dose rate per U by introducing the activity, air kerma strength of the source and appropriate conversion factors in the calculations. Superimposition method A superimposition algorithm was developed to produce the dose distributions of the GZP6 sources No. 1, 2 and 5 from the dose distribution data of the source No. 3. The algorithm was consisted of four steps: (a) The dose distribution data for each pellet in the sources 1, 2 and 5 was obtained from the dose distribution matrix of source 3 through application of matrix shift method.21 The shifting distance was equal to the inter-pellets distance (6.5 mm). Radiol Oncol 2012; 46(2): 170-178. (b) The dose distribution data for each pellet was multiplied by normalized activity of that pel- let to the activity of source No. 3. (c) A summation was then performed over the matrixes of all pellets in each source of 1, 2 ad 5. (d) Dose contours were plotted from the dose distribution matrix of sources 1, 2 and 5. The results of the mentioned algorithm were verified to examine its accuracy. For this purpose the sources 1, 2 and 5 were simulated separately and the obtained dose distributions were com- pared by the dose distributions resulted from the above algorithm. Results and discussion TG-43 dosimetric parameters The calculated values of geometry function for 0.5-5 cm radial distance and 0°-90° angles are presented in the Table 2. The calculated values for geometry function were equal to unity at 6-10 cm distance. To summarize the results, these values were not pre- sented in the Table 2. The geometry function is sym- metrical with reference to the angle of 90°. On the other hand the angular values of the on the either side of the 90° angle, for the angles 100°-180°, are mirror images of the values for 80°-0° angles.22 So as showed in Table 2, the two dimensional geometry function is presented only for angles 0°-90°. Monte Carlo calculated value of air kerma strength is Sk=17240.01 cGyh-1U-1 as worked out ear- lier for the GZP6 source number three.20 The value was used for the calculation of dose rate constant in the present study. Monte Carlo calculated dose rate constants for GZP6 and Ralstron (type 2) and microSelectron sources are presented in Table 3. The dose rate results, in terms of cGyh-1U-1, in Cartesian away (y) and along (z) coordinates are presented in the Table 4. It should be noted that the source center is assumed to be in the origin of the Cartesian coordinates. Radial dose function (RDF) computed values for GZP6 source number 3 are presented in Table 5. The tabulated g(r) data presented in the Table 5 were fitted to a fifth order polynomialin form of: [8]