The first step in this work consisted in to model and validate a brachytherapy source containing ¹²⁵I, Amersham, model 6711 [12] .

The validation was performed by the evaluation of the parameters dose rate constant, anisotropy function and radial dose function, recommended by the dosimetry protocol TG43U1 [13] . This source is constituted by two cylinders, the inner is composed of silver, 𝜌 = 10.5 g/cm³, and has a length of 3 mm and basis of 0.5 mm coated by an emmiter thickness of 1 μm, containing ¹²⁵I in the form of silver iodide (𝜌 = 6.2 g/cm³). The outer cylinder is composed of titanium (𝜌 = 4.54 g/cm³), has a length of 4.5 mm and basis of 0.81 mm closed by two ellipsoides [12] . The energy distribution of the photons emitted by the simulated ¹²⁵I source, used as an input parameter for the simulation, is presented in Table 1.

For the generation and evaluation of the DVHs using the MCNP Monte Carlo code, a prostate treatment plan consisting of 108 ¹²⁵I seeds was elaborated, with seed activities of 0.33 mCi, using the male phantom model recommended by ICRP110 [8] . Considering that the prostate of the simulator has very small volume, the seeds were inserted with spacing of 5 mm.

Figure 1 shows the mentioned model, that represents an adult of 38 years, with a height of 176 cm and weight of about 73 kg. This simulator has voxels dimension of 2.137 × 2.137 × 8 mm³, which corresponds to a volume equal to 36.53 mm³ and contains a total of 122 segmented structures.

The distribution of the ¹²⁵I seeds inside the prostate was obtained using the automatic replication program developed by Boia et al. [14] . The dose in each voxel of interest was obtained setting some plans, in order to define volumetrically the volume of each organ and using the MCNP code tools, that allow the individual calculation of the dose for all voxels delimited by the plans.

The absorbed dose in the volume studied was obtained using the command tally * F8 (MeV) of the MCNP code, applied in each voxel of interest, considering the number (N) of the used sources divided by the mass (g) of each voxel, taking in account the integration of the activity throughout the life of the source (Equation (1)). All simulations were performed considering the transport of photons and electrons (mode p e) with a cutoff energy of 5 keV and the dose of the prostate, bladder and rectum were evaluated using the methodology described above.

Through the analysis of the doses obtained for all voxels in the organ of interest, it became possible to generate the Dose Volume Histogram, taking into account the class interval for the desired dose level and the frequency distribution of voxels for these dose levels. The simulation was performed using the MCNPX code, with uncertainties below 5%, thus guaranteeing satisfactory results according to the limits of reliability presented by the relative error interpretation guidelines of MCNP like can be seen in Table 2 [15] .

Figure 2 illustrates the computational diagram of the metotology for DVHs generation using the MCNP radiation transport code applied to Low Dose Rate Brachytherapy implant using ¹²⁵I sources.

Figure 3 shows two-dimensional cuts, obtained with the Moritz graphic viewer [16] illustrating the shape of different structures constituting the simulated ¹²⁵I source. The titanium encapsulation and silver cylinder of the ¹²⁵I sources are illustrated. The use of

the ptrack card, provided by the MCNP code, permitted the illustration of the particle being emitted by modeled sources in the Figure 3(b).

Table 3 shows the results obtained in this work for the dose rate constant, in comparison with the results taken from the literature [17] - [19] . The good agreement is an indication of computational effectiveness of the performed modeling.

The results presented in this work (Table 3) showed a better agreement with those obtained in references [19] . It should be mentioned that the value associated with the TG-43 report is higher than those obtained in the other references, 4% higher when compared to the present work.

In Figure 4 the results for the anisotropy function are shown for 1 cm distance, compared with other workers results obtained from the literature [13] [18] [19] . It Can be seen a good agreement with the literature results.

Figure 5 is showed the result for the radial dose functions obtained for ¹²⁵I. They are compared with the results of several studies reported in the literature [13] [18] [19] . It can be seen a good agreement with the literature results.

Based on the results obtained for dosimetric parameters it can be concluded that the I-125 irradiation source is validated and can be used for the next steps for this study.

This section presents the DVHs results for the prostate, bladder and rectum using the methodology described above. In Table 4 the distributions of the Dose Volume Fre- quency are presented, considering all voxels of the prostate volume and intervals classes interval equal to 50 Gy. The prostate gland received doses ranging between 0 and 360 Gy when 108 seeds of ¹²⁵I were simulated. The parameters F_Vol, F_ac, represent the volumetric and accumulated frequency, respectively. The volumetric frequency (F_Vol) was obtained by multiplying the number of voxels belonging to a range of dose and the volume of individual voxel. The accumulated frequency (F_ac) was obtained through the sum of the accumulated volumes to the levels of doses considered.

Figure 6 shows the DVH obtained through the distributions of frequency presented in Table 4. We found the values of 50, 145 and 160 Gy for parameters D₁₀₀, D₉₀ and D₈₀,

and 28%, 90%, 92% and 95% for volumetric parameters V₂₀₀, V₁₀₀, V₉₀ and V₈₀, respectively. The DVH shows that 90% of the volume of the prostate receives a value of dose equal to 145 Gy, which is typically used as a reference [20] - [22] for the prescription dose in Low Dose Brachytherapy using ¹²⁵I sources. Based on these dosimetric parameters the implant was considered satisfactory for the purpose of this study.

Figure 7 illustrates the DVHs for the rectum and bladder, using class intervals of 5 Gy. It can be seen that the rectum and bladder received maximum doses equal to 41 and 60 Gy, respectively. The DVH show that 0.1 and 2 cm³ (D_0.1cc and D_2cc) of the rectum received doses of 39 and 22 Gy. The bladder received doses of 58 and 42 Gy in 0.1 and 2 cm³ of volume. These values are in agreement with reference values presented in the literature [20] - [22] .

The isodose curves were obtained in a region of the prostate using the MCNP command mesh tally. The mesh tally was used to quantify the absorbed dose in a matrix of dose defined by voxels of dimensions 0.12 × 0.12 × 0.12 cm³.

The absorbed dose obtained for each voxel of the mesh tally array was recorded in a binary file. The values of doses were obtained primarily in rem/h and subsequently converted to Gy/s per particle emitted by the source. For the construction of the isodose curves a program in MATLAB was developed.

Figure 8 shows that the curve of 145 Gy was used as prescription cover all volumetric extension of the prostate gland.