2.1 103-Pd source description

The source used in this study is the palladium-103 source model IR06-103Pd seed which is designed and fabricated in Agricultural, Medical and Industrial Research School (AMIRS). The production of 103-Pd is carried out via the 103Rh(p,n)103Pd reaction which is well suited to low-energy cyclotrons. 103-Rh target was irradiated via cyclotron (IBA-Cyclone30, Belgium) at the AMIRS. The solid targetry system in this cyclotron is made up of a pure copper backing on which the target materials are electrodeposited. The target that undergoes bombardments by the proton beam at the cyclotron production consists of three layers as follows: (I) rhodium layer, (II) copper layer and (III) copper layer without induced proton beam [21]. All irradiation of the electroplated Rh targets were performed at 200 μA beam current. The rhodium targets were prepared by the electrodeposition technique. Thus, the electrodeposition experiments were performed in acidic sulphate media using RhCl3.3H2O, Rh2(SO4)3. The radiochemical processing of the irradiation targets involved (a) dissolution, (b) radiochemical separation of 103-Pd from the Rh target solution and (c) recovery of 103-Pd as the final product from the organic phases [22]. After the chemical separation process, 103-Pd radioactive material is absorbed uniformly in the resin Amberlite IR-93 resin (20–50 mesh) bead to encapsulate

inside the titanium capsule. The seed contains five resin beads, each in diameter of 0.6 mm with the compositions of (by weight percent) C, 90%; H, 8%; Pd, 1%; Cl, 0.7%; and N, 0.3%, with the density equal to 1.14 g/cm<sup>3</sup> . The resin beads are packed inside a titanium capsule of 4.7 mm length; 0.7 and 0.8 mm internal and external diameters, respectively; and 0.6 mm thick end caps and with an effective length of 3 mm. 103-Pd radioactive material is absorbed uniformly in the resin bead volume [23]. Figure 1 shows a schematic diagram of the IR06-103Pd seed. As the resin beads are free to move within the titanium capsule, their location can vary with seed orientations. Following the TG-43U1 recommendation for "good practice for Monte Carlo calculations" [18], mechanical mobility of the internal component of the seed has been considered in the simulations, and three geometric models (ideal, vertical and diagonal) of the seed were developed as shown in Figure 1a–c.

#### 2.2 Seed Monte Carlo dosimetry

The IR06-103Pd brachytherapy seed has been simulated in the center of a spherical water phantom in 15 cm radius with an array of 1 mm thick detector rings. Detectors were defined at distances of r = 0.25, 0.5, 0.75, 1, 2, 3, 4, 5 and 7 cm, away from the palladium-103 seed and at polar angles relative to the seed longitudinal axis from 0 to 90°. The rings were also bounded with two cones (10°) bisecting the phantom sphere corresponding to points in two-dimensional TG-43U1 dose formalism for ideal orientation and from 0 to 180° for vertical and diagonal orientations, with 10° increment. A cross section of the detector arrangement is shown in Figure 2.

To calculate the dosimetric parameters of the seed, TG43-U1 formalism has been used, which are briefly described by Sadeghi et al. [24].

According to TG43-U1 recommendation, the proposed formula for two-dimensional dose rate is

where:

Figure 2.

G rð Þ ;θ

function as follows:

23

D r \_ ð Þ ; <sup>θ</sup> is the dose rate in the water at the distance r in cm from the source.

G rð Þ <sup>0</sup>;θ<sup>0</sup> is the geometry factor; <sup>r</sup><sup>0</sup> <sup>¼</sup> <sup>1</sup> cm and <sup>θ</sup><sup>0</sup> <sup>¼</sup> <sup>90</sup><sup>0</sup> (reference position). g rð Þ and F rð Þ ; θ are the radial dose function and the anisotropy function, respectively. The dose rate constant, Λ, for the seed was calculated as the ratio of the dose to

water at 1 cm from the seed along the transverse axis to the source's air kerma strength, SK, at distance r from the source center. The air kerma strength was

SK <sup>¼</sup> <sup>K</sup>\_ <sup>δ</sup>ð Þ<sup>r</sup> <sup>r</sup>

As the energy of the photons from 103-Pd are low, in the Monte Carlo calculations, all the generated electrons from the photon collisions are absorbed locally, so it was expected that dose is equal to kerma at all points of interest. The air kerma rate, <sup>K</sup>\_ <sup>δ</sup>ð Þ<sup>r</sup> , of the seed was determined by calculating the dose in 1 mm thick airfilled rings in a vacuum. The rings were bounded by 86 and 94° conics and defined with a radial increment of 5–150 cm along the transverse axis of the source to find the SK that is independent to distance [14]. The dose distributions were calculated from the energy deposition averaged over a cell tally F6 in MeV/g/source photon. For the calculations, the titanium characteristic X-ray production was suppressed with δ = 5 keV (δ is the energy cut-off) [25]. The radial dose function expresses the effect of tissue attenuation on photons emitted from seed and defines the dose falloff along the seed transverse axis due to the attenuation and scattering of the

.

<sup>2</sup> (2)

(3)

U�<sup>1</sup> .

θ is the polar angle specifying the point of interest.

Cross section of the detector arrangement for Monte Carlo calculations.

Λ is the dose rate constant with the unit of cGy h�<sup>1</sup>

calculated using the following equation [18]:

photon. g(r) was calculated by the following equation:

gXð Þ¼ r

D r \_ ð Þ ; <sup>θ</sup><sup>0</sup> D r \_ ð Þ <sup>0</sup>; <sup>θ</sup><sup>0</sup>

Dose variations, as the distribution of seed radioactivity, oblique filtration, and self-absorption in the encapsulating material, are defined by the 2D anisotropy

GLð Þ r0; θ<sup>0</sup> GLð Þ r; θ<sup>0</sup>

SK is the air kerma strength and the unit is <sup>U</sup> <sup>¼</sup> cGy cm<sup>2</sup>h�<sup>1</sup>

Modelling, Simulation and Dosimetry of 103-Pd Eye Plaque Brachytherapy

DOI: http://dx.doi.org/10.5772/intechopen.88144

Figure 1. Schematic diagram of the IR06-103Pd seed in (a) ideal, (b) diagonal and (c) vertical orientation.

Modelling, Simulation and Dosimetry of 103-Pd Eye Plaque Brachytherapy DOI: http://dx.doi.org/10.5772/intechopen.88144

#### Figure 2.

inside the titanium capsule. The seed contains five resin beads, each in diameter of 0.6 mm with the compositions of (by weight percent) C, 90%; H, 8%; Pd, 1%; Cl,

Theory, Application, and Implementation of Monte Carlo Method in Science and Technology

inside a titanium capsule of 4.7 mm length; 0.7 and 0.8 mm internal and external diameters, respectively; and 0.6 mm thick end caps and with an effective length of 3 mm. 103-Pd radioactive material is absorbed uniformly in the resin bead volume [23]. Figure 1 shows a schematic diagram of the IR06-103Pd seed. As the resin beads are free to move within the titanium capsule, their location can vary with seed orientations. Following the TG-43U1 recommendation for "good practice for Monte Carlo calculations" [18], mechanical mobility of the internal component of the seed has been considered in the simulations, and three geometric models (ideal, vertical

. The resin beads are packed

g rð ÞF rð Þ ; θ (1)

0.7%; and N, 0.3%, with the density equal to 1.14 g/cm<sup>3</sup>

used, which are briefly described by Sadeghi et al. [24].

D r \_ ð Þ¼ ; <sup>θ</sup> SK<sup>Λ</sup>

2.2 Seed Monte Carlo dosimetry

two-dimensional dose rate is

Figure 1.

22

and diagonal) of the seed were developed as shown in Figure 1a–c.

The IR06-103Pd brachytherapy seed has been simulated in the center of a spherical water phantom in 15 cm radius with an array of 1 mm thick detector rings. Detectors were defined at distances of r = 0.25, 0.5, 0.75, 1, 2, 3, 4, 5 and 7 cm, away from the palladium-103 seed and at polar angles relative to the seed longitudinal axis from 0 to 90°. The rings were also bounded with two cones (10°) bisecting the phantom sphere corresponding to points in two-dimensional TG-43U1 dose formalism for ideal orientation and from 0 to 180° for vertical and diagonal orientations, with 10° increment. A cross section of the detector arrangement is shown in Figure 2. To calculate the dosimetric parameters of the seed, TG43-U1 formalism has been

According to TG43-U1 recommendation, the proposed formula for

Schematic diagram of the IR06-103Pd seed in (a) ideal, (b) diagonal and (c) vertical orientation.

G rð Þ ; θ G rð Þ <sup>0</sup>; θ<sup>0</sup> Cross section of the detector arrangement for Monte Carlo calculations.

where:

D r \_ ð Þ ; <sup>θ</sup> is the dose rate in the water at the distance r in cm from the source. θ is the polar angle specifying the point of interest.

SK is the air kerma strength and the unit is <sup>U</sup> <sup>¼</sup> cGy cm<sup>2</sup>h�<sup>1</sup> .

Λ is the dose rate constant with the unit of cGy h�<sup>1</sup> U�<sup>1</sup> .

G rð Þ ;θ G rð Þ <sup>0</sup>;θ<sup>0</sup> is the geometry factor; <sup>r</sup><sup>0</sup> <sup>¼</sup> <sup>1</sup> cm and <sup>θ</sup><sup>0</sup> <sup>¼</sup> <sup>90</sup><sup>0</sup> (reference position). g rð Þ and F rð Þ ; θ are the radial dose function and the anisotropy function, respectively.

The dose rate constant, Λ, for the seed was calculated as the ratio of the dose to water at 1 cm from the seed along the transverse axis to the source's air kerma strength, SK, at distance r from the source center. The air kerma strength was calculated using the following equation [18]:

$$\mathcal{S}\_K = \dot{\mathcal{K}}\_\delta(r)r^2 \tag{2}$$

As the energy of the photons from 103-Pd are low, in the Monte Carlo calculations, all the generated electrons from the photon collisions are absorbed locally, so it was expected that dose is equal to kerma at all points of interest. The air kerma rate, <sup>K</sup>\_ <sup>δ</sup>ð Þ<sup>r</sup> , of the seed was determined by calculating the dose in 1 mm thick airfilled rings in a vacuum. The rings were bounded by 86 and 94° conics and defined with a radial increment of 5–150 cm along the transverse axis of the source to find the SK that is independent to distance [14]. The dose distributions were calculated from the energy deposition averaged over a cell tally F6 in MeV/g/source photon. For the calculations, the titanium characteristic X-ray production was suppressed with δ = 5 keV (δ is the energy cut-off) [25]. The radial dose function expresses the effect of tissue attenuation on photons emitted from seed and defines the dose falloff along the seed transverse axis due to the attenuation and scattering of the photon. g(r) was calculated by the following equation:

$$\mathbf{g}\_{X}(r) = \frac{\dot{D}(r, \theta\_{0})}{\dot{D}(r\_{0}, \theta\_{0})} \frac{G\_{L}(r\_{0}, \theta\_{0})}{G\_{L}(r, \theta\_{0})} \tag{3}$$

Dose variations, as the distribution of seed radioactivity, oblique filtration, and self-absorption in the encapsulating material, are defined by the 2D anisotropy function as follows:

$$F(r,\theta) = \frac{\dot{D}(r,\theta)}{\dot{D}(r,\theta\_0)} \frac{G\_L(r,\theta\_0)}{G\_L(r,\theta)}\tag{4}$$

The simulations were performed in water with 1 � 109 histories giving statistical uncertainties of 2.5 and 3.5% at 1 and 5 cm along the long axis and 0.05–0.1% at 1 and 5 cm on the transverse plane. The statistical uncertainty in the air was 1% with 7 � 107 histories. In this study, the Monte Carlo simulation was benchmarked with the brachytherapy seed model Theragenics 200 [18, 26].

#### 2.3 Eye plaque simulation

To determine the dose rate around the eye plaque, eyeball and eye plaque, which are loaded with the seeds, are modelled in the center of 20 � <sup>20</sup> � 15 cm3 water phantom. The seeds were distributed in the Silastic insert. The longitudinal axes of the seeds are perpendicular to the eye phantom central plane.

The total dose is calculated by the following equation [14]:

$$\dot{d}(\mathbf{x}, \mathbf{y}, \mathbf{z}) = {}\_{\text{SP}} \dot{d}(\mathbf{x}, \mathbf{y}, \mathbf{z}) \left[ {}\_{\text{source}} \text{S}\_{\text{K}} \left( \frac{\text{SK}}{\text{A}} \right)^{-1} \text{K} \right] \text{.} n \tag{5}$$

determined by integrating over the treatment time, taking into account the exponential decay of the source". Also, the photoelectric absorption, fluorescent emission and Rayleigh and Compton scattering, of characteristic K- and L-shell X-rays, are all simulated. For variance reduction, the electron and photon transport energy cutoff in all calculations was selected at 1 and 5 keV, respectively [29]. In the simulation 3.8 108 photon histories were simulated, and the statistical uncertainties at 5 and 11 mm (tumour apex) depth of central axis were obtained at 0.7 and 1.1%, respectively. Statistical uncertainties at the opposite side of the eye exceeded 4%

Points of interest for eye plaque dosimetry, given in the center of eye reference frame (scale in centimeters) for a right eye [17]. In the figure a plaque midway between the posterior pole and equator temporal is shown. All points of interest are indicated (with the exception of the lacrimal gland, which does not lie in the plane shown).

which has the greatest uncertainty among the points on interest.

Modelling, Simulation and Dosimetry of 103-Pd Eye Plaque Brachytherapy

DOI: http://dx.doi.org/10.5772/intechopen.88144

In this work, the Monte Carlo simulation was benchmarked with the Theragenics model 200 source. The comparison between the calculated value of Λ

data for the seed [18], 0.686 cGy h<sup>1</sup> <sup>U</sup><sup>1</sup> (0.1% difference), shows the accuracy of our simulation method. The result has been presented in Table 1. Based on the calculations, the dose rate constant for the IR06-103Pd source in ideal orientation is

commercial sources. Calculated SK per contained activity for model 200 in this work

WAFAC simulation, [26] and Melhus et al. [14] calculations. The values of Λ in

three seed orientations ranged from 0.689 to 0.697 cGy h<sup>1</sup> U<sup>1</sup>

. The result was compared to 0.721 U mCi<sup>1</sup> for Williamson's

, and the previously published

, with a 0.34%

<sup>U</sup><sup>1</sup> which is comparable with the other two

3. Results and discussions

Figure 3.

3.1 Seed dosimetry benchmarking

estimated to be 0.692 0.020 cGy<sup>h</sup><sup>1</sup>

was 0.722 U mCi<sup>1</sup>

25

for the model 200 in this study, 0.685 cGy h<sup>1</sup> U<sup>1</sup>

where \_ d xð Þ ; y; z is the dose rate at (x, y, z) position, Sk is the air kerma strength per history calculated by using Monte Carlo methods, A is the activity (mCi), K is the photons emitted per unit activity (photons mCi�<sup>1</sup> ) and n is the number of seeds which are loaded in the eye plaque. The COMS eye plaques which are used in this study are composed of two parts with diameters ranging from 10 to 22 mm in 2 mm increments:


The plaque assumed a standard eye diameter of 24.6 mm by considering lens and homogenized eye materials according to ICRU 46 [28]. The position of the points is followed by Thomson et al. [17] (Figure 3). The lens is modelled in the homogenized eye, and to obtain the dose rate, the plaque and eye ball are then modelled at the center of the spherical water phantom with 30 cm diameter. The plaque backing and Silastic insert effect on dose rate is obtained by replacing water with gold and Silastic insert. Central axis depth dose to water was determined using the F6 tally of MCNP for 0.05 mm radius and 0.01 mm thick cylindrical voxels from the outer sclera (�1 mm) to 11 mm inside the eye in 0.5 mm steps [2]. For the comparison doses to interest points (center of the eye, macula, optic disk, proximal sclera, tumour apex, lacrimal gland and retina opposite the apex) have been determined. The total dose is calculated following Melhus and Rivard [14] and Thomson et al. [17] verbatim: "The Monte Carlo simulations provide the dose in a voxel per history. The dose rate is calculated by dividing this number by the air kerma strength per history for the relevant seed type and multiplying by the number of seeds and the air kerma strength per seed. The air kerma strength per seed is chosen in order to obtain a prescription dose of 85Gy at the tumour apex (5 mm on the central axis) in 168 hours for 103-Pd. The total dose delivered during treatment is then

Modelling, Simulation and Dosimetry of 103-Pd Eye Plaque Brachytherapy DOI: http://dx.doi.org/10.5772/intechopen.88144

#### Figure 3.

F rð Þ¼ ; <sup>θ</sup> D r \_ ð Þ ; <sup>θ</sup>

Theory, Application, and Implementation of Monte Carlo Method in Science and Technology

the brachytherapy seed model Theragenics 200 [18, 26].

2.3 Eye plaque simulation

where \_

increments:

24

\_

and a density of 1.12 g/cm<sup>3</sup> [15]

d xð Þ¼ ; <sup>y</sup>; <sup>z</sup> SP \_

the photons emitted per unit activity (photons mCi�<sup>1</sup>

D r \_ ð Þ ; <sup>θ</sup><sup>0</sup>

To determine the dose rate around the eye plaque, eyeball and eye plaque, which are loaded with the seeds, are modelled in the center of 20 � <sup>20</sup> � 15 cm3 water phantom. The seeds were distributed in the Silastic insert. The longitudinal

d xð Þ ; y; z sourceSK

per history calculated by using Monte Carlo methods, A is the activity (mCi), K is

which are loaded in the eye plaque. The COMS eye plaques which are used in this study are composed of two parts with diameters ranging from 10 to 22 mm in 2 mm

a. The gold backing, with the composition of (by weight) 77% gold, 14% silver,

b.The Silastic insert as a seed career with the composition of (by weight) 6.3% hydrogen, 24.9% carbon, 28.9% oxygen, 39.9% silicon and 0.005% platinum

The plaque assumed a standard eye diameter of 24.6 mm by considering lens and homogenized eye materials according to ICRU 46 [28]. The position of the points is followed by Thomson et al. [17] (Figure 3). The lens is modelled in the homogenized eye, and to obtain the dose rate, the plaque and eye ball are then modelled at the center of the spherical water phantom with 30 cm diameter. The plaque backing and Silastic insert effect on dose rate is obtained by replacing water with gold and Silastic insert. Central axis depth dose to water was determined using the F6 tally of MCNP for 0.05 mm radius and 0.01 mm thick cylindrical voxels from the outer sclera (�1 mm) to 11 mm inside the eye in 0.5 mm steps [2]. For the comparison doses to interest points (center of the eye, macula, optic disk, proximal sclera, tumour apex, lacrimal gland and retina opposite the apex) have been determined. The total dose is calculated following Melhus and Rivard [14] and Thomson et al. [17] verbatim: "The Monte Carlo simulations provide the dose in a voxel per history. The dose rate is calculated by dividing this number by the air kerma strength per history for the relevant seed type and multiplying by the number of seeds and the air kerma strength per seed. The air kerma strength per seed is chosen in order to obtain a prescription dose of 85Gy at the tumour apex (5 mm on the central axis) in 168 hours for 103-Pd. The total dose delivered during treatment is then

8% 159 copper and 1% palladium and a density of 15.8 g/cm<sup>3</sup> [27]

d xð Þ ; y; z is the dose rate at (x, y, z) position, Sk is the air kerma strength

SK A � ��<sup>1</sup>

" #

K

:n (5)

) and n is the number of seeds

axes of the seeds are perpendicular to the eye phantom central plane. The total dose is calculated by the following equation [14]:

The simulations were performed in water with 1 � 109 histories giving statistical uncertainties of 2.5 and 3.5% at 1 and 5 cm along the long axis and 0.05–0.1% at 1 and 5 cm on the transverse plane. The statistical uncertainty in the air was 1% with 7 � 107 histories. In this study, the Monte Carlo simulation was benchmarked with

GLð Þ r; θ<sup>0</sup>

GLð Þ <sup>r</sup>; <sup>θ</sup> (4)

Points of interest for eye plaque dosimetry, given in the center of eye reference frame (scale in centimeters) for a right eye [17]. In the figure a plaque midway between the posterior pole and equator temporal is shown. All points of interest are indicated (with the exception of the lacrimal gland, which does not lie in the plane shown).

determined by integrating over the treatment time, taking into account the exponential decay of the source". Also, the photoelectric absorption, fluorescent emission and Rayleigh and Compton scattering, of characteristic K- and L-shell X-rays, are all simulated. For variance reduction, the electron and photon transport energy cutoff in all calculations was selected at 1 and 5 keV, respectively [29]. In the simulation 3.8 108 photon histories were simulated, and the statistical uncertainties at 5 and 11 mm (tumour apex) depth of central axis were obtained at 0.7 and 1.1%, respectively. Statistical uncertainties at the opposite side of the eye exceeded 4% which has the greatest uncertainty among the points on interest.

### 3. Results and discussions

#### 3.1 Seed dosimetry benchmarking

In this work, the Monte Carlo simulation was benchmarked with the Theragenics model 200 source. The comparison between the calculated value of Λ for the model 200 in this study, 0.685 cGy h<sup>1</sup> U<sup>1</sup> , and the previously published data for the seed [18], 0.686 cGy h<sup>1</sup> <sup>U</sup><sup>1</sup> (0.1% difference), shows the accuracy of our simulation method. The result has been presented in Table 1. Based on the calculations, the dose rate constant for the IR06-103Pd source in ideal orientation is estimated to be 0.692 0.020 cGy<sup>h</sup><sup>1</sup> <sup>U</sup><sup>1</sup> which is comparable with the other two commercial sources. Calculated SK per contained activity for model 200 in this work was 0.722 U mCi<sup>1</sup> . The result was compared to 0.721 U mCi<sup>1</sup> for Williamson's WAFAC simulation, [26] and Melhus et al. [14] calculations. The values of Λ in three seed orientations ranged from 0.689 to 0.697 cGy h<sup>1</sup> U<sup>1</sup> , with a 0.34%


#### Table 1.

Monte Carlo calculated dose rate constant, Λ, of the IR06-103Pd and model 200 seeds in comparison with the measured and calculated values of model MED3633, model 200 and model 2335 seeds.

uncertainty. According to TG-43U1, a standard uncertainty of 3% is acceptable for Monte Carlo studies. The dose rate constant can be calculated by normalizing to the SK of the vertical orientation and the source geometry during the NIST calibration. The values, in this case, are 0.680 � 0.020 cGy h�<sup>1</sup> <sup>U</sup>�<sup>1</sup> , �1.7% lower than the value in the ideal orientation. This result obtained in this study is comparable with Λ values obtained for other 103-Pd sources which are presented in TG-43U1 report. Table 1 shows the calculated dose rate constant for the IR06-103Pd seed and the measured and calculated values of Λ, for NASI model MED3633, Theragenics model 200 and Best model sources.

The calculated line radial dose function gL(r), of the IR06-103Pd for ideal orientation, was fit to a fifth-order polynomial function yielding the following relationship:

$$\mathbf{g}\_L(\mathbf{r}) = \mathbf{a}\_0 + \mathbf{a}\_1 \mathbf{r} + \mathbf{a}\_2 \mathbf{r}^2 + \mathbf{a}\_3 \mathbf{r}^3 + \mathbf{a}\_4 \mathbf{r}^4 + \mathbf{a}\_5 \mathbf{r}^5 \tag{6}$$

Figure 5 shows a comparison between the calculated anisotropy function of the IR06-103Pd seeds at a distance of 2 cm from the source center in water with the other published data (in ideal orientation). The values of the anisotropy function for the new 103-Pd sources agreed with those for the model MED3633, Theragenics model 200 and Best® double-wall 103-Pd sources [18, 26, 30] are found in 4% in angles >20°. Due to the thick end caps of the IR06-103Pd source, the differences in

Monte Carlo calculations for radial dose function, gL(r), for IR06-103Pd and model 200 seeds compared to

Comparison of the calculated radial dose function of IR06-103Pd seeds in water versus other available

Modelling, Simulation and Dosimetry of 103-Pd Eye Plaque Brachytherapy

DOI: http://dx.doi.org/10.5772/intechopen.88144

0.5 1.300 1.330 2 1.333 0.75 1.150 1.170 2 1.144 1.000 1.000 0 1.000 1.5 0.749 0.755 1 0.756 0.555 0.567 2 0.566 0.302 0.305 1 0.318 0.163 0.168 3 0.168 0.089 0.091 3 0.091 0.026 0.027 2 0.026

Theragenics 200 Percent difference (%) IR06-103Pd

r (cm) gL(r)

Ref. [26] Present work

Table 4 shows the calculated central depth dose distribution for COMS eye

smaller angles can be as large as up to 17%.

plaques loaded with IR06-103Pd seeds in the Silastic insert.

3.2 Plaque Monte Carlo simulations

Figure 4.

Table 2.

27

reference Monte Carlo data.

sources [18, 30].

where:

a0 = 1.785, a1 <sup>=</sup> �1.064, a2 = 3.385 � <sup>10</sup>–<sup>1</sup> , a3 <sup>=</sup> �7.062 � <sup>10</sup>–<sup>2</sup> , a4 = 8.469 � <sup>10</sup>–<sup>3</sup> and a5 <sup>=</sup> �4.173 � <sup>10</sup>–<sup>4</sup> define R2 = 9.999 � <sup>10</sup>�<sup>1</sup> .

Figure 4 presents the radial dos�e function, g(r), for IR06-103Pd seed and three other commercial sources. Table 2 shows the differences between the results of this study and AAPM TG-43U1 reference data for model 200. As the differences are <3%, the agreement between these data sets is acceptable. The radial dose function values for two other geometric models, vertical and diagonal, were also calculated, and the disagreement between them varied from <2%. The anisotropy function, F (r,θ), of the IR06-103Pd seed was calculated in the phantom of water, at radial distances of r = 0.25, 0.5, 0.75, 1, 1.5, 2, 3, 4, 5 and 7 cm relative to the seed center and polar angle, θ, ranging from 0 to 180° for vertical and diagonal orientations and 0–90° for ideal orientation, in 10° increment with respect to the seed long axis. The results are shown in Table 3.

Modelling, Simulation and Dosimetry of 103-Pd Eye Plaque Brachytherapy DOI: http://dx.doi.org/10.5772/intechopen.88144

#### Figure 4.

uncertainty. According to TG-43U1, a standard uncertainty of 3% is acceptable for Monte Carlo studies. The dose rate constant can be calculated by normalizing to the SK of the vertical orientation and the source geometry during the NIST calibration.

Monte Carlo calculated dose rate constant, Λ, of the IR06-103Pd and model 200 seeds in comparison with the

measured and calculated values of model MED3633, model 200 and model 2335 seeds.

Source type Method Medium Λ (cGy h�<sup>1</sup> U�<sup>1</sup>

Theory, Application, and Implementation of Monte Carlo Method in Science and Technology

IR06-103Pd Monte Carlo simulation (ideal)<sup>a</sup> Liquid water 0.692 � 0.021

MED3633 TLD dosimetry<sup>b</sup> Solid water 0.688 � 0.05

Theragenics model 200 TLD dosimetry<sup>d</sup> Solid water 0.650 � 0.08

Best model 2335 TLD dosimetry<sup>f</sup> Solid water 0.69 � 0.08

Monte Carlo simulation (diagonal)<sup>a</sup> Liquid water 0.697 � 0.021 Monte Carlo simulation (vertical)a Liquid water 0.689 � 0.021

Monte Carlo simulation<sup>c</sup> Liquid water 0.677 � 0.02

Monte Carlo simulation<sup>e</sup> Liquid water 0.686 � 0.03 Monte Carlo simulation<sup>a</sup> Liquid water 0.685 � 0.02

Monte Carlo simulation<sup>f</sup> Liquid water 0.67 � 0.02

in the ideal orientation. This result obtained in this study is comparable with Λ values obtained for other 103-Pd sources which are presented in TG-43U1 report. Table 1 shows the calculated dose rate constant for the IR06-103Pd seed and the measured and calculated values of Λ, for NASI model MED3633, Theragenics model

tation, was fit to a fifth-order polynomial function yielding the following

gLð Þ¼ r a0 þ a1r þ a2r

a0 = 1.785, a1 <sup>=</sup> �1.064, a2 = 3.385 � <sup>10</sup>–<sup>1</sup>

and a5 <sup>=</sup> �4.173 � <sup>10</sup>–<sup>4</sup> define R2 = 9.999 � <sup>10</sup>�<sup>1</sup>

The calculated line radial dose function gL(r), of the IR06-103Pd for ideal orien-

<sup>2</sup> <sup>þ</sup> a3r

Figure 4 presents the radial dos�e function, g(r), for IR06-103Pd seed and three other commercial sources. Table 2 shows the differences between the results of this study and AAPM TG-43U1 reference data for model 200. As the differences are <3%, the agreement between these data sets is acceptable. The radial dose function values for two other geometric models, vertical and diagonal, were also calculated, and the disagreement between them varied from <2%. The anisotropy function, F (r,θ), of the IR06-103Pd seed was calculated in the phantom of water, at radial distances of r = 0.25, 0.5, 0.75, 1, 1.5, 2, 3, 4, 5 and 7 cm relative to the seed center and polar angle, θ, ranging from 0 to 180° for vertical and diagonal orientations and 0–90° for ideal orientation, in 10° increment with respect to the seed long axis. The

.

<sup>3</sup> <sup>þ</sup> a4r

, a3 <sup>=</sup> �7.062 � <sup>10</sup>–<sup>2</sup>

<sup>4</sup> <sup>þ</sup> a5r

, �1.7% lower than the value

)

<sup>5</sup> (6)

, a4 = 8.469 � <sup>10</sup>–<sup>3</sup>

The values, in this case, are 0.680 � 0.020 cGy h�<sup>1</sup> <sup>U</sup>�<sup>1</sup>

200 and Best model sources.

results are shown in Table 3.

relationship:

a

b Ref. [33]. c Ref. [34]. d Ref. [32]. e Ref. [26]. f Ref. [27].

Table 1.

Present work.

where:

26

Comparison of the calculated radial dose function of IR06-103Pd seeds in water versus other available sources [18, 30].


#### Table 2.

Monte Carlo calculations for radial dose function, gL(r), for IR06-103Pd and model 200 seeds compared to reference Monte Carlo data.

Figure 5 shows a comparison between the calculated anisotropy function of the IR06-103Pd seeds at a distance of 2 cm from the source center in water with the other published data (in ideal orientation). The values of the anisotropy function for the new 103-Pd sources agreed with those for the model MED3633, Theragenics model 200 and Best® double-wall 103-Pd sources [18, 26, 30] are found in 4% in angles >20°. Due to the thick end caps of the IR06-103Pd source, the differences in smaller angles can be as large as up to 17%.

#### 3.2 Plaque Monte Carlo simulations

Table 4 shows the calculated central depth dose distribution for COMS eye plaques loaded with IR06-103Pd seeds in the Silastic insert.

The depth dose distribution has been calculated in 0.5 mm steps between the outer sclera (1 mm) to 3 mm and in 1 mm steps from 4 to 10 mm. The dose distribution is also calculated in water medium to obtain the effect of the Silastic insert and the plaque backing on central axis dose distribution. In this study, the


required air kerma strength per seed (SK) is calculated to deliver prescription dose (85 Gy) to the apex of the tumour (5 mm depth) for 168 hours of implant. In addition, to investigate the effect of different materials constituting the COMS plaque on dose distributions near the plaque, the ratio of dose in three media (discussed above) relative to dose in water medium is shown in Figure 6.

2-D anisotropy functions for the IR06-103Pd seed calculated by Monte Carlo method for the (a) ideal

orientation, (b) vertical orientation and (c) diagonal orientation.

c. 2-D anisotropy function, F(r,θ), in diagonal seed orientation

0.25 1.155 0.471 0.525 0.591 0.567 0.502 0.424 0.352 0.310 1.000 0.5 0.969 0.438 0.485 0.597 0.651 0.673 0.682 0.696 0.723 1.000 0.75 0.941 0.453 0.508 0.631 0.701 0.744 0.775 0.805 0.842 1.000 1 0.918 0.471 0.530 0.657 0.734 0.783 0.822 0.857 0.897 1.000 1.5 0.907 0.497 0.560 0.686 0.767 0.824 0.866 0.906 0.947 1.000 2 0.881 0.515 0.579 0.704 0.786 0.845 0.889 0.930 0.972 1.000 3 0.857 0.540 0.607 0.724 0.806 0.865 0.910 0.953 0.995 1.000 4 0.852 0.556 0.623 0.738 0.817 0.873 0.921 0.962 1.003 1.000 5 0.810 0.577 0.637 0.746 0.825 0.883 0.928 0.969 1.012 1.000 7 0.888 0.610 0.669 0.769 0.846 0.902 0.946 0.979 1.027 1.000

r (cm) 100° 110° 120° 130° 140° 150° 160° 170° 180° 0.25 0.945 0.684 0.879 0.943 0.974 0.993 1.002 1.003 1.004 0.5 0.921 0.652 0.741 0.856 0.935 0.975 0.994 1.002 1.003 0.75 0.889 0.663 0.739 0.837 0.915 0.964 0.989 1.001 1.002 1 0.876 0.673 0.744 0.836 0.910 0.961 0.989 1.000 1.002 1.5 0.860 0.686 0.752 0.837 0.905 0.956 0.985 0.999 1.001 2 0.852 0.697 0.758 0.841 0.905 0.955 0.984 0.999 1.001 3 0.847 0.713 0.769 0.845 0.906 0.954 0.984 0.998 1.002 4 0.843 0.723 0.778 0.848 0.907 0.954 0.983 0.997 1.001 5 0.842 0.733 0.785 0.853 0.908 0.953 0.983 0.996 1.000 7 0.856 0.759 0.806 0.868 0.919 0.963 0.988 1.003 1.005

0° 10° 20° 30° 40° 50° 60° 70° 80° 90°

r (cm) Θ=

DOI: http://dx.doi.org/10.5772/intechopen.88144

Modelling, Simulation and Dosimetry of 103-Pd Eye Plaque Brachytherapy

The effect of 20 mm gold plaque backing on dose distribution along the central axis is shown in Figure 7, which provides central axis depth dose curve for full loaded IR06-103Pd, Theragenics 200 and model 2335 seeds with water replacing the Silastic. This figure demonstrates dose is increased near the plaque; now this wellknown effect is due to L-shell fluorescence photons emitted by atoms in the plaque backing [27]. Emission photons from palladium seeds with an average energy of about 21 keV excite the L-shell in gold and silver [31] which are the composition of the plaque backing. The excitation of these shells results in the emission of fluorescence photons, so this event explains why dose increases near the plaque. About

3.3 Effect of the gold backing

Table 3.


Modelling, Simulation and Dosimetry of 103-Pd Eye Plaque Brachytherapy DOI: http://dx.doi.org/10.5772/intechopen.88144

Table 3.

The depth dose distribution has been calculated in 0.5 mm steps between the outer sclera (1 mm) to 3 mm and in 1 mm steps from 4 to 10 mm. The dose distribution is also calculated in water medium to obtain the effect of the Silastic insert and the plaque backing on central axis dose distribution. In this study, the

Theory, Application, and Implementation of Monte Carlo Method in Science and Technology

a. 2-D anisotropy function, F(r,θ), in ideal seed orientation

0.25 0.053 0.074 0.616 0.854 0.924 0.959 0.979 0.992 0.998 1.000 0.5 0.132 0.165 0.472 0.701 0.845 0.927 0.964 0.985 0.996 1.000 0.75 0.169 0.211 0.480 0.686 0.823 0.912 0.960 0.985 0.997 1.000 1 0.190 0.242 0.491 0.686 0.816 0.903 0.956 0.982 0.996 1.000 1.5 0.229 0.281 0.512 0.692 0.813 0.899 0.952 0.982 0.995 1.000 2 0.265 0.309 0.526 0.696 0.814 0.896 0.950 0.982 0.996 1.000 3 0.294 0.345 0.545 0.705 0.815 0.897 0.949 0.981 0.997 1.000 4 0.319 0.369 0.558 0.709 0.818 0.895 0.948 0.979 0.995 1.000 5 0.337 0.392 0.568 0.715 0.820 0.900 0.948 0.981 0.995 1.000 7 0.405 0.428 0.601 0.730 0.831 0.900 0.948 0.982 1.004 1.000 b. 2-D anisotropy function, F(r,θ), in vertical seed orientation

0° 10° 20° 30° 40° 50° 60° 70° 80° 90°

0° 10° 20° 30° 40° 50° 60° 70° 80° 90°

0.25 1.155 0.471 0.526 0.591 0.568 0.504 0.426 0.351 0.308 1.000 0.5 0.958 0.436 0.485 0.597 0.650 0.672 0.682 0.695 0.720 1.000 0.75 0.931 0.453 0.508 0.631 0.702 0.743 0.775 0.806 0.840 1.000 1 0.907 0.471 0.531 0.656 0.733 0.784 0.823 0.856 0.895 1.000 1.5 0.900 0.497 0.560 0.685 0.767 0.824 0.868 0.905 0.945 1.000 2 0.880 0.514 0.579 0.704 0.786 0.845 0.888 0.928 0.967 1.000 3 0.859 0.541 0.606 0.724 0.810 0.867 0.912 0.952 0.992 1.000 4 0.851 0.557 0.623 0.737 0.817 0.875 0.924 0.961 1.004 1.000 5 0.810 0.577 0.637 0.747 0.826 0.883 0.927 0.968 1.009 1.000 7 0.889 0.610 0.668 0.769 0.846 0.901 0.946 0.977 1.024 1.000

r (cm) 100° 110° 120° 130° 140° 150° 160° 170° 180° 0.25 0.945 0.682 0.877 0.942 0.975 0.993 1.003 1.005 1.002 0.5 0.918 0.652 0.741 0.855 0.933 0.974 0.994 1.003 1.002 0.75 0.887 0.661 0.739 0.837 0.916 0.964 0.989 1.000 1.001 1 0.874 0.673 0.743 0.835 0.908 0.960 0.988 1.000 1.001 1.5 0.856 0.685 0.753 0.837 0.906 0.956 0.985 0.999 1.001 2 0.851 0.696 0.758 0.840 0.905 0.954 0.984 0.998 1.001 3 0.845 0.712 0.768 0.845 0.907 0.954 0.984 0.998 1.001 4 0.842 0.722 0.778 0.848 0.907 0.953 0.983 0.997 1.000 5 0.839 0.733 0.785 0.853 0.909 0.953 0.983 0.996 1.000 7 0.852 0.757 0.805 0.869 0.919 0.963 0.988 1.003 1.004

r (cm) Θ=

r (cm) Θ=

28

2-D anisotropy functions for the IR06-103Pd seed calculated by Monte Carlo method for the (a) ideal orientation, (b) vertical orientation and (c) diagonal orientation.

required air kerma strength per seed (SK) is calculated to deliver prescription dose (85 Gy) to the apex of the tumour (5 mm depth) for 168 hours of implant. In addition, to investigate the effect of different materials constituting the COMS plaque on dose distributions near the plaque, the ratio of dose in three media (discussed above) relative to dose in water medium is shown in Figure 6.
