*Comparative Dosimetric Study between 60Co and 192Ir BEBIG High Dose… DOI: http://dx.doi.org/10.5772/intechopen.102435*

The spectrum of gamma rays used in the simulations was obtained from the (National Nuclear Data Center) [18]; we use a cutoff energy of 10 keV for both of photons and electrons. Up to 2 <sup>10</sup><sup>9</sup> photon histories were simulated in this study using an Intel® Xeon (R) CPU E5620@2.40GH 16, HP-Z600 work station. No technique of variance reduction was used. To calculate the 2D along & away in water, the source was located in the center of a spherical phantom 40 cm in radius; acts like an unbounded phantom up to 20 cm from the source center for both 60Co and 192Ir sources. The density for the liquid water was 0.998 gcm<sup>3</sup> at 22°C according to the HEBD Working Group report. The coordinate axes used are shown in **Figure 1**. To obtain the radial dose function, and the along & away dose rate in the 2D Cartesian look-up table, we use a cylindrical rings system of 400\*800 with 0.05 cm thick concentric to the longitudinal axis.

The high gamma energy of the 60Co source takes electronic disequilibrium up to a distance of about 0.7 cm in water. Thus, we cannot approximate kerma by the dose in the near region to the source as in the case of 192Ir. Consequently, the doses have been scored in distances near the source. The scored values for dose rate were included in the tables given in this study for the located points at distances where electronic disequilibrium exists. For distance greater than 1 cm from the source, to decrease the statistical uncertainty, the dose was approximate by the scored kerma; a previous study of Ballester et al., (2005) mentioned that the differences between dose and kerma are negligible at distances greater than 1 cm [19]. 10<sup>9</sup> Photon histories were


#### **Table 1.**

*Elemental composition used in this study by mass percentage for: sources and water phantom, (international commission on radiation units and measurements, ICRU report 44, 1989) [20].*


#### **Table 2.**

*Per unite source activity and Λ, obtained with MCNPX, compared with the values obtained in other previous studies.*

simulated to obtain dose rate values in the region of electronic disequilibrium and 2.10<sup>9</sup> photon histories to score kerma for the 60Co source. 109 photon histories were used to estimate kerma for the 192Ir source.

To investigate the air-kerma strength, we kept the source in the center of a cubic phantom with 5 � <sup>5</sup> � 5 m<sup>3</sup> in dimensions. Then, the air-kerma was scored at 1 m in the transversal axis of the source using 1 mm thickness cylindrical rings, concentrated from distance 99.5 cm to 100.5 cm, filled with air, with relative humidity of 40% and mass density 0.001205 g cm�<sup>3</sup> . In addition to that, to avoid the correction for photon attenuation and scatter in air, we have considered outside the scoring cells filled with vacuum. Elemental composition of materials used in this simulation is shown in **Table 1**, taken from the (ICRU 44 report) [20].

The dose rate constant was calculated using Eq. (2), by dividing the scored value of dose in a cubic voxel, with 0.1 � 0.1 � 0.1 mm<sup>3</sup> in dimensions by the air-kerma strength. Therefore, the scoring zone located in 1 cm from the active core center in the transversal axis (Y-axis), in a spherical phantom of 40 cm in radius filled with water.

$$
\Lambda = \frac{\dot{D}(r, \theta)}{\mathcal{S}\_k} \tag{2}
$$

The values of and Λ were compared with the published data and presented in **Table 2**.

### **5. Air kerma strength**

The TG-43 formalism and the full report for the HEBD Working Group of the AAPM and ESTRO recommend for HDR brachytherapy specifying photon-emitting sources in terms of the air-kerma strength SK, taking into account correction for attenuation and scattering in air. The relation between SK and Kair is given by Eq. (3) [21]:

$$\mathbf{S}\_{\mathbf{K}} = \mathbf{K}\mathbf{a}\mathbf{i}\_{\text{dref}} \times \mathbf{d}\_{\text{ref}}^2 \tag{3}$$

Where the reference air-kerma rate is defined at *dref* = 1 m. The air-kerma per source photon depends to the photon fluence by the equation:

$$Kair = 1.602 \text{ 10}^{-10} \ast \int\_{Emin}^{Emax} \Phi(E) E \left(\frac{\mu en(E)}{\rho}\right) dE \tag{4}$$

Where Kair is air kerma per source photon in Gy, the factor 1.602 10�<sup>10</sup> converted the result from MeV g�<sup>1</sup> into Gy, photon fluence (cm�<sup>2</sup> ) at the energy E (MeV) per initial source photon at the distance d, and the mass-energy absorption coefficient (cm�<sup>2</sup> g�<sup>1</sup> ) at the energy E [22].

To obtain the total air-kerma, we use the following Eq. (8) [22].

$$
\dot{\mathbf{K}} \dot{a} \dot{r} = \mathbf{1.602 } \mathbf{10}^{-10} \ast \sum\_{E \neq i}^{E \text{max}} \Phi(Ei) E i \left( \frac{\mu \epsilon n(Ei)}{\rho} \right) \Delta E \tag{5}
$$

The total air-kerma per incident photon, *Ei* the midpoint for an energy bin, *ΔE* the bin size in MeV, for this study we use the photon fluence spectrum in 10 keV intervals. Thus, we introduce the Eq. (5) by using the MCNPX F6 tally, which is a track-length estimator [23], providing results in (MeV/g) [10, 24], converted into Gy by using the appropriate FM card tally multiplier (FM = 1.60210�10). The composition for air is taken from the tables of X-ray mass attenuation coefficients and mass energy-absorption coefficients (NIST) [25]. The HEBD recommended a shorthand notation for the air-kerma strength: 1 U = 1μGym2 h�<sup>1</sup> = 1cGycm<sup>2</sup> h�<sup>1</sup> .Then to calculate the air-kerma strength per unit of source activity in (Gym<sup>2</sup> s �<sup>1</sup> Bq�<sup>1</sup> ), we use Eq. (6) below:

$$\frac{\text{Sk}}{A} = \dot{\text{K}} \dot{a} \dot{r} (d\_{\text{ref}}) d\_{\text{ref}^2} \text{N} \tag{6}$$

Where A is the source activity (Bq) and N the number of photons per decay, considered equal 2 for the 60Co source, and 2.21 for the 192Ir source.

### **6. Radial dose function**

The radial dose function gL(r) described in the protocol of the (HEBD) takes into account scattering and absorption in the transversal axis of the source; it was calculated in a spherical phantom filled with water using concentric cylindrical rings to the longitudinal axis, with 0.05 cm thickness for the ranging distance from 0.25 cm to 20 cm for both of the simulated sources in this study. The results obtained are presented in **Table 3**.

### **7. Along & away absorbed dose**

The along & away absorbed dose rates were investigated for the ranging distance from 0.25 cm to 7 cm in the transversal axis and from 0 cm to �7 cm in the longitudinal axis. The 2D along & away was compared with the published data. The results

*Dosimetry*


#### **Table 3.**

*Radial dose function obtained for 60Co and 192Ir using MCNPX in a water.*

are tabulated in the form recommended by the HEBD Working Group report [1], **Tables 4** and **5**, respectively, for 60Co and 192Ir.

### **8. Uncertainties**

The uncertainties evaluated in this study are the type A (k = 1) statistical uncertainty contribution dependent on the Monte Carlo technique. No technique of the variance reduction was used as mentioned before. All MCNPX results are normalized to be per initial particle history printed in the output with an additional number beside, which is the estimated statistical uncertainty. In this work statistical uncertainties are less than 0.8% and 0.4% type A uncertainty (k = 1) respectively for 60Co and 192Ir, derived by considering the contribution of the different simulated parameters for both of the simulated sources. In addition to the contribution of the propagated uncertainty for both of radial dose function and the 2D along & away in the relative uncertainties of the MCNPX output tallies. For the cobalt source dose rates, uncertainties were calculated from the quadrature sum of uncertainties obtained for the dose scored in the near distance to the source, and the scored kerma for the distance where the electronic equilibrium is reached.

Type B uncertainties are difficult to evaluate because of different contributions such as uncertainties of the cross section and energy spectrum, uncertainties in the modeled geometry of the source, and uncertainties in the scoring dose and kerma


*Dose rate along* *the delivery cable).*

*& away per unit air-kerma strength (cGyh1 U1) in liquid water obtained for the BEBIG 60Co source (model: Co0.A86),*

 *(+Z toward the source tip and -Z toward*
