**2. Material and methods**

The Monte Carlo code, PENELOPE®, version 2008 was used to achieve the main objective to simulate tumors with hypoxia. Since the code allows the "construction" of materials by the compound's chemical composition, the soft tissue material from the code, number 262, was modified by adding different concentrations tumors with hypoxia, from knowledge that chemical compounds of the normal tissue are approximately equal to the tumor. The geometry of simulation used was a parallelepiped of 8 × 15 × 21 cm3 containing six identical spherical tumors of 1.2 cm radius, as shown in **Figure 1** [47]. In that work 2 × 109 primary particles and 0.1mm2 pixel size and photon spectra at 6 MV [48], which was applied in the input file of the code, were used. The tumors were located before the buildup region for the

#### **Figure 1.**

*Geometric representation through of the PENELOPE code, for the simulation of six tumors (spheres) spaced within the parallelepiped, in the XY plane.*

**119**

**3. Results**

proposed for [55].

**Figure 2.**

*Evaluation by Monte Carlo Simulation of Doses Distributions in Tumors with Hypoxia*

6 MV beam at 10 cm from the top of the phantom. The simulated material of the parallelepiped was a soft tissue, available in the code, while the tumors had different pressures of oxygen, from 5 to 70 mmHg. Simulation responses were obtained

*Geometric representation of the PENELOPE code, for the simulation of a tumor (sphere) centralized in the* 

This geometry used to simulate the radiation conditions was 22 × 22 cm<sup>2</sup>

tion field, 100 cm source-tumor distance, with a 6 MV energy beam. The obtained results from the simulation were analyzed in terms of deposited energy and values of OER relative to the pressure O2 in terms of mmHg, following the OER equation

The second part of that work published [47] analyzed the oxygen effect in the dose distributions in simulated cranial tumors: one with different oxygen concentrations and the other with normal oxygenation [18, 36–39]. A cylinder with 18 cm in diameter and 20 cm in height was simulated to represent the head of an adult, containing concentric spheres of radii of 0.5–1.2 cm that can represent the dimensions of a glioblastoma tumor. Due the characteristics of localization of this kind of tumor, the simulation tumors were centralized at 10 cm height, beyond the equilibrium range to charged particle for the energy used in this study. The bean incident was simulated in the direction to the phantom, parallel to the Z axis. In **Figure 2** the geometry for radiation for a simulated tumor with different concentrations of oxygen from minor (radius sphere 0.5 cm) to greater is shown (radius sphere 1.2 cm). The simulated material of the tumors and brain structures was soft tissue due to similar chemical compounds present. This material is available in the simulation code. In the spheres (tumors) these materials were modified with different concentrations of oxygen. The radiation conditions used were 1.2 × 1.2 cm radiation field,

0.616)/ (<sup>1</sup> + p O2

radia-

0.616) (1)

through the values average in the whole target or spherical tumors.

OER = 1 + 0.81 (p O2

source-tumor distance of 100 cm, and photon spectra at 6 MV.

From the results obtained to the six spheres inserted in the parallelepiped (**Figure 1**), the deposited energy was plotted for each spherical tumor containing

*DOI: http://dx.doi.org/10.5772/intechopen.90611*

*center of the brain (cylinder), in the ZY plane.*

*Evaluation by Monte Carlo Simulation of Doses Distributions in Tumors with Hypoxia DOI: http://dx.doi.org/10.5772/intechopen.90611*

**Figure 2.**

*Translational Research in Cancer*

**PENELOPE code**

**2. Material and methods**

lelepiped of 8 × 15 × 21 cm3

als that constitute a simulation geometry.

code is based on the published by Alva-Sánchez [47].

radius, as shown in **Figure 1** [47]. In that work 2 × 109

Another executable program comes together with PENELOPE package, the GEOVIEW.exe, which allows the visualization of the defined bodies and the materi-

As some tumors have concentric circles of regions of low concentration of oxygenation, which are deprived of adequate blood supply, the evaluation of those regions becomes essential to guarantee the success of radiotherapy treatments [4]. The study evaluated the hypoxia effect in the dose distribution for simulated cranial tumor with different concentrations of oxygen [18, 36–39] through the PENELOPE simulation code. The code allows the "construction" of tumors through the compound's chemical composition, mass density, mean excitation energy, and energy and oscillator strength [45, 46]. The tumor with different concentrations of oxygen will be compared with one under normal oxygen conditions. The parameter OER was applied to express the decreased radiosensibilty of the tumor with hypoxia. The simulation of the dose distribution in tumors with hypoxia through PENELOPE

The Monte Carlo code, PENELOPE®, version 2008 was used to achieve the main objective to simulate tumors with hypoxia. Since the code allows the "construction" of materials by the compound's chemical composition, the soft tissue material from the code, number 262, was modified by adding different concentrations tumors with hypoxia, from knowledge that chemical compounds of the normal tissue are approximately equal to the tumor. The geometry of simulation used was a paral-

pixel size and photon spectra at 6 MV [48], which was applied in the input file of the code, were used. The tumors were located before the buildup region for the

*Geometric representation through of the PENELOPE code, for the simulation of six tumors (spheres) spaced* 

containing six identical spherical tumors of 1.2 cm

primary particles and 0.1mm2

**1.2 Simulation of the dose distribution in tumors with hypoxia through** 

**118**

**Figure 1.**

*within the parallelepiped, in the XY plane.*

*Geometric representation of the PENELOPE code, for the simulation of a tumor (sphere) centralized in the center of the brain (cylinder), in the ZY plane.*

6 MV beam at 10 cm from the top of the phantom. The simulated material of the parallelepiped was a soft tissue, available in the code, while the tumors had different pressures of oxygen, from 5 to 70 mmHg. Simulation responses were obtained through the values average in the whole target or spherical tumors.

This geometry used to simulate the radiation conditions was 22 × 22 cm<sup>2</sup> radiation field, 100 cm source-tumor distance, with a 6 MV energy beam. The obtained results from the simulation were analyzed in terms of deposited energy and values of OER relative to the pressure O2 in terms of mmHg, following the OER equation proposed for [55].

$$\text{OER} = \mathbf{1} + \mathbf{0.81} \left( \mathbf{p} \, \text{O}\_2^{0.616} \right) / \left( \mathbf{1} + \mathbf{p} \, \text{O}\_2^{0.616} \right) \tag{1}$$

The second part of that work published [47] analyzed the oxygen effect in the dose distributions in simulated cranial tumors: one with different oxygen concentrations and the other with normal oxygenation [18, 36–39]. A cylinder with 18 cm in diameter and 20 cm in height was simulated to represent the head of an adult, containing concentric spheres of radii of 0.5–1.2 cm that can represent the dimensions of a glioblastoma tumor. Due the characteristics of localization of this kind of tumor, the simulation tumors were centralized at 10 cm height, beyond the equilibrium range to charged particle for the energy used in this study. The bean incident was simulated in the direction to the phantom, parallel to the Z axis. In **Figure 2** the geometry for radiation for a simulated tumor with different concentrations of oxygen from minor (radius sphere 0.5 cm) to greater is shown (radius sphere 1.2 cm).

The simulated material of the tumors and brain structures was soft tissue due to similar chemical compounds present. This material is available in the simulation code. In the spheres (tumors) these materials were modified with different concentrations of oxygen. The radiation conditions used were 1.2 × 1.2 cm radiation field, source-tumor distance of 100 cm, and photon spectra at 6 MV.

#### **3. Results**

From the results obtained to the six spheres inserted in the parallelepiped (**Figure 1**), the deposited energy was plotted for each spherical tumor containing

#### *Translational Research in Cancer*

different pressures of oxygen as shown in **Figure 3**. Values of the OER were obtained through Eq. (1) and plotted for each pressure of oxygen, as shown in **Figure 4**.

The *penmain* file of the code generates an output file with generic information, such as number of simulated primary showers, secondary-particle generation probabilities, average deposited energies, and statistical error, etc. Each simulation was written in a separate file. The program computes and delivers the statistical uncertainties (3σ) of all evaluated quantities and distributions. Thus, for all obtained results, an error at least 3.58% was reported by the code used.

**Figure 5a** shows the dose distributions for a simulated tumor of 1.2 cm radius with different pressures of O2, and **Figure 5b** shows the same tumor of **Figure 5a** with normal oxygenation.

These distributions were compared through a dose profile, as shown in **Figure 6**, along the center of the dose maps.

**Figure 3.** *Behavior and deposited energy for six identical spheres with different pressures of O2.*

**121**

*Evaluation by Monte Carlo Simulation of Doses Distributions in Tumors with Hypoxia*

*: (a) tumor 1, with different pressures O2, and (b) tumor 2, normal* 

*DOI: http://dx.doi.org/10.5772/intechopen.90611*

**Figure 5.**

**Figure 6.**

*oxygenation.*

*Dose distribution of the tumor of 7.24 cm3*

**4. Discussions and conclusions**

presented in the literature [36, 49].

Statistical uncertainties at least 3.58% was reported by the code for all simula-

The obtained values of the OER relative to pressure of O2 shown in **Figure 4** have a behavior similar to an increasing logarithm function as found in literature [50–54]. After the 60 mmHg of pressure of O2, the OER values have a trend to value constant. **Figures 3** and **4** confirm the increasing of the deposited energy for tumors with a high concentration of oxygen, because of the oxygen effect that is

The dose distributions shown in **Figure 5** visually show almost the same distribution, but in the field profile of both distributions, shown in **Figure 6**, a difference of 7.29% was found at a radial distance of 0.6 mm of the tumor. The code allowed evaluated the influences of effect of oxygen for tumors with hypoxia that is related

tions. From the results shown in **Figure 3**, we can observe that the deposited energy have an approximately linear behavior with the increases in pressure until 50 mmHg of O2; from this pressure the deposited energy shows a constant trend for higher pressures than 60 mmHg of O2. This behavior was also equivalent to those

*Dose relative profile of tumor 1 (with different pressures of O2) and tumor 2 (with normal oxygenation).*

disregarded in accuracy of the ionization radiation treatment [53, 55].

**Figure 4.** *OER values relative to each of the six identical spheres with different pressures of O2.*

*Evaluation by Monte Carlo Simulation of Doses Distributions in Tumors with Hypoxia DOI: http://dx.doi.org/10.5772/intechopen.90611*

#### **Figure 5.**

*Translational Research in Cancer*

with normal oxygenation.

along the center of the dose maps.

different pressures of oxygen as shown in **Figure 3**. Values of the OER were obtained through Eq. (1) and plotted for each pressure of oxygen, as shown in **Figure 4**.

The *penmain* file of the code generates an output file with generic information, such as number of simulated primary showers, secondary-particle generation probabilities, average deposited energies, and statistical error, etc. Each simulation was written in a separate file. The program computes and delivers the statistical uncertainties (3σ) of all evaluated quantities and distributions. Thus, for all obtained

**Figure 5a** shows the dose distributions for a simulated tumor of 1.2 cm radius with different pressures of O2, and **Figure 5b** shows the same tumor of **Figure 5a**

These distributions were compared through a dose profile, as shown in **Figure 6**,

results, an error at least 3.58% was reported by the code used.

*OER values relative to each of the six identical spheres with different pressures of O2.*

*Behavior and deposited energy for six identical spheres with different pressures of O2.*

**120**

**Figure 4.**

**Figure 3.**

*Dose distribution of the tumor of 7.24 cm3 : (a) tumor 1, with different pressures O2, and (b) tumor 2, normal oxygenation.*

#### **Figure 6.**

*Dose relative profile of tumor 1 (with different pressures of O2) and tumor 2 (with normal oxygenation).*

#### **4. Discussions and conclusions**

Statistical uncertainties at least 3.58% was reported by the code for all simulations. From the results shown in **Figure 3**, we can observe that the deposited energy have an approximately linear behavior with the increases in pressure until 50 mmHg of O2; from this pressure the deposited energy shows a constant trend for higher pressures than 60 mmHg of O2. This behavior was also equivalent to those presented in the literature [36, 49].

The obtained values of the OER relative to pressure of O2 shown in **Figure 4** have a behavior similar to an increasing logarithm function as found in literature [50–54]. After the 60 mmHg of pressure of O2, the OER values have a trend to value constant. **Figures 3** and **4** confirm the increasing of the deposited energy for tumors with a high concentration of oxygen, because of the oxygen effect that is disregarded in accuracy of the ionization radiation treatment [53, 55].

The dose distributions shown in **Figure 5** visually show almost the same distribution, but in the field profile of both distributions, shown in **Figure 6**, a difference of 7.29% was found at a radial distance of 0.6 mm of the tumor. The code allowed evaluated the influences of effect of oxygen for tumors with hypoxia that is related

with the outcome of treatment with radiotherapy. However, the hypoxic tumor cells are resistant to radiation [8]. From the comparisons of the dose distribution in the central plane of the phantom, it was observed that there are regions where the concentration of oxygen was lower (that of sphere of less radius), thus, the energy deposited was lower, unlike the spheres with higher oxygen concentrations.

Despite the fact that the code cannot simulate the physiological factor, which it can modulate a variety of normal developmental and metabolic processes that cause injury to the tumor cell, the present study of tumors with hypoxia plays an important role in dose distribution that can compromise the treatment outcomes and individual prognosis.
