**Abstract**

Radiotherapy is one of the most useful modalities applied for tumor treatments, which use ionization radiation to eradicate the tumor, in major cases. Cells with normal oxygenation are more sensitive to the effects of ionizing radiation than those with hypoxic conditions, because O2 molecules react rapidly with free radicals, produced by irradiation, originating highly reactive radicals. Thus, the different concentrations of hypoxia in tumors can modulate the response of the irradiation through the radioresistance they present and consequently the success of the treatment. This chapter deals with the dose distributions in cranial tumors with different concentrations of hypoxia through a code based on Monte Carlo simulation.

**Keywords:** radiotherapy, tumor hypoxia, dose distribution, Monte Carlo simulations

### **1. Introduction**

The modality of treatment with ionization radiation, specifically, for cancer can be considered routinely in several hospital centers, which must have human and technological resources capable of conforming the radiation dose into the target volumes and trying to avoid high toxicity in the adjuvant tissues. Although all these resources exist, the treatment planning is based on prior knowledge of the structures of the patient that can be obtained through any kind of medical images. Once the tumor has been diagnosed, appropriate treatment is indicated without, often, considering some factors that may influence treatment success, due the limitation of the medical images. Factors known as repair of sublethal DNA damage, cell repopulation, redistribution of cells, and reoxygenation are not considered [1].

Experimental data showed that oxygen is the most component that modified the radiation sensitivity and hypoxic cells that can be 2–3 times more resistant to ionizing radiation, which would imply administering doses higher than doses to achieve the same effect in oxygenated cells under normal conditions [2–4].

An important concept in clinical radiobiology is that the tumor may have subpopulations in hypoxic areas, thus leading to success of radiotherapy. Still, there are concepts related to acute or chronic hypoxic cells that may also alter treatment outcomes [5]. The low concentration of oxygen or hypoxia in the tumor tissues is a radiobiological phenomenon that has been observed since the beginning of the twentieth century [6].

The dependence of oxygen in tissue is related with the generation of free radicals, which came from interacting between the radiation energy and tissues. The quantity that measures the likelihood of this interacting is the cross section, which decreases when the beam energy increases [7]. Thus, few radicals will interact with the DNA of the tumor cell and consequently decreasing the chain reaction. This dependence is known as the oxygen effect that is ignored in the accuracy of ionization radiation treatments [8, 9], which is why hypoxia characterizes a tissue as radioresistant. Therefore, hypoxia and radiosensitivity are related to lower oxygen concentration rate; there will be higher survival cell rate, in postirradiation. On the other hand, there is an optimal oxygenation value wherewith the radiosensitivity increases [10]. Concentrations of oxygen in some tumors can be found in different regions in the same tumor complex. In this case, the tumor hypoxia may occur in a chronic or acute form. A form of oxygen concentration is due to the accelerated growth of the tumor in the most central parts, which are usually originated by the lack of adequate blood supply. In this way, in an axial section of one tumor, have concentric circles of regions of different oxygenation, whose central areas are necrotic [4]. One way to express the decreased radiosensibilty of cell, due to hypoxia, is through the parameter oxygen enhancement ratio (OER), which is defined as the amount of dose reduction required for cell of a given oxygenation level compared to cell with no oxygen to obtain the same effect [11].

One way to study the oxygen effect in tumors is through computational modeling. Thus, different modeling of oxygen effect has been proposed such as a voxelbased multiscale tumor response model [12]. The model used in this work was written in C++ simulating a virtual tumor with considering biological parameters as vascular fraction that is related to the oxygenation of the tumor.

Laura Antonovic and co-authors [13] used a treatment planning system TRiP [14] to simulated spherical tumors in silico based on a biological model of oxygen diffusion [15]. The beam used was carbon ion.

Another publication showed the use of a computational model for trans-vascular oxygen transport and blood vessel networks in tumors [16, 17].

The paper title *Dose prescription and optimisation based on tumor hypoxia* [18] proposed a method to prescribe dose distributions in radioresistant tumors.

The Monte Carlo HYP-RT model was used to simulate tumors considering the repopulation and reoxygenation for hypoxic head and neck tumors [19].

A 4D cellular model was applied to simulate head and neck cancer with oxygenation varying with vascularity and blood oxygenation [20].

An algorithm implemented on Geant4-DNA (codes based on Monte Carlo) was developed to show the effect of oxygen on DNA [21].

The Monte Carlo simulation, specifically the codes based on this method, can also be an effective dosimetric tool for the study of dose deposited. The dose– response from the codes shows an advantage of providing detailed studies in different conditions that involve procedures which are lengthy, complex, and expensive. The most commonly used Monte Carlo simulation codes in radiotherapy simulations are EGS, MCNP, and PENELOPE [22–28]. The quality of the results provided by the different codes is directly related to the accuracy of the implemented transport model and its data libraries associated with the cross section of the transported particles. Thus, the mixed charged particle transport algorithm, implemented by the penetration and energy loss of positron and electrons (PENELOPE) code [29], led to its intense use in radiotherapy [30–35].

This chapter presents a study of dose distribution in simulated cranial tumor with different concentrations of oxygen [18, 36–39] through the PENELOPE simulation code, which is based on the Monte Carlo method [40, 41]. The tumor with different concentrations of oxygen will be compared with one under normal oxygen conditions.

**117**

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

PENELOPE is a code used to simulate the transport of electrons, positrons, and photons considering interactions of photons and charged particles (such as the photoelectric effect, Rayleigh scattering, Compton scattering, production and annihilation of pairs, elastic and inelastic collisions), which are simulated in complex

In the PENELOPE package, there are subroutines written in FORTRAN distributed in various (open) source codes, applications, a database with characteristics of various materials, as well as application examples. The FORTRAN subroutines are organized into four basic files: PENELOPE.f, PENGEOM.f, PENVARED.f, and

PENELOPE.f contains the simulated particle scattering and absorption subroutines, primary and secondary particle generation and storage, and particle transport

PENGEOM.f defines the structures, or geometries, to be simulated, which may consist of several homogeneous bodies, defined by a specified material and also by their limits in space. The bounding surfaces of the geometry bodies are described by quadratic functions. Through these functions surfaces such as planes, plane pairs, spheres, cylinders, cones, ellipsoids, parables, and hyperboloids can be defined. For each body defined in the geometry file of a given simulation, a material index must be defined, corresponding to the material that will be a constituent of the body, having an agreement between the geometry file and the material file. In the material archive, the interaction data of the radiation with the material being used are shown in tables, as interaction coefficients for electrons and photons in energies from 1 eV to 1GeV. A material file is created using the subroutines of the MATERIAL.f and PENELOPE.f source codes. One of the advantages of PENELOPE is that it uses a recent database with the characteristics of various materials of interest in radiological physics [42] and current cross section libraries and other quanti-

The PENVARED.f source code contains subroutines that perform the variational reduction methods of the code, without increasing simulation time and neither the

The simulation algorithm is based on a model that combines numerical and analytical cross section data for the different types of interaction and is applied for initial energies from 1 keV to 1 GeV. Photons transport are simulated by the conventional or detailed, and for electron and positron are simulated using a mixed algorithm. Thus, for electrons and positrons, the PENELOPE code differs from other simulation codes by using a mixed algorithm that implements two simulation models: the detailed, for strong events, defined from angular deflection (scattering angle) or energy loss above a set value, and the condensate for weak interactions with angular deflection or energy loss less than the preset values. Condensed interactions are described by a multiple-scatter approximation consisting of transforming a given number of weak interactions into a single artificial event [44]. To develop a simulation with PENELOPE, the user must edit a FORTRAN file, user.f, with calls from the subroutines PENELOPE.f, PENGEOM.f, PENVARED.fe, and TIMER.f, providing overall simulation management and creating with these five

The simulation is started by running the user.exe file that reaches the usersupplied input information through the input.in file, geometry information through the geometry.geo file, and cross section information for the materials involved in

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

**1.1 PENELOPE-Monte Carlo code**

geometries and arbitrary materials.

management and simulation as a whole.

ties required for particle transport [43].

FORTRAN files a user.exe file.

the simulation through the material.mat file.

statistical uncertainty of the simulated results.

Finally, source code TIMER.f manages the simulation time.

TIMER.f.

## **1.1 PENELOPE-Monte Carlo code**

*Translational Research in Cancer*

The dependence of oxygen in tissue is related with the generation of free radicals, which came from interacting between the radiation energy and tissues. The quantity that measures the likelihood of this interacting is the cross section, which decreases when the beam energy increases [7]. Thus, few radicals will interact with the DNA of the tumor cell and consequently decreasing the chain reaction. This dependence is known as the oxygen effect that is ignored in the accuracy of ionization radiation treatments [8, 9], which is why hypoxia characterizes a tissue as radioresistant. Therefore, hypoxia and radiosensitivity are related to lower oxygen concentration rate; there will be higher survival cell rate, in postirradiation. On the other hand, there is an optimal oxygenation value wherewith the radiosensitivity increases [10]. Concentrations of oxygen in some tumors can be found in different regions in the same tumor complex. In this case, the tumor hypoxia may occur in a chronic or acute form. A form of oxygen concentration is due to the accelerated growth of the tumor in the most central parts, which are usually originated by the lack of adequate blood supply. In this way, in an axial section of one tumor, have concentric circles of regions of different oxygenation, whose central areas are necrotic [4]. One way to express the decreased radiosensibilty of cell, due to hypoxia, is through the parameter oxygen enhancement ratio (OER), which is defined as the amount of dose reduction required for cell of a given oxygenation

level compared to cell with no oxygen to obtain the same effect [11].

vascular fraction that is related to the oxygenation of the tumor.

oxygen transport and blood vessel networks in tumors [16, 17].

ation varying with vascularity and blood oxygenation [20].

developed to show the effect of oxygen on DNA [21].

led to its intense use in radiotherapy [30–35].

diffusion [15]. The beam used was carbon ion.

One way to study the oxygen effect in tumors is through computational modeling. Thus, different modeling of oxygen effect has been proposed such as a voxelbased multiscale tumor response model [12]. The model used in this work was written in C++ simulating a virtual tumor with considering biological parameters as

Laura Antonovic and co-authors [13] used a treatment planning system TRiP [14] to simulated spherical tumors in silico based on a biological model of oxygen

The paper title *Dose prescription and optimisation based on tumor hypoxia* [18]

The Monte Carlo HYP-RT model was used to simulate tumors considering the

A 4D cellular model was applied to simulate head and neck cancer with oxygen-

An algorithm implemented on Geant4-DNA (codes based on Monte Carlo) was

The Monte Carlo simulation, specifically the codes based on this method, can also be an effective dosimetric tool for the study of dose deposited. The dose– response from the codes shows an advantage of providing detailed studies in different conditions that involve procedures which are lengthy, complex, and expensive. The most commonly used Monte Carlo simulation codes in radiotherapy simulations are EGS, MCNP, and PENELOPE [22–28]. The quality of the results provided by the different codes is directly related to the accuracy of the implemented transport model and its data libraries associated with the cross section of the transported particles. Thus, the mixed charged particle transport algorithm, implemented by the penetration and energy loss of positron and electrons (PENELOPE) code [29],

This chapter presents a study of dose distribution in simulated cranial tumor with different concentrations of oxygen [18, 36–39] through the PENELOPE simulation code, which is based on the Monte Carlo method [40, 41]. The tumor with different concentrations of oxygen will be compared with one under normal oxygen conditions.

proposed a method to prescribe dose distributions in radioresistant tumors.

repopulation and reoxygenation for hypoxic head and neck tumors [19].

Another publication showed the use of a computational model for trans-vascular

**116**

PENELOPE is a code used to simulate the transport of electrons, positrons, and photons considering interactions of photons and charged particles (such as the photoelectric effect, Rayleigh scattering, Compton scattering, production and annihilation of pairs, elastic and inelastic collisions), which are simulated in complex geometries and arbitrary materials.

In the PENELOPE package, there are subroutines written in FORTRAN distributed in various (open) source codes, applications, a database with characteristics of various materials, as well as application examples. The FORTRAN subroutines are organized into four basic files: PENELOPE.f, PENGEOM.f, PENVARED.f, and TIMER.f.

PENELOPE.f contains the simulated particle scattering and absorption subroutines, primary and secondary particle generation and storage, and particle transport management and simulation as a whole.

PENGEOM.f defines the structures, or geometries, to be simulated, which may consist of several homogeneous bodies, defined by a specified material and also by their limits in space. The bounding surfaces of the geometry bodies are described by quadratic functions. Through these functions surfaces such as planes, plane pairs, spheres, cylinders, cones, ellipsoids, parables, and hyperboloids can be defined.

For each body defined in the geometry file of a given simulation, a material index must be defined, corresponding to the material that will be a constituent of the body, having an agreement between the geometry file and the material file. In the material archive, the interaction data of the radiation with the material being used are shown in tables, as interaction coefficients for electrons and photons in energies from 1 eV to 1GeV. A material file is created using the subroutines of the MATERIAL.f and PENELOPE.f source codes. One of the advantages of PENELOPE is that it uses a recent database with the characteristics of various materials of interest in radiological physics [42] and current cross section libraries and other quantities required for particle transport [43].

The PENVARED.f source code contains subroutines that perform the variational reduction methods of the code, without increasing simulation time and neither the statistical uncertainty of the simulated results.

Finally, source code TIMER.f manages the simulation time.

The simulation algorithm is based on a model that combines numerical and analytical cross section data for the different types of interaction and is applied for initial energies from 1 keV to 1 GeV. Photons transport are simulated by the conventional or detailed, and for electron and positron are simulated using a mixed algorithm. Thus, for electrons and positrons, the PENELOPE code differs from other simulation codes by using a mixed algorithm that implements two simulation models: the detailed, for strong events, defined from angular deflection (scattering angle) or energy loss above a set value, and the condensate for weak interactions with angular deflection or energy loss less than the preset values. Condensed interactions are described by a multiple-scatter approximation consisting of transforming a given number of weak interactions into a single artificial event [44]. To develop a simulation with PENELOPE, the user must edit a FORTRAN file, user.f, with calls from the subroutines PENELOPE.f, PENGEOM.f, PENVARED.fe, and TIMER.f, providing overall simulation management and creating with these five FORTRAN files a user.exe file.

The simulation is started by running the user.exe file that reaches the usersupplied input information through the input.in file, geometry information through the geometry.geo file, and cross section information for the materials involved in the simulation through the material.mat file.

#### *Translational Research in Cancer*

Another executable program comes together with PENELOPE package, the GEOVIEW.exe, which allows the visualization of the defined bodies and the materials that constitute a simulation geometry.

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

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