Monte Carlo simulations have been applied to determine and study different parameters that are challenged in experimental measurements, due to its capability in simulating the radiation transport with a probability distribution to interact with electrosferic electrons and some cases with the nucleus from an arbitrary material, which such particle track or history can carry out physical quantities providing data from a studied or investigating quantities. For this reason, simulation codes, based on Monte Carlo, have been proposed. The codes currently available are MNCP, EGSnrc, Geant, FLUKA, PENELOPE, as well as GAMOS and TOPAS. These simulation codes have become a tool for dose and dose distributions, essentially, but also for other applications such as design clinical, tool for commissioning of an accelerator linear, shielding, radiation protection, some radiobiologic aspect, treatment planning systems, prediction of data from results of simulation scenarios. In this chapter will be present some applications for radiotherapy procedures with use, specifically, megavoltage x-rays and electrons beams, in scenarios with homogeneous and anatomical phantoms for determining dose, dose distribution, as well dosimetric parameters through the PENELOPE and TOPAS code.
- Monte Carlo
The constant development of medical applications using ionizing radiation requires an understanding of the transport of particles through materials, such as tissues, organs, patients, imaging devices. For this reason, computational simulations, using the Monte Carlo Method, have been extensively used in several areas, specifically, in Radiological Physics, where this tool is applied for modeling a treatment or medical examinations, for example, that for some regions of interest are difficulties and complexities to making experimentally.
Several computational codes, based on Monte Carlo simulation, have been used in radiological protection, radiotherapy source dosimetry, planning systems, and other applications PENELOPE [1, 2, 3, 4, 5, 6], MCNP [7, 8, 9, 10, 11], EGSnrc [12, 13, 14, 15], FLUKA [16, 17, 18, 19, 20], TOPAS [21, 22, 23, 24, 25], GAMOS [26, 27, 28, 29], Geant [30, 31].
In this work, some applications will be presented, in different scenarios to determine dose, relative dose, dose distribution, as well as to determine dosimetric parameters used in radiotherapy, using computational codes through Monte Carlo simulation.
2. Applications of computational codes in radiotherapy
In this section, some applications of computational codes in radiotherapy will be presented.
2.1 Determination of dosimetric parameters of clinical sources of high dose rate brachytherapy using the PENELOPE package
The PENELOPE (PENetration and Energy LOss of Positrons and Electrons) computational code includes several computational codes written in FORTRAN 77 . The package simulates the transport of electrons, photons, and positrons in arbitrary materials and energy values from 100 eV to 1 GeV, in geometries and materials defined by the user . PENELOPE has a database of cross-sections for materials involving elements with atomic numbers from 1 to 92, and 180 other compounds and mixtures of interest in Radiological Physics.
where D is the dose rate; r is the distance from the center of the source to the point of interest (in cm), is the polar angle that specifies the point of interest, 0 is the reference angle (90°); GL is the geometric factor, determined analytically.
Quevedo et al.  determined a dosimetric parameter, using Monte Carlo simulation with the PENELOPE package. The high dose-rate 192Ir brachytherapy source commonly used in gynecological brachytherapy was modeled, and the Anisotropy Function in regions close to the source was determined. Figure 1 shows (a) the source geometry, modeled in the PENELOPE package, and (b) the Anisotropy Function in regions close to the irradiation source.
To validate the results obtained, using Monte Carlo simulation with the PENELOPE package, dose profiles in the longitudinal direction of the source were compared with data from the BrachyVision planning system. Figure 2 shows the comparisons of relative doses, as a function of distances, between the PENELOPE package and the BrachyVision treatment planning system for distances (a) 0.4 cm from the center of the source towards the source cable, (b) center of the source and (c) 0.4 cm from the center of the source towards the top of the source encapsulation, adapted from Quevedo et al. .
From the comparisons in the three plans, it is possible to verify that the data obtained in the simulations with the PENELOPE package shows agreement greater than 98% of the points, with the data obtained from the treatment planning system, indicating that the PENELOPE package has great potential in the determination of dosimetric parameters of high dose rate brachytherapy sources.
2.2 Applications of the TOPAS code in ocular brachytherapy
The TOPAS (Tool for Particle Simulation) computational code is based on physical Geant4 models and low energy electromagnetic models of the PENELOPE code  and has shown great potential for simulations in medical and quality control applications [22, 40, 41, 42, 43].
TOPAS is based on an innovative parameter control system, which allows the modeling of therapy and imaging devices without the need for programming knowledge, in order to reduce user errors. The code has a vast library of predefined modules for geometry, physical models, and detection. Despite this, it is possible for more experienced users to write their own modules in C++. You can also create patient geometries based on computed tomography (CT) images. Therefore, TOPAS presents itself as a highly extensible and accessible tool for medical physicists for modeling therapy and imaging devices.
Another innovative feature of this code is that it handles time-dependent amounts, that is, it has 4D resources through its Time Feature System. Time-varying amounts are essential for modeling advanced radiotherapy treatment techniques, the Image-Guided Radiotherapy (IGRT) technique is an example of this, where the positioning of the patient or target organ varies. Therefore, TOPAS proposes an approach to 4D simulation to deal with various time-dependent quantities in a single simulation, such as volume change, rotational movement, current variation, magnetic field, etc. .
Knoll et al., determined dose deposition from a source of brachytherapy used in ophthalmic treatments . In this work, the applicator used in the treatment, which uses the 90Sr/90Y source, was modeled in the TOPAS code, including the active part, encapsulation, and simulator object filled with water. A relative dose profile was obtained in a high dose gradient region, normalized at the reference point to 1 mm and, for validation purposes, the data obtained with TOPAS were compared with data from the ICRU (International Commission on Radiation & Measurements) with the same conditions. Figure 3 shows (a) geometry of the 90Sr/90Y source with applicator and simulator object and (b) comparison of relative dose, as a function of distance, between TOPAS and ICRU data (Adapted from ).
The greatest uncertainty obtained in computer simulations with the TOPAS code was approximately 0.01% at the point where it was normalized. When compared to the ICRU, the greatest difference found was approximately 4% at 1.6 mm depth. Thus, the TOPAS code has been shown to be a promising tool for dosimetry in brachytherapy and radiological applications.
2.3 Applications of the TOPAS-nBio code
Although the TOPAS code provides a wide range of tools for use in radiotherapy at patient scale or clinically applicable geometries, the fundamental unit of biological response to the effects of ionizing radiation is at the cellular or subcellular scale. For this reason, TOPAS has an extension dedicated to the study of the biological effects of radiation in micrometer and nanometer scale, designed based on Geant4-DNA, the extension of Geant4, the basis of TOPAS, so that very low energy are included in the interactions.
When interacting with matter, excitations and ionizations can be caused due to ionizing radiation. In the context of radiotherapy, incident particles cause radiolysis of water and subsequent chemical interactions, inducing molecular damage to the cell, more specifically to DNA, which is the critical target for most biological effects of radiation . For this reason, TOPAS-nBio has several models of cellular and subcellular geometries (such as blood cells and single and double-stranded DNA models, for example) specialized in a pre-defined way . Furthermore, with regard to biological modeling, the code inherits the chemical parameters provided by the Geant4-DNA toolkit and also includes mechanistic DNA repair models to perform water radiolysis simulations. With this, it is possible to develop complete modeling from the initial physical events to the final observed biological result .
According to Semenenko et al.  the combination of runway structure simulations with core geometry models is considered the gold standard for predicting the spectrum of DNA damage induced by ionizing radiation. Therefore, Hongyu et al.  determined the cellular response after proton irradiation using the TOPAS-nBio code for damage induction and repair modeling with MEDRAS, which is a model capable of predicting the main final biological damage in a variety of cell types, including repair kinetics, chromosomal aberrations, and cell survival.
To determine the DNA damage yield, the results were scored in the SSD format and quantified by strand break (SBs), single-strand break (SSBs), and double-strand break (DSBs) yields, compared to published and experimentally measured data.
The initial DNA damage after proton irradiation (0.5–500 MeV, corresponding to the LET region of 60–0.2 keV/μm) was simulated with the code. The core model used was placed in the center of a cubic world with a side length of 14 μm, containing the core, filled with water. Primary protons were randomly initiated on the surface of the nucleus and propagated within the nucleus in a random direction. Induced DNA damage caused by direct and indirect interactions in the physical and chemical stages was quantified as SBs, SSBs, or DSBs and sent in standard DNA damage data format (SDD). To get enough statistics, 100 stories were performed for each energy point. Each simulation had a fixed number of primary particles and deposited a dose of 1 Gy inside the nucleus. Statistical uncertainty associated with DSB dose and yield was less than 2%.
The average LET was recorded as a radiation quality index and calculated by the equation:
where d is the average length of the proton path inside the nucleus and ε is the energy deposition of primary and secondary particles inside the nucleus.
The initial DNA damage induced by incident protons was simulated by modeling the physical and chemical interactions within the nucleus with standard process models available in TOPAS-nBio.
As a result, a relationship was obtained between the LET of the proton according to literature references and the simulated particle energy in TOPAS-nBio. In low energy regions, the maximum discrepancy between the results was 32.5%, probably due to the size of the scoring volume, and in this low energy region, the protons do not cross the entire nucleus. However, there was an optimal agreement of 96%, as shown in Figure 4.
The results of DNA damage as a function of the LET of the proton simulated with TOPAS-nBio were also obtained, as shown in Figure 5.
The figure shows a relationship between the relative contribution of direct and hybrid damage as a fraction of each type of SB, SSB, and DSB break. Thus, it was shown that most SBs and SSBs would be caused by indirect damage and the indirect contribution rate would increase from approximately 60% to approximately 75% at 4.5 keV/μm (10 MeV proton energy) and, then decrease to higher LET values where radiolysis is denser, causing a greater number of chemical interactions. Furthermore, it was shown that most DSB damage was classified as a hybrid type, caused by the combination of direct and indirect damage. Simulations using TOPAS-nBio showed that Monte Carlo tools can predict DNA damage and can be used to interpret experimental data and design new theories.
Monte Carlo simulations have been applied to determine and study different parameters that are challenged in experimental measurements, due to its capability in simulating the radiation transport. In this chapter were presented applications for radiotherapy procedures, in scenarios with homogeneous and anatomical phantoms determining dose values, dose distribution, and dosimetric parameters through the PENELOPE and TOPAS code, showing itself as a useful tool for radiotherapy.
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