Journal of Medical Physics
: 2020  |  Volume : 45  |  Issue : 2  |  Page : 116--122

Monte carlo calculation of the energy spectrum of a 6 MeV electron beam using penetration and energy loss of positrons and electrons code

Danny Giancarlo Apaza Veliz1, Jorge Homero Wilches Visbal2, Felipe Chen Abrego3, José Luis Vega Ramírez4,  
1 Department of Physics, Faculty of Philosophy, Sciences and Letters, University of São Paulo, Brazil; Department of Physics, National University of San Agustín, Arequipa, Peru
2 Department of Basic Biomedical Sciences, Faculty of Health Sciences, University of Magdalena, Santa Marta, Colombia
3 Center for Natural and Human Sciences, Federal University of ABC, Brazil
4 Department of Physics, National University of San Agustín, Arequipa, Peru

Correspondence Address:
Prof. Danny Giancarlo Apaza Veliz
Department of Physics, Faculty of Philosophy, Sciences and Letters, University of Sao Paulo


Background: The limited bibliographic existence of research works on the use of Monte Carlo simulation to determine the energy spectra of electron beams compared to the information available regarding photon beams is a scientific task that should be resolved. Aims: In this work, Monte Carlo simulation was performed through the PENELOPE code of the Sinergy Elekta accelerator head to obtain the spectrum of a 6 MeV electron beam and its characteristic dosimetric parameters. Materials and Methods: The central-axis energy spectrum and the percentage depth dose curve of a 6 MeV electron beam of an Elekta Synergy linear accelerator were obtained by using Monte Carlo PENELOPE code v2014. For this, the linear accelerator head geometry, electron applicators, and water phantom were simplified. Subsequently, the interaction process between the electron beam and head components was simulated in a time of 86.4x104 s. Results: From this simulation, the energy spectrum at the linear accelerator exit window and the surface of the phantom was obtained, as well as the associated percentage depth dose curves. The validation of the Monte Carlo simulation was performed by comparing the simulated and the measured percentage depth dose curves via the gamma index criterion. Measured percentage depth- dose was determined by using a Markus electron ionization chamber, type T23343. Characteristic parameters of the beam related with the PDD curves such as the maximum dose depth (R100), 90% dose depth (R90), 90% dose depth or therapeutic range (R85), half dose depth (R50), practical range (Rp), maximum range (Rmax), surface dose (Ds), normalized dose gradient (G0) and photon contamination dose (Dx) were determined. Parameters related with the energy spectrum, namely, the most probable energy of electrons at the surface (Ep,0) and electron average energy (E0) were also determined. Conclusion: It was demonstrated that PENELOPE is an attractive and accurate tool for the obtaining of dosimetric parameters of a medical linear accelerator since it can reliably reproduce important clinical data such as the energy spectrum, depth dose, and dose profile.

How to cite this article:
Apaza Veliz DG, Wilches Visbal JH, Abrego FC, Vega Ramírez JL. Monte carlo calculation of the energy spectrum of a 6 MeV electron beam using penetration and energy loss of positrons and electrons code.J Med Phys 2020;45:116-122

How to cite this URL:
Apaza Veliz DG, Wilches Visbal JH, Abrego FC, Vega Ramírez JL. Monte carlo calculation of the energy spectrum of a 6 MeV electron beam using penetration and energy loss of positrons and electrons code. J Med Phys [serial online] 2020 [cited 2020 Oct 22 ];45:116-122
Available from:

Full Text


Radiation therapy is one of the most used treatment modalities of cancer. Its objective is to maximize the dose delivered to cancer while minimizing the delivery in healthy tissues. The choice of the type of radiation (electrons, photons, protons, or heavy ions) and the availability of advanced tools for treatment are crucial to the success of radiotherapy.[1],[2] Electron beams[3],[4] are specially used for the treatment of superficial tumors because of the fast energy loss of the electrons in the first layers of the material.[5],[6],[7] Many efforts have been done both in order to achieve better planning and dosimetry in the electron treatments and to assess the risks and benefits of this procedure.[1],[8],[9] Computational simulations are one of the most common and effective ways used to bring us as close as possible to the conditions and characteristics of the clinical setting. Monte Carlo method (MMC) is a powerful tool to simulate the interaction of ionizing radiation with matter. It also allows to model radiation beams (electrons, photons, positrons, neutrons, and protons) produced in clinical linear accelerators.[10],[11],[12],[13],[14] With this, Monte Carlo simulation (MCS) can be used to obtain and analyze different clinical parameters such as energy spectrum, angular distribution, percentage depth dose (PDD), and other clinical parameters.[15]

The MCS validation is done by comparing the dose distribution obtained from the simulation with the experimental measurements. To perform this validation, the gamma-index can be used. Gamma-index is a mathematical parameter that evaluates the degree of agreement between two dose distributions considering spatial and dose distances under predefined tolerance limits.[16],[17],[18],[19] The report 42 of the International Commission on Radiation Units and Measurements (ICRU)[20] states that, in order to have a high level of precision in the MCS of a beam, there should be no discrepancy between dose distributions >±2% or ± 2 mm.[21] In addition to the considerations given in the report 42, the accuracy of the simulation depends directly on the choice and how well the parameters or input information, the characteristics of the materials immersed in the constructed geometries, and the nominal energies can be represented.[15],[21]

The choice of the Monte Carlo code for the simulation marks a differential in obtaining satisfactory results. Currently, there are several radiation transport simulation codes based on the MMC, some free and others sold. For example, there is the EGSnrc system which is a Monte Carlo code to simulate the transport of electrons and photons in various geometries,[12],[22],[23] and whose valid energy range is between 1 keV and 100 GeV. Geometry ANd Tracking (GEANT4) is a code that simulates the transport of all kinds of particles in the energy range between 250 eV and about 10 TeV.[24] It is mainly used in high-energy physics as well as in medical physics. FLUktuierendeKAskade is used in high-energy physics and medical physics. It is a general-purpose code that reproduces the interaction of ionizing radiation with the matter of up to 60 different particles at the same time, electrons and photons (from 1 keV to 1000 TeV), hadrons (up to 20 TeV), neutrons (including thermal), and heavy ions. Like GEANT4, it presents various applications in high-energy physics and medical physics.[25] Monte Carlo N-Particle is another general-purpose code for the transport of neutrons, photons, and electrons.[26],[27],[28] In this work, the PENetration and Energy LOss of Positrons and Electrons (PENELOPE) code is used. It has extensive information on various applications for radiotherapy and radiodiagnosis.[4],[29],[30],[31],[32],[33],[34] Since its first version launched in 1996, the MCS PENELOPE code has become a flexible and reliable tool to describe the coupled transport of photons and electrons in complex material structures,[35],[36] presenting simplicity and versatility to be used in the two most used programming platforms such as Windows and Linux without the necessity of the usage of an intermediary interface. Moreover, the results obtained are presented in.dat extension which is easy to read in any code for statistical analysis such as Origin, Matlab, and Gnuplot.

The main motivation of this work is related to there are few research papers about the use of MCS to determine energy spectra of electron beams[21],[31],[37],[38] and its characteristic dosimetric parameters in comparison to those existent for photon beam,[11],[31],[33],[39],[40],[41],[42],[43],[44],[45],[46] especially for linear accelerators still used in developing countries. Thus, in this work, an Elekta Synergy Platform linear accelerator was used as a reference, since the Synergy is still one of the most used accelerators in the Latin-American market and other developing regions of the world. The novelty of the present work consists of a complete description of how to simulate the Synergy Elekta linear accelerator head using PENELOPE. It was also demonstrated that PENELOPE is a cheap and powerful computational tool for the radiation external source modeling in radiotherapy since it reliably reproduced the relevant dosimetric data of the electron beam studied.

 Materials and Methods

Monte Carlo simulation codes

MMC is any probabilistic method that is based on random sampling and provides numerical results. This method is widely applied for simulations in physics, biology, chemistry, and mathematics[12],[22],[36],[47] since it can give numerical solutions of very complex functions. One of the many Monte Carlo versions utilized for studying the radiation transport in a material is the PENetration and Energy LOss of Positrons and Electrons code. Thus, PENELOPE is a general-purpose open code for the transport of electrons, photons, and positrons with a range of energies between 50 eV and 1 GeV. Because of this, its main fields of use are applications in medical physics, namely external radiotherapy, radiodiagnostic, nuclear medicine, and brachytherapy.

The several geometries used are constructed from quadratic surfaces, and variance reduction techniques are incorporated to have better adaptability and greater precision.[30],[33],[36],[47],[48] PENELOPE allows creating materials with a single component, alloys, or mixed materials that are present in the constitution of a clinical linear accelerator. All these help to make better reproductions and representations of experimental conditions. PENELOPE's stop simulation criteria depend on the real time of the simulation or the events/simulated shower number. In this work, the PENELOPE version 2014 was used.

Modeling of the electron radiation source using PENetration and Energy LOss of Positrons and Electrons

PENELOPE code was used to reproduce the physical, geometrical, and material characteristics that make up the head of an Elekta Synergy Platform linear accelerator. The technical detail of each of the mentioned characteristics is described in the phase spaces extracted from the manual provided by the manufacturer, and for commercial reasons, this information is omitted. Based on the geometric information and composition of the elements and components of the linear accelerator head provided in the manufacturer's manual, the virtual simulation was performed in PENELOPE. Both materials of the primary and secondary collimators and those of the scattering foils used in the virtual geometry are composed of the same alloys and densities as the actual accelerator materials. The precision in the replication of these details allowed determining the characteristics of the energy spectrum of the electron beam both in the exit window after interacting with the head components as well as the spectrum on the surface of the phantom.

[Figure 1] shows the virtual geometry of the Elekta linear accelerator built-in PENELOPE. To do this, three-dimensional gview software was used since it is the graphic display extension of PENELOPE. [Figure 1]a details the locations of the radiation source, the scattering foils, and the collimators inside the accelerator head. The geometry configuration shown in [Figure 1]b was used to simulate the interaction of the electron beam with the surface of the water phantom: gantry angle of 0°, nominal energy of 6 MeV, field size of 10 cm × 10 cm, 100 cm of source-skin distance (SSD), applicators of 10 cm × 10 cm, and a phantom water of 40 cm × 40 cm × 40 cm. The simulation time employed was 86.4 × 104 s, number of simulated showers of 3.5 × 109, and a confidence level of 99%. To carry out the simulations, the Educational Cluster of the University of São Paulo-Ribeirão Preto was used. All simulations were performed with respect to the central axis of the electron beam. For the experimental dosimetric measurements, the accelerator position was configured as follows: 0° gantry angle, 6 MeV nominal energy, 10 cm × 10 cm field size, 100 cm SSD with 10 cm × 10 cm applicators, and an automated tank, and a parallel flat ionization chamber was used Markus model with 3.05 mm detector radius. Throughout all the work, we will call the PENELOPE simulation as MCS.{Figure 1}

Relationships between beam characteristics and depth-dose distribution

There are several dosimetric parameters to fully characterize an electron beam from the PDD curve recommended by ICRU. These parameters are: maximum dose depth (R100), 90% dose depth (R90), 85% dose depth (R85), 50% dose depth (R50), practical range (Rp), maximum range (Rmax), the most probable energy of electrons on the surface (Ep, 0), average energy of electrons (E–0) on the surface, the dose gradient (G0), percentage of doses of contaminating photons (Dx), and percentage of surface dose (Ds). In the Technical Report Series No. 381 reports of IAEA[49] and the report 32 of the AAPM,[6] empirical relationships between the parameters and the PDD curve are shown. The two best known relationships between E0 and R50 are:



Eq. (1) is recommended in the technical report 381 of the IAEA (1997)[49] while Eq. (2) is recommended in report 32 of the AAPM.[6] Both allow calculating the average energy of the electrons from R50.

A very useful relationship is Ep, 0 and Rp, which has the same form of Eq. (1) but with different constants and in relation to Rp.[6],[49]


Another characteristic parameter that can be calculated is the standardized dose gradient (G0), which describes the slope of the fall region of the PDD curve. This gradient is related to Rq and Rp,


All parameters R100, R90, R85, R50, Rq, Rp, Rmax, Ep, 0, E–0 and G0 were obtained for the measured depth-dose distribution curve and also for the one generated by simulation with PENELOPE code, in order to validate the simulation and have a comparison between both curves.

In order to validate the PDD curve obtained from the simulation, it is compared to the measured PDD which was previously determined by employing an ionization chamber. The comparing method utilized was the gamma-index since it is widely known and used criterion in radiotherapy. The gamma-index (Γ) is determined by:


where [INSIDE:1] is the distance between the analyzed points, being [INSIDE:2] the obtained from simulation and [INSIDE:3] the experimentally measured, and [INSIDE:4] represents the dose difference (DD) between the simulated and measured PDD curves at [INSIDE:2] and [INSIDE:3] respectively. The distance-to-agreement and DD values are scale values that adjust the gamma-index to the acceptance level required, i.e., they are the predefined tolerance values.[16],[18]

 Results and Discussions

Electron energy spectrum derived from Monte Carlo simulation

The simulated energy spectra at the linear accelerator exit window and at the water phantom surface are shown in [Figure 2]. The spectrum at the exit window was measured after the second scattering foil. The spectra were normalized to its most probable maximum energy value.{Figure 2}

[Figure 2]a is observed the energy spectrum at the exit window with a narrow central peak and the presence of an additional small peak to its left. The narrowness of the central peak is because the electron beam has not interacted with most of the accelerator head structures and the entire air column. The small peak is generated as the beam passing through the first linear accelerator head metal structures (collimator and scattering foils) and interacting with them for producing this secondary radiation. [Figure 2]b shows the energy spectrum at phantom surface whose shape resembles a slightly asymmetric Gaussian distribution and with a width central peak. There is also observed a small peak to the left of the central peak in the energy range of 0–0.250 MeV which may be due to the contaminating photons that reach the water phantom surface. From [Figure 2], two important spectral parameters can be obtained: the most probable energy, E0, and the full width at half maximum (FWHM) of the central peak, γ0. Not to be confused E0 with Ep, 0, since while both mean the same, E0 is the most probable energy obtained from the analysis of the spectrum, while Ep, 0 represents the most probable energy from R50 in the PDD curve.

[Table 1] shows the values of E0 and γ0 for the spectra at the exit window and at the phantom surface. The value of γ0, as well as its value respect to E0, is shown as well. From [Table 1] data, it is noted that as the beam approaches, the surface of the water phantom decreases the most probable energy and increases the FWHM of the spectrum. This is because of the low-energy electrons, generated by the interaction among the beam and the accelerator structures and air, reduce the hardness of the beam and they are more easily scattered.[21]{Table 1}

Comparison of depth-dose distribution curves and dose profiles

[Figure 3] shows the simulated and measured PDD curves for the electron beam of 6 MeV nominal energy. Vertical open circle lines are the values of the gamma-index in each depth.{Figure 3}

At the build-up region (0–1 cm depth), a noticeable discrepancy in terms of DD is observed. The contribution of contamination photons is noted at the final part of PDD curves, specifically, from the 3.2 cm depth. Contamination photons are generated by the deflection of primary and secondary electrons passing through accelerator structures.[50] It was found that the contribution of contamination photon dose in the measured PDD curve is greater than the simulated one because of the inefficiency of the simulation to calculate the contamination photons amount. It is possible that such inefficiency obeys to the discrepancies in the constitution of the alloys of the accelerator materials simulated in PENELOPE and those of the real accelerator. ICRU recommendation is that the differences between the treatment (measured) and planning (simulated) PDD curves were within ± 2%/±2 mm.[21] Keeping this in mind, the DDs between the measured and simulated PDD curves were analyzed using the gamma-index. The largest differences are found at the shallow region of the water phantom. In fact, the DD between the PDD curves reached up to 3% in that region, while for the rest, it was not >1%. The acceptance percentage of the simulated PDD curve was 100% and 98% according to the gamma-index criterion of >95% of simulated curve within 2%/2 mm and 1%/1 mm, respectively.

[Figure 4]a displays the measured and simulated PDD curves in the build-up region. In this region, DDs are ranged from 1% to 3%. The largest difference occurs in the depth of the surface dose. This indicates that the simulated spectrum could not reproduce the dose data in this region with high accuracy. However, this is a really hard task since the experimental measurements of the dose at the build-up region are highly probabilistic due to here occur the first interaction of beam electrons with the water surface.{Figure 4}

In [Figure 4]b, the measured and simulated dose profiles are compared. Dose profiles allow detailing the off-axis DDs between the dose profiles at a reference depth. The reference depth was stated in 1.3 cm. Moreover, from [Figure 4]b, A good agreement between measured and simulated dose profiles is observed, except in the field edge region. In the edge region, the differences are higher than the other regions of dose profiles because the incident electrons possess a greater angular spread.

Beam characteristics derived from the percentage depth-dose curves

An additional way to evaluate the accuracy of the simulated electron energy spectrum is comparing the values of dosimetric parameters obtained from the measured and simulated PDD curves. The values of dosimetric parameters found are shown in [Table 2].{Table 2}

From [Table 2], a good approximation between the values of the measured and simulated characteristic parameter is observed. The highest deviations were found for G0 and DX.


Monte Carlo PENELOPE code represents a powerful tool to study the effects and characteristics of a medical electron beam. A good agreement between the measured and simulated depth-dose distributions was observed according to the gamma passing rate criterion. It was also seen a good agreement between the measured and simulated dose profiles excepting the field edge region. The small discrepancies found are related to the limited representation of the geometrical and the composition of accelerator head structures as well as the behavior of the simulated energy beam as it traverses such structures and the air. Most of the characteristic parameters of the simulated PDD relative are in accordance with those of the measured PDD. The dose gradient and the photon contamination dose were the characteristic parameters of PDD curves with the highest discrepancies. Therefore, it can be concluded that PENELOPE v2014 is an accurate tool to obtain the electron energy spectrum and other important dosimetric characteristics of an electron beam.

Financial support and sponsorship


Conflicts of interest

There are no conflicts of interest.


1AAPM AA of P in M. Radiation treatment planning. Vol. 74, American Institute of Physics. New York: American Institute of Physics; 1995. p. 2118.
2Fraass B, Doppke K, Hunt M, Kutcher G, Starkschall G, Stern R, et al. American Association of Physicists in Medicine Radiation Therapy Committee Task Group 53: Quality assurance for clinical radiotherapy treatment planning. Med Phys 1998;25:1773-829.
3Blomquist M, Karlsson MG, Zackrisson B, Karlsson M. Multi leaf collimation of electrons – Clinical effects on electron energy modulation and mixed beam therapy depending on treatment head design. Phys Med Biol 2002;47:1013-24.
4Brualla L, Zamora RP, Wittig A, Sempau J, Sauerwein W. Comparison between PENELOPE and electron Monte Carlo simulations of electron fields used in the treatment of conjunctival lymphoma. Phys Med Biol 2009;54:5469-81.
5American Association of Physicists in Medicine. A protocol for the determination of absorbed dose from high energy photon and electron beams. Med Phys 1983;10:741-71.
6Khan FM, Doppke KP, Hogstrom KR, Kutcher GJ, Nath R, Prasad SC, et al. Clinical electron-beam dosimetry: Report of AAPM Radiation Therapy Committee Task Group No. 25. Med Phys 1991;18:73-109.
7Almond PR, Biggs PJ, Coursey BM, Hanson WF, Huq MS, Nath R, et al. AAPM's TG-51 protocol for clinical reference dosimetry of high-energy photon and electron beams. Med Phys 1999;26:1847-70.
8Al-Yahya K, Verhaegen F, Seuntjens J. Design and dosimetry of a few leaf electron collimator for energy modulated electron therapy. Med Phys 2007;34:4782-91.
9Strydom W, Parker W, Olivares M. Electron Beams: Physical and Clinical Aspects. In: Radiation oncology physics: A handbook for teachers and students (E.B. Podgorsak Edt). International Atomic Energy Agency (IAEA), Viena 2005;1:273-299.
10Durán-Nava OE, Torres-García E, Oros-Pantoja R, Hernández-Oviedo JO. Monte Carlo simulation and experimental evaluation of dose distributions produced by a 6 MV medical linear accelerator. J Phys Conf Ser, Ciudad de México, México 2018;1221:1-6.
11Samir D, Zerfaoui M, Moussa A, Benkhouya Y, El Ouartiti M. Grid Monte Carlo Simulation of a medical linear accelerator. Eur J Eng Res Sci 2018;3:40-3.
12Doucet R, Olivares M, DeBlois F, Podgorsak EB, Kawrakow I, Seuntjens J. Comparison of measured and Monte Carlo calculated dose distributions in inhomogeneous phantoms in clinical electron beams. Phys Med Biol 2003;48:2339-54.
13Siantar CL, Moses EI. The peregrine TM program: Using physics and computer simulation to improve radiation therapy for cancer. Eur J Phys 1998;19:513-21.
14Lux I, Koblinger L, editors. Monte Carlo Particle Transport Methods: Neutron and Photon Calculations. Boca Raton: CRC Press; 2018. p. 513.
15Björk P, Knöös T, Nilsson P, Larsson K. Design and dosimetry characteristics of a soft-docking system for intraoperative radiation therapy. Int J Radiat Oncol Biol Phys 2000;47:527-33.
16Hussein M, Clark CH, Nisbet A. Challenges in calculation of the gamma index in radiotherapy – Towards good practice. Phys Medica 2017;36:1-11.
17Hussein M, Clementel E, Eaton DJ, Greer PB, Haworth A, Ishikura S, et al. A virtual dosimetry audit – Towards transferability of gamma index analysis between clinical trial QA groups. Radiother Oncol 2017;125:398-404.
18Low DA, Dempsey JF. Evaluation of the gamma dose distribution comparison method. Med Phys 2003;30:2455-64.
19Sumida I, Yamaguchi H, Kizaki H, Aboshi K, Tsujii M, Yoshikawa N, et al. Novel radiobiological gamma index for evaluation of 3-dimensional predicted dose distribution. Int J Radiat Oncol Biol Phys 2015;92:779-86.
20ICRU. Use of computers in external beam radiotherapy procedures with high-energy photons and electrons. Thirth. Measurements International Commission on Radiation Units and Measurements, editor. Maryland; 1987. p. 70. Available from: [Last accessed on 2020 Apr 09].
21Björk P, Knöös T, Nilsson P. Influence of initial electron beam characteristics on Monte Carlo calculated absorbed dose distributions for linear accelerator electron beams. Phys Med Biol 2002;47:4019-41.
22Kawrakow I, Mainegra-Hing E, Rogers DWO, Tessier F, Walters BR. EGSnrc: The EGSnrc code system: Monte Carlo simulation of electron and photon transport. NRCC Report. 2015. Ottawa, National Research Council Canada.
23Sahoo S, Selvam T, Sharma SD, Das T, Dey AC, Patil BN, et al. Dosimetry of indigenously developed 192Ir high-dose rate brachytherapy source: An EGSnrc Monte Carlo study. J Med Phys 2016;41:115-22.
24Agostinelli S, Allison J, Amako K, Apostolakis J, Araujo H, Arce P, et al. GEANT4 – A simulation toolkit. Nucl Instrum Methods Phys Res A 2003;506:250-303.
25Ferrari A, Sala PR, Fasso A, Ranft J. FLUKA: A Multi-Particle Transport Code. 2014th ed. European Organization for Nuclear Research, editor. Vol. 773, Geneve; 2005. p. 406. Available from: [Last accessed 2020 Apr 01].
26Waters LS, McKinney GW, Durkee JW, Fensin ML, Hendricks JS, James MR, et al. The MCNPX Monte Carlo radiation transport code. AIP Conf Proc 2007;896:81-90.
27Jabbari K, Seuntjens J. A fast Monte Carlo code for proton transport in radiation therapy based on MCNPX. J Med Phys 2014;39:156-63.
28Jabbari I, Monadi S. Development and validation of MCNPX-based Monte Carlo treatment plan verification system. J Med Phys 2015;40:80-9.
29Sánchez MS, Pianoschi TA. Study of the distribution of doses in tumors with hypoxia through the PENELOPE code. Radiat Phys Chem 2020;167:22-5.
30Merk R, Kröger H, Hornung LE, Hoffmann B. PENELOPE-2008 Monte Carlo simulation of gamma exposure induced by 60Co and NORM-radionuclides in closed geometries. Appl Radiat Isot 2013;82:20-7.
31Brualla L, Rodriguez M, Sempau J, Andreo P. PENELOPE/primo-calculated photon and electron spectra from clinical accelerators. Radiat Oncol 2019;14:6.
32Sheikh-bagheri D, Rogers DWO. Monte Carlo calculation of nine megavoltage photon beam spectra using the BEAM code. Med Phys 2002;29:391-402.
33Gallardo S, Querol A, Pozuelo F, Verdú G, Ródenas J. Application of the Monte Carlo codes PENELOPE and MCNP5 to unfold X-ray spectra in the diagnostic energy range. Radiat Phys Chem 2014;95:166-9.
34Merk R, Mielcarek J, Döring J, Lange B, Lucks C. Estimating contamination monitor efficiency for beta radiation by means of PENELOPE-2008 Monte Carlo simulation. Appl Radiat Isot 2017;127:87-91.
35Salvat F, Varea JM, Sempau J. PENELOPE 2011: A Code System for Monte Carlo Simulation of Electron and Photon Transport. Nuclear Energy Agency; 2011.
36Salvat F. The PENELOPE code system. Specific features and recent improvements. Ann Nucl Energy 2014;82:98-109.
37Pimpinella M, Mihailescu D, Guerra AS, Laitano RF. Dosimetric characteristics of electron beams produced by a mobile accelerator for IORT. Phys Med Biol 2007;52:6197-214.
38Björk P, Nilsson P, Knöös T. Dosimetry characteristics of degraded electron beams investigated by Monte Carlo calculations in a setup for intraoperative radiation therapy. Phys Med Biol 2002;47:239-56.
39Jiménez JS, Lagos MD, Martinez-Ovalle SA. A Monte Carlo study of the photon spectrum due to the different materials used in the construction of flattening filters of LINAC. Comput Math Methods Med 2017;2017:3621631.
40Qomariyah N, Wirawan R, Mardiana L, Hadi K Al. Distributions dose analysis for 6 MV photon beams using Monte Carlo-GEANT4 simulation. AIP Conf Proc 2019;2169:1-6.
41Sheikh-bagheri D, Rogers DWO. Monte Carlo calculation of nine megavoltage photon beam spectra using the BEAM code. Med Phys 2002;29:391-402.
42Lin SY, Chu TC, Lin JP. Monte Carlo simulation of a clinical linear accelerator. Appl Radiat Isot 2001;55:759-65.
43Serrano B, Hachem A, Franchisseur E, Hérault J, Marcié S, Costa A, et al. Monte Carlo simulation of a medical linear accelerator for radiotherapy use. Radiat Prot Dosimetry 2006;119:506-9.
44Jabbari K, Anvar H, Tavakoli M, Amouheidari A. Monte carlo simulation of siemens oncor linear accelerator with beamnrc and dosxyznrc code. J Med Signals Sens 2013;3:172-9.
45Sadrollahi A, Nuesken F, Licht N, Rübe C, Dzierma Y. Monte-Carlo simulation of the Siemens Artiste linear accelerator flat 6 MV and flattening-filter-free 7 MV beam line. PLoS One 2019;14:e0210069.
46Anderson R, Lamey M, MacPherson M, Carlone M. Simulation of a medical linear accelerator for teaching purposes. J Appl Clin Med Phys 2015;16:5139.
47Chin MP, Böhlen TT, Fassò A, Ferrari A, Ortega PG, Sala PR. FLUKA and PENELOPE simulations of 10keV to 10MeV photons in LYSO and soft tissue. Radiat Phys Chem. 2014;95:170-3.
48Almansa JF, Guerrero R, Al-Dweri FM, Anguiano M, Lallena AM. Dose distribution in water for monoenergetic photon point sources in the energy range of interest in brachytherapy: Monte Carlo simulations with PENELOPE and GEANT4. Radiat Phys Chem 2007;76:766-73.
49International Atomic Energy Agency. The Use of Plane Parallel Ionization Chambers in High Energy Electron and Photon Beams: An International Code of Practice for Dosimetry. Technical Reports Series No. 381. Vienna, 1997.
50Zhengming L, Jette D. On the possibility of determining an effective energy spectrum of clinical electron beams from percentage depth dose (PDD) data of broad beams. Phys Med Biol 1999;44:N177-82.