

ORIGINAL ARTICLE 



Year : 2018  Volume
: 43
 Issue : 1  Page : 18 

Monte carlo investigation of photon beam characteristics and its variation with incident electron beam parameters for indigenous medical linear accelerator
Subhalaxmi Mishra^{1}, PK Dixit^{2}, T Palani Selvam^{1}, Sanket S Yavalkar^{3}, DD Deshpande^{4}
^{1} Radiological Physics and Advisory Division, Bhabha Atomic Research Centre; Homi Bhabha National Institute, Training School Complex, Anushaktinagar, Mumbai, India ^{2} Radiological Safety Division, Atomic Energy Regulatory Board; Homi Bhabha National Institute, Training School Complex, Anushaktinagar, Mumbai, India ^{3} Technology Innovation Department, Society for Applied Microwave Electronics Engineering and Research, Mumbai, India ^{4} Department of Medical Physics, Tata Memorial Hospital, Mumbai, India
Date of Submission  13Oct2017 
Date of Decision  21Dec2017 
Date of Acceptance  02Jan2018 
Date of Web Publication  12Mar2018 
Correspondence Address: Subhalaxmi Mishra Radiological Physics and Advisory Division, Bhabha Atomic Research Centre, Safety and Environment Group, Mumbai  400 09, Maharashtra India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/jmp.JMP_125_17
Abstract   
Purpose: A Monte Carlo model of a 6 MV medical linear accelerator (linac) unit built indigenously was developed using the BEAMnrc user code of the EGSnrc code system. The model was benchmarked against the measurements. Monte Carlo simulations were carried out for different incident electron beam parameters in the study. Materials and Methods: Simulation of indigenously developed linac unit has been carried out using the Monte Carlo based BEAMnrc usercode of the EGSnrc code system. Using the model, percentage depth dose (PDD), and lateral dose profiles were studied using the DOSXYZnrc user code. To identify appropriate electron parameters, three different distributions of electron beam intensity were investigated. For each case, the kinetic energy of the incident electron was varied from 6 to 6.5 MeV (0.1 MeV increment). The calculated dose data were compared against the measurements using the PTW, Germany make RFA dosimetric system (water tank MP3M and 0.125 cm^{3} ion chamber). Results: The best fit of incident electron beam parameter was found for the combination of beam energy of 6.2 MeV and circular Gaussian distributed source in X and Y with FWHM of 1.0 mm. PDD and beam profiles (along both X and Y directions) were calculated for the field sizes from 5 cm × 5 cm to 25 cm × 25 cm. The dose difference between the calculated and measured PDD and profile values were under 1%, except for the penumbra region where the maximum deviation was found to be around 2%. Conclusions: A Monte Carlo model of indigenous linac (6 MV) has been developed and benchmarked against the measured data.
Keywords: Beamnrc, dosxyznrc, egsnrc code system, linear accelerator, measurement, monte Carlo
How to cite this article: Mishra S, Dixit P K, Selvam T P, Yavalkar SS, Deshpande D D. Monte carlo investigation of photon beam characteristics and its variation with incident electron beam parameters for indigenous medical linear accelerator. J Med Phys 2018;43:18 
How to cite this URL: Mishra S, Dixit P K, Selvam T P, Yavalkar SS, Deshpande D D. Monte carlo investigation of photon beam characteristics and its variation with incident electron beam parameters for indigenous medical linear accelerator. J Med Phys [serial online] 2018 [cited 2019 Jul 22];43:18. Available from: http://www.jmp.org.in/text.asp?2018/43/1/1/227064 
Introduction   
Linear accelerator (linac) has several advantages in comparison to telecobalt units.^{[1],[2],[3],[4],[5]} Department of Science and Technology, Government of India, has entrusted the responsibility of development of indigenous linac to one of its constituent units, Society for Applied Microwave Electronics Engineering and Research (SAMEER) under Jai Vigyan National Science and Technology Mission. Due to its development under indigenous technology, the machine has the potential of delivering costeffective radiotherapy treatments in India. The linac unit is named as Siddharth and is capable of producing photon beam energy of 6 MV. Details can be found at https://www.sameer.gov.in/linearaccelerators.
Benchmarking of photon beams generated from radiotherapy equipment are extensively carried out with the help of Monte Carlo radiation transport simulations.^{[6],[7],[8],[9],[10],[11],[12],[13]} The first step of dose calculation using Monte Carlo code is to develop the Monte Carlo beam model for the linac. Tuning of the incident electron beam parameters is an important task to benchmark the calculated dose data against the measured data.^{[14],[15],[16],[17]} Detailed studies by Sheikh–Bagheri and Rogers ^{[14]} showed that optimum tuning of the beam energy and its width can be performed by using PDD and inair offaxis factors. A study by Lin et al.^{[18]} found that it is possible to tune the beam width by the 10 cm × 10 cm beam profile measured in a water phantom. Verhaegen and Seuntjens ^{[19]} identified suitable electron beam width based on larger fields and shallower depths. Recently, Sangeetha and Surekha ^{[20]} used EGSnrc code system ^{[21]} to simulate Varian 600 C/D linac of photon energy 6 MV (for both with flattening filter and without flattening filter). Several studies on determination of incident beam parameters are reported in the literature.^{[15],[22],[23],[24],[25],[26],[27],[28],[29]}
The purpose of the present study is to develop Monte Carlo model of 6 MV Siddharth linac unit using the Monte Carlobased BEAMnrc usercode ^{[30]} of the EGSnrc ^{[21]} Monte Carlo code system and benchmark this model against the measured data. The calculated dose data are based on the DOSXYZnrc user code ^{[31]} of the EGSnrc code system.^{[21]} In the study, simulations were carried out for different incident electron beam parameters.
Materials and Methods   
Simulation of medical linear accelerator (Siddharth)
The geometry of the linac unit was simulated based on the manufacturer's detailed information using the BEAMnrc user code ^{[30]} of the Monte Carlobased EGSnrc code system.^{[21]} In this study, different components of the treatment head such as target, primary collimator, flattening filter, monitor chamber, mirror, and secondary collimator were modeled. [Figure 1] shows the display of linac modeled in the present study using the BEAMnrc user code.^{[30]} In this simulation, the zaxis is taken along the beam axis, and the origin is taken at the front face of the target.  Figure 1: Detailed head structure of Siddharth medical linear accelerator. The dashed line is the Zaxis, with the positive X direction to the right and the Y direction coming out of the page. The origin is on the target surface at position 0. The linac head consists of six main component modules including the target, primary collimator, flattening filter, ion chamber, mirror, and secondary collimator
Click here to view 
Incident electron beam parameters
Incident electron parameters play an important role in the dose distributions. To identify appropriate electron parameters, following three cases were studied. For each case, the kinetic energy of the incident electron was varied from 6 to 6.5 MeV (0.1 MeV increment).
Case 1
As per the manufacturer's specification, the electron beam is a point and divergent with a halfangle of 14°. The source is positioned on Zaxis and 4 mm above the target [Figure 2]. The radius of the beam at the target is 1 mm.  Figure 2: Point divergent source on Zaxis (Case 1) showing the electron beam divergence angle which is the half angle of the circular field at the point of incidence (14°) and the directions of X, Y and Z axes. The beam is centered on the Z axis
Click here to view 
Case 2
In this case, the incident electron beam is a circular parallel beam with a diameter of 2 mm [Figure 3]. The electron beam is incident in the XY plane.  Figure 3: Parallel Circular Beam (Case 2) showing the beam diameter (2 mm) measured perpendicular to the beam central axis and the directions of X, Y and Z axes. The beam is along the Zaxis
Click here to view 
Case 3
In this case, the beam is circular, and the spatial distribution of electrons is defined by a Gaussian intensity distribution [Figure 4]. The Full Width Half Maximum (FWHM) of the incident beam is considered to be 1 mm in both X and Y directions.  Figure 4: Circular Beam with Gaussian distributions in X and Y (Case 3). The shape of the circle is defined by FWHM (1 mm) of the Gaussian intensity distributions in the Xand Ydirections respectively
Click here to view 
BEAMnrc and DOSXYZnrc simulations
The Monte Carlo simulations were done in two steps. To identify the incident electron beam parameters, initial simulations were carried out for 10 cm × 10 cm field size and depth of 10 cm. In the first step, phase space file for each of the above cases was scored at 100 cm from the target using the BEAMnrc usercode.
In the BEAMnrc simulations, the electron transport cutoff (ECUT) and photon transport cutoff (PCUT) energies were set to 0.7 and 0.01 MeV, respectively. Secondary electron production cutoff (AE) and bremstrahlung production cutoff (AP) values were set to 0.521 and 0.01 MeV, respectively. Range rejection was turned on with ESAVE value of 0.7 MeV in the target and 2 MeV in other components of the linac.^{[14]} The number of histories for Monte Carlo calculation was set 6 × 10^{9} particles.
In the second step, the phase space data from aforementioned simulations served as the source for the simulations using the DOSXYZnrc user code. This user code is capable of performing 3D absorbed dose calculations in Cartesian coordinates in the water phantom. In DOSXYZnrc, the water phantom size was 50 cm × 50 cm × 50 cm and the phase space source was positioned on the water surface, i.e. at Z = 100 cm. [Figure 5] represents the voxel phantom set up in the DOSXYZnrc simulations. The water phantom was divided into a number of voxels. For highdose gradients regions, small voxel sizes were adapted.^{[32]} For central axis PDD simulation, up to a depth of 2 cm, absorbed dose was scored in voxel dimension of 1.0 cm × 1.0 cm × 0.05 cm and for depths from 2 to 25 cm, voxel dimension of 1.0 cm × 1.0 cm × 0.1 cm were considered. The beam profiles (both X and Y directions) were calculated at three different depths such as d_{max} (1.5 cm), 5 cm and 10 cm. For beam profile simulations, different voxel dimensions were chosen for the shoulder, penumbra, and flattened regions. For example, for dose profile simulation in Xdirection for a field size of 10 cm × 10 cm voxel dimensions of 0.1 cm × 1.0 cm × 0.1 cm (from −4.0 to +4.0) for flattened region and 0.05 cm × 1.0 cm × 0.1 cm for shoulder and penumbra regions (from −7.5 to −4.0 and +7.5 to +4.0) were used. The EGSnrc parameters set for DOSXYZnrc simulation were ECUT = AE = 0.521 MeV, PCUT = AP = 0.01 MeV.  Figure 5: The voxel water phantom of dimension 50 cm × 50 cm × 50 cm used for DOSXYZnrc simulation. The size of voxels set for PDD and beam profile calculations (for 10 cm × 10 cm field size) are also shown
Click here to view 
All the simulations utilized PRESTAII electron step length algorithm. Up to 6 × 10^{9} particle histories were followed in the simulation. The statistical uncertainties associated with the absorbed dose values were <0.5%.
Measurement of photon beam dosimetric parameters
Dose measurements were carried out by a PTW MP3 Water Scanning System and ionization chamber (Semiflex 0.125 cm ^{3}). The measurements were performed with 1 mm resolution for both PDD and beam profiles. Field sizes considered were from 5 cm x 5 cm to 25 cm x 25 cm at a SSD of 100 cm. Beam profiles were measured at three different depths, i.e. depth of maximum dose (d_{max}), 5 cm and 10 cm for both X and Y directions. The overall uncertainty in the dose measurement using the water phantom scanning system is estimated up to a maximum value of 2%. This uncertainty is attributed to positioning inaccuracy of the chamber up to 1 mm and fluctuations of chamber and electrometer, air pressure, and temperature during the time frame of one scan.
Results and Discussion   
Incident electron beam characteristics
Analysis of central axis percentage depth dose (PDD) data for 10 cm × 10 cm suggests that for a given incident electron beam energy, PDD is almost insensitive to the incident electron beam parameters. PDD values also do not differ significantly with the investigated incident electron beam energies of 6–6.5 MeV. The relative difference between the calculated depthdose distributions (10 cm × 10 cm field size) for beam energies 6 and 6.5 MeV was <1.5%. The PDD values at a depth of 10 cm, %dd (10), for a field size of 10 cm × 10 cm, corresponds to the beam quality.^{[33]} [Figure 6] presents the %dd (10) values for the investigated electron beam energies which have Gaussian distribution (FWHM = 1 mm). As the energy increases, there is a marginal increase in the value of %dd (10). The same trend was observed for the cases 1 and 2. For the incident electron beam energy of 6.2 MeV (Gaussian with FWHM = 1 mm), the calculated value %dd (10) is 66.3% which is in close agreement with the measured value of 67% carried out in the present study. The overall conclusion is that for the incident electron beam energy of 6.2 MeV, irrespective of the cases investigated (cases 1–3), the agreement between the calculated PDD values and the measurements is <1%.  Figure 6: Comparison of percent depth dose value at a depth of 10 cm, %dd (10), in water, Monte Carlocalculated values for various incident electron beam energies and measurement for a field size of 10 cm × 10 cm
Click here to view 
However, the beam profiles are sensitive to the incident electron beam parameters. [Figure 7]a presents the comparison of Monte Carlocalculated profile in Xdirection for incident electron beam energies 6.0, 6.2, 6.5 MeV and measured data for a field size of 10 cm × 10 cm and at a depth of 10 cm for point divergent source (case 1). [Figure 7]b and c present the above comparison for the parallel circular beam (case 2) and Gaussian distribution (case 3), respectively. It was observed that beam profile horns were reduced as the incident electron beam energy increases. Lower energy beams produce horns at the edge of the radiation field while higher ones correspond to flat profiles. An energy difference of 0.1 MeV causes a dose difference at the edge of the field by about 1%. Above discussion demonstrates that the dose profile resulting from 6.2 MeV of electrons with Gaussian distribution (case 3) provides optimum agreement with the measurements. [Figure 7]d compares the investigated cases with incident electron beam energy of 6.2 MeV with measured data.  Figure 7: Comparison of Monte Carlocalculated beam profiles and measured values for incident electron beam energies 6.0, 6.2, 6.5 MeV and measured data for a field size of 10 cm × 10 cm and at a depth of 10 cm (a) Point divergent source placed on the Zaxis (b) parallel circular beam (c) circular beam with Gaussian distributions. (d) Comparison of Monte Carlocalculated beam profiles of all the investigated radial intensity distributions for incident electron beam energy 6.2 MeV and measured data
Click here to view 
For all the investigated cases, beam parameters such as left penumbra (LP), right penumbra (RP), beam flatness and beam symmetry were investigated. [Table 1] presents these parameters analyzed from the calculated beam profiles of all the investigated electron beam parameters for the field size of 10 cm × 10 cm. Measured data are also included for comparison. For case 1, both RP and LP were <6 mm which is less than the measured values of 6.9 mm. Beam symmetry and flatness were observed to be higher than the measured as well as the tolerance values (103% and 106%) as quoted by the IEC protocol.^{[34]} For case 2, both RP and LP were <5.5 mm which is less than the measured values of 6.9 mm. Beam flatness was observed to be higher than the measured as well as the tolerance values. However, beam symmetry was within the acceptable range for all the beam energies. For case 3, all the parameters such as RP, LP, symmetry, and flatness were in good agreement with the measured values at beam energy 6.2 MeV with the Gaussian distribution.  Table 1: The parameters analyzed from the beam profiles for all the combinations of incident electron beam parameters along with the measured parameters for a field size of 10 × 10 cm^{2} and at a depth of 10 cm
Click here to view 
[Figure 6] and [Figure 7] and [Table 1] demonstrate that Monte Carlo calculations using the incident electron beam energy of 6.2 MeV with Gaussian distribution (FWHM = 1 mm) produce dose distributions which agree with the measurements. [Table 2] presents the incident electron beam parameters concluded by the other investigators which result in dose distribution comparable to the measurements.  Table 2: Comparison of incident electron beam parameters which resulted in good agreement with the measured dose profiles (published and this study)
Click here to view 
Measured and calculated photon beam dosimetric characteristics
Further Monte Carlo simulations were carried out for other field sizes such as 5 cm × 5 cm, 15 cm × 15 cm, 20 cm × 20 cm and 25 cm × 25 cm for a monoenergetic electron beam of kinetic energy 6.2 MeV with the Gaussian distribution of FWHM = 1 mm. PDDs were calculated for depths from 0 to 25 cm, and beam profiles (both X and Y directions) were calculated at three different depths of d_{max} (1.5 cm), 5 cm and 10 cm for the above field sizes. The calculated PDD and beam profiles for all the above field sizes were compared with the measured data and a good agreement was found.
The dose difference between the calculated and measured PDD values were under 1% for all the investigated field sizes. Both Monte Carlocalculated and measured depth of d_{max} was found to be at 1.52 cm for a field size of 10 cm × 10 cm. The differences between calculated and measured values were <1% in the tail region and <0.5% in the superficial depth region for all the investigated field sizes. Calculated and measured PDD values are shown in [Figure 8], [Figure 9], [Figure 10] for field sizes of 5 cm × 5 cm, 10 cm × 10 cm and 25 cm × 25 cm, respectively.  Figure 8: Comparison of Monte Carlocalculated and measured percentage depth dose values for a field size of 5 cm × 5 cm
Click here to view 
 Figure 9: Comparison of Monte Carlocalculated and measured percentage depth dose values for a field size of 10 cm × 10 cm
Click here to view 
 Figure 10: Comparison of Monte Carlocalculated and measured percentage depth dose values for a field size of 25 cm × 25 cm
Click here to view 
For beam profiles, the difference between calculated and measured dose values was <1%, except for the border points where the maximum deviation between calculated and measured dose values were found to be around 1.8%. [Table 3] presents the comparison of Monte Carlocalculated and measured beam profile parameters such as LP, RP, flatness, and symmetry for all the investigated field sizes. Monte Carlocalculated values were found to be in excellent agreement with the measured values for the field sizes. Calculated and measured Xprofiles and Yprofiles for all the investigated field sizes at a depth of 10 cm are presented in [Figure 11] and [Figure 12], respectively. Statistical uncertainties on the calculated dose values for each voxel were mostly below 0.2% and about 0.7% for regions near field edge.  Table 3: Comparison of Monte Carlocalculated and measured beam profile parameters such as left penumbra, right penumbra, flatness, and symmetry for the investigated field sizes for incident electron beam energy of 6.2 MeV with a Gaussian distribution of Full Width Half Maximum 1 mm
Click here to view 
 Figure 11: Comparison of Monte Carlocalculated and measured Xprofiles for all the investigated field sizes at a depth of 10 cm
Click here to view 
 Figure 12: Comparison of Monte Carlocalculated and measured Yprofiles for all the investigated field sizes at a depth of 10 cm
Click here to view 
Conclusions   
The indigenous linac unit Siddharth of photon energy 6 MV was simulated using the Monte Carlobased BEAMnrc code. The dosimetric parameters such as PDD and beam profile were calculated using the DOSXYZnrc usercode of the EGSnrc code system, and the results were compared with the measured data. In the study of the influence of electron beam parameters on photon beam characteristics, five different incident electron beam energies (66.5 MeV) and three different type of radial intensity distribution of electron beam (case 1, 2 and 3) were chosen. It was found that the central axis relative depth dose values, i.e. PDDs are quite insensitive to variations in the electron beam radial intensity distribution. However, the beam profiles are sensitive to the incident electron energy as well as the radial intensity distribution of the incident electron beam. The calculated PDD and lateral beam profiles for 5 cm × 5 cm, 10 cm × 10 cm, 15 cm × 15 cm, 20 cm × 20 cm and 25 cm × 25 cm field sizes were compared with the measured data and a good agreement was found when the calculated dose profiles utilized the combination of incident electron beam energy of 6.2 MeV and the Gaussian distribution with FWHM of 1.0 mm.
Acknowledgment
The authors would like to Dr. D. Datta, Head, Radiological Physics and Advisory Division, Bhabha Atomic Research Centre, and Dr. A. U. Sonawane, Head, Directorate of Regulatory Affairs and Commumnications, Atomic Energy Regulatory Board for their encouragement and support throughout the study. The authors would also like to thank Dr. K. P. Ray, Program Director, SAMEER Mumbai, India for his technical support in the study.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
References   
1.  Matcalfe P, Kron T, Hoban P. The Physics of Radiotherapy XRays from Linear Accelerators. Madison, Wisconsin: Medical Physics Publishing; 1997. 
2.  Adams EJ, Warrington AP. A comparison between cobalt and linear acceleratorbased treatment plans for conformal and intensitymodulated radiotherapy. Br J Radiol 2008;81:30410. [ PUBMED] 
3.  Thwaites DI, Tuohy JB. Back to the future: The history and development of the clinical linear accelerator. Phys Med Biol 2006;51:R34362. [ PUBMED] 
4.  Khan FM. The Physics of Radiation Therapy. 4 ^{th} ed. Baltimore: Lippincott; 2010. 
5.  Page BR, Hudson AD, Brown DW, Shulman AC, AbdelWahab M, Fisher BJ, et al. Cobalt, linac, or other: What is the best solution for radiation therapy in developing countries? Int J Radiat Oncol Biol Phys 2014;89:47680. [ PUBMED] 
6.  Andreo P. Monte Carlo techniques in medical radiation physics. Phys Med Biol 1991;36:861920. [ PUBMED] 
7.  Rogers DW, Faddegon BA, Ding GX, Ma CM, We J, Mackie TR, et al. BEAM: A Monte Carlo code to simulate radiotherapy treatment units. Med Phys 1995;22:50324. 
8.  DeMarco JJ, Solberg TD, Wallace RE, Smathers JB. A verification of the Monte Carlo code MCNP for thick target bremsstrahlung calculations. Med Phys 1995;22:116. 
9.  Keall PJ, Siebers JV, Arnfield M, Kim JO, Mohan R. Monte Carlo dose calculations for dynamic IMRT treatments. Phys Med Biol 2001;46:92941. 
10.  Solberg TD, DeMarco JJ, Chetty IJ, Mesa AV, Cagnon CH, Li AN, et al. A review of radiation dosimetry application using the MCNP Monte Carlo code. Radiochim Acta 2001;89:33755. 
11.  Fix MK, Manser P, Born EJ, Mini R, Rüegsegger P. Monte Carlo simulation of a dynamic MLC based on a multiple source model. Phys Med Biol 2001;46:324157. 
12.  Das IJ, Kassaee A, Verhaegen F, Moskvin VP. Interface dosimetry: Measurement and Monte Carlo simulations of lowenergy photon beams. Radiat Phys Chem 2001;61;5935. 
13.  Ma CM, Pawlicki T, Jiang SB, Li JS, Deng J, Mok E, et al. Monte Carlo verification of IMRT dose distributions from a commercial treatment planning optimization system. Phys Med Biol 2000;45:248395. 
14.  SheikhBagheri D, Rogers DW, Ross CK, Seuntjens JP. Comparison of measured and Monte Carlo calculated dose distributions from the NRC linac. Med Phys 2000;27:225666. 
15.  Jiang SB, Kapur A, Ma CM. Electron beam modeling and commissioning for Monte Carlo treatment planning. Med Phys 2000;27:18091. 
16.  Deng J, Jiang SB, Kapur A, Li J, Pawlicki T, Ma CM, et al. Photon beam characterization and modelling for Monte Carlo treatment planning. Phys Med Biol 2000;45:41127. 
17.  Mesbahi A, Fix M, Allahverdi M, Grein E, Garaati H. Monte Carlo calculation of Varian 2300C/D linac photon beam characteristics: A comparison between MCNP4C, GEANT3 and measurements. Appl Radiat Isot 2005;62:46977. 
18.  Lin SY, Chu TC, Lin JP. Monte Carlo simulation of a clinical linear accelerator. Appl Radiat Isot 2001;55:75965. 
19.  Verhaegen F, Seuntjens J. Monte Carlo modelling of external radiotherapy photon beams. Phys Med Biol 2003;48:R10764. 
20.  Sangeetha S, Sureka CS. Comparison of flattening filter (FF) and flatteningfilterfree (FFF) 6 MV photon beam characteristics for small field dosimetry using EGSnrc Monte Carlo code. Radiat Phys Chem 2017;135:6375. 
21.  Rogers DW, Kawrakow I, Seuntjens JP, Walters BR, MainegraHing E. NRC User Codes for EGSnrc. NRCC Report PIRS702 (revB). Ottawa, ON: National Research Council of Canada; 2010. 
22.  Keall PJ, Siebers JV, Libby B, Mohan R. Determining the incident electron fluence for Monte Carlobased photon treatment planning using a standard measured data set. Med Phys 2003;30:57482. 
23.  Aljarrah K, Sharp GC, Neicu T, Jiang SB. Determination of the initial beam parameters in Monte Carlo linac simulation. Med Phys 2006;33:8508. 
24.  Almberg SS, Frengen J, Kylling A, Lindmo T. Monte Carlo linear accelerator simulation of megavoltage photon beams: Independent determination of initial beam parameters. Med Phys 2012;39:407. 
25.  Tzedakis A, Damilakis JE, Mazonakis M, Stratakis J, Varveris H, Gourtsoyiannis N, et al. Influence of initial electron beam parameters on Monte Carlo calculated absorbed dose distributions for radiotherapy photon beams. Med Phys 2004;31:90713. 
26.  Pena J, GonzálezCastaño DM, Gómez F, SánchezDoblado F, Hartmann GH. Automatic determination of primary electron beam parameters in Monte Carlo simulation. Med Phys 2007;34:107684. 
27.  Bush K, Zavgorodni S, Beckham W. Inference of the optimal pretarget electron beam parameters in a Monte Carlo virtual linac model through simulated annealing. Med Phys 2009;36:230919. 
28.  Fix MK, Stampanoni M, Manser P, Born EJ, Mini R, Rüegsegger P, et al. A multiple source model for 6 MV photon beam dose calculations using Monte Carlo. Phys Med Biol 2001;46:140727. 
29.  Björk 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;47:401941. 
30.  Rogers DW, Walters B and Kawrakow I. BEAMnrc users Manual. PIRS 509(A) Rev. Ottawa, ON: National Research Council of Canada; 2016. 
31.  Walters B, Kawrakow I, Rogers DW. DOSXYZnrc users Manual. PIRS 794(B) Rev. Ottawa, ON: National Research Council of Canada; 2016. 
32.  Yani S, Dirgayussa I, Gde E, Rhani MF, Haryanto F, Arif I. The effect of voxel size on dose distribution in Varian Clinac i×6 MV photon beam using Monte Carlo simulation. AIP Conf Proc 2015;1677:040002. 
33.  Almond PR, Biggs PJ, Coursey BM, Hanson WF, Huq MS, Nath R, et al. AAPM's TG51 protocol for clinical reference dosimetry of highenergy photon and electron beams. Med Phys 1999;26:184770. 
34.  International Electrotechnical Commission IEC 609772. Medical Electrical Equipment – Medical Electron Accelerators – Guidelines for Functional Performance Characteristics. IEC/TR 60977; 2008. 
[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8], [Figure 9], [Figure 10], [Figure 11], [Figure 12]
[Table 1], [Table 2], [Table 3]
