

ORIGINAL ARTICLE 

Year : 2019  Volume
: 15
 Issue : 8  Page : 127134 

A Monte Carlo evaluation of dose distribution of commercial treatment planning systems in heterogeneous media
Mohsen Hasani^{1}, Kheirollah Mohammadi^{2}, Mahdi Ghorbani^{3}, Soraya Gholami^{1}, Courtney Knaup^{4}
^{1} Department of Radiotherapy Physics, Cancer Research Centre, Tehran University of Medical Sciences, Cancer Institute, Tehran, Iran ^{2} Department of Physics, Malek Ashtar University of Technology, Tehran, Iran ^{3} Department of Biomedical Engineering and Medical Physics, Faculty of Medicine, Shahid Beheshti University of Medical Sciences, Tehran, Iran ^{4} Comprehensive Cancer Centers of Nevada, Las Vegas, Nevada, USA
Date of Web Publication  22Mar2019 
Correspondence Address: Dr. Kheirollah Mohammadi Department of Physics, Faculty of Science, Malek Ashtar University of Technology, Shahid Babaei Highway, Lavizan, Tehran Iran
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/jcrt.JCRT_1210_16
Introduction: Calculations from a treatment planning system (TPS) in heterogeneous regions may present significant inaccuracies due to loss of electronic equilibrium. The purpose of this study is to evaluate and quantify the differences of dose distributions computed by some of the newest dose calculation algorithms, including collapsed cone convolution (CCC), fast Fourier transform (FFT) convolution, and superposition convolution, in heterogeneity of the lung. Materials and Methods: A 6MV Siemens Primus linear accelerator was simulated by MCNPX Monte Carlo (MC) code, and the results of percentage depth dose (PDD) and dose profile values were compared with measured data. The ISOgray TPS was used and PDDs of CCC, FFT, and superposition convolution algorithms were compared with the results obtained by MCNPX code. CT2MCNP software was used to convert the computed tomography images of the lung tissue to MC input files, and dose distributions from the three algorithms were compared to MC method. Results: For PDD curves in buildup region, the maximum underdosage of ISOgray TPS was at the surface (19%) and comes in closer agreement when depth increases (average 7.08%). Dose differences (DD) between different algorithms and MC were typically 4.81% (range: 1.95% to 7.30%), −1.55% (range: −5.14% to 5.26%) and 4.96% (range: 2.00% to 7.4%) in the lung for the CCC, FFT, and superposition algorithms, respectively. The difference between monitor units and maximum dose calculated using the three algorithms were 0.5% and 1.61%, respectively. The maximum DD of 7% was observed between MC and TPS results. Conclusion: Significant differences were found when the calculation algorithms were compared with MC method in lung tissue, and this difference is not negligible. It is recommended to use of MCbased TPS for the treatment fields including lung tissue.
Keywords: CT2MCNP, dose calculation algorithm, heterogeneity, Monte Carlo, treatment planning system
How to cite this article: Hasani M, Mohammadi K, Ghorbani M, Gholami S, Knaup C. A Monte Carlo evaluation of dose distribution of commercial treatment planning systems in heterogeneous media. J Can Res Ther 2019;15, Suppl S1:12734 
How to cite this URL: Hasani M, Mohammadi K, Ghorbani M, Gholami S, Knaup C. A Monte Carlo evaluation of dose distribution of commercial treatment planning systems in heterogeneous media. J Can Res Ther [serial online] 2019 [cited 2021 Apr 13];15:12734. Available from: https://www.cancerjournal.net/text.asp?2019/15/8/127/243475 
> Introduction   
In radiation therapy, several treatment planning systems (TPSs) are available to deliver a prescribed dose to a tumor while minimizing dose to the critical structures.^{[1]} Many different types of dose calculation algorithm are used in modern TPSs.^{[2],[3],[4]} The accuracy of algorithms for prediction of dose depends on the assumptions and approximations that the algorithms make. These approximations cause uncertainty in the delivered dose, especially in heterogeneous organs such as the bone and lung.^{[5],[6]} According to recommendation by the International Commission on Radiation Units and Measurements, the error in delivered dose should be <±5%,^{[7]} including quality control of machine, patient positioning, and dose calculation. For dose calculation, accuracy in the range of 2%–3% is required.^{[8],[9]}
The most modern calculation algorithms implemented in threedimensional (3D) TPSs are the modelbased algorithms, which attempt to model from first principles the photon beam and its interaction with the patient, such as the pencil beam convolution, anisotropic analytical algorithm, and collapsed cone convolution (CCC).^{[4],[5],[10]} For these calculation algorithms, there is not much difference of accuracy in homogeneous media such as water. For heterogeneous media, the difference in the accuracy of dose calculation is determined by how well the kernels of these algorithms can simulate the actual radiation scattering.^{[1],[11]} Monte Carlo (MC) dose calculations will not show inaccuracy for heterogeneous media when enough particles are transported. The aim of this study is to evaluate the accuracy of different algorithms of ISOgray TPS, including CCC, fast Fourier transform (FFT) and superposition convolution by MC simulation in water and lung as samples of homogeneous and heterogeneous media, respectively.
> Materials and Methods   
Siemens Primus linear accelerator was simulated by use of MCNPX code (Los Alamos National Laboratory, Los Alamos, USA) and the simulation accuracy was validated by measurement data. Percentage depth dose (PDD) and beam profile curves from three different algorithms of ISOgray TPS in homogeneous medium were obtained and compared with the results of the MC calculation.
In the second stage of this work, to assess the accuracy of ISOgray TPS in heterogeneous media, CT2MCNP software was used and isodose curves from TPS algorithms and MC calculations were compared.
Monte Carlo simulation validation of Siemens Primus linear accelerator
MCNPX (version 2.6.0) radiation transport MC code was used in this study to simulate a Siemens Primus medical linear accelerator (Siemens AG, Erlangen, Germany). This code allows development of a detailed 3D modeling of a linear accelerator's treatment head and dose calculation in complex geometries and materials.^{[12]}
In this study, a 6MV photon beam from a Siemens Primus linear accelerator was simulated using the geometric information provided by the manufacturer. The main parts of the linear accelerator in 6MV photon mode are target (9 layers), primary collimator (6 layers), absorber (4 layers), flattening filter (16 layers), photon ionization chamber (5 layers), mirror (2 layers), and two secondary collimators which are used for definition of radiation field in X and Y directions. The target consists of various layers including stainless steel, graphite, gold, water, and air. The primary collimator is made of tungsten, and it is located under the target. The absorber and the flattening filter are made of aluminum and stainless steel, respectively. The ionization chamber body is made of aluminum oxide and it includes air. The secondary collimators are composed of tungsten.
To verify the simulation, PDD values and beam profiles were acquired from simulations of various field sizes and a phantom, and then, the simulation values were compared with analogous values obtained by measurements. To accomplish depth dose calculation for various depths of the water phantom, a cylinder was defined with 1 cm in radius at a water phantom of 40 × 40 × 40 cm^{3} in dimensions that were positioned under the treatment head at a sourcetosurface distance (SSD) of 100 cm (for 6 × 6 cm^{2}, 10 × 10 cm^{2} and 15 × 15 cm^{2} field sizes). The cylinder axis was assumed to be positioned on the beam's central axis. The cylinder was then divided into 61 cells, with 2 mm in height, named scoring cells. To calculate beam profiles, 51 cubic scoring cells were utilized as the main axes of the scoring cells, which were perpendicular to the central axis of the beam and their dimensions were 0.2 × 1 × 1 cm^{3}. The cubes were positioned at 5 cm, 10 cm, and 15 cm depths of the water phantom, for 10 × 10 cm^{2} field size. In calculations of PDD and dose profile, the energy cutoffs for electrons and photons were defined as 0.5 MeV and 10 Kev, respectively. All input files were run by *F8 tally for 2 × 10^{9} particle histories and the maximum combined MC statistical uncertainty in PDD and dose profile calculations were equal to 1.2% and 1.9%, respectively.
To verify our simulation data, the obtained MC results were compared with the corresponding measured values using the gamma function method. Measurements were performed on a Siemens Primus medical linear accelerator with 6MV nominal photon energy. Dosimetry was performed using an automated (PTW, Freiburg Germany) dosimetry system and a water phantom (IEC 610101, Germany) at Teb Parto Sadra company (TPS Co.). This equipment is controlled by MEPHYSTO Navigator (version 3.2, PTW, Freiburg Germany) software. The depth measurements were performed using a diode detector (TM31010, 0.125 cc). The dimensions of the water phantom were 80 × 80 × 70 cm. The measurements were performed according to Technical Reports Series No. 398 reported by the International Atomic Energy Agency^{[13]} and based on this report, the average uncertainty in the measurements was 1.05%.
The comparison of the simulation and dosimetry data was performed by use of gamma function algorithm which was first developed by Low et al.^{[14]} In the gamma function method, if the gamma value is between 0 and 1, it is considered a pass or agreement of two dose distributions which are being compared. On the other hand, values exceeding 1 are considered a fail or disagreement. This algorithm is a computation method for comparison of two dose distributions which one of them is intended as a reference dose distribution.^{[14]} In this study, a gamma function software (Gamma_index.exe) was used and the evaluation criteria considered were 3% for dose difference (DD) and 3 mm for distance to agreement (DTA).^{[15],[16],[17]} In the MC and measurement comparisons, the measured data were chosen as the reference.
Dose calculation algorithms
The speed and quality of any TPS is dependent on the type of algorithms used.^{[4]} In this study, ISOgray TPS was used and it employs three different algorithms: FFT, CCC, and superposition convolution for calculation of dose distribution in a 3D space.
A radiation beam is divided into initial and scattered components by the CCC algorithm and dispersion values are calculated in nonuniform organs in the body inherently.^{[18]} This computation method has an acceptable accuracy in areas such as softtissuebone or softtissueair interfaces, where there is not an electronic equilibrium.^{[19],[20]} The FFT convolution algorithm transfers total energy released per unit mass (TERMA) from the spherical coordination to the Cartesian coordination based on a kernel. The distribution of radiation scattering in each part of the body mainly depends on the scattered radiation from the surrounding medium. Therefore, such a 3D calculation method is of paramount importance in this algorithm.^{[1]} Reports have indicated that the required volume for the FFT convolution algorithm calculation is 30 cm forward, 5 cm backward for the returning electrons, and twice the size of the radiation field at the field edges.^{[8],[21],[22]} Application of such large volume leads to long computation time needed for dose calculation by this algorithm. The superposition algorithm, which has been adapted from CCC algorithm, done calculation dose in beam coordinates as the FFT convolution. The superposition algorithm utilizes the kernel calculation that calculates TERMA at the interaction point, to the point in the volume of interest, and then transfers the results in a space which is selected by user.^{[23],[24]}
To evaluate the differences between the three algorithms of ISOgray TPS in a homogeneous medium, the images of a water phantom with dimensions of 30 × 30 × 30 cm^{3} were acquired by a computed tomography (CT) machine (Neusoft Neu Viz 16 slice). The PDD of a 6MV photon beam in SSD = 100 cm and 10 × 10 cm^{2} field size was obtained and compared with the results of the MC calculation. For evaluation of the algorithms in heterogeneous medium, a 6MV direct field was used for irradiation of lung tissue. The prescription characteristics were 200 cGy prescribed dose at depth of 3 cm, beam dimensions of 18 × 9 cm^{2}, and source axis distance technique. The dimension of each voxel in TPS was 0.5 × 0.5 × 0.5 cm^{3} and the dose distribution, monitor unit (MU), and maximum dose delivered by each algorithm were obtained.
Monte Carlo simulation of the heterogeneous media
CT2MCNP software was used to insert the materials and geometry of the body in the MCNPX code. This software converts the CT images to the required input files in the MCNP code via the following steps:
 Reading the CT files and ensuring they are 3D
 Assigning a specific material, density, and composition to each voxel
 Connecting the adjacent cells through the same square mesh to reduce the number of cells and assigning new material compositions and densities to the new cells
 Combining adjacent cells if they are made of same materials.
In this program, materials including air, soft tissue, lung, bone, and fat can be defined.^{[25]}
In this study, 27 CT images with 0.5cm slice thickness and 256 × 256 dimensions were used. The images were inserted into the CT2MCNP software, and the integrated matrices of the cells were obtained. The output file of CT2MCNP was positioned under the treatment head at a SSD of 97 cm with 18 × 9 cm^{2} field size (the same as TPS conditions). [Figure 1] shows a slice of this simulation geometry. The energy cutoffs for electrons and photons were defined as 0.5 MeV and 10 keV, respectively, and input files were run for 2 × 10^{9} particle histories by mesh tally (Type 3). The maximum uncertainty in the MC calculations was 1.3%. Finally, a comparison between the results of different TPS algorithms and simulation data was performed. To calculate percentage DD formula was used, where D_{MC} and D_{TPS} are dose results from MC and TPS calculations, respectively.  Figure 1: A view of simulation geometry plotted by CT2MCNP software for obtaining isodose curves
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> Results   
Monte Carlo simulation validation
PDD values which were obtained by MC simulations and measurements for 6MV photon beam are plotted in [Figure 2]. The data in the figure are related to 5 × 5 cm^{2}, 10 × 10 cm^{2}, and 15 × 15 cm^{2} field sizes and SSD of 100 cm. As it was mentioned in the previous section, comparisons of the simulation and measurement data were based on gamma function calculations. The resulting gamma function values used for PDD comparisons for these three field sizes are plotted in [Figure 3]. Gamma calculations were performed using DD and DTA criteria of 3% and 3 mm, respectively. As it can be seen from the gamma data in [Figure 3], only a few points show gamma values greater than unity, which is interpreted as fail or disagreement of the dose distributions at these points. The number of points with gamma index of higher than unity was 12, 2, and 5 points for 5 × 5 cm^{2}, 10 × 10 cm^{2}, and 15 × 15 cm^{2} field sizes, respectively.  Figure 2: Percent depth dose values for 6MV photon beam calculated by Monte Carlo code versus measurement data (source to surface distance = 100). The curves (a), (b), and (c) are corresponding to 5 × 5 cm^{2}, 10 × 10 cm^{2}, and 15 × 15 cm^{2} field sizes, respectively. For more clarification, the data for 5 × 5 cm^{2} and 10 × 10 cm^{2} field sizes are scaled 0.8 and 0.9, respectively
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 Figure 3: Gamma function results for percentage depth dose values for: 5 × 5 cm^{2} (a), 10 × 10 cm^{2} (b), and 15 × 15 cm^{2} (c) field sizes. Dose differences and distance to agreement criteria were set as to 3% and 3 mm in the gamma calculations, respectively
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Dose profiles related to the field size of 10 × 10 cm^{2} for three depths of 5, 10, and 15 cm, obtained from MC simulations and measurements are plotted in [Figure 4]a,[Figure 4]b,[Figure 4]c, respectively. The corresponding gamma values for dose profile data for the three depths are plotted in [Figure 5]. [Figure 5]a,[Figure 5]b,[Figure 5]c illustrate gamma function results for dose profiles at 5, 10, and 15 cm depths, respectively. All the gamma calculations were performed by defining 3% DD and 3 mm DTA criteria. The maximum number of points with gamma index of higher than unity was 14 points, which is related to depth of 15 cm. As it can be seen in [Figure 5], only gamma function values related to the penumbra regions, in which there exist highdose gradients, are greater than unity.  Figure 4: Dose profile data for 6MV photon beam calculated by Monte Carlo code versus measurement data (source to surface distance = 100, 10 × 10 cm^{2} field size). Dose profiles for 5, 10, and 15 cm depths are plotted in each part of (a), (b), and (c), respectively. For more clarification, the data for 5 and 10 cm depths are scaled 0.8 and 0.9, respectively
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 Figure 5: Gamma function results for dose profile data for: depth of 5 cm (a), depth of 10 cm (b), and depth of 15 cm (c) in 10 × 10 cm^{2} field size. Dose differences and distance to agreement criteria were defined as 3% and 3 mm in the gamma calculations, respectively
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Evaluation of the treatment planning system algorithms in homogeneous media
[Figure 6] displays PDD curves of ISOgray TPS's algorithms including the CCC, FFT, and superposition convolution in homogeneous water phantom (at depth 0 cm–38 cm, field size of 10 × 10 cm^{2}, and SSD = 100 cm). To evaluate the deviation of the three algorithms, the results were compared with MC simulation by gamma function and plotted in [Figure 7]a,[Figure 7]b,[Figure 7]c. All the gamma calculations were performed by defining 3% DD and 3 mm DTA. It is evident from [Figure 7] that the PDD curves of the three algorithms are in good agreement with each other. However, in comparison of the MC simulation, there is a deviation in the results of the ISOgray TPS's algorithms. In the region of buildup (at depths 0–1.6 cm), these three algorithms predict underdosage as compared with MC simulation. The maximum underdosage of the ISOgray algorithms is on the surface (19%), and it decreases for greater depths (average 7%). After buildup (depth >1.6 cm), PDD curves are shifted slightly to the right and up. The result reveals 1%–2% overdosage of the TPS algorithms in comparison by the MC. The numbers of points with gamma index of higher than unity are 21, 16, and 13 points for CCC, FFT, and superposition convolution, respectively.  Figure 6: Percentage depth dose values for 10 × 10 cm^{2} field size of 6MV photon beam calculated by collapsed cone convolution, fast Fourier transform, and superposition convolution algorithms; and the corresponding measurement data in homogeneous water phantom (source to surface distance = 100 cm)
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 Figure 7: Gamma function results for: collapsed cone convolution (a), fast Fourier transform (b), and superposition convolution algorithm (c). The results were obtained in homogenous water phantom (10 × 10 cm^{2} field size and sourcetosurface distance = 100 cm)
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Evaluation of the treatment planning system algorithms in heterogeneous media
[Figure 8]a shows the isodose curve of MC method for the anteriorposterior field (SSD = 97 cm and 18 × 9 cm^{2} field size) in the chest wall region. These results were obtained from CT2MCNP software in the presence of a Siemens Primus head for 6MV photon beam. Comparisons between TPS's algorithms and MC isodose curves are presented in [Figure 8]b,[Figure 8]c,[Figure 8]d.  Figure 8: Dose distributions obtained by different algorithms in ISOgray treatment planning system and Monte Carlo simulation. (a) Dose distribution from MCNPX code, (b) Dose distribution from collapsed cone convolution algorithm compared to MCNPX code, (c) Dose distribution from fast Fourier transform algorithm compared to MCNPX code, (d) Dose distribution from superposition convolution algorithm compared to MCNPX code
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Analysis of the isodose curves for TPS's algorithms shows that CCC and superposition convolution algorithms are closer to each other, and there are no clinically significant differences between them. On the other hand, FFT has more variation compared to the other algorithms.
The comparison between the TPS calculation and MC simulations indicates that in CCC and superposition convolution, the MC surpasses the algorithms dose for 100%, 95%, and 90% isodose curve. The FFT presents a different behavior from the others algorithms for 95% and 90% isodose curves and predicts lower dose than MC simulation, whereas in 100% isodose curve is similar to the other algorithms.
Taking the MC data as the reference doses, [Table 1] shows comparison between MC and algorithms values of the four isodose curves. These results were obtained from a comparison of isodose curves from a beam in the center of the left lung [Figure 8]. It can be seen that the FFT has differences ranging from 0.75% to 10% and 0.8% to 10.25% with CCC and superposition convolution algorithms, respectively. The results are in accordance with the results of Butts and Foster^{[5]} that compared the results of TPS algorithms and measurement in a Computerized Imaging Reference Systems phantom for a 6MV photon beam.  Table 1: A summary of the comparison between monte carlo values and treatment planning system algorithms values of the four isodose curves
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There is no clinically significant difference between the number of MUs and maximum doses calculated by the algorithms [Table 2]. Each algorithm has differences less 0.5% and 1.61% in MU and maximum doses with other algorithms, respectively. However, the maximum doses of MC in the chest wall are 5.55%–7.08% more than the algorithms.  Table 2: Monitor units and maximum dose calculated by collapsed cone convolution, fast Fourier transform, and superposition convolution algorithms and MCNPX code
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> Discussion   
It is evident from [Figure 2] and [Figure 3] that there is a good agreement between our PDD values obtained by MC simulations of the linear accelerator head and the measured values. There are only a few points in the gamma function data which have gamma values greater than unity. For dose profiles, as plotted in [Figure 5], it can be noted that there are few points with gamma indexes greater than unity. These points are those located in the penumbra region or out of the radiation field. Generally speaking, there is a good agreement between the simulations and measurements of PDDs and dose profiles. Therefore, the MC modeling of the linear accelerators head in the present study is validated.
Evaluations of the calculations in the homogeneous media [Figure 6] and [Figure 7] show a little underdosage from algorithms compared to MC in buildup region. Maximum value is observed on the surface (19%) and decreases by depth increasing (average 7%). When a photon beam passes through an absorbing medium, various physical processes are underway due to the interaction between the particles and the media. At any point of interest, the dose is contributed by primary beam particles interacting at the point, then scattering from other interacting points in the medium. However, TPS's algorithms use assumptions and approximations to predict dose distribution, and this can cause limitations in modeling the charged particle generation and photon scattering from various materials will result in significant discrepancies in their dose calculations.^{[25],[26],[27],[28]} Therefore, it can be expected that TPS calculations neglect the scattered radiation and predict low dose in comparison with MC method.
Quite generally, the differences between the three dose algorithms in inhomogeneities were studied here are small in MU (<0.5%) and maximum dose (<1.61%) [Table 2]. Small differences in isodose curves between the CCC and superposition convolution algorithms are evident; however, FFT has obvious differences as compared to the other algorithms. In this comparative study, it is observed that CCC (range 1.95% to 7.30%), FFT (range − 5.14% to 5.26%), and superposition (range 2% to 7.4%) have differences compared to MC simulations which is assumed to be the best representation of the real dose distributions under the limitations of the present study [Table 1]. However, the maximum doses of MC in the chest wall were 5.55%–7.08% more than those from the algorithms. The aforementioned differences can be attributed to the lack of precise calculation of the lateral scattered radiations by the algorithms and the difference in the accuracy of dose calculation in heterogeneous media is determined by how well the kernels of these algorithms can simulate the actual radiation scattering.^{[1],[27]}
> Conclusion   
In the present study, a 6MV photon beam of a Siemens Primus linear accelerator was simulated by MCNPX MC code, and then the accuracy of the ISOgray TPS's algorithms (CCC, FFT, and superposition convolution) were evaluated and compared to MC calculations in homogeneous (water) and heterogeneous (lung) media. In homogeneous media, all three of the TPS algorithms accurately computed the central axis entrance doses to within 2% after maximum dose depths. In the buildup region, three algorithms failed to account for the lack of scattered photons, which resulted in 7% discrepancy in the central axis (range: 2.3%–19%).
For a single beam which passes through the lung, this study shows that CCC and superposition convolution predict lower doses than MC calculations, but FFT has different flexibility for the dose calculation. For greater depths, the results reveal that the FFT (isodose curve: 90% and 95%) surpasses the MC dose and this is opposite the other algorithms. The neglected scattering of radiation and lack of electronic equilibrium in the lung can explain this difference.^{[5],[29]}
The accuracy of the three algorithms' for prediction of maximum dose is not acceptable with the MC with observed discrepancies up to 7.08%. There is no clinically significant difference between the numbers of MUs calculated by the algorithms.
The results of the present work clearly show that in actual radiotherapy practice, relying solely on ISOgray TPS's algorithms for dose calculation, particularly for lung cancer cases, may be inappropriate since the tolerance level for TPS's algorithms is commonly set at 3.5%. The dose discrepancy for heterogeneities must be considered to avoid falsepositive results. To have accurate dose calculation for lung tissue, it is recommended that MCbased TPS's be used.
Financial support and sponsorship
This work was financially supported by Malek Ashtar University of Technology.
Conflicts of interest
There are no conflicts of interest.
> References   
1.  Lu L. Dose calculation algorithms in external beam photon radiation therapy. Int J Cancer Ther Oncol 2013;1:01025. 
2.  Constine LS, Milano M, Friedman D, Morris M, Williams J, Rubin P, et al. Late effects of cancer treatment on normal tissues. In: Halperin EC, Brady LW, Perez CA, David E, Wazer DE, editors. Perez and Brady's Principles and Practice of Radiation Oncology. 5 ^{th} ed. Philadelphia, Pa: Lippincott Williams & Wilkins; 2008. p. 32055. 
3.  Bucci MK, Bevan A, Roach M 3 ^{rd}. Advances in radiation therapy: Conventional to 3D, to IMRT, to 4D, and beyond. CA Cancer J Clin 2005;55:11734. 
4.  Animesh. Advantages of multiple algorithm support in treatment planning system for external beam dose calculations. J Cancer Res Ther 2005;1:1220. 
5.  Butts JR, Foster AE. Comparison of commercially available threedimensional treatment planning algorithms for monitor unit calculations in the presence of heterogeneities. J Appl Clin Med Phys 2001;2:3241. 
6.  Lin MH, Li J, Price RA Jr., Wang L, Lee CC, Ma CM, et al. The dosimetric impact of dental implants on headandneck volumetric modulated arc therapy. Phys Med Biol 2013;58:102740. 
7.  International Commission on Radiation Units and Measurements. Report No. 24. Determination of Absorbed Dose in a Patient Irradiated by Beams of X or Gamma Rays in Radiotherapy Procedures. Bethesda, MD: International Commission on Radiation Units and Measurements; 1976. 
8.  Hasenbalg F, Neuenschwander H, Mini R, Born EJ. Collapsed cone convolution and analytical anisotropic algorithm dose calculations compared to VMC++ Monte Carlo simulations in clinical cases. Phys Med Biol 2007;52:367991. 
9.  Fraass BA, Smathers J, Deye J. Summary and recommendations of a national cancer institute workshop on issues limiting the clinical use of Monte Carlo dose calculation algorithms for megavoltage external beam radiation therapy. Med Phys 2003;30:320616. 
10.  Xing L, Hamilton RJ, Spelbring D, Pelizzari CA, Chen GT, Boyer AL, et al. Fast iterative algorithms for threedimensional inverse treatment planning. Med Phys 1998;25:18459. 
11.  Tan YI, Metwaly M, Glegg M, Baggarley S, Elliott A. Evaluation of six TPS algorithms in computing entrance and exit doses. J Appl Clin Med Phys 2014;15:22940. 
12.  Hendricks JS, McKinney GW, Fensin ML, James MR, Johns RC, Durkee JW, et al. MCNPX 2.6. 0 extensions. Los Alamos National Laboratory, LAUR082216. Los Alamos:USA;2008. 
13.  International Atomic Energy Agency. Absorbed dose Determination in External Beam Radiotherapy: An International Code of Practice for Dosimetry Based on Standards of Absorbed Dose to Water. Vienna: International Atomic Energy Agency; 1997. 
14.  Low DA, Harms WB, Mutic S, Purdy JA. A technique for the quantitative evaluation of dose distributions. Med Phys 1998;25:65661. 
15.  Van Esch A, Depuydt T, Huyskens DP. The use of an aSibased EPID for routine absolute dosimetric pretreatment verification of dynamic IMRT fields. Radiother Oncol 2004;71:22334. 
16.  Agazaryan N, Solberg TD, DeMarco JJ. Patient specific quality assurance for the delivery of intensity modulated radiotherapy. J Appl Clin Med Phys 2003;4:4050. 
17.  McDermott LN, Wendling M, van Asselen B, Stroom J, Sonke JJ, van Herk M, et al. Clinical experience with EPID dosimetry for prostate IMRT pretreatment dose verification. Med Phys 2006;33:392130. 
18.  Dobler B, Walter C, Knopf A, Fabri D, Loeschel R, Polednik M, et al. Optimization of extracranial stereotactic radiation therapy of small lung lesions using accurate dose calculation algorithms. Radiat Oncol 2006;1:45. 
19.  Nisbet A, Beange I, Vollmar HS, Irvine C, Morgan A, Thwaites DI, et al. Dosimetric verification of a commercial collapsed cone algorithm in simulated clinical situations. Radiother Oncol 2004;73:7988. 
20.  Sharpe MB, Battista JJ. Dose calculations using convolution and superposition principles: The orientation of dose spread kernels in divergent xray beams. Med Phys 1993;20:168594. 
21.  Mackie TR, elKhatib E, Battista J, Scrimger J, Van Dyk J, Cunningham JR, et al. Lung dose corrections for 6 and 15MV xrays. Med Phys 1985;12:32732. 
22.  Mackie TR, Scrimger JW, Battista JJ. A convolution method of calculating dose for 15MV xrays. Med Phys 1985;12:18896. 
23.  Irvine C, Morgan A, Crellin A, Nisbet A, Beange I. The clinical implications of the collapsed cone planning algorithm. Clin Oncol (R Coll Radiol) 2004;16:14854. 
24.  Cho W, Suh TS, Park JH, Xing L, Lee JW. Practical implementation of a collapsed cone convolution algorithm for a radiation treatment planning system. J Korean Phys Soc 2012;61:207383. 
25.  Mehranian A, Ay M, Zaidi H. CT2MCNP: An integrated package for constructing patientspecific voxelbased phantoms dedicated for MCNP (X) Monte Carlo code. IFMBE Proc 2010;29:31922. 
26.  Fogliata A, Vanetti E, Albers D, Brink C, Clivio A, Knöös T, et al. On the dosimetric behaviour of photon dose calculation algorithms in the presence of simple geometric heterogeneities: Comparison with Monte Carlo calculations. Phys Med Biol 2007;52:136385. 
27.  Fogliata A, Nicolini G, Clivio A, Vanetti E, Cozzi L. Critical appraisal of acuros XB and anisotropic analytic algorithm dose calculation in advanced nonsmallcell lung cancer treatments. Int J Radiat Oncol Biol Phys 2012;83:158795. 
28.  Bush K, Gagne IM, Zavgorodni S, Ansbacher W, Beckham W. Dosimetric validation of acuros XB with Monte Carlo methods for photon dose calculations. Med Phys 2011;38:220821. 
29.  Miften M, Wiesmeyer M, Monthofer S, Krippner K. Implementation of FFT convolution and multigrid superposition models in the FOCUS RTP system. Phys Med Biol 2000;45:81733. 
[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8]
[Table 1], [Table 2]
