

ORIGINAL ARTICLE 

Year : 2018  Volume
: 14
 Issue : 2  Page : 351356 

Underdosing of the maxillary sinus for small fields used in newer radiotherapy techniques: Comparison of thermoluminescent dosimeter and Monte Carlo data
Navin Singh^{1}, Sunil Dutt Sharma^{2}, Nirmal Kumar Painuly^{1}, Abhijit Mandal^{3}, Lalit Mohan Agarwal^{3}, Ashutosh Sinha^{4}
^{1} Department of Radiotherapy, King George's Medical University, Lucknow, India ^{2} Radiological Physics and Advisory Division, Bhabha Atomic Research Center, CTCRS, Mumbai, Maharashtra, India ^{3} Department of Radiotherapy and Radiation Medicine, Institute of Medical Sciences, Banaras Hindu University, Varanasi, India ^{4} Department of Radiotherapy, U.P. Rural Institute of Medical Sciences and Research, Etawah, Uttar Pradesh, India
Date of Web Publication  8Mar2018 
Correspondence Address: Navin Singh Department of Radiotherapy, King George's Medical University, Lucknow  226 003, Uttar Pradesh India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/09731482.183195
Aims: To evaluate the underdosing of the maxillary sinus at its distal end produced by air cavity in the path of the 6 MV photon beam. Materials and Methods: A cubic solid water slab phantom of dimensions 18 cm × 18 cm × 18 cm with 4 cm × 4 cm × 4 cm air cavity 3 cm away from its anterior surface was used in this study. The percentage depth dose (PDD) for 6 MV Xrays along the central axis of the cubical air cavity was measured using thermoluminescent dosimeter100 chips. The EGSnrc/DOSXYZnrc Monte Carlo (MC) code was used to estimate the PDD values in both homogeneous and inhomogeneous conditions. The dose data were generated for 1 cm × 1 cm, 2 cm × 2 cm, 3 cm × 3 cm, and 5 cm × 5 cm field sizes. Results: Average percentage dose reductions at 1 mm beyond the distal surface of the maxillary sinus for the field sizes 1 × 1, 2 × 2, and 3 × 3 cm^{2} are 42.4%, 39.5%, and 29.4%, respectively. However, for 5 cm × 5 cm field size, there is a dose enhancement (i.e., overdosing) at 1 mm from the distal surface of the maxillary sinus and the average percentage dose enhancement is 5.9%. Also, beyond 1 cm from the airwater interface, there is dose enhancement for all the field sizes. Conclusion: This study showed that the significant dose reduction occurs near the airwater interface for the treatment techniques using small photon fields such as intensitymodulated radiotherapy or other newer techniques. MCbased treatment planning calculation predicts realistic dose distribution while using small photon fields in the treatment of maxillary sinus.
Keywords: Dose enhancement, dose reduction, maxillary sinus, Monte Carlo, small field, thermoluminescent dosimeter
How to cite this article: Singh N, Sharma SD, Painuly NK, Mandal A, Agarwal LM, Sinha A. Underdosing of the maxillary sinus for small fields used in newer radiotherapy techniques: Comparison of thermoluminescent dosimeter and Monte Carlo data. J Can Res Ther 2018;14:3516 
How to cite this URL: Singh N, Sharma SD, Painuly NK, Mandal A, Agarwal LM, Sinha A. Underdosing of the maxillary sinus for small fields used in newer radiotherapy techniques: Comparison of thermoluminescent dosimeter and Monte Carlo data. J Can Res Ther [serial online] 2018 [cited 2020 Jun 1];14:3516. Available from: http://www.cancerjournal.net/text.asp?2018/14/2/351/183195 
> Introduction   
Small fields are commonly used for radiation therapy because of the development of intensitymodulated radiotherapy (IMRT) and stereotactic radiosurgery. Both conventional nondedicated medical linear accelerators and specialized dedicated accelerators are used in such treatments. IMRT was introduced in the 1990s and is increasingly being used in the treatment of head and neck tumors. Compared to conventional therapy, IMRT conforms to the highdose region to the shape of the target volume while minimizing the dose to the surrounding normal tissues.
The presence of air cavity in the head and neck region creates conditions of electronic disequilibrium near the airtissue interfaces.^{[1],[2],[3],[4]} Due to this phenomenon, radiation dose builddown and buildup occur near proximal and distal airtissue interfaces. Thus, an increased risk of recurrence of cancer may exist near the airtissue interfaces. Li et al.^{[1]} performed Monte Carlo (MC) simulations to investigate the effect of beam quality, field size, cavity shape and dimensions, and depth of the cavity in water and demonstrated that the dose reduction (i.e., underdosing) increases with beam energy and decreases with size of the radiation field.
For small photon fields, which suffer already from lateral electronic disequilibrium in a homogeneous water medium, the increased electron range in air will result in a dramatic reduction of the central axis dose just beyond the cavity.^{[5]} The relatively large area of electronic disequilibrium in narrow photon fields affects the dosimetry accuracy by a larger magnitude in comparison to interface dosimetry in conventional radiotherapy beams. This disequilibrium effect can be exacerbated in areas of tissue heterogeneity. Also, the dosimetry in the subcentimeter field can result in substantial uncertainties because of the presence of electron disequilibrium due to highdose gradients in the field.
In IMRT, a number of beamlets (i.e., small fields) are used to deliver significant part of the prescribed radiation dose. When calculating the dose in a lowdensity medium such as maxillary sinus using narrow beams, tissue density variations can introduce significant perturbations that are energy and density dependent and affect the accuracy of the dose calculation. This problem is more pronounced when the treatment planning system (TPS) uses simple, onedimensional density scaling.^{[6],[7],[8]} The level of accuracy improves with the use of more sophisticated treatment planning algorithms^{[9],[10],[11],[12],[13],[14],[15]} where multisource modeling is included, allowing a more accurate dose prediction for small fields and nonequilibrium conditions.^{[16],[17]}
In the studies on interface dosimetry reported so far, the investigators have measured the dose reduction near the airtissue interfaces of openended longitudinal air gaps such as the air gap created by trachea in head and neck region and by airfilled rectal balloons in prostate cases.^{[1],[2],[3],[4]} To date, there have been a few experimental measurements available on interface dosimetry near closed air cavities due to the challenges associated with dose measurements in interface region around closed air cavities.
We have carried out the dosimetric evaluations at the distal end of maxillary sinus experimentally using thermoluminescent dosimeter (TLD) and theoretically using EGSnrc MC code. The objective of this work was to evaluate the underdosing of the maxillary sinus at the distal end produced by air cavity in the path of the 6 MV photon beam. This study reports the results of TLD measurements and MC simulations and a comparison of the experimental and theoretical dose values.
> Materials and Methods   
The maxillary sinus is a pyramidal cavity, the base of which lies lateral to the nasal cavity. In adults, the dimensions of the sinus are approximately 33 mm in height, 23–25 mm in width, and 34 mm in length (anteroposterior axis). A cubic solid water slab phantom of dimensions 18 cm × 18 cm × 18 cm was used in this study. A 4 cm × 4 cm × 4 cm air cavity was created in this phantom which is 3 cm away from the anterior surface [Figure 1]. This phantom was irradiated by 6 MV photon beam (UNIQUE Performance, Varian Medical Systems, USA) with source to surface distance of 100 cm. The treatment dose of 1 Gy was prescribed at the depth of dose maximum (d_{m}= 1.5 cm) with single anterior beam (gantry angle 0°).  Figure 1: Schematic diagram of the experimental setup showing 4 cm × 4 cm × 4 cm air cavity 3 cm away from the anterior surface of the solid water cubical (18 cm × 18 cm × 18 cm) phantom
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Thermoluminescent dosimetry
Experimental measurement of the dose in water, airwater interface, and air cavity was carried out using lithium fluoride TLDs (LiF: Mg, Ti; TLD100, Victoreen, USA). The dimension of the TLD chips used in this work was 3.2 mm × 3.2 mm × 0.9 mm. The effective atomic number of this TLD material is 8.2 which is nearly tissue equivalent. During the experiment, the TLD chips were placed along the central axis of the beam at the depths of 1.5, 2, 2.5, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 cm. The field sizes of 1 cm × 1 cm, 2 cm × 2 cm, 3 cm × 3 cm, and 5 cm × 5 cm were used for irradiating the TLD chips.
TLD chips of a single batch were used in this study. Several dosimeters from the same batch were designated “control” dosimeters and were used for the calibration and the remaining as “experimental” dosimeters and were used for the measurements.
Individually identifiable TLD chips were located at 13 measurement locations in water, waterair interface, and air cavity. The TLDs for the cavity measurements were placed at fixed locations in a single strip of a plastic wrap. The plastic strip was then suspended inside the cavity using tapes at each end.
Before each irradiation, the TLDs were annealed in a laboratory oven (Thermolyne 47900, Barnsted Thermolyne, Iowa, USA) at a temperature of 400°C for 1 h, followed by 100°C for 2 h. The postirradiation annealing protocol was 100°C for 10 min. The thermoluminescent response was assessed 24 h after irradiation using a standard TLD reader (TL10091, Nucleonix, Hyderabad, India). During the readout, the TLD reader was operated at a high voltage supply of 700 Volts. The heating profile recommended for LiF: Mg, Ti (TLD100) was used. The total area of the glow curve was taken as the reading of TLD. The TLD measured dose data were normalized with respect to the dose at d_{m} for obtaining the percentage depth dose (PDD).
Monte Carlo simulation
In this study, 4 cm × 4 cm × 4 cm air cavity in 18 cm × 18 cm × 18 cm water phantom was modeled using the EGSnrc MC code.^{[18],[19]} MC dose calculations were performed using the DOSXYZnrc code which uses the cubical voxels. The dimension of the grid size used for the simulation was 2 mm. MC simulations were performed for a single field irradiations with 6 MV photon beam. Dose calculations were performed for beam sizes 1 cm × 1 cm, 2 cm × 2 cm, 3 cm × 3 cm, and 5 cm × 5 cm. The global electron cutoff energy (ECUT) and global photon cutoff energy (PCUT) of 0.521 MeV and 0.01 MeV were used in the simulations, respectively. Photon and electron interaction crosssection data (PEGS data set 521icru.pegs4dat) were used in this study.
Published spectra of 6 MV Xrays were used as input in the simulations to generate the radiation fields within the DOSXYZ code.^{[20]} About 1 × 10^{9}–2 × 10^{9} histories were traced in the MC simulations to achieve statistical errors ≤1%. MC simulations were repeated for homogeneous water phantom with identical voxel matrices to provide the reference doses for comparison. As MC calculations give dose to medium and thermoluminescent detectors give dose to water, MC results were converted into dose to water by applying the corresponding stopping power ratios of water and air.
For benchmarking of the MC calculated dose data, PDDs of 6 MV Xrays for field sizes 1 cm × 1 cm, 2 cm × 2 cm, 3 cm × 3 cm, and 5 cm × 5 cm were measured using a radiation field analyzer (ScanditronixWellhofer with Omnipro Accept 7.0, Sweden) and 0.13 cm^{3} ionization chamber (CC13, ScanditronixWellhofer, Sweden).
> Results   
PDDs of 1 cm × 1 cm, 2 cm × 2 cm, 3 cm × 3 cm, and 5 cm × 5 cm fields in a homogeneous water phantom obtained using MC simulation were compared with measured data obtained from the radiation field analyzer (RFA). The MC calculated PDDs were found to be in close agreement to the RFA measured PDDs (within ±2%) for all the field sizes.
The PDDs obtained using TLD measurements in inhomogeneous phantom and PDDs obtained using MC simulations in inhomogeneous and homogeneous conditions for field sizes 1 cm × 1 cm, 2 cm × 2 cm, 3 cm × 3 cm, and 5 cm × 5 cm are shown in [Figure 2], [Figure 3], [Figure 4], [Figure 5], respectively. It is observed from these [Figure 2], [Figure 3], [Figure 4], [Figure 5] that PDDs obtained using MC simulations are very close to the PDDs measured using TLD (within ±3%). The secondary buildup effect is observed for all the fields at airwater interface. A higher depth dose is observed beyond this interface due to reduced attenuation of the radiation beam in the air and is more pronounced for the smaller fields.  Figure 2: The percentage depth dose to water, airwater interface, and air cavity obtained using thermoluminescent dosimeter measurement and Monte Carlo simulation for 1 cm × 1 cm field size of 6 MV Xrays. The percentage depth dose obtained using Monte Carlo simulation for homogeneous water phantom is also included in this plot
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 Figure 3: The percentage depth dose to water, airwater interface, and air cavity obtained using thermoluminescent dosimeter measurement and Monte Carlo simulation for 2 cm × 2 cm field size of 6 MV Xrays. The percentage depth dose obtained using Monte Carlo simulation for homogeneous water phantom is also included in this plot
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 Figure 4: The percentage depth dose to water, airwater interface, and air cavity obtained using thermoluminescent dosimeter measurement and Monte Carlo simulation for 3 cm × 3 cm field size of 6 MV Xrays. The percentage depth dose obtained using Monte Carlo simulation for homogeneous water phantom is also included in this plot
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 Figure 5: The percentage depth dose to water, airwater interface, and air cavity obtained using thermoluminescent dosimeter measurement and Monte Carlo simulation for 5 cm × 5 cm field size of 6 MV Xrays. The percentage depth dose obtained using Monte Carlo simulation for homogeneous water phantom is also included in this plot
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Percentage dose reduction (PDR) or percentage dose enhancement (PDE) at a point beyond the distal surface of the maxillary sinus was calculated by subtracting the dose to the point in inhomogeneous condition from the dose to the point in homogeneous condition (PDR (or PDE) = PDD_{homo}− PDD_{inhomo}). The positive sign of the numerical value of this difference indicates the dose reduction (i.e., PDR) while negative sign indicates the dose enhancement (i.e., PDE). The PDRs/PDEs at 1 mm from the airwater interface (i.e., 1 mm from the distal surface of the maxillary sinus) are shown in [Table 1]. It is observed from [Table 1] that there is a dose reduction (i.e., under dosing) at 1 mm from the distal surface of the maxillary sinus in case of irradiation by small fields (1 cm × 1 cm, 2 cm × 2 cm, and 3 cm × 3 cm). The average PDR data (arithmetic mean of MC and TLD data) at 1 mm beyond the distal surface of the maxillary sinus for the field size 1 cm × 1 cm, 2 cm × 2 cm, and 3 cm × 3 cm are 42.4%, 39.5%, and 29.4%, respectively. However, in case of 5 cm × 5 cm field (conventional field), there is a dose enhancement (i.e., overdosing) at 1 mm from the distal surface of the maxillary sinus and the average PDE is 5.9%.  Table 1: Percentage dose reduction/percentage dose enhancement at 1 mm from the airwater interface of different field sizes with respect to the Monte Carlo calculated dose in homogeneous medium (i.e., without air cavity)
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[Table 2] presents the PDEs at 1 cm from the airwater interface (i.e., 1 cm from the distal surface of the maxillary sinus). It is also observed here that there is a dose enhancement for all the field sizes (whether small or conventional fields).  Table 2: Percentage dose enhancement at 1 cm from the airwater interface of different field sizes with respect to the Monte Carlo calculated dose in homogeneous medium (i.e., without air cavity)
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The relation between the data obtained by the MC simulation with and without air cavity and TLD measured data was analyzed by means of post hoc test (multiple comparison). When we compare MC simulated data for inhomogeneous condition (i.e., the case of phantom with air cavity) with TLD measured data for 1 cm × 1 cm field size, P = 0.996 (P > 0.05) shows that there is no significant difference between MC simulated and TLD measured data. However, when we compare MC simulated data of inhomogeneous condition (i.e., the case of phantom with air cavity) with MC simulated data of homogeneous condition (i.e., the case of phantom without air cavity) for 1 cm × 1 cm field size, P = 0.034 (P< 0.05) shows that there is a significant difference between two values. Similar trends were found on comparison of the dose data of other field sizes.
> Discussion   
The experimental and MC results of the current study indicate the significant underdosing of the maxillary sinus when treated with small photon fields which are commonly used in newer radiotherapy techniques. The results of our study are also in good agreement with the results of similar studies conducted on the subject of small fields in radiation therapy of head and neck cancers. The outcome of our work clearly indicates that while planning a treatment by newer radiotherapy techniques (e.g., IMRT and tomotherapy), the effect of dose reductions in the interface regions around air cavities should be given serious considerations and need to be compensated during the optimization. However, dose calculation algorithms of many commercial TPSs encounter severe limitations in the conditions of electronic disequilibrium,^{[21],[22],[23]} particularly in IMRT techniques.^{[24],[25]} The issues related to the accuracy of dose calculations near the air cavities in head and neck region have been discussed in many recent studies.^{[8],[23],[24],[25]}
[Figure 6] shows the variation in PDD of 6 MV Xrays with depth for 1 cm × 1 cm, 2 cm × 2 cm, 3 cm × 3 cm, and 5 cm × 5 cm fields across the cubical air cavity of size 4 cm × 4 cm × 4 cm. At the interface of waterair/airwater, the absorbed dose fluctuates because of the density variations and difference in secondary electron generation rate in different media. This phenomenon is exacerbated in conditions of small fields and high energy photon beams currently being used in radiation therapy. In lowdensity material such as air, the absorbed dose reduces abruptly due to the reduction in the number of secondary electrons coming from upstream in the air and the dose builddown region is created after waterair interface. On the other hand, at airwater interface, the dose buildup region is created due to the increased production of secondary electrons in the unit density medium and electronic equilibrium exists at a short distance. Overall, the interface effect is pronounced for the highenergy photon beam because of the longer range of secondary electrons.  Figure 6: Variation in percentage depth dose of 6 MV Xrays with depth across the cubical air cavity of size 4 cm × 4 cm × 4 cm
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Our results show that the magnitude of dose reduction near the airwater interface decreases with increase in the size of radiation beams. For the field size of 1 cm × 1 cm, the average PDR at 1 mm beyond the airwater interface is 42.4% whereas for the field size of 2 cm × 2 cm, this value is 39.5%. However, 1 cm beyond the airwater interface, there is dose enhancement for all field sizes considered in this study because of the increased production of secondary electrons in unit density medium.
Although the shape of the maxillary sinus is irregular, we have represented this irregular geometry of the maxillary sinus by the simple cubic geometry to understand the complexity of dose distribution in this situation. The excellent agreement of TLD measurements with MC results indicates that subcentimeter dosimetry by experimental method would be a good choice for testing the accuracy of dose calculation algorithms of commercial TPS in such situations. The testing of dose calculation algorithms in such situations is highly required, especially for the small photon fields, because dose calculation algorithms of many commercial TPS are unable to predict the dose accurately near the airtissue interface.
Further, we have generated dosimetry data for single beam irradiation in this study. However, in a realistic IMRT treatment, a combination of multiple of subfields within fields from many beam directions is employed. Thus, the magnitude of dose reduction at interface will be smaller than that recorded during single small field irradiation. However, with the increasing use of techniques employing small field irradiations (IMRT and tomotherapy), the interface dose reduction may remain relevant in the context of local control of lesions situated in the close vicinity of air cavities.
The measurements in the solid water phantom were made with TLD100 chips of thickness 0.9 mm, thus the TLD results were average values over the first 1 mm depth near the airwater interface. The TLD results are not exactly the doses at the interface.
Stathakis et al. measured the dose reduction near the airtissue interface with air thickness of 5 cm for 6 MV photon beams.^{[26]} They used the BEAMnrc/DOSXYZnrc code for calculating the dose in their study and two other anisotropic analytical algorithms (AAAs) were assessed against the MC results. The difference in dose reduction for the case of air inhomogeneity between AAA and MC was about 50% for 1 cm × 1 cm field. For the same geometry, Acuros XB and Collapsed cone convolution superposition algorithm (CCCS) showed differences that ranged from 3% to 15%.
Joshi et al. studied the dosimetry of interface region near closed air cavities for Co60, 6 MV, and 15 MV photon beams using MC simulations.^{[27]} They investigated the dose reductions near the airwater interfaces of closed cubic air cavities of size 3 cm × 3 cm typically encountered in the treatment of head and neck cancers. They observed that the dose reduction on the distal surface was 38.7% and 18.2% for field size 2 cm × 2 cm and 10 cm × 2 cm, respectively.
Martens et al. assessed dose rebuildup behind air cavity for small fields in case of head and neck tumors.^{[28]} They simulated the trachea by a 2 cm diameter cylindrical air cavity inside a tissueequivalent solid phantom and 6 MV photon beams of size 10 cm × 2 cm and 10 cm × 1 cm were used for irradiation. They observed that collapsed cone convolution (CCC) algorithm of HelaxTMS TPS overestimated the interface dose by 13% and 31% for field sizes 10 cm × 2 cm and 10 cm × 1 cm, respectively. The overestimation of the interface dose was 9% and 54% for field size 10 cm × 2 cm and 10 cm × 1 cm by the Pinnacle CCC calculations, respectively.
Kan et al. measured and calculated depth dose data for 5 cm × 5 cm × 30 cm and 3 cm × 3 cm × 30 cm air cavity phantoms irradiated by 6 MV photon beams of size 2 cm × 2 cm, 3 cm × 3 cm, and 5 cm × 5 cm.^{[29]} The dose at the distal surface of the cavity was measured using TLD and calculated using pencil beam (PB) and AAAs. Although the AAA produced considerably accurate results than the PB algorithm, it still overestimated the distal interface dose significantly for small fields (2 cm × 2 cm and 3 cm × 3 cm fields). For 2 cm × 2 cm, the overestimation at the distal interface was 265% and 179% for the larger cavity phantom and smaller cavity phantom, respectively. For 3 cm × 3 cm, it was 163% and 94% for the larger cavity phantom and smaller cavity phantom, respectively. It shows that AAA did not model the effect of lateral electronic disequilibrium properly in extreme cases.
> Conclusion   
Significant dose reduction occurs near the airwater interface for the treatment techniques using small fields such as IMRT or other newer techniques. TLD placed along the central axis is found to be useful for measuring the dose inside the cavity and near the interfaces. MC simulation results correspond very well to the measurements. From this study, we can conclude that MCbased TPS will be able to predict the accurate dose values with small fields near the airwater (or lowdensity) interface or even in case of extreme cases.
Acknowledgment
The authors would like to thank Mr. Arun Chairmadurai, Department of Radiotherapy, Jaypee Hospital, Noida, Uttar Pradesh, for his guidance.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
> References   
1.  Li XA, Yu C, Holmes T. A systematic evaluation of air cavity dose perturbation in megavoltage Xray beams. Med Phys 2000;27:10117. 
2.  WadiRamahi SJ, Bernard D, Chu JC. Effect of ethmoid sinus cavity on dose distribution at interface and how to correct for it: Magnetic field with photon beams. Med Phys 2003;30:155665. 
3.  Behrens CF. Dose buildup behind air cavities for Co60, 4, 6 and 8 MV. Measurements and Monte Carlo simulations. Phys Med Biol 2006;51:593750. 
4.  Klein EE, Chin LM, Rice RK, Mijnheer BJ. The influence of air cavities on interface doses for photon beams. Int J Radiat Oncol Biol Phys 1993;27:41927. 
5.  De Vlamynck K, De Wagter C, De Neve W. Diamond detector measurements near simulated air channels for narrow photon beams. Radiother Oncol 1999;53:1559. 
6.  Saitoh H, Fujisaki T, Sakai R, Kunieda E. Dose distribution of narrow beam irradiation for small lung tumor. Int J Radiat Oncol Biol Phys 2002;53:13807. 
7.  Chetty IJ, Charland PM, Tyagi N, McShan DL, Fraass BA, Bielajew AF. Photon beam relative dose validation of the DPM Monte Carlo code in lungequivalent media. Med Phys 2003;30:56373. 
8.  AlHallaq HA, Reft CS, Roeske JC. The dosimetric effects of tissue heterogeneities in intensitymodulated radiation therapy (IMRT) of the head and neck. Phys Med Biol 2006;51:114556. 
9.  GarcíaVicente F, Miñambres A, Jerez I, Modolell I, Pérez L, Torres JJ. Experimental validation tests of fast Fourier transform convolution and multigrid superposition algorithms for dose calculation in lowdensity media. Radiother Oncol 2003;67:23949. 
10.  Scholz C, Schulze C, Oelfke U, Bortfeld T. Development and clinical application of a fast superposition algorithm in radiation therapy. Radiother Oncol 2003;69:7990. 
11.  Bragg CM, Conway J. Dosimetric verification of the anisotropic analytical algorithm for radiotherapy treatment planning. Radiother Oncol 2006;81:31523. 
12.  Gagné IM, Zavgorodni S. Evaluation of the analytical anisotropic algorithm in an extreme waterlung interface phantom using Monte Carlo dose calculations. J Appl Clin Med Phys 2006;8:3346. 
13.  Craig J, Oliver M, Gladwish A, Mulligan M, Chen J, Wong E. Commissioning a fast Monte Carlo dose calculation algorithm for lung cancer treatment planning. J Appl Clin Med Phys 2008;9:2702. 
14.  Kunieda E, Deloar HM, Kishitani N, Fujisaki T, Kawase T, Seki S, et al. Variation of dose distribution of stereotactic radiotherapy for smallvolume lung tumors under different respiratory conditions. Phys Med 2008;24:20411. 
15.  Tillikainen L, Helminen H, Torsti T, Siljamäki S, Alakuijala J, Pyyry J, et al. A3D pencilbeambased superposition algorithm for photon dose calculation in heterogeneous media. Phys Med Biol 2008;53:382139. 
16.  Zhu TC, Bjärngard BE. The headscatter factor for small field sizes. Med Phys 1994;21:658. 
17.  Zhu TC, Bjärngard BE. The fraction of photons undergoing head scatter in xray beams. Phys Med Biol 1995;40:112734. 
18.  Kawrakow I, Rogers DW. The EGSnrc Code System: Monte Carlo Simulations of Electron and Photon Transport, Technical Report PIRS701. Ottawa, Ontario: National Research Council of Canada; 2003. 
19.  Walters B, Kawrakow I, Rogers DW. DOSXYZnrc Users Manual. Ionizing Radiation Standards, National Research Council of Canada, NRCC Report PIRS794revB; 2005. 
20.  Mohan R, Chui CS. Validity of the concept of separating primary and scatter dose. Med Phys 1985;12:72630. 
21.  Heath E, Seuntjens J, SheikhBagheri D. Dosimetric evaluation of the clinical implementation of the first commercial IMRT Monte Carlo treatment planning system at 6 MV. Med Phys 2004;31:27719. 
22.  Haraldsson P, Knöös T, Nyström H, Engström P. Monte Carlo study of TLD measurements in air cavities. Phys Med Biol 2003;48:N2539. 
23.  Linthout N, Verellen D, Van Acker S, Voordeckers M, Bretz A, Storme G. Evaluation of dose calculation algorithms for dynamic arc treatments of head and neck tumors. Radiother Oncol 2002;64:8595. 
24.  Yoon M, Lee DH, Shin D, Lee SB, Park SY, Cho KH. Accuracy of inhomogeneity correction algorithm in intensitymodulated radiotherapy of headandneck tumors. Med Dosim 2007;32:4451. 
25.  Sohn JW, Dempsey JF, Suh TS, Low DA. Analysis of various beamlet sizes for IMRT with 6 MV photons. Med Phys 2003;30:24329. 
26.  Stathakis S, Esquivel C, Quino LS, Myers P, Calvo O, Mavroidis P, et al. Accuracy of the small field dosimetry using the acuros XB dose calculation algorithm within and beyond heterogeneous media for 6 MV photon beams. Int J Med Phys Clin Radiat Oncol 2012;1:7887. 
27.  Joshi CP, Darko J, Vidyasagar PB, Schreiner LJ. Dosimetry of interface region near closed air cavities for Co60, 6 MV and 15 MV photon beams using Monte Carlo simulations. J Med Phys 2010;35:7380. [ PUBMED] [Full text] 
28.  Martens C, Reynaert N, De Wagter C, Nilsson P, Coghe M, Palmans H, et al. Underdosage of the upperairway mucosa for small fields as used in intensitymodulated radiation therapy: A comparison between radiochromic film measurements, Monte Carlo simulations, and collapsed cone convolution calculations. Med Phys 2002;29:152835. 
29.  Kan MW, Cheung JY, Leung LH, Lau BM, Yu PK. The accuracy of dose calculations by anisotropic analytical algorithms for stereotactic radiotherapy in nasopharyngeal carcinoma. Phys Med Biol 2011;56:397413. 
[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6]
[Table 1], [Table 2]
