

ORIGINAL ARTICLE 

Year : 2014  Volume
: 10
 Issue : 4  Page : 896902 

A Monte Carlo approach to lung dose calculation in small fields used in intensity modulated radiation therapy and stereotactic body radiation therapy
Asghar Mesbahi^{1}, Habib Dadgar^{2}, Nahideh GharehAghaji^{3}, Mohammad Mohammadzadeh^{4}
^{1} Department of Medical Physics, Medical School, Tabriz University of Medical Sciences; Department of Radiation Oncology, Imam Hospital, Tabriz, Iran ^{2} Department of Medical Physics, Medical School, Tabriz University of Medical Sciences, Tabriz, Iran ^{3} Department of Radiology, Paramedical School, Tabriz University of Medical Sciences, Tabriz, Iran ^{4} Department of Radiation Oncology, Imam Hospital, Tabriz, Iran
Date of Web Publication  9Jan2015 
Correspondence Address: Asghar Mesbahi Department of Medical Physics, Medical School, Tabriz University of Medical Sciences, Attare Neishabouri Street, Tabriz Iran
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/09731482.137989
Aims: In the current study, the effect of electronic disequilibrium on lung dose with small photon beams was verified. Materials and Methods: The central axis absorbed dose in lung phantom was calculated by Monte Carlo (MC) method. The 6 and 18 MV photon beams of Varian Clinac 2100EX were simulated using MCNPX MC Code (Los Alamos national lab, USA). The MC model was used to calculate the depth doses water and low density water resembling the softtissue and lung, respectively. Four small field sizes including 0.5 cm ^{2} × 0.5 cm ^{2} , 1 cm ^{2} × 1 cm ^{2} , 2 cm ^{2} × 2 cm ^{2} , and 3 cm ^{2} × 3 cm ^{2} were used in this study. Results: Percentage of dose reduction in lung region relative to homogenous phantom for 6 MV photon beam were 44.6%, 39%, 13%, and 7% for 0.5 cm ^{2} × 0.5 cm ^{2} , 1 cm ^{2} × 1 cm ^{2} , 2 cm ^{2} × 2 cm ^{2} , and 3 cm ^{2} × 3 cm ^{2} fields, respectively. For 18 MV photon beam, the results were found to be 82%, 69%, 46%, and 25.8% for the same field sizes, respectively. The solid tumor dose inside lung was reduced considerably between 17% and 35% for 18 MV beam, while there was only 9% dose reduction for tumor dose for 0.5 and 1 cm field sizes. Conclusion: Our study showed that the dose reduction with small fields in the lung was very enormous. Thus, inaccurate prediction of absorbed dose inside lung and also lung softtissue interfaces with small photon beams may lead to critical consequences for treatment outcome. 蒙特卡罗法计算小野调强放疗和立体定向放疗的肺剂量 摘要 目的：验证小光子束电子不平衡对肺剂量的影响。
材料与方法：中心轴在肺部吸收剂量是通过Monte Carlo计算模型（MC）方法算出的。瓦里安医用直线加速器2100EX使用MCNPX MC代码模拟产生了6MV和18 MV光子束（洛斯阿拉莫斯国家实验室，美国）。MC模型被用来分别计算水、低密度似水软组织和肺的深度剂量。研究中使用四小野，尺寸包括0.5 cm^{2} × 0.5 cm^{2}, 1 cm^{2} × 1 cm^{2}, 2 cm^{2} × 2 cm^{2}, 3 cm^{2} × 3 cm^{2}。
结果：肺区域相对于同质的虚构区域，剂量降低百分比分别为：6 MV光子束为44.6%、39%、13%和7%，对应野大小分别为0.5 cm^{2} × 0.5 cm^{2}, 1 cm^{2} × 1 cm^{2}, 2 cm^{2} × 2 cm^{2} 和3 cm^{2} × 3 cm^{2}。18 MV光子束，结果是82%、69%、46%和25.8%，对应相同野。肺内实体瘤剂量大大减少，18 MV光束为17%35%之间，而0.5和1cm野的剂量减少仅为9%。
结论：在肺内小野照射的剂量减少是非常多的。因此，对于小光子束在肺内和肺软组织间吸收剂量的不准确预测，可能导致危险的治疗结果。
关键词：电子不平衡，蒙特卡罗计算，放射治疗肺癌，小场剂量学
Keywords: Electronic disequilibrium, monte carlo calculations, radiotherapy of lung, small field dosimetry
How to cite this article: Mesbahi A, Dadgar H, GharehAghaji N, Mohammadzadeh M.
A Monte Carlo approach to lung dose calculation in small fields used in intensity modulated radiation therapy and stereotactic body radiation therapy. J Can Res Ther 2014;10:896902 
How to cite this URL: Mesbahi A, Dadgar H, GharehAghaji N, Mohammadzadeh M.
A Monte Carlo approach to lung dose calculation in small fields used in intensity modulated radiation therapy and stereotactic body radiation therapy. J Can Res Ther [serial online] 2014 [cited 2020 Jul 10];10:896902. Available from: http://www.cancerjournal.net/text.asp?2014/10/4/896/137989 
> Introduction   
Application of small fields in intensity modulated radiation therapy (IMRT) and stereotactic body radiation therapy (SBRT) of lung cancers has been received more attention by researchers. ^{[1],[2],[3],[4],[5],[6]} However, the application of these new modalities with small beams for lung cancers has made the dose calculations more intricate and sophisticated. In general, the main goal of small field irradiation is to provide a desired dose distribution to a fine described small target with the slightest dose to the neighboring normal tissue of the lung. ^{[1],[7]} However, in these techniques such as IMRT and SBRT of lung cancers, small fields are used routinely as a part of the series of small beamlets to provide a nonhomogenous dose distribution inside planning target volume. The use of small photon fields, normally in the presence of low density heterogeneous substances, may become a complicated scenario to be studied by the treatment planning system (TPS) in order to resolve dose portions. Because, as it is known that a photon beam with field size larger than 4 cm ^{2} × 4 cm ^{2} may produce lateral electronic equilibrium in tissueequivalent media, but fails while entering the low density inhomogeneity such as air and lung. ^{[8]}
Application of small fields in waterequivalent causes underdosage of target volume due to lateral electronic disequilibrium (LED). On the other hand, the problem of LED becomes more pronounced in low density media, due to the existence of fewer atoms along the pathway of photons, and it causes the lack of secondary electrons accordingly. ^{[9],[10],[11]}
It has been reported that the precision of small field dosimetry is greatly improved when Monte Carlo (MC) calculations are used, particularly for a beam with apertures less than 3 cm ^{2} × 3 cm ^{2} in homogeneous media. Jones and Das studied the effect of lung heterogeneity on small beamlets for 6, 15 and 24 MV photon beams by the EGSnrc MC (NRC, Canada) code. Their data suggested that current TPS may dramatically over or underestimate the dose in inhomogeneous media for small field sizes that are used for IMRT. ^{[9]} In a study, on lung in the small field sizes, a large dose reduction was seen for points inside lung and MC results agreed with measurements within the measurement and computational uncertainties. ^{[10]}
Arnfield et al. examined the results of lung heterogeneities on depth dose and lateral beam profiles for 6 and 18 MV photon beams for field sizes 4 cm ^{2} × 4 cm ^{2} and 10 cm ^{2} × 10 cm ^{2} . ^{[12]} Dose calculations were done with a generalized Batho model, the Pinnacle collapsed cone convolution model (CCC), and the Peregrine MC dose calculation algorithm. Absolute central axis and off axis dose data at various depths relative to interfaces of inhomogeneities were compared. Their results confirmed that for a Batho correction, dose errors in the calculated depth dose arise from the neglect of electron transport. This effect increases as the field size decreases, as the density of the heterogeneous decreases, and with the energy of incident photons. The CCC calculations were closer to measurements than the Batho model, but important differences remain. MC results agreed with measurements within the measurement and computational uncertainties.
In all previous studies, it was concluded that MC method is capable to predict the dose variation with depth inside inhomogeneous media like lung as well as lung softtissue interfaces. While, the other algorithms were not capable to predict the lung dose accurately in the conditions of electronic disequilibrium with high energy photons. ^{[3],[13],[14]} Otherwise, the presence of small sold lung tumor would make more difficult situation for TPSs to predict the dose inside the tumor. To address these issues we planned a MC study for depth dose variations in the lung with and without a small tumor resembling the situations occur in IMRT of lung tumors. The results also can be used for other techniques utilizing very small fields for radiation therapy of lung tumors. In the current research, the extent of dose reduction inside the lung with and without solid tumor was studied and the purpose was to show the dose reduction factor for a solid tumor inside lung which can be treated with IMRT or other types of radiotherapy techniques like Cyberknife with small fields as small as 0.5 cm ^{2} × 0.5 cm ^{2} .
> MaterialS and Methods   
The MCNP × 2.4.0 MC (Los Alamos national lab, USA) code was applied for dose calculations. We used a validated MC model of Varian 2100EX model for our dose calculations in lung and water phantoms. ^{[10],[15],[16]} The components of a linear accelerator for 6 and 18 MV photon beams are shown in [Figure 1]. The multileaf collimator (MLC) with 80 leafs was molded with thickness of 6.1 cm. The projected width of every leaf was 1 cm in the isocentric plane. A phasespace (PS) file was generated above the secondary collimator with running 10 ^{8} primary particles for each energy and then this PS was used for dose calculations with different field sizes for 6 and 18 MV photon beams. The MLC with 80 leafs was molded to create small fields used as beamlets in IMRT. The round front end of leafs was modeled as an inclined plane surfaces according to beam divergence.
In running PS file the secondary collimator, MLC and phantom were simulated and the absorbed dose was scored inside scoring cells filled with water. A water phantom with dimension of 30 cm ^{3} × 30 cm ^{3} × 30 cm ^{3} was simulated under treatment head with sourcesurface distance of 100 cm. The lattice feature of MCNPX code was utilized in our simulation and the scoring cells with the dimension of 2 mm ^{2} × 2 mm ^{2} × 2 mm ^{2} .  Figure 1: Schematic representation of simulated linac head and phantom used for dose scoring
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The percentage depth dose (PDD) for 0.5 cm ^{2} × 0.5 cm ^{2} , 1 cm ^{2} × 1 cm ^{2} , 2 cm ^{2} × 2 cm ^{2} and 3 cm ^{2} × 3 cm ^{2} field sizes were calculated using MC method for homogenous water and inhomogeneous phantom containing lung. The photon and electron lowenergy cutoff was 10 and 500 keV respectively. The water used with 1g/cm ^{3} density as material resembling the softtissue. For lung material, we used water with 0.25 g/cm ^{3} density.
The *F8 tally was used for dose calculations in water and lung phantom. The PDD curves for both energies are shown in [Figure 2],[Figure 3],[Figure 4],[Figure 5] and [Figure 6]. Depth dose curves were normalized to d_{max} and were scaled for inclusion on the same graph.  Figure 2: Comparison of depth dose calculations for homogeneous water phantom and lung phantom. The MC calculations were performed for field sizes of (a) 0.5 cm2× 0.5 cm2, (b) 1 cm2 × 1 cm2, (c) 2 cm2 × 2 cm2, and (d) 3 cm2 × 3 cm2 for 6 MV photon beam
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 Figure 3: Comparison of depth dose calculations for homogeneous water phantom and lung phantom. The MC calculations were performed for field sizes of (a) 0.5 cm2 × 0.5 cm^{2}, (b) 1 cm^{2} × 1 cm^{2}, (c) 2 cm^{2} × 2 cm^{2}, and (d) 3 cm^{2} × 3 cm^{2} for 18 MV photon beam
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 Figure 4: Comparison of depth dose calculations for homogeneous water phantom and lung phantom containing a solid cubic tumor with dimension of 1 cm3 × 1 cm3 × 1 cm3. The MC calculations were performed for field sizes of (a) 0.5 cm2 × 0.5 cm2, (b) 1 cm2 × 1 cm2, (c) 2 cm2 × 2 cm2, and (d) 3 cm2 × 3 cm2 for 6 MV photon beam
Click here to view 
 Figure 5: Comparison of depth dose calculations for homogeneous water phantom and lung phantom containing a solid cubic tumor with dimension of 1 cm3 × 1 cm3 × 1 cm3. The MC calculations were performed for field sizes of (a) 0.5 cm2 × 0.5 cm2, (b) 1 cm2 × 1 cm2, (c) 2 cm2 × 2 cm2, and (d) 3 cm2 × 3 cm2 for 18 MV photon beam
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 Figure 6: Comparison percentage depth dose for 0.5 cm2 × 0.5 cm2 to 3 cm2 × 3 cm2 field sizes at 6 and 18 MV photon beam: (a and b) 6, 18 MV without tumor and (c and d) 6, 18 MV with tumor, respectively
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The dose reduction percentage was calculated using the following formula (1) at a given depth for all cases:
> Results   
In this study, we applied MC simulation for obtaining PDD in lung phantom with and without tumor. PDD curves for both energies 6 and 18 MV and field sizes 0.5 cm ^{2} × 1 cm ^{2} × 1 cm ^{2} , 2 cm ^{2} × 2 cm ^{2} , and 3 cm ^{2} × 3 cm ^{2} were calculated.
In all [Figure 2],[Figure 3],[Figure 4] and [Figure 5] the effect of waterlung interface is apparent, while its dosimetric magnitude and spatial spread differ considerably for different photon energies and field sizes. In other words, the dose begins to dropoff at the waterlung interface and decreases steadily with depth inside lung, then at the second lungwater interface, the dose builds up and reaches to its second maximum in water. However, this pattern of dose variation with depth becomes very pronounced with decreasing the field size. Otherwise, the dose beyond the lung increases significantly compared with homogenous water phantom.
[Figure 2] illustrates the depth dose variation with depth for homogeneous water and inhomogeneous lung phantom for 6 MV photon beam. For this geometry, the maximum dose reduction percentage was calculated at the depth of 7 cm, just after the build down region. The dose reduction in lung compared with water was obtained 44%, 39%, 13%, and 7% for 0.5 cm ^{2} × 0.5 cm ^{2} , 1 cm ^{2} × 1 cm ^{2} , 2 cm ^{2} × 2 cm ^{2} , and 3 cm ^{2} × 3 cm ^{2} field sizes, respectively. Meanwhile, it can be noticed that the dose inside lung is getting similar to water dose in field size of 3 cm ^{2} × 3 cm ^{2} .
[Figure 3] illustrates the comparison of depth dose calculations for homogeneous water and lung phantoms for 18 MV beam. In all field sizes, there is a sharp decline in the depth dose which starts from waterlung interface and reaches to a relatively steady state inside lung similar to 6 MV beam. The dose reduction percentage was calculated at 10 cm depth for 18 MV beam and there were higher dose reductions in lung relative to water with 82%, 70%, 46%, and 26% for 0.5 cm ^{2} × 0.5 cm ^{2} , 1 cm ^{2} × 1 cm ^{2} , 2 cm ^{2} × 2 cm ^{2} , and 3 cm ^{2} × 3 cm ^{2} field sizes, respectively.
For the 18 MV beam, due to the higher range of secondary electrons, the forward electronic disequilibrium becomes more pronounced relative to 6 MV beam and consequently the depth dose reduces considerably for smaller fields sizes.
In [Figure 4] and [Figure 5], the results for another case were illustrated. The geometry is similar to the previous case, but there was a small lung tumor with the size of 2 cm ^{3} × 2 cm ^{3} × 2 cm ^{3} in the middle of the lung. The density of the lung tumor was considered to be 1 g/cm ^{3} like water. The aim was to evaluate the effect of electronic disequilibrium on the tumor received a dose as treated by the smallest fields provided by Cyberknife or micro MLCs including of 0.5 cm ^{2} × 0.5 cm ^{2} and 1 cm ^{2} × 1 cm ^{2} . The dose reduction was calculated for both energies at the center of solid tumor. The results for 6 MV beam is seen in [Figure 3] for studied fields sizes. Despite the considerable absorbed dose dropoff inside the lung for 0.5 cm ^{2} × 0.5 cm ^{2} and 1 cm ^{2} × 1 cm ^{2} field sizes, the tumor absorbed dose was very comparable to water phantom dose at the same depth of 10 cm and only a difference of 9% was observed for 1 × 1 field size [Figure 3]b. On the other hand, there was a considerable tumor underdosage at the tumorlung interface because of electronic disequilibrium again for these field sizes. While this was not the case for 2 × 2 and 3 × 3 field sizes.
In [Figure 5], the results have been shown for 18 MV beam. As it can be seen all beams were capable to cover the tumor except 0.5 cm ^{2} × 0.5 cm ^{2} . However, it was found that the tumor underdosage was higher for larger field sizes and the maximum value of 35% was seen for 2 cm ^{2} × 2 cm ^{2} and the minimum value of 17% underdosage was seen for 0.5 cm ^{2} × 0.5 cm ^{2} field size. The dose reduction percentages for 1 cm ^{2} × 1 cm ^{2} and 3 cm ^{2} × 3 cm ^{2} were 32% and 20%, respectively.
In [Figure 6], the comparison of depth dose variations with field size and energy have been shown with emphasis on field size effect in each case. It is apparent that field size affects the lung dose very prominently in 18 MV photon beam compared to 6 MV. For the solid tumor case, the electronic equilibrium does not establish in the center of tumor due the high range of secondary electrons for all field sizes, but for 0.5 cm ^{2} × 0.5 cm ^{2} field where the tumor size is larger than field size, the depth dose in the center of tumor increases and have a small difference with homogenous water dose at the same location.
> Discussion   
The results of the current study was compatible with results of previous investigation on the subject of small fields in radiation therapy of lung cancers both experimental and MC studies. Nonetheless, there were small discrepancies concerning the amount of dose reduction percentages in the lung as well as the solid tumor inside lung. We think these slight differences can be attributed to the differences in MC code used comparing the MCNP with BEAM and EGSnrc. Furthermore, there were small differences in the geometry simulated in the current study with others. There was another different case in our study resembling the Cyberknife or SBRT treatments with small fields, in which the field size can be as small as 0.5 cm ^{2} × 0.5 cm ^{2} and also can used to treat the larger tumor (1 cm ^{3} × 1 cm ^{3} × 1 cm ^{3} ). For this case, results showed that the dose at the center tumor becomes comparable to homogenous case. The reason for that dose build up inside the tumor in that in this case the electrons generated at the edge of beam coming from unit density material not from lung. Hence, their number could be enough to produce higher dose build up inside the tumor.
In waterlung interface the absorbed dose fluctuates because of the density variations and 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 low density material such as lung, the absorbed dose reduces abruptly due the reduction of secondary electrons coming from upstream in the lung and the dose build down region is created after waterlung interface. On the other hand, in lungwater interface the dose build up region is generated due to more secondary electrons production in unit density medium; and, at a short distance, the electronic equilibrium was created. Overall, the interface effect was very pronounced for the 18 MV photon beam, since the range of secondary electrons was longer.
Jones and Das studied the effect of lung heterogeneity on small beamlets for 6, 15 and 24 MV photon beams by the EGSnrc MC code. ^{[9]} Their simulations showed a dose decrease for small fields in the presence of low density media due to the lack of lateral electronic equilibrium. As the density and field size increased, the dose reduction was less pronounced and for the 10 cm field there was an increased dose as expected due to lack of attenuation. Their data suggested that current TPS may dramatically over or underestimate the dose in inhomogeneous media for small field sizes that are used for IMRT.
In a study on lung in the small field sizes, a large dose reduction was reported in the lung for field size of 2 cm ^{2} × 2 cm ^{2} due to the LED and it reached up to 16.2% and 33.3% for 6 and 18 MV beams, respectively. ^{[11]}
Carrasco et al. assessed the absorbed dose by measurements, MC simulations, and TPS calculations for 10 cm ^{2} × 10 cm ^{2} , 5 cm ^{2} × 5 cm ^{2} , 2 cm ^{2} × 2 cm ^{2} , and 1 cm ^{2} × 1 cm ^{2} field sizes and Xray spectrum of 6 and 10 MV. Where, the collapsed cone overestimated the dose inside the lung heterogeneity about 35%. ^{[17]}
In a similar study by da Rosa et al., they compared the accuracy of different inhomogeneity correction methods in a lung phantom. ^{[13]} Analyzing their pertinent data on the MC and the curves without correction revealed that the dose reduction inside the lung at the depth 10 cm (the comparable depth with our results, 5 cm distance from interface) was 50% and 90% respectively for 2 cm × 2 cm and 1 cm × 1 cm field sizes respectively for 15 MV photon beam. Comparing to our results of 46% and 70% for the same field sizes, the differences were acceptable with consideration of differences in used MC code, geometries, and photon beams energies.
We compared our 6 MV results with the study of Stathakis et al. on a similar geometry with lung thickness of 5 cm. ^{[18]} The BEAMnrc/DOSXYZnrc code calculations were used in their study and two other analytical algorithms were assessed against MC results. The dose reduction inside lung was obtained for 1 cm × 1 cm, 2 cm × 2 cm and 3 cm × 3 cm field sizes. Its maximum value was approximately 50%, 16% and 11% respectively, while our results were 39%, 13%, and 7% for the similar geometry. As we can deduce from our results, the obtained dose reductions were consistent with their results and like other cases the observed discrepancies can be attributed the small differences in MC code and geometries.
In a recent study by Disher et al. effects of lateral disequilibrium was studied for lung with different density ranging from 0.001 to 5 g/cm ^{3} . Their study showed that sever LED small fields in ultralow density of lung can lead to significant dose reduction inside lung and cause large underdosage of solid tumor inside lung. ^{[3]}
Our results were consistent with the recent studies on SBRT fields used for lung cancer and it revealed enormous tumor underdosage in small fields due to LED. Consequently, in accordance with previous studies, application of more accurate dose calculation engines seems an essential prerequisite for lung cancer treatment to lower the uncertainty associated with delivered dose to the small solid tumor.
> Conclusion   
Dose calculations inside lung was performed for small fields used in IMRT or SBRT using MC method. The results were in accordance with the previous studies and large dose reduction was found for lung tissue as well as a small solid tumor inside lung. Thus, accurate dose calculation for these techniques has crucial importance for radiation therapy outcome and its shortcomings may compromise the expected survival for treated patients. Application of either MC method or other algorithms capable of considering the complex dosimetric situation in lung tumors is recommended.
> Acknowledgments   
The authors would like to thank research office of Tabriz University of Medical Sciences for their financial support of this project.
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[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6]
