

ORIGINAL ARTICLE 

Year : 2012  Volume
: 8
 Issue : 3  Page : 367372 

Influence of smoothing algorithms in Monte Carlo dose calculations of cyberknife treatment plans: A lung phantom study
H Sudahar^{1}, PG Gopalakrishna Kurup^{1}, V Murali^{1}, J Velmurugan^{2}
^{1} Department of Radiotherapy, Apollo Speciality Hospital, Chennai, India ^{2} Department of Medical Physics, Anna University, Chennai, India
Date of Web Publication  17Nov2012 
Correspondence Address: H Sudahar Department of Radiotherapy, Apollo Speciality Hospital, 320, Padma Complex, Mount Road, Chennai Pin: 600035 India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/09731482.103514
Aim: The Monte Carlo dose calculation algorithm yields accurate dose distributions in heterogeneous media and interfaces. The Monte Carlo calculation algorithm provided in the Multiplan Cyberknife treatment planning system (Accuray, Sunnyvale, CA, USA) has five different dosesmoothing algorithms in it. As the principle of smoothing of these algorithms is different, they can produce a disparity in the final dose distribution. The aim of the present study is to analyze the influence of these Monte Carlo smoothing algorithms in the final dose distribution of cyberknife treatment plans. Materials and Methods: An anthropomorphic lung phantom with a tumor mimicking ball target was taken for this study. The basic optimization was performed with the Ray tracing algorithm. The Monte Carlo calculations were introduced with each smoothing algorithm on the basic plan and the plans were compared. Results: The Monte Carlo doses were found to be lesser than the Ray tracing doses. The dose conformity index was above 4 for all the smoothing algorithms, while it was only 1.19 for Ray tracing. The least coverage of 6.34 was obtained for a weighted average algorithm. The deviation between the V100% values of different smoothing algorithms was higher than the deviation in V80%. Conclusion: The deviations between the smoothing algorithms are higher in the highdose regions, including the prescribing isodose, than the lowdose regions of the target, as well as in the organs at risk (OAR). Keywords: Cyberknife, dosesmoothing algorithm, Gaussian algorithm, Monte Carlo dose, Ray tracing
How to cite this article: Sudahar H, Gopalakrishna Kurup P G, Murali V, Velmurugan J. Influence of smoothing algorithms in Monte Carlo dose calculations of cyberknife treatment plans: A lung phantom study. J Can Res Ther 2012;8:36772 
How to cite this URL: Sudahar H, Gopalakrishna Kurup P G, Murali V, Velmurugan J. Influence of smoothing algorithms in Monte Carlo dose calculations of cyberknife treatment plans: A lung phantom study. J Can Res Ther [serial online] 2012 [cited 2019 Nov 13];8:36772. Available from: http://www.cancerjournal.net/text.asp?2012/8/3/367/103514 
> Introduction   
For determining the dose distribution in radiotherapy, treatment planning systems (TPS) use dose calculation algorithms. Accuracy of the treatment dose calculations is determined by the algorithm used in the TPS. In a homogeneous medium, these algorithms calculate nearly similar dose distributions. However, they do not yield similar results in a heterogeneous media. ^{[1],[2]} There are several algorithms introduced to improvize the dose calculations in a heterogeneous interface or medium. ^{[3],[4],[5],[6],[7],[8]} The Monte Carlo algorithm is considered to be the finest dose calculating algorithms among all other commercially available algorithms. ^{[9],[10]} Multiplan (Accuray Inc., Sunnyvale, CA, USA) TPS is one among the treatment planning systems that uses the Monte Carlo dose calculation algorithm. Multiplan is the dedicated Cyberknife (Accuray Inc, Sunnyvale, CA, USA) stereotactic radiosurgery TPS. There are few studies available on the implementation of Monte Carlo algorithms in cyberknife treatment planning. ^{[9],[10],[11],[12],[13],[14],[15]} According to Wilcox et al., ^{[9]} the discrepancies between the Ray tracing and Monte Carlo algorithms are larger for plans using smaller collimator sizes. The depthdose studies of Yamamoto et al. ^{[11]} state that the discrepancy between the Monte Carlo calculated and the measured depthdose curves increase with decreasing field size. According to Sharma et al., ^{[15]} there can be significant differences between Ray tracing and Monte Carlo calculations in a heterogeneous medium. The Monte Carlo calculations in the Multiplan treatment planning system are associated with a smoothing algorithm. These algorithms are prone to create a discrepancy in the final dose distribution, as the smoothing principles are different in each smoothing algorithm. The influence of these Monte Carlo dosesmoothing algorithms has not yet been studied in depth. The aim of present study is to analyze the influence of these Monte Carlo dosesmoothing algorithms in a lung phantom, which has a greater extent of heterogeneity.
> Materials and Methods   
The Xsight^{®} Lung Tracking (XLT) lung phantom (Computerized Imaging Reference Systems, Norfolk, VA, USA), which is used for performing the endtoend test of dynamic lung tumor tracking in cyberknife, was considered for this study. This XLT lung phantom contained an anthropomorphic spine, with a cortical and trabecular bone, ribs, lung lobes, and a lung tumorsimulating target. The computed tomography (CT) images of this phantom were acquired in 1 mm thickness and loaded into the Multiplan TPS. The lung target, which was the target mimicked ball in the XLT phantom, was drawn. The volume of the target was 7023.81 mm ^{3} . The organs at risk (OAR), the ipsilateral (Left) lung, contralateral (Right) lung, and spine, were also marked on the CT images. The treatment plans were made for this target with proper constraints to the OARs.
All the cyberknife treatment plans are associated with a tracking method. The lung tumors, having a definite size, can also be used as tracking objects, and this lung tracking method is called, sight lung tracking. Although it is a lung tracking method, the initial alignment is done by aligning the spine. As a part of the planning the initial Spine Tracking Volume was drawn. Following this, the alignment of the spine in the DRR (Digitally Reconstructed Radiograph) (generated by the TPS) was confirmed. The lung tumor simulating target was taken as the Tumor Tracking Volume. Sequential optimization was selected for the treatment planning. The collimators were selected by the automatic collimator selection tool for optimal conformity. This tool suggested 10 mm and 15 mm collimators for the lung target. Then four doselimiting shell volumes were created around the target. The first shell covered a radial width of 2 mm around the target. The second shell covered a 3 mm radial width around the first shell. The third shell covered a 5 mm radial width from the second shell. Similarly the final fourth shell covered a radial width of 15 mm around the third shell. The dose limit set for the first shell was 100% of the target dose. Similarly, the limiting dose of 85, 60, and 25% of the target dose was set for the second, third, and the fourth shells, respectively. The goal to the target dose coverage was set as 60 Gy in the four fractions and it was set for optimal conformity. The Ray tracing algorithm was selected for the dose calculations. The optimization was executed in low resolution. Once the optimization was completed the high resolution calculations were performed. In the Multiplan planning system the maximum dose was taken as the default normalization dose. The isodose covering 95% of the target was selected for the prescription, and the prescription dose in this study was 60 Gy.
In cyberknife the Monte Carlo dose calculations are performed after the basic dose calculations by the Ray tracing algorithm. Hence, the high resolution Ray tracing doses were introduced for Monte Carlo calculations with the same beam parameters estimated by the basic Ray tracing−based sequential optimization. The Monte Carlo doses were smoothed by the smoothing algorithms. The smoothing algorithms available in Multiplan TPS were: The Average, Weighted average, Gaussian, Clipped Gaussian, and DesparkledOnly algorithm.
The average smoothing algorithm computes the average value within a 3 x 3 x 3 voxel cube surrounding the calculation voxel. The weighted average also does the same, but with weighting factors, which decreases with distance from the central voxel. The Gaussian algorithm gives the convolution of dose distribution with a 3D Gaussian function and the standard deviation σ of the Gaussian function can be selected by the user. Two different standard deviations (σ = 0.2 and σ = 3) were taken for the present study. Clipped Gaussian also does the same, but the outcome of the Gaussian function is modified so that the difference between the raw dose and the smoothed dose exists within the statistical uncertainty in dose calculation, at each voxel. The DesparkledOnly algorithm removes the artificial hot spots at voxels with greater uncertainty.
All the smoothing algorithms were introduced in the Monte Carlo dose calculations independently, and the results were analyzed and compared.
The cyberknife treatment plans of different Monte Carlo dose smoothing algorithms were evaluated for target coverage and sparing of the OAR. The formulae used to calculate the conformity index and the homogeneity index are given below.
Conformity index CI = (V _{RI} / TV _{RI} ) x (TV / TV _{RI} )
Where V _{RI} is the actual volume including the target receiving the prescription isodose or more, TV is the volume of the target, TV _{RI} is the volume of the target that receives the prescription isodose or more.
Homogeneity Index HI = (D _{2%}  D _{98%} ) / D _{50%} For the OARs spine, ipsilateral lung, and contralateral lung, V _{100%} , V _{80%} , V _{50%} , V _{30%} , V _{10%} , and V _{5%} were evaluated in terms of the volume, in cubic millimeters.
The Pvalues were calculated from the twotailed Student's ttest and tabulated accordingly.
> Results   
The target doses D _{98%} , D _{95%,} D _{90%} , D _{50%} , D _{10%} , and D _{2%} are shown in [Table 1] for the Ray tracing algorithm and for all the Monte Carlo smoothing algorithms. Monte Carlo smoothed doses were found to be lesser than the doses calculated by the Ray tracing algorithm. The Ray tracing−calculated dose distribution is shown in [Figure 1]. The Gaussian, Clipped Gaussian, and Desparkledonly algorithms showed the same results when the standard deviations selected were low. However, they were differing in smoothing when high standard deviation was selected. D _{98%} was the lowest for the Clipped Gaussian algorithm and it was 50.56 Gy. Except D _{98%,} all other volume doses were smoothed to the lowest by the Average smoothing algorithm. The dose distribution that was smoothed by the Average algorithm is shown in [Figure 2]. The lowest values of the volume doses were 51.27 Gy, 52.52 Gy, 57.52 Gy, 60.65 Gy, and 61.28 Gy, respectively, for D _{95%,} D _{90%} , D _{50%} , D _{10%} , and D _{2%.} The corresponding values calculated by the Ray tracing algorithms were 60.00 Gy, 60.67 Gy, 62.67 Gy, 64.00 Gy, and 65.33 Gy, respectively. Similarly the highest value of D _{98%} was obtained by the Weighted Average smoothing algorithm, and it was 50.82 Gy. However, D _{95%,} D _{90%} , D _{50%} , D _{10%} ,and D _{2%} were the highest for the Gaussian and Clipped Gaussian algorithms, with a low standard deviation, and also for the Desparkledonly algorithm. The highest values of D _{95%,} D _{90%} , D _{50%} , D _{10%} , and D _{2%} were 52.03 Gy, 53.40 Gy, 58.20 Gy, 61.63 Gy, and 63.67 Gy, respectively. The volumes covered by 100% of the prescribed dose differed vastly between the Ray tracing and Monte Carlo smoothed doses. The V _{100%} calculated by the Ray tracing algorithm was 94.31%. However, the deviations between the Monte Carlo smoothed doses were lower. The minimum V _{100%} value was obtained for the weighted average algorithm and it was 15.78%. The Gaussian and Clipped Gaussian algorithms with a low standard deviation and the Desparkledonly algorithms showed the same maximum V _{100%} and the value was 24.9%. The smoothed dose distribution by the Gaussian algorithm with σ = 0.2 is shown in [Figure 3]. Although there were huge differences between Ray tracing and the Monte Carlo smoothed doses in V _{100%,} the deviations progressively reduced for V _{95%} , V _{90%} , V _{85%,} and V _{80%} . The minimum V _{80%} was 99.90% and it was for the weighted average smoothing algorithm. V _{100%,} V _{95%} , V _{90%} , V _{85%,} and V _{80%} of the target are shown in [Table 2].  Figure 2: Axial Monte Carlo dose distribution smoothed by the Average smoothing algorithm
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 Figure 3: Axial Monte Carlo dose distribution smoothed by the Gaussian (σ = 0.2) smoothing algorithm
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 Table 1: Analysis of volume dose distribution in the target for different Monte Carlo smoothing algorithms and the ray tracing calculation algorithm
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 Table 2: Analysis of dose volumes of the target for different Monte Carlo smoothing algorithms and the ray tracing calculation algorithm
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The target dose conformity index of the smoothed dose distributions were between 4.01 and 6.34. However, the conformity index of the Ray tracing dose distribution was 1.19. Similarly the homogeneity index of the Monte Carlo smoothed doses were between 0.18 and 0.22, while it was 0.11 for Ray tracing. The conformity index and homogeneity index are tabulated in [Table 3].
In the ipsilateral lung, V _{100%} was 123.98 mm ^{3} for Ray tracing, while it was zero for all the Monte Carlo Smoothing algorithms. The difference between the smoothed doses and Ray tracing was low for larger volumes involving small doses. Although there was a difference between the smoothed doses, the difference was very low. The dose volumes of the ipsilateral lung are given in [Table 4]. In case of contralateral lung and spine, the dose volumes from V _{100%} to V _{30%} were not appreciable to quantify for both Ray tracing and Monte Carlo calculations. The V _{10%} and V _{5%} analysis of the contralateral lung and spine are shown in [Table 5].  Table 4: Ipsilateral lung dose volumes for different Monte Carlo smoothing algorithms and the ray tracing calculation algorithm
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 Table 5: Spine and contralateral lung dose volumes for different Monte Carlo smoothing algorithms and the ray tracing calculation algorithm
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> Discussion   
The Monte Carlo algorithm is the proven algorithm for accurate dose calculations in radiotherapy. ^{[3],[4],[9],[16],[17]} Sharma et al. ^{[16]} studied the dose calculation accuracy of the Cyberknife Monte Carlo dose calculation algorithm with other commercially available algorithms. According to that study the gamma analysis showed a better match in more than 97% of the area with a 3% dose and 3 mm distance to the agreement criteria. Another study by Sharma et al. ^{[15]} showed a greater degree of difference between Ray tracing and Monte Carlo doses, especially in the lung target. According to that study, the target coverage was 97.3% for Ray tracing, while it was only 71.3% for the Monte Carlo calculations.
The results of the present study show that the Ray tracing dose coverage is 94.31%, while the average dose coverage value of all the smoothing algorithms is only 21.08%. This difference is much higher than that reported in their study. Studies by Wilcox et al. ^{[9]} state that the maximum doses calculated by Ray tracing are larger than the Monte Carlo plans by up to a factor of 1.63. In the present study the D _{98%} of the Ray tracing dose is 97.8% and the mean D _{98%} value of all smoothing algorithms is 84.5%. This difference is lesser than the difference quoted by Wilcox et al. ^{[9]} The Gaussian smoothing algorithm, with a standard deviation of 1, was taken in those studies by Sharma et al. ^{[15]} However, the role of all other dose smoothing algorithms in the Cyberknife Monte Carlo calculations is not addressed explicitly in any of the Monte Carlo studies reported to date. The present study shows that there is a disparity in the conformity index between the different dose smoothing algorithms.
The dose conformity index is the measure of conformity of the prescribed dose within the target. Variation in the conformity index shows that there is a nonuniformity in the dose coverage between the Monte Carlo smoothed dose distributions. Values of more than 4 indicate the degree of under coverage of the prescribed dose. The weighted average algorithm gives the least dose conformity with a maximum conformity index of 6.34. For an ideal dose distribution, the conformity index should be 1. Interestingly the conformity index of the Ray tracing calculation is closer to 1 and it is 1.19.
Homogeneity in dose distribution within the target is quantified with the homogeneity index. For an ideal dose distribution, the homogeneity index must be zero. This means that D _{2%} and D _{98%} must be the same for an ideal dose distribution. In reality, for a good plan, the homogeneity index must be closer to zero. In the present study, the homogeneity index for the Ray tracing algorithm is 0.11. However, the homogeneity index for all the Monte Carlo smoothing algorithms is about 0.20. The least value of the homogeneity index has been obtained for the Average, Weighted average, and Gaussian (σ = 3) algorithms, with the homogeneity index being 0.18.
Although there is a difference in the target covering dose, the difference between the smoothing algorithms in D _{95%} , D _{90%} , D _{50%,} and D _{2%} are found to be small. Disparity between the Monte Carlo smoothing algorithms is higher for the V _{100%} values than the V _{80%} values. This was seen in the OAR dose distributions too.
These results show that the smoothing algorithms create appreciable discrepancies in the higher dose regions than in the lower dose regions.
According to Sharma et al., ^{[15]} the difference between the Ray tracing and Monte Carlo doses are also decided by the location of the tumor in the lung. The present study was a phantom study, and the target positions at different places could not be accounted for. Further studies on real patients should be made, to analyze the role of the location, in Monte Carlo Smoothing algorithms.
> Conclusion   
The Monte Carlo dose smoothing doses in all the five available algorithms in the Multiplan treatment planning system resulted in reduced doses when compared with the Ray tracing doses. The major differences between the algorithms were predominant in the higher dose regions and in the target dose conformity index. In the regions of lower doses, the smoothing algorithms produced similar results, with lesser discrepancy. Desparkledonly, Gaussian, and Clipped Gaussian algorithms, with a smaller standard deviation yielded the same results. However, they differed when the selected standard deviation was on the higher side.
As the dose smoothing algorithms create discrepancies in the final dose distributions in lung targets, it is essential to select an accurate and optimal dose smoothing algorithm in the Monte Carlo dose calculations of Cyberknife radiosurgery treatment planning of lung cancer. An inappropriate choice of a smoothing algorithm may lead to under or over dosage in lung targets.
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[Figure 1], [Figure 2], [Figure 3]
[Table 1], [Table 2], [Table 3], [Table 4], [Table 5]
