148 CHAPTER 9 INFLUENCE OF SMOOTHING ALGORITHMS IN MONTE CARLO DOSE CALCULATIONS OF CYBERKNIFE TREATMENT PLANS: A LUNG PHANTOM STUDY 9.1 INTRODUCTION 9.1.1 Dose Calculation Algorithms Dose calculation algorithms are used in the TPS for determining the dose distribution in radiotherapy. Accuracy of the treatment dose calculations is determined by the algorithm used in the TPS. In a homogeneous medium these algorithms are calculating nearly similar dose distributions. However they are not yielding similar results in heterogeneous media (Fotina et al 2009; Knöös et al 1995). There are several algorithms introduced to improvise the dose calculations in a heterogeneous interface or medium (Krieger and Sauer 2005; Vanderstraeten et al 2006; Carrasco et al 2004; Deng et al 2003; Deng et al 2004; Francescon et al 2009). Monte Carlo algorithm is considered to be the finest of the dose calculating algorithms among all other commercially available algorithms (Wilcox et al 2010; Wilcox and Daskalov 2008). CyberKnife radiosurgery is performed for intracranial as well as extra cranial targets. Lung target is one among the extracranial site which is treated with dedicated tracking methods. Anatomy of lung is highly inhomogeneous and it requires accurate dose calculation algorithms like Monte Carlo algorithm.
149 9.1.2 Monte Carlo Dose Calculation Algorithm in CyberKnife Treatment Planning Multiplan is the dedicated CyberKnife stereotactic radiosurgery TPS. Multiplan TPS is one among the treatment planning systems which uses Monte Carlo dose calculation algorithm. Multiplan system has Ray Tracing dose calculations algorithm also, in addition with the Monte Carlo algorithm. There are few studies available on implementation of Monte Carlo algorithms in CyberKnife treatment planning (Wilcox et al 2010; Wilcox and Daskalov 2008; Yamamoto et al 2002; Sánchez-Doblado et al 2003; Yu et al 2004, Araki 2006; Sharma et al 2010; Sharma et al 2011; Craig et al 2008). According to Wilcox et al (2010) the discrepancies between the Ray tracing and Monte Carlo algorithms are larger for plans using smaller collimator sizes. Depth dose studies of Yamamoto et al (2002) state that the discrepancy between the Monte Carlo calculated and measured depth dose curve increases with decreasing field size. According to Sharma et al (2010) there can be significant differences between Ray tracing and Monte Carlo calculations in a heterogeneous medium. 9.1.3 Monte Carlo Dose Smoothing Algorithms The Monte Carlo calculations in the Multiplan treatment planning system are associated with a smoothing algorithm. These algorithms are prone to create discrepancy in the final dose distribution as the smoothing principles are different in each smoothing algorithm. The influence of these Monte Carlo dose smoothing algorithms are not yet studied in depth. The present study is to analyze the influence of these Monte Carlo dose smoothing algorithms in a lung phantom which has the greater extent of heterogeneity.
150 9.2 MATERIALS AND METHODS 9.2.1 The Lung Phantom The X-sight Lung Tracking lung phantom (Computerized Imaging Reference Systems, Norfolk, VA, USA) which is used for performing the end to end test of dynamic lung tumor tracking in CyberKnife, was considered for this study. This XLT lung phantom (Figure 9.1) contains anthropomorphic spine with cortical and trabecular bone, ribs, lung lobes and a lung tumor-simulating target. Figure 9.1 X-sight lung phantom with the insert which contains the lung target The CT images of this phantom were acquired in 1mm thickness and loaded into the Multiplan TPS. The lung target which is the target mimicked ball in the XLT phantom was contoured. The volume of the target was 7023.81mm 3.The organs at risk (OAR) ipsi-lateral (Left) lung, contra-
151 lateral (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. 9.2.2 Treatment Planning and the Dose Calculations for the Lung Phantom in the Multiplan TPS All the CyberKnife treatment plans are associated with a tracking method. The lung tumors having definite size can also be used as a tracking object and this lung tracking method is called as X-sight lung tracking. Though it is lung tracking method the initial alignment is done by aligning the spine. As the part of the planning, the initial Spine Tracking Volume was contoured. Then the alignment of the spine in the DRR (generated by the TPS) was confirmed. The lung tumor simulating the target was taken as the Tumor Tracking Volume. The sequential optimization was selected for the treatment planning. The collimators were selected by the automatic collimator selection tool for optimal conformity.this tool suggested 10mm and 15mm collimator for the lung target. Then four dose limiting shell volumes were created around the target. The first shell covered a radial width of 2 mm around the target. The second shell covered 3mm radial width around the first shell. The third shell covered 5mm from the second shell. Similarly the final fourth shell covered a radial with of 15mm 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 were set for the second shell, third shell and the fourth shell respectively. The goal to the target dose coverage was set as 60Gy in 4 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 Multiplan planning system the maximum dose was taken as the default normalization dose. The isodose
152 covering the 95% of the target was selected for 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 are Average, Weighted average, Gaussian, Clipped Gaussian and Desparkled- Only algorithm. 9.2.3 Principles of the Dose Smoothing Algorithms The average smoothing algorithm computes the average value within a 3x3x3- voxel cube surrounding the calculation voxel. Weighted averagealso does the same but with weighting factors which decreases with distance from the central voxel. Gaussian algorithm gives the convolution of the dose distribution with a 3D Gaussian function and the standard deviation of the Gaussian function can be selected by the user. Two different standard deviations ( = 0.2 and = 3) are 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. Desparkled-Only algorithm removes the artificial hot spots at voxels with greater uncertainty.
153 All the smoothing algorithms were introduced in the Monte Carlo dose calculations independently and the results were analyzed and compared. 9.2.4 Treatment Plan Evaluation for Comparison 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, and TV RI is the volume of the target which receives the prescription isodose or more. The homogeneity index is given by, Homogeneity Index HI = (D 2% - D 98%)/ D 50% Where, D 2% is the dose received by only 2% of the target volume, D 98% is the dose received by 98% of the target volume and D 50% is the dose received by 50% of the target volume. For the OARs spine, ipsi- lateral lung and contra lateral lung the V 100%, V 80%, V 50%, V 30%, V 10%, V 5% were evaluated in terms of the volume in cubic millimeters. The P-values were calculated from the two tailed Student s T test and tabulated accordingly.
154 9.3 RESULTS The target doses D 98%, D 95%, D 90%, D 50%, D 10% and D 2% are shown in Table 9.1 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 9.2. Figure 9.2 Dose distribution calculated by the Ray tracing algorithm Gaussian, Clipped Gaussian and Desparkled-only algorithms were showing same results when the standard deviations selected was low. However they were differing in smoothing when high standard deviation was selected. D 98% was the lowest for Clipped Gaussian algorithm and it was 50.56Gy. Except D 98%, all other volume doses were smoothed for a lowest by the Average smoothing algorithm. The dose distribution which was smoothed by the Average algorithm is shown in Figure 9.3. The lowest values of the volumes doses were 51.27Gy, 52.52Gy, 57.52Gy, 60.65Gy and 61.28Gy respectively for D 95%, D 90%, D 50%, D 10% and D 2%. The corresponding values
155 calculated by the Ray tracing algorithms were 60.00Gy, 60.67Gy, 62.67Gy, 64.00Gy and 65.33Gy respectively. The DVHs of Average, Weighted average, Gaussian with two values, Clipped Gaussian with two values and Desparkled-only algorithms are shown in Figure 9.5, 9.6, 9.7, 9.8, 9.9, 9.10 and 9.11 respectively. Figure 9.3 Monte Carlo dose distribution smoothed by the Average smoothing algorithm Similarly the highest value of D 98% was obtained by the Weighted Average smoothing algorithm and it was 50.82Gy. The highest values of D 95%, D 90%, D 50%, D 10% and D 2% were 52.03Gy, 53.40Gy, 58.20Gy, 61.63Gy and 63.67Gy respectively. The volumes covered by 100% of the prescription dose were vastly differing 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 lesser.
156 Figure 9.4 Monte Carlo dose distribution smoothed by the Gaussian smoothing algorithm The minimum V 100% value was obtained for weighted average algorithm and it was 15.78%. Gaussian, Clipped Gaussian algorithms with low standard deviation and Desparkled-only algorithms were showing the same maximum V 100% and the value was 24.9%. The smoothed dose distribution by Gaussian algorithm with =0.2 is shown in Figure 9.4. Though there was a huge difference between Ray tracing and Monte Carlo smoothed doses in V 100%, the deviations progressively reducing for V 95%, V 90%, V 85% and V 80%. The minimum V 80% was 99.90% and it was for weighted average smoothing algorithm. The V 100%, V 95%, V 90%, V 85% and V 80% of the target are shown in Table 9.2. The target dose conformity index of the smoothed dose distributions were between 4.01 and 6.34. However the conformity index of 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
157 0.11 for Ray tracing. The conformity index and homogeneity index are tabulated in Table 9.3. Table 9.1 Volume doses of the target calculated by different smoothing algorithms Dose calculation/smoothing Monte Carlo smoothing Algorithms Algorithm Target Volume doses in Gy D 98% D 95% D 90% D 50% D 10% D 2% Ray Tracing 58.67 60 60.67 62.67 64 65.33 Average 50.64 51.27 52.52 57.52 60.65 61.28 Weighted Average 50.82 51.45 52.71 57.73 60.86 61.49 Gaussian(=0.2) 50.67 52.03 53.4 58.2 61.63 63.67 Gaussian (=3) 50.69 51.32 52.57 57.58 60.71 61.34 ClippedGaussian(=0.2) 50.67 52.03 53.4 58.2 61.63 63.67 Clipped Gaussian (=3) 50.56 51.87 52.53 57.78 61.07 61.72 Desparkled-only 50.67 52.03 53.4 58.2 61.63 63.67 P-value 0.0158 0.0173 0.0118 0.0006 <0.0001 0.0002 In the ipsilateral lung, the 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. Though there was a difference between the smoothed doses, the difference was very low. In the case of contra lateral lung and spine the dose volumes from V 100% to V 30% were not appreciable to quantify for both in Ray tracing and Monte Carlo calculations. V 10% and V 5% analysis of contra lateral lung and spine are shown in Table 9.4. The dose volumes of the ipsilateral lung are given in Table 9.5.
158 Table 9.2 smoothing algorithms Dose volumes of the target calculated by different Dose calculation/smoothing algorithm Monte Carlo smoothing Algorithms Target Dose Volumes in percentage V 100% V 95% V 90% V 85% V 80% Ray Tracing 94.31 99.93 100.00 100.00 100.00 Average 17.24 54.13 82.59 96.10 100.00 Weighted Average 15.78 58.52 83.50 97.79 99.90 Gaussian(=0.2) 24.90 58.98 86.46 96.58 99.92 Gaussian (=3) 16.58 57.79 82.76 96.12 99.96 Clipped Gaussian(=0.2) 24.90 58.98 86.46 96.58 99.92 Clipped Gaussian (=3) 23.26 58.72 84.62 96.74 99.97 Desparkled-only 24.90 58.98 86.46 96.58 99.92 P-value 0.8931 0.4863 0.0329 <0.0001 <0.0001 Table 9.3 Conformity and homogeneity indices calculated by different smoothing algorithms Dose calculation/smoothing algorithm Monte Carlo smoothing Algorithms Conformity Index Homogeneity Index Ray Tracing 1.19 0.11 Average 5.80 0.18 Weighted Average 6.34 0.18 Gaussian(=0.2) 4.01 0.22 Gaussian (=3) 6.03 0.18 Clipped Gaussian(=0.2) 4.01 0.22 Clipped Gaussian (=3) 4.30 0.19 Desparkled-only 4.01 0.22 p value 0.6544 0.4210
159 Table 9.4 Spine and contra-lateral lung dose volumes for different Monte Carlo smoothing algorithms and Ray tracing calculation algorithm Monte Carlo smoothing Algorithms Dose calculation/smoothing algorithm Spine Dose volumes in mm 3 Contra-lateral (Right)Lung V 10% V 5% V 10% V 5% Ray Tracing 858.31 4404.07 77903.75 185400.01 Average 30.52 367.69 3196.72 86472.51 Weighted Average 32.42 3616.33 3557.21 87102.89 Gaussian(=0.2) 268.94 4141.81 7039.07 112191.20 Gaussian (=3) 29.56 3656.39 3275.87 86572.65 Clipped Gaussian(=0.2) 268.94 4141.81 7039.07 112191.20 Clipped Gaussian (=3) 196.46 3403.66 5495.07 78414.92 Desparkled-only 268.94 4141.81 7039.07 112191.20 P- value 0.8808 0.6576 0.9259 0.6047 Table 9.5 Ipsi-lateral lung dose volumes for different Monte Carlo smoothing algorithms and Ray tracing calculation algorithm Dose calculation/smoothing algorithm Monte Carlo smoothing Algorithms Ipsi-lateral (Left) Lung dose volumes in mm 3 V 100% V 80% V 50% V 30% V 10% V 5% Ray Tracing 123.98 6729.13 21890.64 52158.36 331079.50 574212.11 Average 0.00 531.20 16341.21 44845.58 260334.97 555864.32 Weighted Average 0.00 521.60 16209.60 47410.01 259840.97 554157.28 Gaussian(=0.2) 0.00 905.04 16349.79 49522.40 270144.40 613836.32 Gaussian (=3) 0.00 527.38 16305.92 47614.10 260173.81 555432.30 Clipped Gaussian(=0.2) Clipped Gaussian (=3) 0.00 905.04 16349.79 49522.40 270144.40 613836.32 0.00 678.06 16048.43 49477.58 279426.56 526952.76 Desparkled-only 0.00 905.04 16349.79 49522.40 270144.40 613836.32 P-value 0.9529 0.9089 0.1823 0.0056 0.0832 0.0214
160 Figure 9.5 DVH of the treatment plan smoothed by the average algorithm Figure 9.6 DVH of the treatment plan smoothed by the weighted average algorithm
161 Figure 9.7 DVH of the treatment plan smoothed by the Gaussian (=0.2) algorithm Figure 9.8 DVH of the treatment plan smoothed by the Gaussian (=3) algorithm
162 Figure 9.9 DVH of the treatment plan smoothed by the Clipped Gaussian (=0.2) algorithm Figure 9.10 DVH of the treatment plan smoothed by the Clipped Gaussian (=3) algorithm
163 Figure 9.11 DVH of the treatment plan smoothed by the Desparkledonly algorithm 9.4 DISCUSSION Monte Carlo algorithm is the proven algorithm for accurate dose calculations in radiotherapy (Krieger T. and Sauer O.A2005; Vanderstraeten et al 2006; Wilcox et al 2010;Sharma et al 2011; Craig et al 2008). Sharma et al (2011) studied the dose calculation accuracy of CyberKnife Monte Carlo dose calculation algorithm with other commercially available algorithms. According to that study the gamma analysis shows a better match in more than 97% area with 3% dose difference and 3mm distance to agreement criteria. Another study by Sharma et al (2010) shows a greater degree of difference between Ray tracing and Monte Carlo doses especially in lung target. According to that study the target coverage is 97.3% for Ray tracing while it is only 71.3% for 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 smoothing algorithm is only 21.08% only. This difference is much higher than that reported in their study.
164 Studies by Wilcox et al (2010) say that the maximum doses calculated by the Ray tracing are higher than the Monte Carlo plans by up to a factor of 1.63. In the present study the D 98% of 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 (2010). Gaussian smoothing algorithm with standard deviation of 1 is taken in those studies by Sharma et al (2010). However the role of all other dose smoothing algorithms in CyberKnife Monte Carlo calculations is not addressed explicitly in any of the Monte Carlo studies reported till now. The present study shows that there is a disparity in the conformity index among the different dose smoothing algorithms. The dose conformity index is the measure of conformity of the prescribed dose to the target. Variation in the conformity index shows that there is a non-uniformity in the dose coverage between the Monte Carlo smoothed dose distributions. The values are 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 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 should be zero. This means the D 2% and D 98% should be the same for an ideal dose distribution. In reality for a good plan the homogeneity index should 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 it is about 0.20. The least value of homogeneity index is obtained for Average, Weighted average and Gaussian (=3) algorithms with a homogeneity index of 0.18. Though there is a
165 difference in the target covering dose, the difference among the smoothing algorithms in the D 95%, D 90%, D 50% and D 2% are found to be small. Disparity between the Monte Carlo smoothing algorithms is higher for V 100% values than the V 80% values. This is seen in the OAR dose distributions too. These results are showing that the smoothing algorithms are creating appreciable discrepancies in the higher dose regions than in the lower dose regions. According to Sharma et al (2010) 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 is a phantom study and the target position at different places couldn t be accounted. Further studies on real patient should be made to analyze the role of location in Monte Carlo Smoothing algorithms. 8.5 CONCLUSION Monte Carlo smoothed doses for all the five available algorithms in the Multiplan treatment planning system are resulting in reduced doses when compared with the Ray tracing doses. The differences between the algorithms are predominant in the higher doses regions and in the target dose conformity index. In regions of lower doses the smoothing algorithms are giving similar results with lesser discrepancy. Desparkled only and Gaussian, Clipped Gaussian algorithms with smaller standard deviation are yielding same results. However they are differing when the selected standard deviation is in the higher side. As the dose smoothing algorithms are creating discrepancies in the final dose distributions in lung targets, it is essential to select an accurate and optimal dose smoothing algorithm in Monte Carlo dose calculations of CyberKnife radiosurgery treatment planning of lung cancer. Inappropriate choice of smoothing algorithm may lead to under or over dosage in lung targets.