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A modified formula for dose calculations of stereotactic ablative body radiotherapy for non–small cell lung cancer
ARTICLE IN PRESS Medical Dosimetry ■■ (2017) ■■–■■
Medical Dosimetry j o u r n a l h o m e p a g e : w w w. m e d d o s . o r g
Medical Physics Contribution:
A modified formula for dose calculations of stereotactic ablative body radiotherapy for non–small cell lung cancer Yangsen Cao, M.D.,* Xiaofei Zhu, M.D.,* Yu Zhang, M.D.,† Chunshan Yu, M.D.,* Yongming Liu, M.D.,* Yongjian Sun, M.D.,* Zhitao Dai, M.D.,* Xueling Guo, M.D.,* Xiaoping Ju, M.D.,* and Huojun Zhang, M.D.* *Department of Radiation Oncology, Changhai Hospital Affiliated to Second Military Medical University, Shanghai, China; and † Department of Radiology, Changhai Hospital Affiliated to Second Military Medical University, Shanghai, China
A R T I C L E
I N F O
Article history:
Received 31 May 2017 Received in revised form 22 August 2017 Accepted 25 August 2017 Keywords:
Stereotactic ablative body radiotherapy Ray-tracing Monte Carlo Dose distribution Non–small cell lung cancer
A B S T R A C T
To provide a modified formula consistent with the Monte Carlo (MC) algorithm for dose calculations during stereotactic ablative body radiotherapy for non–small cell lung cancer. Seventy CyberKnife treatment plans were calculated and analyzed by MC and ray-tracing (RT) algorithms, separately. Parameters of treatment plans were compared, and those associated with differences of dose distributions were analyzed to establish a modified formula. Gross tumor volume and tumor tracking volume (TTV) were defined as the evident disease on the sequences of the window width and level of the lung and the mediastinum. Additionally, the formula was validated by another 20 plans. The prescription dose of the 90 patients was 60 Gy/5f. The RT algorithm overestimated the planning target volume (PTV) D95 by an average of 8.59 Gy and the gross tumor volume D99 by an average of 5.84 Gy. The homogeneity index of PTV was underestimated by 0.11 on average, whereas the conformity index and new conformity index was underestimated by 0.05. The RT algorithm overestimated the dose distribution to the spinal cord by 2.23 Gy, the esophagus by 1.96 Gy, the trachea by 1.89 Gy, the left-sided bronchus by 1.77 Gy, the right-sided bronchus by 1.64 Gy, and the heart by 2.16 Gy. The average whole-lung dose volumes of lung tissues and dose volumes of V5 were overestimated by 2.69 Gy and 7.52%, respectively. A power function distribution (R2 = 0.8626) was confirmed between PTV D95 and TTV volumes. PTV D95 calculated by the MC algorithm could be computed easily with TTV and PTV D95 calculated by the RT algorithm based on the formula. The modified equation was more consistent with MC algorithm than with other formula, which could be a reference to those not accessible to the MC algorithm. © 2017 American Association of Medical Dosimetrists.
Yangsen Cao, Xiaofei Zhu, and Yu Zhang contributed equally to this article. Reprint requests to Xiaoping Ju, M.D., Department of Radiation Oncology, Changhai Hospital Affiliated to Second Military Medical University, 168 Changhai Road, Yangpu District, Shanghai 200433, China. E-mail: [email protected] Reprint requests to Huojun Zhang, M.D., Department of Radiation Oncology, Changhai Hospital Affiliated to Second Military Medical University, 168 Changhai Road, Yangpu District, Shanghai 200433, China. E-mail: [email protected] https://doi.org/10.1016/j.meddos.2017.08.008 0958-3947/Copyright © 2017 American Association of Medical Dosimetrists
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Introduction Lung cancer is the leading cause of cancer deaths worldwide.1 For patients with non–small cell lung cancer (NSCLC), surgery is the preferred treatment. However, for inoperable patients, such as those with other diseases or intolerable to surgeries, radiation therapy is the only alternative curative treatment.2 More than 95% of patients with early-stage NSCLC treated with stereotactic ablative body radiotherapy (SABR) achieved good local control, with a median survival time of 34 to 45 months. SABR has already become the standard treatment option for medically inoperable patients with early-stage NSCLC.3-5 The CyberKnife system (Xsight Lung Tracking System) can track tumors located in the lungs when their diameters in all planes are greater than 15 mm. Tumor movement during inhalations and exhalations is traced in real time during the treatment, and simultaneously the treatment beams can be modified automatically, rendering SABR noninvasive for lung cancer with sub-millimeter accuracy. Real-time tracking further reduces the collateral irradiation doses to normal lung tissues and the probability of developing radiation-induced pneumonitis.6 The CyberKnife treatment planning system is equipped with ray-tracing (RT) and Monte Carlo (MC) algorithms.7,8 The dose distributions in non-homogeneous media could be modified by the MC algorithm, which is the most accurate method for calculating dose distributions.9-11 The RT algorithm, meanwhile, overestimated the planning target volume (PTV) doses by an average of ~19% to 21%.8,12-14 Up to May 2016, in mainland China, a total of 21 hospitals have introduced CyberKnife. Among them, the third generation of CyberKnife (G3) was not equipped with the MC algorithm. In addition, only part of the fourth (G4) and fifth generation (VSI) CyberKnife provided the MC algorithm. Therefore, the aim of our study was to establish a modified formula for dose calculation.
Methods and Materials Patient selection Seventy patients with NSCLC who had received CyberKnife between June 2013 and June 2015 were retrospectively analyzed. Patients who met the following criteria were included: a diagnosis of NSCLC confirmed by biopsy specimen; aged 18 to 80 years; with an inoperable condition or refusing surgeries; with 1 peripheral lesion, the diameter of which was between 1.5 cm and 8 cm (8 cm was included); with an expected survival of more than 6 months; with an Eastern Cooperative Oncology Group scale no more than 2; no previous radiotherapy; no multiple lesions; and no distant metastases. Forty-two male and 28 female patients were included in the study, with a median age of 64 years. The study
set consisted of 3 cases of large cell lung cancer, 27 cases of squamous cell carcinoma, and 40 cases of adenocarcinoma. Of the 70 foci, 11 were located within the right upper lobe, 15 within the right middle lobe, 7 within the right lower lobe, 25 within the left upper lobe, and 12 within the left lower lobe. The average diameter of tumors was 3.40 cm, and the median was 3.21 cm. Definition of variables Gross tumor volume (GTV) was delineated as a radiographically evident gross disease acquired from the image sequences of the window width and level of the lung. PTV was the expansion of 5 mm outside the GTV. Tumor tracking volume (TTV) was defined as the contour of the tumor on the sequences of the window width and level of the mediastinum (Fig. 1). PTV D95 and GTV D99 were defined as the dose to 95% volumes of PTV and 99% volumes of GTV, respectively. The conformity index (CI) was calculated with the equation: CI =
Viso (Viso: volumes covered by isodose line; Voverlap
Voverlap: overlap volumes of Viso and PTV). The new conformity index (nCI) was calculated with the following formula:
CI . The homogeneity index (HI) was deterCoverage D mined by the equation: HI = max (RxDose: prescription dose). R xDose The definition of whole-lung V5 was the percentage of the irradiated lung volume receiving a radiation dose exceeding 5 Gy. Esophagus D5cc, trachea D4cc, bronchia D0.5cc, heart D15cc, and spinal cord D0.35cc were the doses to 5 cc of the esophagus, 4 cc of the trachea, 0.5 cc of the bronchia, 15 cc of the heart, and 0.35 cc of the spinal cord, respectively.
nCI =
Treatment planning The patients adopted a supine position, and were scanned with a large-aperture computed tomography (CT) simulator (Brilliance CT Big Bore Oncology; Philips Medical System, The Netherlands) during inhalation. Scanning conditions were as follows: 120 kVp, 400 mAs, 1.5 mm slice thickness without image intervals (helical), and a 0.938 pitch. The scanning range was set from 15 cm outside of the lower boundary of the tumor to 15 cm outside of the upper boundary of the tumor, including the whole lung. After the CT simulation images with and without contrast were imported into the CyberKnife Data Management System, the GTV and organs at risk (OARs) were delineated. The OARs included the left and right lungs, esophagus, trachea, left-sided and rightsided bronchi, pericardium, and spinal cord. Afterward, the spine tracking volume (STV) (Fig. 2) and TTV were contoured. STV and TTV were used for primary image-guided setup and tracing positions of the tumor during treatment
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Fig. 1. (A) The contour of TTV on the sequence of window width and level of the mediastinum. The tumor encompassed by the red line was TTV. (B) The contour of GTV on the sequence of window width and level of the lung. The tumor encompassed by the purple line was GTV, inside which was the gray line that covered TTV.
to establish respiratory tracing models. The outline of STV was completed via STV tools in the contour task. TTV sketches were done manually, directly with the tools of the volumes of interest module in the contour task. Next, the Xsight Lung Tracking mode was adopted in all 70 cases. The doses to OARs were determined after referral to the recommendations of the American Association of Physicists in Medicine Task Group 101.15 The RT algorithm was used first for low resolution during the dose optimization. Next, the dose distribution was calculated based on high resolution by the RT algorithm. The prescription dose was 60 Gy/5f with the isodose line covering at least 95% of the PTV. The maximum dose was defined by the 100% isodose
Fig. 2. STV contains the whole vertebrae, which is used for global patient alignment in treatment position before treatment. The gray line demonstrated by the arrow encompassed the STV.
line. Finally, the plan was then recalculated via the MC algorithm with the same parameters including beam arrangements and monitor units and 1% uncertainty.
Formula establishment and validation Firstly, 70 treatment plans were calculated using both MC and RT algorithm. Variables including PTV D95, GTV D99, CI of PTV, the nCI, the HI, the mean lung dose, whole lung V5, esophagus D5cc, trachea D4cc, bronchia D0.5cc, heart D15cc, and spinal cord D0.35cc were analyzed to clarify the differences between these 2 algorithms. Next, the correlation between potential factors and PTV D95 were evaluated to establish a modified formula. Sharma et al. showed that the difference between the 2 algorithms was mainly determined by the location of the tumor and the proportion of lung tissue that PTV encompassed.8 Besides, it was elucidated that GTV, the density of lung tissue, and the location of the tumor influenced the PTV dose distributions calculated by the 2 algorithms.13 Another study also confirmed that with the increase of the diameters of the GTV and PTV, the differences of the PTV D99, D95, and Dmean in the 2 algorithms would be less significant.16 Moreover, the beam penetration distance in the lung, the size of the collimator, was correlated with the dose differences calculated by the 2 algorithms.12 Therefore, the correlation between the PTV, GTV, TTV, total monitor units, beam numbers, the horizontal (x), and vertical (y) distances from the tumor to the ipsilateral chest wall and PTV D95 were analyzed. The modified formula was then validated by another 20 plans. Those 20 patients (validation group) with lung cancer were treated with CyberKnife from June 2015 to March 2016.
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The entry criteria of the validation group were the same as patient selection criteria for proposal of the formula. When the prescription dose calculated by the RT algorithm was 60 Gy, the prescription doses to the tumor in the revised RT algorithm proposed in van der Voort van Zyp et al.16 (revised RT algorithm) were as follows: 48 Gy (tumor diameter <3 cm), 51 Gy (tumor diameter was 3-5 cm), and 54 Gy (tumor diameter>5 cm). The MC algorithm was applied as the standard to compare doses calculated by the RT algorithm, revised RT algorithm, and the modified formula in our study.
Data analysis Statistical Analysis System 9.4 (SAS Institute, Cary, NC) was used for all data processing, with exception to the scatter plots (TTV volumes vs PTV D95), which were modeled within Microsoft Office Excel 2013 (Microsoft Corporation, Santa Rosa, CA). Paired differences were tested for normality. Subsequently, the paired t test (t, P) and Wilcoxon signed rank test (S, P) were used for normally and abnormally distributed data, respectively. A P value <0.05 was considered statistically significant. The correlation analysis was carried out using the generalized additive model. The establishment of the formula was dependent on the trend lines calculated by the quadratic polynomial, cubic polynomial, the quartic polynomial, the exponential function, the logarithmic function, and the power function, after which the R2 values were evaluated.
Results Comparison between dose distributions calculated by the RT and MC algorithm The PTV D95 and GTV D99 were significantly reduced (p < 0.0001), whereas the CI, nCI, and HI increased calculated by the MC algorithm (p < 0.0001) when compared with those of the RT algorithm (Table 1). The average whole-lung dose volume of lung tissues, whole-lung V5 (the percentage of the irradiated lung volume receiving a radiation dose exceeding 5 Gy), the dose volume of the spinal cord, the esophagus, the trachea, the leftsided and the right-sided bronchi, and the heart were all significantly lower when calculated by the MC algorithm (Table 2) (p < 0.0001).
Potential factors associated with differences of dose distributions There was no linear correlation between those 7 parameters (PTV, GTV, TTV, total monitor units, number of beams, and the horizontal, and vertical distance from the ipsilateral chest wall to the tumor) and the PTV D95 (R2 <0.5). However, the deviation analysis of smoothing models showed that only the TTV affected PTV D95 (χ2 = 156.2710; p < 0.0001) (Table 3), when a generalized additive model was applied
Table 1 Dose differences in target volumes calculated by RT and MC algorithms (n = 70) Structure
Parameter
RT
MC
GTV PTV
D99 (Gy) D95 (Gy) CI nCI HI
75.68 ± 4.50 (58.42-86.77) 60.00 ± 0.00 (60.00-60.00) 1.16 ± 0.08 (1.04-1.29) 1.21 ± 0.08 (1.09-1.35) 1.44 ± 0.07 (1.23-1.59)
69.84 ± 4.47 (53.66-79.75) 51.41 ± 3.60 (42.19-57.83) 1.21 ± 0.10 (1.07-1.54) 1.26 ± 0.11 (1.11-1.61) 1.55 ± 0.10 (1.28-1.82)
GTV, gross tumor volume; PTV, planning target volume; RT, ray-tracing; MC, Monte Carlo. All data were presented with the mean ± SD. The values in the parentheses represent the ranges.
Table 2 Differences between the doses to OARs calculated by RT and MC algorithms (n = 70) Structure
Parameter
RT
MC
Lung
Dmean (Gy) V5 (%) D0.35cc (Gy) D5cc (Gy) D4cc (Gy) D0.5cc (Gy) D0.5cc (Gy) D15cc (Gy)
7.89 ± 3.31 (2.99-16.61) 28.43 ± 12.44 (7.31-77.50) 3.73 ± 1.37 (0.95-7.21) 4.41 ± 2.17 (1.39-13.82) 4.50 ± 2.40 (1.38-14.80) 4.56 ± 2.52 (1.41-12.10) 4.65 ± 2.74 (1.21-12.50) 4.35 ± 2.41 (0.70-12.60)
5.20 ± 2.34 (1.38-12.37) 20.91 ± 8.30 (5.13-46.75) 1.50 ± 0.83 (0.23-3.89) 2.45 ± 1.83 (0.43-11.58) 2.61 ± 2.31 (0.05-11.28) 2.79 ± 2.40 (0.18-10.78) 3.01 ± 2.52 (0.20-10.98) 2.19 ± 1.82 (0.04-10.45)
Spinal cord Esophagus Trachea Left bronchus Right bronchus Heart
All data were presented the mean ± SD. The values in the parentheses represented the ranges.
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Table 3 Smoothing model analysis (analysis of deviance) (n = 70) Source
DF
Sum of Square
χ2
P value
Spline (PTV volume) Spline (GTV volume) Spline (TTV volume) Spline (Total MUs) Spline (Beams) Spline (X) Spline (Y)
0.000008 0.000006 9.675710 0.000011 0.000006 0.000052 0.000046
. . 295.49808 0.0000083 . 0.0000846 0.0000447
. . 156.2710 0.0000 . 0.0000 0.0000
. . <0.0001 . . . .
DF, degree of freedom; χ2, chi-square.
for a nonlinear regression analysis, using generalized crossvalidation to select smoothing parameters. Scatter plots of TTV volumes vs PTV D95 were shown (Fig. 3). Trend lines were drawn and calculated by quadratic polynomial, cubic polynomial, quartic polynomial, exponential, logarithmic function, and power function models. The analysis indicated that R2 value of each model was as follows: 0.6532 (the quadratic polynomial), 0.7329 (the cubic polynomial), 0.7945 (the quartic polynomial), 0.3970 (the exponential function), 0.8487 (logarithmic function), and 0.8626 (power function). Among them, power function fitted the best. In our study, PTV D95_RT was 60 Gy. Therefore, the modified formula was as follows:
PTV D95 _MC = 45.395 × TTV 0.0448
Regarding different PTV D95_RT, the modified formula was amended as follows:
PTV D95 _MC = 0.7566 × TTV 0.0448 × PTV D95 _RT (PTV D95_MC: dose calculated by MC algorithm; PTV D95_RT: dose calculated by RT algorithm) (Fig. 3)
Validation of the modified formula The comparison of the PTV D95 calculated by the RT algorithm, revised RT algorithm, and formula in this study was performed based on the PTV D95 derived from the MC algorithm (Table 4). The dose error of the 2 algorithms was 8.52 Gy before modification (t = 10.89, p < 0.0001). The dose errors calculated by the revised RT algorithm and modified
Fig. 3. The data fitting of TTV volume and PTV D95 calculated by power function.
Table 4 Different PTV D95 calculated by different algorithms (n = 20) Structure
PTV
Parameter
D95 (Gy)
MC
51.48 ± 3.50 (45.26-56.12)
RT Pre-modification
Revised RT algorithm*
Modified formula of this study
60.00 ± 0.00 (60.00-60.00)
49.80 ± 2.26 (48.00-54.00)
50.50 ± 3.57 (43.53-56.76)
All data were given in mean ± SD. The values in the parentheses represented the ranges for the corresponding quantities. * Revised RT algorithm was introduced from van der Voort van Zyp NC et al.16
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Fig. 4. PTV D95 of 20 cases calculated by the RT algorithm, MC algorithm, revised RT algorithm, and modified model.
formula in our study were −1.68 Gy (t = −3.58, p = 0.002) and −0.98 Gy (t = −2.86, p = 0.010), respectively. Regarding consistency of results calculated by the MC algorithm, the revised RT algorithm and the modified formula in this study were evaluated by intraclass correlation coefficient. The value of intraclass correlation coefficient between the MC algorithm and the modified formula, the MC algorithm and the revised RT algorithm was 0.903 (0.826 to 0.947) and 0.757 (0.590 to 0.862), respectively. Therefore, the modified formula in our study was more favorable than the revised RT algorithm in van der Voort van Zyp et al. (Fig. 4). Discussion Although it was proven that there were differences between dose distributions calculated by the RT and MC algorithm, especially for heterogeneous tissues, relevant factors contributing to the difference remained unclear. Only van der Voort van Zyp et al. have proposed a 3-stage simple modified model, whereas the remaining studies raised only possible candidate factors correlated with the dose differences, but failed to create a modified formula.16 In our study, potential factors were identified to form a modified formula for conversion of PTV D95 calculated by the RT algorithm. Computed with the formula, the subsequent dose distributions could be consistent with those directly calculated by the MC algorithm. Besides, only TTV correlated with PTV D95 after introduction and analysis of those parameters. This may be owing to fewer differences between dose distributions calculated by the RT and MC algorithm attributable to fewer low density lung tissues that target volumes encompassed. As a result, TTV, with the least proportion of lung tissues compared with GTV and PTV, could be the best variable in the formula for modification of dose distributions calculated by the RT algorithm.
Because of sparse data regarding larger TTV (more than 100 cm3), TTV of smaller sizes had more weight during formula fitting. Nevertheless, during the establishment of the formula, a high-order polynomial may result in worse goodness of fit when the weight of larger TTV equaled to that of smaller TTV compared with other functions. Therefore, quintic and sextic polynomial was precluded for formula fitting. The study included 70 patients with NSCLC. The sample size was therefore large, and the results were convincing. Related factors of tumor targets and normal lung tissues were compared. Additionally, the volumes of doses to the spinal cord, esophagus, trachea, left-sided and right-sided bronchi, and heart calculated by 2 algorithms were analyzed when dose differences of 2 algorithms were studied, ensuring that the doses delivered to these OARs complied with the limiting amount recommended by the American Association of Physicists in Medicine Task Group 101. Sharma et al. reported the verification of the accuracy of the MC algorithm of the 2.1.0 Multiplan treatment planning system with an inhomogeneous phantom.8 The mean percentages of pixels passing of MC were 96% ~ 100%. Additionally, Computerized Imaging Reference Systems’ nonuniform chest phantom, EBT2 film, and Pro FilmQA were used to verify the accuracy of the MC algorithm in another study.17 The results showed that 98.4%~100% of the MC algorithm calculated points pass a γ (3%, 2 mm) criteria, whereas only 27.1%~49.7% of the RT algorithm calculated points pass the γ (3%, 2 mm) criteria. Mark et al. used Computerized Imaging Reference Systems’ programmable synchronous movement of the nonuniform chest phantom.18 The localizations of 4-dimensional CT in the model were carried out with 7 kinds of motion models respectively, to verify the accuracy of the 4D scheme for the 4.0.× MC version of the Multiplan algorithm of the
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CyberKnife. The results indicated that the mean percentages of pixels passing 5%/3 mm of the MC algorithm were more than 95% in the nonuniform medium. These studies have proven that the higher accuracy of the MC algorithm of the Multiplan treatment planning system in the dose calculation in inhomogeneous media with the actual measurement from different versions, different modules, and different verification methods compared with that of RT algorithm. The limitation of the study was that lung tissue phantoms and films were excluded from the point and surface doses verification of treatment plans. Differences between the 2 algorithms would have been more persuasive if doses were verified under the above conditions. The TTV of patients mainly focused on those less than 100 cm3, and there were only 5 samples with the TTV more than 100 cm3. The impact derived from the weight of larger TTV on data fitting must be taken into account, and TTV more than 100 cm3 should be expected in further studies. Better modified formula could be established via identification of more relevant factors of large tumors and data fitting based on TTV. Conclusions A modified formula was established based on the correlations between TTV and PTV D95. Validation of the formula indicated that PTV D95 calculated by this formula was more consistent with that calculated by the MC algorithm compared with the revised RT algorithm from van der Voort van Zyp et al., which could be a reference to those not accessible to the MC algorithm. Conflict of Interest The authors declare no conflict of interest. References 1. Siegel, R.L.; Miller, K.D.; Jemal, A. Cancer statistics, 2016. CA Cancer J. Clin. 66:7–30; 2016. 2. Ha, I.B.; Jeong, B.K.; Jeong, H.; et al. Effect of early chemoradiotherapy in patients with limited stage small cell lung cancer. Radiat. Oncol. J. 31:185–90; 2013. 3. Andratschke, N.; Zimmermann, F.; Boehm, E.; et al. Stereotactic radiotherapy of histologically proven inoperable stage I non-small cell lung cancer: Patterns of failure. Radiother. Oncol. 101:245–9; 2011.
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4. Onishi, H.; Shirato, H.; Nagata, Y.; et al. Stereotactic body radiotherapy (SBRT) for operable stage I non-small-cell lung cancer: Can SBRT be comparable to surgery? Int. J. Radiat. Oncol. Biol. Phys. 81:1352–8; 2011. 5. Xia, T.; Li, H.; Sun, Q.; et al. Promising clinical outcome of stereotactic body radiation therapy for patients with inoperable stage I/II non-small-cell lung cancer. Int. J. Radiat. Oncol. Biol. Phys. 66:117–25; 2006. 6. Park, H.J.; Griffin, R.J.; Hui, S.; et al. Radiation-induced vascular damage in tumors: Implications of vascular damage in ablative hypofractionated radiotherapy (SBRT and SRS). Radiat. Res. 177:311– 27; 2012. 7. Fox, C.; Romeijn, H.E.; Dempsey, J.F. Fast voxel and polygon raytracing algorithms in intensity modulated radiation therapy treatment planning. Med. Phys. 33:1364–71; 2006. 8. Sharma, S.C.; Ott, J.T.; Williams, J.B.; et al. Clinical implications of adopting Monte Carlo treatment planning for CyberKnife. J. Appl. Clin. Med. Phys. 11:3142; 2010. 9. Fippel, M.; Haryanto, F.; Dohm, O.; et al. A virtual photon energy fluence model for Monte Carlo dose calculation. Med. Phys. 30:301– 11; 2003. 10. Vanderstraeten, B.; Reynaert, N.; Paelinck, L.; et al. Accuracy of patient dose calculation for lung IMRT: A comparison of Monte Carlo, convolution/superposition, and pencil beam computations. Med. Phys. 33:3149–58; 2006. 11. Takahashi, W.; Yamashita, H.; Saotome, N.; et al. Evaluation of heterogeneity dose distribution for stereotactic radiotherapy (SRT): Comparison of commercially available Monte Carlo dose calculation with other algorithms. Radiat. Oncol. 7:20; 2012. 12. Wilcox, E.E.; Daskalov, G.M.; Lincoln, H.; et al. Comparison of planned dose distributions calculated by Monte Carlo and Ray-Trace algorithms for the treatment of lung tumors with CyberKnife: A preliminary study in 33 patients. Int. J. Radiat. Oncol. Biol. Phys. 77:277–84; 2009. 13. Miura, H.; Masai, N.; Oh, R.J.; et al. Clinical introduction of Monte Carlo treatment planning for lung stereotactic body radiotherapy. J. Appl. Clin. Med. Phys. 15:38–46; 2014. 14. Kang, K.M.; Jeong, B.K.; Choi, H.S.; et al. Combination effects of tissue heterogeneity and geometric targeting error in stereotactic body radiotherapy for lung cancer using CyberKnife. J. Appl. Clin. Med. Phys. 16:193–204; 2015. 15. Benedict, S.H.; Yenice, K.M.; Followill, D.; et al. Stereotactic body radiation therapy: The report of AAPM Task Group 101. Med. Phys. 37:4078–101; 2010. 16. van der Voort van Zyp, N.C.; Hoogeman, M.S.; van de Water, S.; et al. Clinical introduction of Monte Carlo treatment planning: A different prescription dose for non-small cell lung cancer according to tumor location and size. Radiother. Oncol. 96:55–60; 2010. 17. Xiang, H.F.; Fisher, K.; Russo, G.A.; et al. Measurements of CyberKnife stereotactic body radiation therapy (SBRT) dose to target volumes in a dynamic lung phantom and comparison with Monte Carlo versus ray-tracing dose calculations. Int. J. Radiat. Oncol. Biol. Phys. 81:S868; 2011. 18. Chan, M.K.; Kwong, D.L.; Ng, S.C.; et al. Accuracy and sensitivity of four-dimensional dose calculation to systematic motion variability in stereotatic body radiotherapy (SBRT) for lung cancer. J. Appl. Clin. Med. Phys. 13:303–17; 2012.
Medical Dosimetry j o u r n a l h o m e p a g e : w w w. m e d d o s . o r g
Medical Physics Contribution:
A modified formula for dose calculations of stereotactic ablative body radiotherapy for non–small cell lung cancer Yangsen Cao, M.D.,* Xiaofei Zhu, M.D.,* Yu Zhang, M.D.,† Chunshan Yu, M.D.,* Yongming Liu, M.D.,* Yongjian Sun, M.D.,* Zhitao Dai, M.D.,* Xueling Guo, M.D.,* Xiaoping Ju, M.D.,* and Huojun Zhang, M.D.* *Department of Radiation Oncology, Changhai Hospital Affiliated to Second Military Medical University, Shanghai, China; and † Department of Radiology, Changhai Hospital Affiliated to Second Military Medical University, Shanghai, China
A R T I C L E
I N F O
Article history:
Received 31 May 2017 Received in revised form 22 August 2017 Accepted 25 August 2017 Keywords:
Stereotactic ablative body radiotherapy Ray-tracing Monte Carlo Dose distribution Non–small cell lung cancer
A B S T R A C T
To provide a modified formula consistent with the Monte Carlo (MC) algorithm for dose calculations during stereotactic ablative body radiotherapy for non–small cell lung cancer. Seventy CyberKnife treatment plans were calculated and analyzed by MC and ray-tracing (RT) algorithms, separately. Parameters of treatment plans were compared, and those associated with differences of dose distributions were analyzed to establish a modified formula. Gross tumor volume and tumor tracking volume (TTV) were defined as the evident disease on the sequences of the window width and level of the lung and the mediastinum. Additionally, the formula was validated by another 20 plans. The prescription dose of the 90 patients was 60 Gy/5f. The RT algorithm overestimated the planning target volume (PTV) D95 by an average of 8.59 Gy and the gross tumor volume D99 by an average of 5.84 Gy. The homogeneity index of PTV was underestimated by 0.11 on average, whereas the conformity index and new conformity index was underestimated by 0.05. The RT algorithm overestimated the dose distribution to the spinal cord by 2.23 Gy, the esophagus by 1.96 Gy, the trachea by 1.89 Gy, the left-sided bronchus by 1.77 Gy, the right-sided bronchus by 1.64 Gy, and the heart by 2.16 Gy. The average whole-lung dose volumes of lung tissues and dose volumes of V5 were overestimated by 2.69 Gy and 7.52%, respectively. A power function distribution (R2 = 0.8626) was confirmed between PTV D95 and TTV volumes. PTV D95 calculated by the MC algorithm could be computed easily with TTV and PTV D95 calculated by the RT algorithm based on the formula. The modified equation was more consistent with MC algorithm than with other formula, which could be a reference to those not accessible to the MC algorithm. © 2017 American Association of Medical Dosimetrists.
Yangsen Cao, Xiaofei Zhu, and Yu Zhang contributed equally to this article. Reprint requests to Xiaoping Ju, M.D., Department of Radiation Oncology, Changhai Hospital Affiliated to Second Military Medical University, 168 Changhai Road, Yangpu District, Shanghai 200433, China. E-mail: [email protected] Reprint requests to Huojun Zhang, M.D., Department of Radiation Oncology, Changhai Hospital Affiliated to Second Military Medical University, 168 Changhai Road, Yangpu District, Shanghai 200433, China. E-mail: [email protected] https://doi.org/10.1016/j.meddos.2017.08.008 0958-3947/Copyright © 2017 American Association of Medical Dosimetrists
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Introduction Lung cancer is the leading cause of cancer deaths worldwide.1 For patients with non–small cell lung cancer (NSCLC), surgery is the preferred treatment. However, for inoperable patients, such as those with other diseases or intolerable to surgeries, radiation therapy is the only alternative curative treatment.2 More than 95% of patients with early-stage NSCLC treated with stereotactic ablative body radiotherapy (SABR) achieved good local control, with a median survival time of 34 to 45 months. SABR has already become the standard treatment option for medically inoperable patients with early-stage NSCLC.3-5 The CyberKnife system (Xsight Lung Tracking System) can track tumors located in the lungs when their diameters in all planes are greater than 15 mm. Tumor movement during inhalations and exhalations is traced in real time during the treatment, and simultaneously the treatment beams can be modified automatically, rendering SABR noninvasive for lung cancer with sub-millimeter accuracy. Real-time tracking further reduces the collateral irradiation doses to normal lung tissues and the probability of developing radiation-induced pneumonitis.6 The CyberKnife treatment planning system is equipped with ray-tracing (RT) and Monte Carlo (MC) algorithms.7,8 The dose distributions in non-homogeneous media could be modified by the MC algorithm, which is the most accurate method for calculating dose distributions.9-11 The RT algorithm, meanwhile, overestimated the planning target volume (PTV) doses by an average of ~19% to 21%.8,12-14 Up to May 2016, in mainland China, a total of 21 hospitals have introduced CyberKnife. Among them, the third generation of CyberKnife (G3) was not equipped with the MC algorithm. In addition, only part of the fourth (G4) and fifth generation (VSI) CyberKnife provided the MC algorithm. Therefore, the aim of our study was to establish a modified formula for dose calculation.
Methods and Materials Patient selection Seventy patients with NSCLC who had received CyberKnife between June 2013 and June 2015 were retrospectively analyzed. Patients who met the following criteria were included: a diagnosis of NSCLC confirmed by biopsy specimen; aged 18 to 80 years; with an inoperable condition or refusing surgeries; with 1 peripheral lesion, the diameter of which was between 1.5 cm and 8 cm (8 cm was included); with an expected survival of more than 6 months; with an Eastern Cooperative Oncology Group scale no more than 2; no previous radiotherapy; no multiple lesions; and no distant metastases. Forty-two male and 28 female patients were included in the study, with a median age of 64 years. The study
set consisted of 3 cases of large cell lung cancer, 27 cases of squamous cell carcinoma, and 40 cases of adenocarcinoma. Of the 70 foci, 11 were located within the right upper lobe, 15 within the right middle lobe, 7 within the right lower lobe, 25 within the left upper lobe, and 12 within the left lower lobe. The average diameter of tumors was 3.40 cm, and the median was 3.21 cm. Definition of variables Gross tumor volume (GTV) was delineated as a radiographically evident gross disease acquired from the image sequences of the window width and level of the lung. PTV was the expansion of 5 mm outside the GTV. Tumor tracking volume (TTV) was defined as the contour of the tumor on the sequences of the window width and level of the mediastinum (Fig. 1). PTV D95 and GTV D99 were defined as the dose to 95% volumes of PTV and 99% volumes of GTV, respectively. The conformity index (CI) was calculated with the equation: CI =
Viso (Viso: volumes covered by isodose line; Voverlap
Voverlap: overlap volumes of Viso and PTV). The new conformity index (nCI) was calculated with the following formula:
CI . The homogeneity index (HI) was deterCoverage D mined by the equation: HI = max (RxDose: prescription dose). R xDose The definition of whole-lung V5 was the percentage of the irradiated lung volume receiving a radiation dose exceeding 5 Gy. Esophagus D5cc, trachea D4cc, bronchia D0.5cc, heart D15cc, and spinal cord D0.35cc were the doses to 5 cc of the esophagus, 4 cc of the trachea, 0.5 cc of the bronchia, 15 cc of the heart, and 0.35 cc of the spinal cord, respectively.
nCI =
Treatment planning The patients adopted a supine position, and were scanned with a large-aperture computed tomography (CT) simulator (Brilliance CT Big Bore Oncology; Philips Medical System, The Netherlands) during inhalation. Scanning conditions were as follows: 120 kVp, 400 mAs, 1.5 mm slice thickness without image intervals (helical), and a 0.938 pitch. The scanning range was set from 15 cm outside of the lower boundary of the tumor to 15 cm outside of the upper boundary of the tumor, including the whole lung. After the CT simulation images with and without contrast were imported into the CyberKnife Data Management System, the GTV and organs at risk (OARs) were delineated. The OARs included the left and right lungs, esophagus, trachea, left-sided and rightsided bronchi, pericardium, and spinal cord. Afterward, the spine tracking volume (STV) (Fig. 2) and TTV were contoured. STV and TTV were used for primary image-guided setup and tracing positions of the tumor during treatment
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Fig. 1. (A) The contour of TTV on the sequence of window width and level of the mediastinum. The tumor encompassed by the red line was TTV. (B) The contour of GTV on the sequence of window width and level of the lung. The tumor encompassed by the purple line was GTV, inside which was the gray line that covered TTV.
to establish respiratory tracing models. The outline of STV was completed via STV tools in the contour task. TTV sketches were done manually, directly with the tools of the volumes of interest module in the contour task. Next, the Xsight Lung Tracking mode was adopted in all 70 cases. The doses to OARs were determined after referral to the recommendations of the American Association of Physicists in Medicine Task Group 101.15 The RT algorithm was used first for low resolution during the dose optimization. Next, the dose distribution was calculated based on high resolution by the RT algorithm. The prescription dose was 60 Gy/5f with the isodose line covering at least 95% of the PTV. The maximum dose was defined by the 100% isodose
Fig. 2. STV contains the whole vertebrae, which is used for global patient alignment in treatment position before treatment. The gray line demonstrated by the arrow encompassed the STV.
line. Finally, the plan was then recalculated via the MC algorithm with the same parameters including beam arrangements and monitor units and 1% uncertainty.
Formula establishment and validation Firstly, 70 treatment plans were calculated using both MC and RT algorithm. Variables including PTV D95, GTV D99, CI of PTV, the nCI, the HI, the mean lung dose, whole lung V5, esophagus D5cc, trachea D4cc, bronchia D0.5cc, heart D15cc, and spinal cord D0.35cc were analyzed to clarify the differences between these 2 algorithms. Next, the correlation between potential factors and PTV D95 were evaluated to establish a modified formula. Sharma et al. showed that the difference between the 2 algorithms was mainly determined by the location of the tumor and the proportion of lung tissue that PTV encompassed.8 Besides, it was elucidated that GTV, the density of lung tissue, and the location of the tumor influenced the PTV dose distributions calculated by the 2 algorithms.13 Another study also confirmed that with the increase of the diameters of the GTV and PTV, the differences of the PTV D99, D95, and Dmean in the 2 algorithms would be less significant.16 Moreover, the beam penetration distance in the lung, the size of the collimator, was correlated with the dose differences calculated by the 2 algorithms.12 Therefore, the correlation between the PTV, GTV, TTV, total monitor units, beam numbers, the horizontal (x), and vertical (y) distances from the tumor to the ipsilateral chest wall and PTV D95 were analyzed. The modified formula was then validated by another 20 plans. Those 20 patients (validation group) with lung cancer were treated with CyberKnife from June 2015 to March 2016.
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The entry criteria of the validation group were the same as patient selection criteria for proposal of the formula. When the prescription dose calculated by the RT algorithm was 60 Gy, the prescription doses to the tumor in the revised RT algorithm proposed in van der Voort van Zyp et al.16 (revised RT algorithm) were as follows: 48 Gy (tumor diameter <3 cm), 51 Gy (tumor diameter was 3-5 cm), and 54 Gy (tumor diameter>5 cm). The MC algorithm was applied as the standard to compare doses calculated by the RT algorithm, revised RT algorithm, and the modified formula in our study.
Data analysis Statistical Analysis System 9.4 (SAS Institute, Cary, NC) was used for all data processing, with exception to the scatter plots (TTV volumes vs PTV D95), which were modeled within Microsoft Office Excel 2013 (Microsoft Corporation, Santa Rosa, CA). Paired differences were tested for normality. Subsequently, the paired t test (t, P) and Wilcoxon signed rank test (S, P) were used for normally and abnormally distributed data, respectively. A P value <0.05 was considered statistically significant. The correlation analysis was carried out using the generalized additive model. The establishment of the formula was dependent on the trend lines calculated by the quadratic polynomial, cubic polynomial, the quartic polynomial, the exponential function, the logarithmic function, and the power function, after which the R2 values were evaluated.
Results Comparison between dose distributions calculated by the RT and MC algorithm The PTV D95 and GTV D99 were significantly reduced (p < 0.0001), whereas the CI, nCI, and HI increased calculated by the MC algorithm (p < 0.0001) when compared with those of the RT algorithm (Table 1). The average whole-lung dose volume of lung tissues, whole-lung V5 (the percentage of the irradiated lung volume receiving a radiation dose exceeding 5 Gy), the dose volume of the spinal cord, the esophagus, the trachea, the leftsided and the right-sided bronchi, and the heart were all significantly lower when calculated by the MC algorithm (Table 2) (p < 0.0001).
Potential factors associated with differences of dose distributions There was no linear correlation between those 7 parameters (PTV, GTV, TTV, total monitor units, number of beams, and the horizontal, and vertical distance from the ipsilateral chest wall to the tumor) and the PTV D95 (R2 <0.5). However, the deviation analysis of smoothing models showed that only the TTV affected PTV D95 (χ2 = 156.2710; p < 0.0001) (Table 3), when a generalized additive model was applied
Table 1 Dose differences in target volumes calculated by RT and MC algorithms (n = 70) Structure
Parameter
RT
MC
GTV PTV
D99 (Gy) D95 (Gy) CI nCI HI
75.68 ± 4.50 (58.42-86.77) 60.00 ± 0.00 (60.00-60.00) 1.16 ± 0.08 (1.04-1.29) 1.21 ± 0.08 (1.09-1.35) 1.44 ± 0.07 (1.23-1.59)
69.84 ± 4.47 (53.66-79.75) 51.41 ± 3.60 (42.19-57.83) 1.21 ± 0.10 (1.07-1.54) 1.26 ± 0.11 (1.11-1.61) 1.55 ± 0.10 (1.28-1.82)
GTV, gross tumor volume; PTV, planning target volume; RT, ray-tracing; MC, Monte Carlo. All data were presented with the mean ± SD. The values in the parentheses represent the ranges.
Table 2 Differences between the doses to OARs calculated by RT and MC algorithms (n = 70) Structure
Parameter
RT
MC
Lung
Dmean (Gy) V5 (%) D0.35cc (Gy) D5cc (Gy) D4cc (Gy) D0.5cc (Gy) D0.5cc (Gy) D15cc (Gy)
7.89 ± 3.31 (2.99-16.61) 28.43 ± 12.44 (7.31-77.50) 3.73 ± 1.37 (0.95-7.21) 4.41 ± 2.17 (1.39-13.82) 4.50 ± 2.40 (1.38-14.80) 4.56 ± 2.52 (1.41-12.10) 4.65 ± 2.74 (1.21-12.50) 4.35 ± 2.41 (0.70-12.60)
5.20 ± 2.34 (1.38-12.37) 20.91 ± 8.30 (5.13-46.75) 1.50 ± 0.83 (0.23-3.89) 2.45 ± 1.83 (0.43-11.58) 2.61 ± 2.31 (0.05-11.28) 2.79 ± 2.40 (0.18-10.78) 3.01 ± 2.52 (0.20-10.98) 2.19 ± 1.82 (0.04-10.45)
Spinal cord Esophagus Trachea Left bronchus Right bronchus Heart
All data were presented the mean ± SD. The values in the parentheses represented the ranges.
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Table 3 Smoothing model analysis (analysis of deviance) (n = 70) Source
DF
Sum of Square
χ2
P value
Spline (PTV volume) Spline (GTV volume) Spline (TTV volume) Spline (Total MUs) Spline (Beams) Spline (X) Spline (Y)
0.000008 0.000006 9.675710 0.000011 0.000006 0.000052 0.000046
. . 295.49808 0.0000083 . 0.0000846 0.0000447
. . 156.2710 0.0000 . 0.0000 0.0000
. . <0.0001 . . . .
DF, degree of freedom; χ2, chi-square.
for a nonlinear regression analysis, using generalized crossvalidation to select smoothing parameters. Scatter plots of TTV volumes vs PTV D95 were shown (Fig. 3). Trend lines were drawn and calculated by quadratic polynomial, cubic polynomial, quartic polynomial, exponential, logarithmic function, and power function models. The analysis indicated that R2 value of each model was as follows: 0.6532 (the quadratic polynomial), 0.7329 (the cubic polynomial), 0.7945 (the quartic polynomial), 0.3970 (the exponential function), 0.8487 (logarithmic function), and 0.8626 (power function). Among them, power function fitted the best. In our study, PTV D95_RT was 60 Gy. Therefore, the modified formula was as follows:
PTV D95 _MC = 45.395 × TTV 0.0448
Regarding different PTV D95_RT, the modified formula was amended as follows:
PTV D95 _MC = 0.7566 × TTV 0.0448 × PTV D95 _RT (PTV D95_MC: dose calculated by MC algorithm; PTV D95_RT: dose calculated by RT algorithm) (Fig. 3)
Validation of the modified formula The comparison of the PTV D95 calculated by the RT algorithm, revised RT algorithm, and formula in this study was performed based on the PTV D95 derived from the MC algorithm (Table 4). The dose error of the 2 algorithms was 8.52 Gy before modification (t = 10.89, p < 0.0001). The dose errors calculated by the revised RT algorithm and modified
Fig. 3. The data fitting of TTV volume and PTV D95 calculated by power function.
Table 4 Different PTV D95 calculated by different algorithms (n = 20) Structure
PTV
Parameter
D95 (Gy)
MC
51.48 ± 3.50 (45.26-56.12)
RT Pre-modification
Revised RT algorithm*
Modified formula of this study
60.00 ± 0.00 (60.00-60.00)
49.80 ± 2.26 (48.00-54.00)
50.50 ± 3.57 (43.53-56.76)
All data were given in mean ± SD. The values in the parentheses represented the ranges for the corresponding quantities. * Revised RT algorithm was introduced from van der Voort van Zyp NC et al.16
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Fig. 4. PTV D95 of 20 cases calculated by the RT algorithm, MC algorithm, revised RT algorithm, and modified model.
formula in our study were −1.68 Gy (t = −3.58, p = 0.002) and −0.98 Gy (t = −2.86, p = 0.010), respectively. Regarding consistency of results calculated by the MC algorithm, the revised RT algorithm and the modified formula in this study were evaluated by intraclass correlation coefficient. The value of intraclass correlation coefficient between the MC algorithm and the modified formula, the MC algorithm and the revised RT algorithm was 0.903 (0.826 to 0.947) and 0.757 (0.590 to 0.862), respectively. Therefore, the modified formula in our study was more favorable than the revised RT algorithm in van der Voort van Zyp et al. (Fig. 4). Discussion Although it was proven that there were differences between dose distributions calculated by the RT and MC algorithm, especially for heterogeneous tissues, relevant factors contributing to the difference remained unclear. Only van der Voort van Zyp et al. have proposed a 3-stage simple modified model, whereas the remaining studies raised only possible candidate factors correlated with the dose differences, but failed to create a modified formula.16 In our study, potential factors were identified to form a modified formula for conversion of PTV D95 calculated by the RT algorithm. Computed with the formula, the subsequent dose distributions could be consistent with those directly calculated by the MC algorithm. Besides, only TTV correlated with PTV D95 after introduction and analysis of those parameters. This may be owing to fewer differences between dose distributions calculated by the RT and MC algorithm attributable to fewer low density lung tissues that target volumes encompassed. As a result, TTV, with the least proportion of lung tissues compared with GTV and PTV, could be the best variable in the formula for modification of dose distributions calculated by the RT algorithm.
Because of sparse data regarding larger TTV (more than 100 cm3), TTV of smaller sizes had more weight during formula fitting. Nevertheless, during the establishment of the formula, a high-order polynomial may result in worse goodness of fit when the weight of larger TTV equaled to that of smaller TTV compared with other functions. Therefore, quintic and sextic polynomial was precluded for formula fitting. The study included 70 patients with NSCLC. The sample size was therefore large, and the results were convincing. Related factors of tumor targets and normal lung tissues were compared. Additionally, the volumes of doses to the spinal cord, esophagus, trachea, left-sided and right-sided bronchi, and heart calculated by 2 algorithms were analyzed when dose differences of 2 algorithms were studied, ensuring that the doses delivered to these OARs complied with the limiting amount recommended by the American Association of Physicists in Medicine Task Group 101. Sharma et al. reported the verification of the accuracy of the MC algorithm of the 2.1.0 Multiplan treatment planning system with an inhomogeneous phantom.8 The mean percentages of pixels passing of MC were 96% ~ 100%. Additionally, Computerized Imaging Reference Systems’ nonuniform chest phantom, EBT2 film, and Pro FilmQA were used to verify the accuracy of the MC algorithm in another study.17 The results showed that 98.4%~100% of the MC algorithm calculated points pass a γ (3%, 2 mm) criteria, whereas only 27.1%~49.7% of the RT algorithm calculated points pass the γ (3%, 2 mm) criteria. Mark et al. used Computerized Imaging Reference Systems’ programmable synchronous movement of the nonuniform chest phantom.18 The localizations of 4-dimensional CT in the model were carried out with 7 kinds of motion models respectively, to verify the accuracy of the 4D scheme for the 4.0.× MC version of the Multiplan algorithm of the
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CyberKnife. The results indicated that the mean percentages of pixels passing 5%/3 mm of the MC algorithm were more than 95% in the nonuniform medium. These studies have proven that the higher accuracy of the MC algorithm of the Multiplan treatment planning system in the dose calculation in inhomogeneous media with the actual measurement from different versions, different modules, and different verification methods compared with that of RT algorithm. The limitation of the study was that lung tissue phantoms and films were excluded from the point and surface doses verification of treatment plans. Differences between the 2 algorithms would have been more persuasive if doses were verified under the above conditions. The TTV of patients mainly focused on those less than 100 cm3, and there were only 5 samples with the TTV more than 100 cm3. The impact derived from the weight of larger TTV on data fitting must be taken into account, and TTV more than 100 cm3 should be expected in further studies. Better modified formula could be established via identification of more relevant factors of large tumors and data fitting based on TTV. Conclusions A modified formula was established based on the correlations between TTV and PTV D95. Validation of the formula indicated that PTV D95 calculated by this formula was more consistent with that calculated by the MC algorithm compared with the revised RT algorithm from van der Voort van Zyp et al., which could be a reference to those not accessible to the MC algorithm. Conflict of Interest The authors declare no conflict of interest. References 1. Siegel, R.L.; Miller, K.D.; Jemal, A. Cancer statistics, 2016. CA Cancer J. Clin. 66:7–30; 2016. 2. Ha, I.B.; Jeong, B.K.; Jeong, H.; et al. Effect of early chemoradiotherapy in patients with limited stage small cell lung cancer. Radiat. Oncol. J. 31:185–90; 2013. 3. Andratschke, N.; Zimmermann, F.; Boehm, E.; et al. Stereotactic radiotherapy of histologically proven inoperable stage I non-small cell lung cancer: Patterns of failure. Radiother. Oncol. 101:245–9; 2011.
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