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**Purpose**
: To investigate the feasibility of applying ANOVA newly proposed by Yukinori to verify the setup errors, PTV (Planning Target Volume) margins, DVH for lung cancer with SBRT. **Methods**: 20 patients receiving SBRT to 50 Gy in 5 fractions with a Varian iX linear acceleration were selected. Each patient was scanned with kV-CBCT before the daily treatment to verify the setup position. Two other error calculation methods raised by Van Herk and Remeijer were also compared to discover the statistical difference in systematic errors (Σ), random errors (σ), PTV margins and DVH. **Results:** Utilizing two PTV margin calculation formulas (Stroom, Van Herk), PTV calculated by Yukinori method in three directions were (5.89 and 3.95), (5.54 and 3.55), (3.24 and 0.78) mm; Van Herk method were (6.10 and 4.25), (5.73 and 3.83), (3.51 and 1.13) mm; Remeijer method were (6.39 and 4.57), (5.98 and 4.10), (3.69 and 1.33) mm. The volumes of PTV using Yukinori method were significantly smaller (P < 0.05) than Van Herk method and Remeijer method. However, dosimetric indices of PTV (D98, D50, D2) and for OARs (Mean Dose, V20, V5) had no significant difference (P > 0.05) among three methods.** Conclusions**: In lung SBRT treatment, due to fraction reduction and high level of dose per fraction, ANOVA was able to offset the effect of random factors in systematic errors, reducing the PTV margins and volumes. However, no distinct dose distribution improvement was founded in target volume and organs at risk.

Compared to Intensity Modulated Radiation Therapy (IMRT), Stereotactic Body Radiation Therapy (SBRT) is characterized by potent ablative doses and highly conformal dose distributions delivered in a few fractions with a short overall treatment time [

In order to reduce toxicity of normal tissues, the planning target volume (PTV) should be minimized by keeping margins for setup and inter-fractional position errors as low as possible. Hence, calculation of the setup errors and PTV margins plays an important role in Stereotactic Body Radiation Therapy (SBRT), especially in lung tumor treatment.

Van Herk et al. and Remeijer et al. had introduced various methods to calculate systematic and random errors in radiation therapy [

Variance component analysis has been in use since the 1910s. Searle [

In this study, we focused on the verification of variance component analysis raised by Yukinori in Lung Stereotactic Body Radiation Therapy (SBRT) with immobilization devices [

Twenty patients (12 men, 8 women) receiving lung SBRT between February 2013 and August 2016 at Zhongnan hospital were retrospectively analyzed in this study. Patients were excluded if previous chemo- or thoracic radiotherapy had been administered. In these cases, sixteen targets were primary early-stage lung tumors, and four were metastases of other solid tumors. All patients were treated with prescription dose (50 Gy) in five fractions every other day. In all, the scale of the treatment involved 100 fractions. Patients’ ages ranged from 47 to 70 years with average age of 52.5 years.

Patients were fixed using R624-SCF immobilization devices [

All patients were treated on the iX linear accelerator (Varian Medical Systems, Palo Alto, CA). Prior to daily treatment, kV-CBCT was used to verify the position of target area. Analyzed shifts were applied for setup correction and CBCT was repeated. If a large shift (>3 mm) occurred in any direction, the treatment would not start until an additional CBCT was employed for verification after localization. The criterion for image registration between the CT simulation image and CBCT image was soft tissue registration. Due to the size of lung tumor and organ motion in the lung, the rigid registration is not ultilized here with the assistance of immobilization equipment. The setup errors of each patient in three directions were obtained from the variation between CT and CBCT.

1) Yukinori method

Yukinori introduced variance component analysis with the calculation methods of standard deviation (SD) of systematic and random errors.

2) Van Herk method

Van Herk proposed the method of calculating standard deviation of systematic and random errors. The standard deviation (SD) of systematic errors were represented by standard deviation (SD) of mean interfractional errors per patient. The standard deviation (SD) of random errors was represented by standard deviation (SD) of root mean square of interfractional errors per patient.

3) Remeijer method

The method of calculating systematic and random errors introduced by Remeijer was:

σ = 1 a ( n − 1 ) ∑ i = 1 a ∑ j = 1 n ( x i j − m i ) 2 (1)

∑ = 1 n ( a − 1 ) ∑ i = 1 a n ( m i − M ) 2 (2)

Note: a: number of patients; n: number of measurements per patient; x_{ij}: a measured value in fraction j for patient i; M: overall mean of the dataset; m_{i}: individual mean in patient i; σ: standard deviation of random error; ∑: standard deviation of systematic error

To discover more general principle in PTV differences, two margin recipes of Stroom and Van Herk were used to calculate the PTV margin form the CTV. ∑ is the standard deviation of total systematic errors and σ is the standard deviation of total random errors. In this work, we consider the interfractional error is the main source of the systematic and random errors.

Source of Variation | DF | SS | MS | EMS |
---|---|---|---|---|

Patient | a − 1 | S S A = ∑ i = 1 a n ( m i − M ) 2 | M S A = S S A a − 1 | n ∑ 2 + σ 2 |

Within Patient | a (n − 1) | S S E = ∑ i a ∑ j = 1 n n ( x i j − m i ) 2 | M S E = S S E a ( n − 1 ) | σ 2 |

Total | an − 1 | S S T = ∑ i a ∑ j = 1 n n ( x i j − M ) 2 | M S T = S S T a n − 1 |

Note: DF = degree of freedom; SS = sum of squares; MS = mean square; EMS = expected mean square; a = number of patients; n = number of measurements per patient; x_{ij} = a measured value in fraction j for patient i; M = overall mean of the dataset; m_{i} = individual mean in patient i; σ^{2} = random error variance; ∑^{2} = systematic error variance. Systematic error (∑): Within 95% confidence interval, ∑^{2} = (MS_{A} − MS_{E})/n, Random error (σ): Within 95% confidence interval, σ^{2} = MS_{E}.

Patient1 | Patient 2 | Patient 3 | Patient 4 | ||
---|---|---|---|---|---|

Day 1 | 2 | 4 | 1 | 3 | |

Day2 | 1 | −2 | −1 | −3 | |

Day 3 | 1 | 2 | 2 | −2 | |

Day 4 | 1 | 0 | 2 | 1 | Mean = M = 0.75 |

Mean | 1.25 | 1 | 1 | −0.25 | SD = ∑ = 0.68 |

SD | 0.50 | 2.58 | 1.41 | 2.75 | RMS = σ = 2.03 |

Note: Quote from VanHerk [

So Stroom [

Stroom formula = 2 ∑ + 0.7 σ (3)

Van Herk [

Van Herk formula = 2.5 ∑ + 0.7 σ − 3mm (4)

In the procedure of dose calculation in Lung Stereotactic Body Radiation therapy, two groups (group 1 and group 2) were divided by Equation (3), Equation (4), respectively. In each group, the dose analysis and comparison among Yukinori, Remeijer and Van Herk were all achieved. However, all PTV margins obtained had to been adjusted before dose recalculation due to the numerical precision of Varian Eclipse treatment planning system. Thus, in group 1, the actual PTV margins in three directions were Yukinori (6 mm, 6 mm, 3 mm), Van Herk (6 mm, 6 mm, 4 mm), Remeijer (6 mm, 6 mm, 4 mm), and in group 2, the PTV margins were Yukinori (4 mm, 4 mm, 1mm), Van Herk (4 mm, 4 mm, 1 mm), Remeijer (5 mm, 4 mm, 1 mm). In group 1 On account of the same numerical precision of Van Herk and Remeijer, we only compare Yukinori method with Remeijer method. In group 2 Yukinori method share the same precision with Van Herk so the comparison between Yukinori method and Remeijer is valid. Four treatment plans (plan441, plan541, plan663, plan664) were generated in the Eclipse system with the progressive resolution optimizer 3. Dose distributions were calculated using the anisotropic analytic algorithm (AAA, ver.11.0.31, Varian Medical Systems, Palo Alto, CA) with a dose calculation grid of 2 mm. R programming language (R Development Core Team 2010) was used for all dose parameters analysis.

20 patients’ setup errors were all analyzed with IBM SPSS 19.0. The distributions of interfractional errors including mean errors and standard deviation in lateral (X), longitudinal (Y), vertical (Z) dimensions are shown in

Systematic Error (∑) | Random Error (σ) | |||
---|---|---|---|---|

Mean | SD | Mean | SD | |

Lateral (x-axis) [mm] | 1.11 | 2.11 | 1.82 | 2.39 |

Longitudinal (y-axis) [mm] | 0.28 | 2.02 | 1.66 | 2.14 |

Vertical (z-axis) [mm] | −0.65 | 1.06 | 1.25 | 1.61 |

However, variance component analysis can only provide the whole discrepancy of errors in three directions instead of pairwise comparison. In this work, the Dunnett test were used to verify the difference between certain two directions.

95%CI | ||||||
---|---|---|---|---|---|---|

(I) group | (J) group | Mean Difference (I-J) | Standard Error | Significance | Lower Limit | Upper Limit |

x-axis | y-axis | 0.083 | 0.431 | 0.157 | −0.021 | 0.187 |

z-axis | 0.176 | 0.369 | <0.05 | 0.087 | 0.265 | |

y-axis | x-axis | −0.083 | 0.431 | 0.157 | −0.187 | 0.021 |

z-axis | 0.093 | 0.349 | 0.025 | 0.009 | 0.177 | |

z-axis | x-axis | −0.176 | 0.369 | <0.05 | −0.265 | −0.087 |

y-axis | −0.093 | 0.349 | 0.025 | −0.177 | −0.009 |

SD | Yukinori | Van Herk | ||
---|---|---|---|---|

∑ | σ | ∑ | σ | |

Lateral (x-axis) [mm] | 2.11 | 2.39 | 2.30 | 2.14 |

Longitudinal (y-axis) [mm] | 2.02 | 2.14 | 2.19 | 1.93 |

Vertical (z-axis) [mm] | 1.06 | 1.61 | 1.25 | 1.43 |

Yukinori | Van Herk | Rate of change | ||||
---|---|---|---|---|---|---|

PTV Margins | (3) | (4) | (3) | (4) | (3) | (4) |

Lateral (x-axis) [mm] | 5.89 | 3.95 | 6.10 | 4.25 | 3.44% | 7.06% |

Longitudinal (y-axis) [mm] | 5.54 | 3.55 | 5.73 | 3.83 | 3.32% | 7.31% |

Vertical (z-axis) [mm] | 3.25 | 0.78 | 3.51 | 1.13 | 7.41% | 30.97% |

Note: (3), (4) is Equation (3), Equation (4) respectively; Rate of change = (Van Herk − Yukinori)/Van Herk.

The application of Remeijer method on errors in Lung SBRT was also achieved and comparisons with Yukinori method are shown in

The results in

SD | Yukinori | Remeijer | ||
---|---|---|---|---|

∑ | σ | ∑ | σ | |

Lateral (x-axis) [mm] | 2.11 | 2.39 | 2.36 | 2.39 |

Longitudinal (y-axis) [mm] | 2.02 | 2.14 | 2.24 | 2.14 |

Vertical (z-axis) [mm] | 1.06 | 1.61 | 1.28 | 1.61 |

Yukinori | Remeijer | Rate of change | ||||
---|---|---|---|---|---|---|

PTV Margins | (3) | (4) | (3) | (4) | (3) | (4) |

Lateral (x-axis) [mm] | 5.89 | 3.95 | 6.39 | 4.57 | 7.82% | 13.57% |

Longitudinal (y-axis) [mm] | 5.54 | 3.55 | 5.98 | 4.10 | 7.36% | 13.41% |

Vertical (z-axis) [mm] | 3.25 | 0.78 | 3.69 | 1.33 | 11.92% | 41.35% |

Yukinori method in three directions were 3.95 mm, 3.55 mm, 0.78 mm, respectively, and PTV margins by Remeijer were 4.57 mm, 4.10 mm, 1.33 mm, respectively. The rate of change of PTV margins with Equation (4) in vertical direction is about 41.35%, the largest among three directions while with Equation (3), the rate of change of PTV margins is also largest in vertical direction, and the reduction rate is nearly 11.92%. Generally, Yukinori method indeed reduced the PTV margins no matter which formula was selected.

^{3} and 17.66 ± 8.69 cm^{3}, which shows significant difference (P < 0.001) between them. The mean volume of PTV 663 and PTV664 are 23.78 ± 3.19 cm^{3} and 25.19 ± 4.33 cm^{3}, which shows significant difference (P < 0.001) between them. This analysis indicates a meaningful decrease of PTV volume using Yukinori method compared to Van Herk method and Remeijer Method. The boxplot (

During Lung SBRT procedure, due to the influence of setup uncertainty, breathing, heart beat and organ geometric transformation, location deviation of tumor and normal structure, it tend to cause the insufficient dose distribution in target area and excessive dose distribution in normal tissues, which aggravated radiation damage. To improve tumor local control, PTV margins should be calculated as accurate as possible for higher dose gradient, especially in Lung SBRT.

According to AAPM-TG83 report, lung dose parameters (mean dose, V5, V20) are recorded.

PTV | Number |
---|---|

PTV Volume < 10 cm^{3} | 2 |

PTV Volume > 100 cm^{3} | 1 |

PTV Volume (10 - 50 cm^{3}) | 17 |

PTV441 Mean Volume (cm^{3}) | 16.79 ± 8.35 |

PTV541Mean Volume (cm^{3}) | 17.66 ± 8.69 |

t (Z) | −5.03 |

P | 0.001 |

PTV | Number |
---|---|

PTV Volume < 10 cm^{3} | 2 |

PTV Volume > 100 cm^{3} | 1 |

PTV Volume (10 − 50 cm^{3}) | 17 |

PTV663 Mean Volume (cm^{3}) | 23.78 ± 3.19 |

PTV664Mean Volume (cm^{3}) | 25.19 ± 4.33 |

t (Z) | −4.49 |

P | 0.001 |

Lung | PLAN441 | PLAN541 | t (z) | P |
---|---|---|---|---|

AVE (Gy) | 4.75 ± 1.35 | 4.85 ± 1.45 | −1.61 | 0.129^{ } |

V5 (%) | 23.22 ± 7.95 | 23.57 ± 8.30 | −1.17 | 0.261^{ } |

V20 (%) | 6.71 ± 2.19 | 6.92 ± 2.34 | −2.01 | 0.063^{ } |

Lung | PLAN663 | PLAN664 | t (z) | P |
---|---|---|---|---|

AVE (Gy) | 5.02 ± 1.44 | 5.07 ± 1.45 | −1.30 | 0.212^{ } |

V5 (%) | 24.17 ± 8.12 | 24.70 ± 8.54 | −1.66 | 0.117^{ } |

V20 (%) | 7.23 ± 2.31 | 7.32 ± 2.33 | −1.30 | 0.214^{ } |

Gy, 23.22% and 6.71% respectively and in plan541, mean dose, V5 and V20 were 4.85 Gy, 23.57% and 6.92% respectively. There is no significant difference (P > 0.05) between these two plans. In plan663 of group 2, mean dose, V5 and V20 are 5.02 Gy, 24.17% and 7.23% respectively and in plan664, mean dose, V5 and V20 are 5.07 Gy, 24.70% and 7.32% respectively. The difference of two plans is also not significant (P > 0.05).

PTV parameters D98, D50 and D2 are also recorded according to AAPM-TG83 report.

Variance component analysis (ANOVA) in radiotherapy introduced by Yukinori is not popular mainly because the validity and effectiveness still require to be verified in large amount of experiments systematically. The purpose of this paper is to verify effectiveness of this methodology on the Lung SBRT, which belongs to hypofractionated radiotherapy referred in the previous paper. We studied the variance component analysis in radiotherapy to explore its effect on PTV margins and cumulative dose distribution in lung SBRT compared with other two conventional methods raised by Van Herk and Remeijer.

However, recent work has demonstrated the limitations of the Van Herk formula for setup errors calculation. Based on the method raised by Van Herk, Gordon [

Tumor | PLAN441 | PLAN541 | P |
---|---|---|---|

D98 (Gy) | 49.53 ± 0.48 | 49.48 ± 0.53 | 0.359^{ } |

D50 (Gy) | 51.71 ± 1.56 | 51.77 ± 1.61 | 0.148 |

D2 (Gy) | 53.61 ± 3.13 | 53.70 ± 3.23 | 0.135^{ } |

Tumor | PLAN663 | PLAN664 | P |
---|---|---|---|

D98 (Gy) | 49.30 ± 0.51 | 49.09 ± 0.96 | 0.139^{ } |

D50 (Gy) | 52.45 ± 2.07 | 52.69 ± 2.98 | 0.520 |

D2 (Gy) | 54.90 ± 5.06 | 55.00 ± 4.39 | 0.836^{ } |

random errors, especially for SBRT. This method introduced effective systematic errors, the purpose of which is to add an offset to the isocenter, and effective

random errors to fully explain correlation between average deviation for isocenter location and each fraction of treatment, and Equation (5) gave the detailed formula:

∑ e f f 2 = ∑ 2 + σ 2 n , σ e f f 2 = σ 2 ( 1 − 1 n ) (5)

Yukinori also argued that in Remeijer method, the systematic errors would be overestimated if the number of fractions is limited. In hypofractionated schedules [

∑ new = ∑ old 2 − σ old 2 n , σ new = σ old (6)

∑ new , σ new , ∑ old , σ old are standard deviation of systematic and random errors in Yukinori and Remeijer method respectively.

Considering the rectification of degrees of freedom [

Actually, in Lung Stereotactic Body Radiation Therapy (SBRT), the accuracy request for setup errors and PTV margins is more strict so decreased PTV margins calculated with Yukinori method indeed may cut down the dose in normal tissue compared to the Van Herk and Remeijer Method. However, the findings on dose distribution in Lung and PTV shows no significant difference (P > 0.05), which indicates the similarity of the Yukinori method and Remeijer method in dose calculation. One possible reason is that the comparison of PTV margins seems to be insufficient without statistical meaning and it still need more samples to do further verification. Also, the statistical method like Bootstrap with no parameters [

In this work, we ignored the intrafrational errors like random motion of tumor and patients on account of the lack of 4D CT simulation and 4D CBCT. However, in the fractional treatment, the image registration method is the soft tissue method (tumor), which can to some extent fully extract a comprehensive effect of setup errors and error of tumor random motion. Some papers have proposed that the CTV-PTV margin formula is not linear because the normal tissues around tumor are inhomogeneous in the actual treatment while the normal tissues in lung around tumor are nearly homogeneous. This research only concentrated on the verification of the new methodology of variance component analysis and we merely selected the most popular CTV-PTV formula raised by Stroom. Although, Van Herk’s CTV-PTV margin formula was mainly used in prostate tumor, the ultilization of it provides a reference to better understand the effectiveness of variance component analysis in Lung SBRT.

In future work, multi-factors variance component analysis will be applied to the calculation of the interfractional setup uncertainties and PTV margins in Stereotactic Body Radiation Therapy (SBRT), to find out whether there exists other factors influencing cumulative dose distribution due to the setup uncertainties and PTV margins. Precision of PTV margins may be dependent on the variation of Treatment Planning System. The examination on brain, liver or other organs should be implemented as well to obtain a more general conclusion. Except for these observations, in this work, we did not find strong relationship between variance component analysis and dose cumulative distribution but expanding sample size is probably a good choice to get better results.

This study evaluated the setup uncertainties of 20 patients treated with Lung SBRT and applied variance component analysis proposed by Yukinori to calculate CTV-PTV margins and corresponding dose distribution. The Yukinori method showed a distinguished effect on the reduction of PTV volumes compared with other two methods (Van Herk and Remeijer). However, with the reduction of PTV margins, there is no evidence showing an outstanding improvement and optimization of dose distribution on PTV and OARs using Yukinori method. Thus, the methodology of variance component analysis, as a novel approach to Stereotactic Body Radiation Therapy, still requires more clinical verification.

The authors declare no conflicts of interest regarding the publication of this paper.

Huang, X.T., Zhang, J., Xie, C.H., Zhou, Y.F. and Quan, H. (2018) Application of Variance Component Analysis (ANOVA) in Setup Errors and PTV Margins for Lung Cancer with Stereotactic Body Radiation Therapy (SBRT). International Journal of Medical Physics, Clinical Engineering and Radiation Oncology, 7, 522-538. https://doi.org/10.4236/ijmpcero.2018.74044