# Simulation of dosimetry impact of 4DCT uncertainty in 4D dose calculation for lung SBRT

- 209 Downloads

**Part of the following topical collections:**

## Abstract

### Background

Due to the heterogeneity of patient’s individual respiratory motion pattern in lung stereotactic body radiotherapy (SBRT), treatment planning dose assessment using a traditional four-dimensional computed tomography (4DCT_traditional) images based on a uniform breathing curve may not represent the true treatment dose delivered to the patient. The purpose of this study was to evaluate the accumulated dose discrepancy between based on the 4DCT_traditional and true 4DCT (4DCT_true) that incorporated with the patient’s real entire breathing motion. The study also explored a novel 4D robust planning strategy to compensate for such heterogeneity respiratory motion uncertainties.

### Methods

Simulated and measured patient specific breathing curves were used to generate 4D targets motion CT images. Volumetric-modulated arc therapy (VMAT) was planned using two arcs. Accumulated dose was obtained by recalculating the plan dose on each individual phase image and then deformed the dose from each phase image to the reference image. The “4 D dose” (*D*^{4D}) and “true dose” (D^{true}) were the accumulated dose based on the 4DCT_traditional and 4DCT_true respectively. The average worse case dose discrepancy (\( \overline{\Delta D} \)) between *D*^{4D} and D^{true} in all treatment fraction was calculated to evaluate dosimetric /planning parameters and correlate them with the heterogeneity of respiratory-induced motion patterns. A novel 4D robust optimization strategy for VMAT (4D Ro-VMAT) based on the probability density function(pdf) of breathing curve was proposed to improve the target coverage in the presence of heterogeneity respiratory motion. The data were assessed with a paired t-tests.

### Results

With increasing breathing amplitude from 5 to 20 mm, target \( \overline{\Delta {D}_{99}} \), \( \overline{\Delta {D}_{95}} \) increased from 1.59,1.39 to 10.15%,8.66% respectively. When the standard deviation of breathing amplitude increased from 15 to 35% of the mean amplitude, \( \overline{\Delta {D}_{99}} \), \( \overline{\Delta {D}_{95}} \) increased from 4.06,3.48 to 10.25%,6.63% respectively. The 4D Ro-VMAT plan significantly improve the target dose compared to VMAT plan.

### Conclusion

When the breathing curve amplitude is more than 10 mm and standard deviation of amplitude is higher than 25% of mean amplitude, special care is needed to choose an appropriated dose accumulation approach to evaluate lung SBRT plan target coverage robustness. The proposed 4D Ro_VMAT strategy based on the pdf of patient specific breathing curve could effectively compensate such uncertainties.

## Abbreviations

- \( \overline{\Delta D} \)
The average worse case dose discrepancy

- 4D Ro-VMAT
4D robust optimization strategy for VMAT

- 4DCT_traditional
Traditional four-dimensional computed tomography

- 4DCT_true
True 4DCT

- AVG CT
Average CT

- CBCT
Cone beam CT

- CC
Collapsed cone

*D*^{4 D}4D dose

- D
^{true} True dose

- DVH
Dose volume histogram

*D*_{x}The largest dose level percentage covering

*x*% volume of the target- GTV
Gross target volume

- IMPT
Intensity-modulated proton therapy

- IMRT
Intensity modulated radiotherapy

- ITV
Internal target volume

- MLC
Multi-Leaf Collimator

- PA
Posterior anterior

Probability density function

- PTV
Planning target volume

- RL
Right left

- SBRT
Stereotactic body radiotherapy

- SI
Superior inferior

- TPS
Treatment Planning System

- VMAT
Volumetric-modulated arc therapy

## Background

Stereotactic body radiotherapy (SBRT) has demonstrated a significant improvement in local tumor control and overall survival of early-stage lung cancer patients [1, 2, 3, 4]. However, dose uncertainty may happen due to the substantial respiratory-induced geometric changes. Currently, the most popular method to compensate for such respiratory-induced target motion in treatment planning is to use four-dimensional computed tomography (4DCT) images with an internal target volume (ITV) design [5]. The patient is commonly in a free-breathing status during the 4DCT simulation. However, the tumor positions manifested on 4DCT images are most likely within a single breathing cycle which is assuming a uniform breathing pattern [6, 7].

However, for lung cancer patients, breathing curve is very likely irregular, the tumor positions shown on the 4DCT images used for treatment planning under estimated the actual tumor motion positions [8, 9]. The traditional 4DCT(4DCT_tradiational) is reconstructed by using 10 phase images to represent a periodic motion which may come from any single breathing cycle and may not fully represent true tumor position and motion [10, 11]. Such uncertainties will introduce variations of the dose in the target particularly in the lung patient with irregular breathing curve/who cannot breathe homogeneously.

Flampouri et al. investigated the dose deviation between planned dose and delivered dose due to respiratory motion and free breathing helical CT artefacts for lung intensity modulated radiotherapy(IMRT) treatments [12]. While the result demonstrated dose difference occurred, delivered dose was only approximated by the deforming and summing of the dose distributions from the ten 4DCT’s phase images [12].

In the presence of irregular breathing curve, it may not be practical achievable to acquire and reconstruct a true and artifact-free 4DCT due to the limited information and image acquisition technique [13]. In this study, we proposed a novel method to generate a true 4DCT(4DCT_true) using a patient’s digital phantom incorporating the irregular patient specific respiratory motion. In order to estimate the delivered dose and evaluate the plan robustness for lung SBRT, clinically a 4D dose accumulation method based on a deformation algorithm and workflow was introduced by Guckenberger et al. in 2006 [14]. However, limited 4DCT_traditional reconstruction, a true dose is difficult to acquire [15]. In order to overcome the limitation of image acquisition on 4DCT patient data, James et al. introduced the digital phantom concept simulating the irregular tumor motion and reconstructed a true dose accumulation [15]. However, the dose discrepancy between the “4D dose” (D^{4D}) calculated using 4DCT _traditional and the “true dose” (D^{true}) calculated based on 4DCT_true is never studied.

To our best of knowledge, it is very first comprehensive study to investigate the dose discrepancy between the D^{4D} and D^{true} simulating different tumor size, different breathing pattern including amplitude, breathing cycle and heterogeneity of the breathing pattern using simulated a digital tumor phantom. Then three real patients’ breathing curve were used to validate this model result. In addition, we proposed a novel probability density function (pdf) of 4DCT based robust optimization strategy for lung SBRT to improve the target coverage in the presence of such irregular breathing pattern.

## Methods

### Digital lung cancer phantom

*i*represents the sphere position in SI direction, [] represents taking the integer portion,

*P*represents

*P*× 10% phase.

In this study, three different sphere diameters (2, 3 and 4 cm) were used to investigate the effect of the target volume. Therefore, a total of 93 digital sample images were created to mimic the tumors with different volumes at different positions along the SI direction. These sample images were matched with the corresponding breathing phases and were used to mimic variations of the tumor motion pattern as well as real patient’s heterogeneous irregular breathing motion.

### Tumor motion simulation

*Z*is the tumor displacement (unit: mm). The parameter

*A*represents the motion amplitude, which is a random variable with a Gaussian distribution

*N*(

*μ*

_{A},

*σ*

_{A}), where

*δ*

_{A}=

*n*⋅

*u*

_{A}, in which

*n*is a determined proportionality coefficient.

*P*represents the duty cycle of one breathing cycle, which is also a random variable with a Gaussian distribution

*N*(

*μ*

_{P},

*σ*

_{P}), where

*δ*

_{P}=

*m*⋅

*u*

_{p}, in which

*m*is also a determined proportionality coefficient. Each heterogeneous breathing motion curve in this study comprised several respiratory cycles. Each respiratory cycle within a session varied by changing the peak-to-peak amplitude (

*A*) and duty cycle (

*P*) sampled from a random generator utilizing the corresponding Gaussian distribution described above. A different number of seeds in the random generator was selected to simulate the respiratory motion among sessions.

Combination of simulation for the breathing curves

No. | Mean excursion (mm) | Standard deviation of excursion/mean excursion | Mean period (s) | Standard deviation of period/mean period |
---|---|---|---|---|

1 | 5 | 0.25 | 4 | 0.2 |

2 | 10 | 0.25 | 4 | 0.2 |

3 | 15 | 0.25 | 4 | 0.2 |

4 | 20 | 0.25 | 4 | 0.2 |

5 | 15 | 0.15 | 4 | 0.2 |

6 | 15 | 0.35 | 4 | 0.2 |

7 | 15 | 0.25 | 3 | 0.2 |

8 | 15 | 0.25 | 5 | 0.2 |

9 | 15 | 0.25 | 4 | 0.1 |

10 | 15 | 0.25 | 4 | 0.3 |

### Tumor motion in actual patient

Three patient’s breathing curves were used for validation purpose. 1.5-mm-diameter gold fiducial markers was implanted into the lungs of three early-stage lung cancer patients. During SBRT treatment, stereoscopic X-ray fluoroscopy images of the gold fiducial markers at a frequency of 30 Hz were acquired over multiple days to determine the marker positions at a 1-mm spatial accuracy [20]. The tumor motion data in the SI direction of three patients with five fractions were acquired during treatment.

To reduce the influence of noise on the observed data and easily acquire peaks and valleys, a low-pass filter that passes signals with a frequency lower than a certain cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency was applied to process real tumor motion data. The exact frequency response of the filter depends on the filter design using fdatool in Matlab (version R2015a, Mathworks). Each actual breathing curve last more than 300 s, but only the previous 100 s were adopted in the present simulation after filtering. The respiratory motion image in actual patient was generated using the phase images that reflect the heterogeneity breathing pattern of the corresponding patient.

### 4DCT reconstruction and treatment planning

*P*= 4 s were generated using formula (1). The 4DCT_traditional images were created utilizing phase based sorting. The detailed selection of phase images was described as follows [21]: the displacement

*Z*was denoted as a function of time

*Z(t)*in present study. The time stamps at the peaks and valleys of the respiratory curves are identified. A neighboring peak and valley points represent a cycle, which will be divided into 10 equal time intervals. The symbol

*t*

^{i}

_{S},

*t*

^{i}

_{E}are the starting and ending time of phase

*i*then the sampling point will be

The average CT (AVG CT) image was generated by averaging the voxel intensities of all phase image and the ITV was created by adding all phase gross target volume (GTV). To study the dosimetric impact of tumor motion amplitude, four SBRT plans were generated based on the 4DCT_traditional with breathing amplitude from 5 to 20 mm.

^{3}.

The detail of plan

No. | Amplitude (mm) | Duty cycle (s) | Target diameter (cm) | Prescription dose level |
---|---|---|---|---|

1 | 5 | 4 | 3 | 80% |

2 | 10 | 4 | 3 | 80% |

3 | 15 | 4 | 2 | 80% |

4 | 15 | 4 | 3 | 80% |

5 | 15 | 4 | 4 | 80% |

6 | 15 | 4 | 3 | 70% |

7 | 15 | 4 | 3 | 90% |

8 | 20 | 4 | 3 | 80% |

9 | 10 | 4 | 3 | 80% |

### 4D robust optimization based on the pdf strategy

### Treatment dose construction

*e*, in the tumor can be written as [26].

*x*

_{i}

*(e)*indicates the tumor sub-volume position of a sample image, with the index

*i*representing the

*i-*th target motion/image sample.

*d (x*

_{i}

*(e))*represents the point dose at the tumor sub-volume position,

*x*

_{i}

*(e)*, calculated using a treatment plan based on the sample image.

*D*

^{4D}indicates the accumulated dose calculated using the sample images produced using 4DCT_traditional (10 phase images were used) while

*D*

^{true}indicates a true accumulated dose based on the whole sample images throughout the heterogeneity breathing cycle.

*I*is the total number of phase images, set to 10 for

*D*

^{4D}and the total number of phase images

*D*

^{true}calculations (~ 250 phase images in 4DCT_true), respectively. The treatment dose construction considered the tumor sub-volume displacements, but it did not consider the MLC interplay effect.

### Evaluation

*D*_{x} was defined as largest dose level percentage covering *x*% volume of the target. *D*^{true}_{x,j} was defined as the true cumulative dose for the *j*-th curve that covers *x*% of the target volume, while *D*^{4D}_{x, j, k} was defined as the cumulative dose for the *k*-periodic segment of the *j*-th curve that covers *x*% of the target volume.

*j*-th curve for the worst case was define as:

*J*is the simulation times or fractions and

*J*= 10 in tumor motion simulation, while

*J*= 5 from actual patient treatment fractions, and

*K*

_{j}is the periodic amount included in the

*j*-th curve. Linear regression was used to fit the \( \overline{\Delta {D}_{99}} \) and \( \overline{\Delta {D}_{95}} \) relationship between cumulative dose deviation and the variance of the respiratory motion pattern.

The data were assessed with a paired t-tests (non-parametric Wilcoxon signed rank test) using SPSS 19.0 software (International Business Machines, Armonk, New York), and *p* values equal to or less than 0.05 were considered statistically significant.

## Results

### Digital lung cancer phantom simulation and dose accumulation

^{nominal}and D

^{true}. Where D

^{nomial}represents the accumulated dose based on the 4DCT_traditional which was used for planning with a uniform breathing pattern, D

^{true}represents the accumulated dose incorporated heterogeneity breathing pattern with mean amplitude 15 mm, standard deviation of amplitude 3.75 mm, mean period 4 s and standard deviation of period 0.8 s. There was a slightly dose degradation on target due to heterogeneous respiratory motion.

The study also found that \( \overline{\Delta {D}_{99}} \) and \( \overline{\Delta {D}_{95}} \) has a weak correlation with the period time as well as standard deviation of the period time. \( \overline{\Delta {D}_{99}} \), \( \overline{\Delta {D}_{95}} \) decreased from 6.71, 4.98 to 6.13%, 4.62%, while the standard deviation of the period varied from 10 to 30% of the average period, 5.97% %<\( \overline{\Delta {D}_{99}} \)< 6.25%,4.60% %<\( \overline{\Delta {D}_{95}} \)< 4.76% .\( \overline{\Delta {D}_{99}} \), \( \overline{\Delta {D}_{95}} \) varied along the average and standard deviation of the period as displayed in Fig. 5c and d, respectively.

The relationship between \( \overline{\Delta {D}_{99}} \), \( \overline{\Delta {D}_{95}} \) and prescription dose level and target volume are shown in Fig. 5e and f, respectively. When the prescription isodose level varied from 70 to 90%, all \( \overline{\Delta {D}_{99}} \) values were less than 8.45% and greater than 6.25%, all \( \overline{\Delta {D}_{95}} \) were less than 6.89% and greater than 4.51%. When the tumor diameter varied from 2 to 4 cm, \( \overline{\Delta {D}_{99}} \) was 10.1%, 6.25 and 10.63%, \( \overline{\Delta {D}_{95}} \) was 8.84, 4.76 and 9.23%. These results indicated that there is no strong correlation between the dose deviation and the prescription isodose line (dose gradient) or the target volume.

### Tumor motion in actual patient and dose accumulation

Characteristics of the respiratory motion in three patients

No. | Fraction | Mean excursion (mm) | Standard deviation of excursion/mean excursion | Mean period (s) | Standard deviation of period/mean period |
---|---|---|---|---|---|

1 | 1 | 10.11 | 0.12 | 4.85 | 0.12 |

2 | 10.32 | 0.09 | 4.65 | 0.09 | |

3 | 10.14 | 0.12 | 4.95 | 0.08 | |

4 | 9.88 | 0.11 | 5.15 | 0.09 | |

5 | 8.59 | 0.09 | 5.05 | 0.12 | |

2 | 1 | 10.21 | 0.23 | 3.78 | 0.05 |

2 | 9.92 | 0.20 | 3.81 | 0.09 | |

3 | 10.53 | 0.23 | 3.85 | 0.09 | |

4 | 10.62 | 0.25 | 3.39 | 0.15 | |

5 | 10.05 | 0.22 | 3.78 | 0.05 | |

3 | 1 | 15.28 | 0.23 | 2.71 | 0.08 |

2 | 14.36 | 0.20 | 2.79 | 0.08 | |

3 | 16.21 | 0.21 | 3.18 | 0.11 | |

4 | 15.88 | 0.23 | 3.11 | 0.10 | |

5 | 15.20 | 0.22 | 3.06 | 0.10 |

\( \overline{\Delta {D}_{99}} \), \( \overline{\Delta {D}_{95}} \) for the three patients were 2.15,1.98% for patient #1, 3.48%, 2.68% for patient #2, and 6.63%, 4.74% for patient #3 based on the simulation. D^{4D} evaluation approach may not be appropriate in the presence of the accumulated dose with heterogeneous breathing motion. Although a complicated respiratory pattern was calculated from the actual patient, the results are consistent with those from the phantom study.

#### 4D Ro-VMAT outcome

_{99}vs tumor position in each phase image was displayed in Fig. 7 from patient #3. The pdf based 4D-Ro-VMAT could effectively compensate the target dose degradation which was out of ITV boundary. When the respiratory pattern is severely irregular, 4D-Ro-VMAT shows a significant improvement in those in these extreme target positions although the chance of such displacement is rare or very lightly weighted. Compared to the VMAT plan, the target accumulated dose \( {D}_{99}^{true} \) significantly increased 1.9% (

*p*< 0.01) and 2.1% (p < 0.01) on average throughout the 5 fractions in the 4D Ro-VMAT plan for patient #2 and #3 respectively, the 4D Ro-VMAT plan significantly improve the accumulated dose coverage. However, when the mean amplitude is less than 10 mm or the amplitude standard deviation is less than 1 mm for patient #1, the accumulated dose \( {D}_{99}^{true} \) increases 0.1%(

*p*= 0.21) on average during 5 fractions, 4D Ro-VMAT may not be necessary.

## Discussion

The study found that the heterogeneity breathing pattern with a greater mean amplitude or the standard deviation of the amplitude led towards a larger variations of target motion and position (Fig. 3a and b). Such phenomena resulted in a significant deviation of the accumulated dose between D^{4D} and D^{true} evaluation approaches, especially when the average breath amplitude is larger than 10 mm or standard deviation of amplitude is larger than 25% of mean amplitude. In order to minimize the breathing curve standard deviation, Blomgren et al. have reported that a passive pressure technique can limit the movement of the diaphragm-by-diaphragm pressure plate, thereby reducing the amplitude of the tumor motion [27]. In addition, respiratory motion is a semi-autonomous and irregular motion, patient breathing training may be helpful to improve the reproducibility of the respiratory amplitude and frequency. Shallow breathing control or high frequency breathing technique can be utilized as well [28]. Therefore, the use of the above techniques can reduce the uncertainty caused by breathing motion thus achieve to improve the accuracy of the accumulated dose calculated with 4DCT_traditionl.

The study found that the accumulated dose discrepancy slightly varies along with the variation of mean and the standard deviation of the period cycle. However, it should be noted that such phenomena might varies if treatment time delivery and tumor motion interplay effect is considered. The study also showed that the target absolute volume doesn’t affect the accumulated dose evaluation approach using D^{4D} or D^{true}. Furthermore, the accumulated dose discrepancy is independent of the prescription isodose line (dose gradient) as well [29], since dose gradient described dose variation along with voxel position variation, while *D*_{x} discribed the largest dose level percentage covering *x*% target volume.

This study assuming the real-time tumor position is available for D^{true} evaluation approach. However, in the current clinical practice, 4DCT_traditional simulation may not fully represents true tumor position and motion [11]. In order to achieve the real-time tumor position tracking, Zhuang et al. proposed an accurately method to extract tumor respiratory motion using the cone beam CT (CBCT) projections during VMAT treatment of lung tumor recently [30]. The result demonstrated that the 3D (x, y, z) mean tumor position and 3D trajectory reconstruction are accurate within ±0.5 mm. Such approach could be implemented into clinical practice and provide the real-time target tracking during the virtual simulation. The study demonstrated a practical feasible way to use D^{true} to evaluate the patient specific tumor motion and provide a more accurate treatment plan robustness analysis using D^{true} approach in case of the patient with a potential larger heterogeneity in breathing pattern and amplitude.

To overcome and mitigate the uncertainties a novel planning strategy was introduced in this study combining the 4D robust optimization approach and the probability density function of breathing pattern. Several 4D robust optimization methods were introduced to address this breathing induced issue. For example, the strategy was implemented by incorporating the min-max optimization of the GTV dose on all phases included in the 4DCT_traditioanl [25]. The similar study from Archibald et al. also showed that such 4D robustness optimization approach could provide a greater stability in both maximum (< 3%) and minimum dose variations (< 2%) over all other techniques included planning target volume (PTV) expansions, ITV with and without tissue override [31]. However, these previous studies using the 4D robust optimization was based on the assumption that respiratory motion throughout the treatment maintained the same pattern manifested on the 4DCT_traditional. In the presence of the heterogeneous breathing pattern in some patients, Chan et al. developed a robust optimization approach incorporating with the convolution of motion pdf variation with static dose distribution, which could mitigate breathing uncertainty as well [32]. However, such approach to calculate the accumulated dose using convolution may not represent the dose distribution with motion accurately [33].

In this study, we proposed to use additional phase images to cover 80% of probability density function for 4D robust optimization. The preliminary result demonstrated that it could significantly reduce the dose uncertainty compared to the VMAT plan when the target mean amplitude was greater or equal to 10 mm and the standard deviation of amplitude was greater or equal to 25% of mean amplitude. This study also indicated that when the standard deviation of amplitude was less than 15% of mean amplitude, the 4D-Ro-VMAT approach may not be effective since the discrepancy between D^{4D} and D^{true} is very minimum. But the selection of appropriate additional phase images to spare normal tissue need to be further studied.

Other limitations in the study are that only rigid motion was investigated; thus, non-rigid motions, such as anatomic changes, needs to be included in the future study. The MLC interplay effect is not considered either.

## Conclusions

Traditional D^{4D} approach might not provide a comprehensive dose accumulation when the respiratory-induced target/organ motion has a larger heterogeneous pattern (more than 10 mm amplitude or 25% mean amplitude as standard deviation of amplitude). D^{true} is preferred in these scenarios. The study suggested that the 4D-Ro-VMAT could be a potential planning strategy to mitigate patient’s breathing pattern heterogeneity.

## Notes

### Acknowledgements

This study was supported by the Natural Science Foundation of China, the Natural Science Foundation of Hubei Province of China and the Natural Science Foundation of Union Hospital, Tongji Medical College, Huazhong University of Science and Technology.

### Funding

This study was supported by the Natural Science Foundation of China (No. 10875092 and 31271511), the Natural Science Foundation of Hubei Province of China (No. 2012 KB04449), and the Natural Science Foundation of Union Hospital, Tongji Medical College, Huazhong University of Science and Technology (No.02.03.2017–289).

### Availability of data and materials

The datasets during and/or analyzed during the current study available from thecorresponding author on reasonable request.

### Authors’ contributions

Conception and design: GL, HQ. Acquisition of data: QS, JY, XL. Analysis of data: GL, FH, XD. Draw Boxplot: YW. Writing, review and/or revision of the manuscript: GL, FH. All authors reviewed, read and approved the final manuscript.

### Ethics approval and consent to participate

This study was approved by the Institutional Review Board at the Tongji Medical College of Huazhong University of Science and Technology. All methods were carried out in accordance with the relevant guidelines and regulations. Written informed consent was obtained from all participants.

### Consent for publication

Written informed consent for publication of their clinical details was obtained from the patient.

### Competing interests

The authors declare that they have no competing interests.

### Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## References

- 1.Fakiris AJ, McGarry RC, Yiannoutsos CT, Papiez L, Williams M, Henderson MA, et al. Stereotactic body radiation therapy for early-stage non-small-cell lung carcinoma: four-year results of a prospective phase II study. Int J Radiat Oncol Biol Phys. 2009;75:677–82.CrossRefGoogle Scholar
- 2.Onishi H, Shirato H, Nagata Y, Hiraoka M, Fujino M, Gomi K, et al. Hypofractionated stereotactic radiotherapy (HypoFXSRT) for stage I non-small cell lung cancer: updated results of 257 patients in a Japanese multi-institutional study. J Thorac Oncol. 2007;2:S94–100.CrossRefGoogle Scholar
- 3.Uematsu M, Shioda A, Suda A, Fukui T, Ozeki Y, Hama Y, et al. Computed tomography-guided frameless stereotactic radiotherapy for stage I non-small cell lung cancer: a 5-year experience. Int J Radiat Oncol Biol Phys. 2001;51:666–70.CrossRefGoogle Scholar
- 4.Martini N, Bains MS, Burt ME, Zakowski MF, McCormack P, Rusch VW, et al. Incidence of local recurrence and second primary tumors in resected stage I lung cancer. J Thorac Cardiovasc Surg. 1995;109:120–9.CrossRefGoogle Scholar
- 5.Hof H, Rhein B, Haering P, Kopp-Schneider A, Debus J, Herfarth K. 4D-CT-based target volume definition in stereotactic radiotherapy of lung tumours: comparison with a conventional technique using individual margins. Radiother Oncol. 2009;93:419–23.CrossRefGoogle Scholar
- 6.Castillo SJ, Castillo R, Balter P, Pan T, Ibbott G, Hobbs B, et al. Assessment of a quantitative metric for 4D CT artifact evaluation by observer consensus. J Appl Clin Med Phys. 2014;15:4718.CrossRefGoogle Scholar
- 7.Guckenberger M, Wilbert J, Meyer J, Baier K, Richter A, Flentje M. Is a single respiratory correlated 4D-CT study sufficient for evaluation of breathing motion? Int J Radiat Oncol. 2007;67:1352–9.CrossRefGoogle Scholar
- 8.Hugo G, Vargas C, Liang J, Kestin L, Wong JW, Yan D. Changes in the respiratory pattern during radiotherapy for cancer in the lung. Radiother Oncol. 2006;78:326–31.CrossRefGoogle Scholar
- 9.Lu W, Parikh PJ, Hubenschmidt JP, Bradley JD, Low DA. A comparison between amplitude sorting and phase-angle sorting using external respiratory measurement for 4D CT. Med Phys. 2006;33:2964–74.CrossRefGoogle Scholar
- 10.Zhang F, Kelsey CR, Yoo D, Yin F-F, Cai J. Uncertainties of 4-dimensional computed tomography-based tumor motion measurement for lung stereotactic body radiation therapy. Pract Radiat Oncol. 2014;4:e59–65.CrossRefGoogle Scholar
- 11.Sonke J-J, Lebesque J, van Herk M. Variability of four-dimensional computed tomography patient models. Int J Radiat Oncol. 2008;70:590–8.CrossRefGoogle Scholar
- 12.Flampouri S, Jiang SB, Sharp GC, Wolfgang J, Patel AA, Choi NC. Estimation of the delivered patient dose in lung IMRT treatment based on deformable registration of 4D-CT data and Monte Carlo simulations. Phys Med Biol. 2006;51:2763–79.CrossRefGoogle Scholar
- 13.Watkins WT, Li R, Lewis J, Park JC, Sandhu A, Jiang SB, et al. Patient-specific motion artifacts in 4DCT. Med Phys. 2010;37:2855–61.Google Scholar
- 14.Guckenberger M, Wilbert J, Krieger T, Richter A, Baier K, Meyer J, et al. Four-dimensional treatment planning for stereotactic body radiotherapy. Int J Radiat Oncol. 2007;69:276–85.CrossRefGoogle Scholar
- 15.James SS, Seco J, Mishra P, Lewis JH. Simulations using patient data to evaluate systematic errors that may occur in 4D treatment planning: a proof of concept study: simulations using patient data to evaluate systematic errors. Med Phys. 2013;40:091706.CrossRefGoogle Scholar
- 16.Shah C, Grills IS, Kestin LL, McGrath S, Ye H, Martin SK, et al. Intrafraction variation of mean tumor position during image-guided Hypofractionated stereotactic body radiotherapy for lung Cancer. Int J Radiat Oncol. 2012;82:1636–41.CrossRefGoogle Scholar
- 17.Bissonnette J-P, Franks KN, Purdie TG, Moseley DJ, Sonke J-J, Jaffray DA, et al. Quantifying Interfraction and Intrafraction tumor motion in lung stereotactic body radiotherapy using respiration-correlated cone beam computed tomography. Int J Radiat Oncol. 2009;75:688–95.CrossRefGoogle Scholar
- 18.Suryanto A, Herlambang K, Rachmatullah P. Comparison of tumor density by CT scan based on histologic type in lung cancer patients. Acta Med Indones. 2005;37:195–8.PubMedGoogle Scholar
- 19.Mutaf YD, Scicutella CJ, Michalski D, Fallon K, Brandner ED, Bednarz G, et al. A simulation study of irregular respiratory motion and its dosimetric impact on lung tumors. Phys Med Biol. 2011;56:845.CrossRefGoogle Scholar
- 20.Koybasi O, Mishra P, St. James S, Lewis JH, Seco J. Simulation of dosimetric consequences of 4D-CT-based motion margin estimation for proton radiotherapy using patient tumor motion data. Phys Med Biol. 2014;59:853–67.CrossRefGoogle Scholar
- 21.Chi Y, Liang J, Qin X, Yan D. Respiratory motion sampling in 4DCT reconstruction for radiotherapy: respiratory motion sampling in 4DCT reconstruction for radiotherapy. Med Phys. 2012;39:1696–703.CrossRefGoogle Scholar
- 22.Chang BK, Timmerman RD. Stereotactic body radiation therapy: a comprehensive review. Am J Clin Oncol. 2007;30:637–44.CrossRefGoogle Scholar
- 23.Liu W, Zhang X, Li Y, Mohan R. Robust optimization of intensity modulated proton therapy: robust optimization of IMPT. Med Phys. 2012;39:1079–91.CrossRefGoogle Scholar
- 24.Miura H, Ozawa S, Nagata Y. Efficacy of robust optimization plan with partial-arc VMAT for photon volumetric-modulated arc therapy: a phantom study. J Appl Clin Med Phys. 2017;18:97–103.CrossRefGoogle Scholar
- 25.Liu W, Schild SE, Chang JY, Liao Z, Chang Y-H, Wen Z, et al. Exploratory study of 4D versus 3D robust optimization in intensity modulated proton therapy for lung Cancer. Int J Radiat Oncol. 2016;95:523–33.CrossRefGoogle Scholar
- 26.Glide-Hurst CK, Hugo GD, Liang J, Yan D. A simplified method of four-dimensional dose accumulation using the mean patient density representation. Med Phys. 2008;35:5269–77.CrossRefGoogle Scholar
- 27.Blomgren H, Lax I, Näslund I, Svanström R. Stereotactic high dose fraction radiation therapy of extracranial tumors using an accelerator. Clinical experience of the first thirty-one patients. Acta Oncol Stockh Swed. 1995;34:861–70.CrossRefGoogle Scholar
- 28.Gagel B, Demirel C, Kientopf A, Pinkawa M, Piroth M, Stanzel S, et al. Active breathing control (ABC): determination and reduction of breathing-induced organ motion in the chest. Int J Radiat Oncol. 2007;67:742–9.CrossRefGoogle Scholar
- 29.Tyler MK. Quantification of interplay and gradient effects for lung stereotactic ablative radiotherapy (SABR) treatments. J Appl Clin Med Phys. 2016;17:158–66.CrossRefGoogle Scholar
- 30.Zhuang L, Liang J, Yan D, Zhang T, Marina O, Ionascu D. An optimization algorithm for 3D real-time lung tumor tracking during arc therapy using kV projection images: 3D real-time lung tumor tracking. Med Phys. 2013;40:101710.CrossRefGoogle Scholar
- 31.Archibald-Heeren BR, Byrne MV, Hu Y, Cai M, Wang Y. Robust optimization of VMAT for lung cancer: Dosimetric implications of motion compensation techniques. J Appl Clin Med Phys. 2017;18:104–16.CrossRefGoogle Scholar
- 32.Chan TCY, Bortfeld T, Tsitsiklis JN. A robust approach to IMRT optimization. Phys Med Biol. 2006;51:2567–83.CrossRefGoogle Scholar
- 33.Song W, Battista J, Van Dyk J. Limitations of a convolution method for modeling geometric uncertainties in radiation therapy: the radiobiological dose-per-fraction effect: modeling geometric uncertainties in radiation therapy. Med Phys. 2004;31:3034–45.CrossRefGoogle Scholar

## Copyright information

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.