Effect of Breathing Phase Number on the 4D Robust Optimization for Pancreatic Cancer Intensity Modulated Proton Therapy

doi:10.21203/rs.3.rs-4867185/v1

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Research Article

Effect of Breathing Phase Number on the 4D Robust Optimization for Pancreatic Cancer Intensity Modulated Proton Therapy

https://doi.org/10.21203/rs.3.rs-4867185/v1

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Purpose

Respiratory movement, as one of the main challenges in proton therapy for pancreatic cancer patients, could not only lead to harm to normal tissues but also lead to failure of the tumor control, resulting in irreversible consequences. Including respiratory movements into the plan optimization, i.e. 4D robust optimization, may mitigate the interplay effect. However, 4D robust optimization considering images of all breathing phases is time-consuming and less efficient. This work aims to investigate the effect of the breathing phase number on the 4D robust optimization for pancreatic cancer intensity modulated proton therapy (IMPT) by examining plan quality and computational efficiency.

Methods

A total of 15 pancreatic cancer patients were retrospectively analyzed. For each patient, five four-dimensional (4D) robust treatment planning strategies with different numbers of respiratory phases and one three-dimensional (3D) treatment plan were created. Optimization of the plans were performed on all ten phases (10phase plan), two extreme phases (2phase plan), two extreme phases plus an intermediate state (3phase plan), six phases during the exhalation stage (6Exphase plan), six phases during the inhalation stage (6Inphase plan) and 3D Computed Tomography (CT) scan image (3D plan), respectively. 4D dynamic dose (4DDD) was then calculated to access the interplay effect by considering respiratory motion and dynamic beam delivery. Plan quality and dosimetric parameters for the target and organs at risk (OARs) were then analyzed.

Results

Compared to the 4D plans, 3D plan only showed lower maximum dose of the small intestine while performing worse on all other aspects. All five 4D treatment planning strategies showed similar protection of the OARs. Both the 6Exphase and 6Inphase plans demonstrated similar performance as the 10phase plan in target coverage, outperforming the other three plans. Compared with the 10phase plan, the average decline rates of the optimization time of the five plans of 2phase, 3phase, 6Exphase, 6Inphase, and 3D were 73.26 ± 6.54%, 65.80 ± 7.89%, 42.14 ± 13.57%, 37.72 ± 11.70% and 75.52 ± 8.21%, respectively. With the decrease of the number of phases selected for optimization, the decline rates increased, while the other dosimetry parameters generally showed a deterioration trend.

Conclusion

This study highlighted that the dosimetric performances of the 6Exphase and 6Inphase plans closely aligned with that of the 10phase plan. These plans offered a feasible alternative to 10phase optimization by reducing optimization time while maintaining dose coverage of the target and protection of OARs.

Pancreatic cancer

4D robust optimization

4D dynamic dose

Intensity Modulated Proton Therapy

Pancreatic cancer is a significant contributor to the global cancer-related mortality with a mortality rate nearly equal to its morbidity rate. Despite the rapid development of the treatment method, long-term survival rates remain low, typically ranging from 9–11% over a 5-year period^[1]. Early detection of pancreatic cancer is challenging leading to the diagnosis at advanced stages. Radiation therapy involves the use of high-energy radiation to target and destroy tumor cells, slowing tumor growth. In the case of pancreatic cancer, radiotherapy plays a crucial role in various clinical treatment approaches, including postoperative adjuvant chemoradiotherapy and radical concurrent chemoradiotherapy. This treatment modality is essential in reducing patient symptoms, improving survival rates, and enhancing overall quality of life^{[2, 3]}.

However, radiotherapy for pancreatic cancer often comes with challenges due to the deep anatomical location of the pancreas in the abdominal cavity surrounded by organs like the duodenum and small intestine. This complicates the precise targeting of the tumor and sparing of the normal tissue. Proton therapy, a novel technique, offers the advantage of delivering prescribed doses to the tumor target with better spare of the surrounding tissues. This ability to minimize radiation exposure to normal tissues enhances therapeutic outcomes and reduces the risk of toxic side effects^[4]. Research by Thompson et al. demonstrated that proton therapy, in comparison to traditional photon therapy, notably reduces medium and low doses to critical organs near the tumor site^[5]. As a result, proton therapy is increasingly being utilized in the treatment of pancreatic cancer^{[6, 7]}.

Although proton therapy shows potentials in the treatment of pancreatic cancer, challenges remain considering the impact of patients' respiratory movement and dynamic proton beam delivery, i.e. interplay effect. The uncertainty of tumor movement significantly affects the actual radiation dose delivered to the tumor, potentially resulting in inadequate coverage of tumor target or severe damage to the nearby critical organs ^[8–10]. To mitigate the effects of motion uncertainty, incorporating tumor movement into the treatment planning optimization process was proposed. Four-dimensional (4D) optimization considering the dynamic anatomy changes of the tumor results in a 4D robust treatment plan^[11–13]. However, 4D robust optimization, while performing better in mitigating the effects of motion uncertainty, is less efficient and time-consuming compared to traditional 3D optimization, limiting its clinical use.

This work aims to investigate if strategies considering less number of optimization phases in pancreatic cancer IMPT treatment planning could maintain tumor target coverage and plan quality, thus saving time and enhancing efficiency. In this study, different numbers of respiration phases were selected for 4D optimization. Merits of the optimization results were evaluated through the 4D dynamic dose(4DDD), so as to select the optimization strategy that was closest to the 10phase plan optimization strategy. This study also explored the optimal number of optimization phases. This research provides guidelines to reduce optimization time and improve clinical efficiency for pancreatic cancer IMPT.

2.1、 Patients and Contouring: Fifteen pancreatic patients were recruited from Shandong Cancer Hospital and Institute. Treatment planning for these patients were then conducted with intensity-modulated proton treatment (IMPT) planning techniques. Inclusion criteria were as follows: (1) unresected pancreatic cancer patients; (2) No previous history of radiotherapy or chemotherapy. Exclusion criteria were as follows: (1) change of radiotherapy regimen during radiotherapy; (2) combination of other malignant tumors. All patients were scanned with calm breathing using Philips Big Core CT (Phillips Medical Systems, 96 Highland Heights, OH) and reconstructed 4D CT image sets of 10 respiratory phases. The thickness of the image scanning layer was 3mm. Table 1 summarizes patient number, position, tumor location, volume, motion amplitude and field angle in this study. The clinical tumor volume (CTV) ranged from 16.27 to 690.97cc, and the tumor movement amplitude (specified as the largest displacement of the tumor mass center in the three coordinate directions in all the phases of the 4D CT dataset) was between 0.938 and 10.662 mm.

The end-expiratory phase (0%Ex) in 4D CT served as the reference phase in this work. The gross target volume (GTV) and organs at risk (OARs) were contoured in the Raystation11B(RaySearch Laboratories AB, Stockholm, Sweden)treatment planning system by the certificated radiation oncologists in our center on all phases of the 4D CT. CTV was determined to be the GTV plus a margin of 5mm ^{[14, 15]}. Based on the deformation algorithm, CTVs on all other phases in 4D CT were registered to the reference phase. The internal clinical target volume (ICTV) was then defined as the envelope of CTVs from all the breathing phases on the reference phase.

Table.1. Patient number, position, tumor location, volume, motion amplitude and field angles utilized during treatment planning.

Patient ID	Tumor location	Patient position	Tumor Volume(cc)	Motion Mag(mm)	Field angle(degree)
1	Head	HSF	52.75	3.473	20,350
2	Body, Tail	HSF	95.85	1.265	20,350
3	Body	HSF	97.14	1.616	20,350
4	Body	HSF	45.62	10.662	20,350
5	Body, Tail	HSF	136.36	3.763	20,350
6	Tail	HSF	38.13	8.526	20,350
7	Tail	HSF	82.90	5.210	20,350
8	Head	HSF	202.67	3.158	20,350
9	Head	HSF	92.32	0.938	20,350
10	Head, Body	HSF	690.97	2.211	0,240,300
11	Body	HSF	251.84	1.992	0,240,300
12	Head	HSF	234.47	3.506	0,240,300
13	Head	HSF	46.23	2.683	20,350
14	Tail	HSF	69.29	6.938	20,350
15	Body	HSF	16.27	7.132	20,350

HFS: Head First Supine.

2.2、Treatment planning: The clinical beam model of ProBeam (Varian Medical Systems, CA, USA) used in the Proton Center of Shandong Cancer Hospital, with the nominal energies range of 70-240MeV in spot scanning mode was adopted. The size of the dose grid for dose calculation is 3x3x3 mm³. The Raystation11B treatment planning system was used to design the IMPT plans with 2–3 fields. To maintain consistency in results analysis, the same beam configuration was applied to most of the patients. Three patients were planned with three fields due to the large tumor size. The beam angles for all 3D and 4D robust treatment plans were identical for the same patient with all patients positions of the Head First Supine (HFS). The relative biologic effectiveness (RBE) weighted dose was determined using a fixed RBE value of 1.1 for proton. A prescription dose of 45Gy (RBE) for 25 fractions was administered to 95% volume of the CTV ^{[12, 15, 16]}.

2.3、4D optimization: 4D robust optimization considering set S of scenarios was implemented using minimax optimization. The objective function was

$$\:\underset{x\in\:X}{\text{min}}\left\{\underset{s\in\:S}{\text{max}}\sum\:_{i=1}^{N}{w}_{i}{f}_{i}\left[d\left(x,s\right)\right]\right\}$$

where X is the set of feasible variables (e.g., spot weights for IMPT), and d(x,s) is the dose distribution as a function of the variables x and the scenario s. Functions applied only to the nominal scenario can also be added to the objective. Moreover, nominal and robust constraints can be used in combination with formulation^[17]. The robust optimization functions were set as follows: The minimum dose of CTV was 45 Gy(RBE) with the weight of 100. The maximum dose of CTV was 47.25 Gy(RBE) with the weight of 100. The maximum dose of duodenal was 48 Gy(RBE) with the weight of 60. The maximum dose of small intestine was 45 Gy(RBE) with the weight of 60.

Five 4D robust plans optimized with various selections of respiratory phases were designed: (1) 10phase plan: all phases of the respiratory cycle (10 phases in this study) were used for standard 4D optimization; (2) 2phase plan: the end of expiratory (0%Ex) and the end of inspiratory (100%In) phases were used for optimization ^[18]. (3) 3phase plan: two extreme phases and an intermediate phase were used for optimization. Three breathing phases of 0%Ex, 100%In and 60%Ex were used in this study. (4) 6Exphase plan: all exhalation phases, including 0%Ex, 20%Ex, 40%Ex, 60%Ex, 80%Ex, 100%In were used for optimization; (5) 6Inphase plan: all inspiratory phases, including 0%Ex, 20%In, 40%In, 60%In, 80%In, 100%In were used for optimization. Besides, the 3D robust plan considering the single reference phase was also conducted. The beam configuration and restriction function were the same for all plans.

2.4、4D dynamic dose (4DDD) calculation: A scheme for the process of 4DDD calculation is shown in Fig. 1. This study took into account the interplay effect, which involved the interaction between dynamic pencil beam delivery and respiratory movement. Utilizing the Monte Carlo (MC) dose algorithm in Raystation, an in-house script for 4DDD calculation was developed. Parameters in the script include: (1) energy layer switching time was 1s; (2) beam spot moving speed was 10m/s; (3) the dose rate during the beam delivery was 800MU/s; (4) Total duration of respiratory cycle was 5s.

2.5、4D dose evaluation: for each patient (with five 4D robust plans and one 3D plan), all plans were normalized before running the script so that 100% of the prescription dose covered 95% volume of CTV. For CTV, the dose metrics were chosen as D₉₈ (the prescribed dose received by at least 98% of the volume), D₉₅ (the prescribed dose received by at least 95% of the volume), D₂ (the minimum dose received by 2% of the volume), the target heterogeneity index (HI), as calculated by the formula:

$$\:\text{H}\text{I}=\left({\text{D}}_{2}-{\text{D}}_{98}\right)/{\text{D}}_{\text{p}\text{r}\text{e}}$$

Where D_pre represents the prescription dose. The HI ranged from 0 to 1, where 0 is the ideal value, the higher the HI, the worse the homogeneity^[19].

The conformability index (CI):

$$\:\text{C}\text{I}=\frac{{\text{T}\text{V}}_{95}}{\text{T}\text{V}}\times\:\frac{{\text{T}\text{V}}_{95}}{{\text{V}}_{95}}$$

Where TV₉₅ and V₉₅ represent the target volume receiving the 95% of the prescription dose and the total volume receiving at least 95% of the prescription dose, respectively. TV indicates the target volume. The CI ranged from 0 to 1, the smaller the CI, the better the conformation ^[20].

The maximum dose to the duodenum and small intestine (D_max) was treated as D₂ in this work^[20]. Volume size irradiated by 15 Gy(RBE) in small intestine was denoted as V_15Gy(RBE). Normal tissue V^’₃₆ referred to the volume of normal tissue exposed to 80% of the prescription dose. To standardize evaluation criteria, this parameter was expressed as a proportion taking the 10phase plan as a reference plan, the formula is:

$$\:{\text{V}}_{36}^{{\prime\:}}={\text{V}}_{\text{x}36}/{\text{V}}_{10\text{p}\text{h}\text{a}\text{s}\text{e}36}$$

Where V_x36 represents the V₃₆ value in various treatment planning strategies, including 2phase, 3phase, 6Exphase, 6Inphase and 3D plans. V_10phase36 indicated the V₃₆ value in the 10phase plan. A higher value of V^’₃₆ indicated a much similar V₃₆ value as the 10phase plan.

The time decline rate is calculated according to the formula below:

$$\:{\text{T}}_{\text{d}\text{e}\text{c}\text{l}\text{i}\text{n}\text{e}}=\left({\text{T}}_{10\text{p}\text{h}\text{a}\text{s}\text{e}}-{\text{T}}_{\text{x}}\right)/{\text{T}}_{10\text{p}\text{h}\text{a}\text{s}\text{e}}$$

Where T_10phase represents the optimization time of the 10phase treatment planning strategy. T_x represents the optimization time of each treatment planning strategy (2phase, 3phase, 6Exphase, 6Inphase or 3D plan). The decline rate ranged from 0 to 100, the higher the value, the less of the time required for the optimization.

Statistical analysis was carried out using the SPSS software with the reference of 10phase plan. Wilcoxon signed-rank sum test was used to evaluate statistical differences between dose metrics. A two-tailed p value < 0.05 was considered statistically significant, and the p value < 0.001 was considered more significant.

Considering dynamic beam delivery and respiratory motion, 4DDD was calculated for all treatment planning strategies (10phase plan, 2phase plan, 3phase plan, 6Exphase plan, 6Inphase plan, 3D plan) of each patient. Dose metrics calculated from dose-volume histogram (DVH) of the 4DDD were analyzed.

Figure 2. illustrates the impact of 4D robust optimization on dose metrics of CTV, including D₉₈, D₉₅ and D₂ for various optimization strategies. The values of D₉₈ and D₉₅ were similar for 2phase and 3phase plans. Conversely, the average values for other plans increased with increasing the number of optimized phases. For D₉₈, the average values of 10phase, 2phase, 3phase, 6Exphase, 6Inphase and 3D plans were 43.75 ± 0.63, 43.48 ± 0.77, 43.45 ± 0.80, 43.51 ± 0.76, 43.59 ± 0.74 and 41.14 ± 2.44 Gy(RBE), respectively; The average values of D₉₅ were 44.18 ± 0.50, 43.99 ± 0.64, 43.95 ± 0.67, 44.01 ± 0.61, 44.02 ± 0.70 and 42.98 ± 1.71 Gy(RBE), respectively. The differences of D₉₈ and D₉₅ for all optimization strategies compared with the scenario of 10 phases were statistically significant (p < 0.05). For D₂, the doses of 2phase, 3phase, 6Exphase and 6Inphase plans were similar. The average dose of the 3D optimized method was significantly higher than that of the other five 4D optimization strategies, while the 10phase strategy had the lowest mean value. The mean values of D₂ of 10phase, 2phase, 3phase, 6Exphase, 6Inphase and 3D plans were 47.91 ± 1.19, 48.32 ± 0.87, 48.25 ± 0.82, 48.21 ± 0.80, 48.24 ± 0.84 and 48.26 ± 0.85 Gy(RBE), respectively. The differences between 10phase and 2phase, 3phase and 6Inphase were statistically significant (p < 0.05).

Figure 3 shows dose metrics HI, CI and the average decline rate of the optimization time. For HI, the value of HI increased with increasing the number of phases during plan optimization. The differences among the six plans were statistically significant (p < 0.05). The value of HI for the 3D plan was significantly higher than the values of other plans. The difference for HI was statistically more significant (p < 0.001). The average values of 10phase, 2phase, 3phase, 6Exphase, 6Inphase and 3D plans were 0.09 ± 0.04, 0.11 ± 0.04, 0.11 ± 0.03, 0.10 ± 0.03, 0.10 ± 0.03 and 0.16 ± 0.06, respectively.

For CI, the value of CI decreased as the number of phases during plan optimization increased. There was statistical significance between the other five plans and the 10phase plan (p < 0.05). The statistical differences between 2phase, 3phase, 6Inphase and 10phase plans were more significant (p < 0.001). The average values of CI for 10phase, 2phase, 3phase, 6Exphase, 6Inphase and 3D plans were 0.53 ± 0.10, 0.59 ± 0.07, 0.58 ± 0.07, 0.56 ± 0.07, 0.56 ± 0.08 and 0.60 ± 0.08, respectively.

Panel (c) shows the average decline rate of the optimization time of the five plans of 2phase, 3phase, 6Exphase, 6Inphase and 3D compared with the 10phase plan. Points in the graph showed the decline rate for all patients’ studies. The inflection points of the polyline were the average of the decline rate of all for the six optimization strategies. Obviously, the fewer the number of breathing phases considered during optimization, the higher the decline rate and the shorter the time consumed. The average values of 10phase, 2phase, 3phase, 6Exphase, 6Inphase and 3D plans were 73.26 ± 6.54%, 65.80 ± 7.89%, 42.14 ± 13.58%, 37.72 ± 11.70% and 75.52 ± 8.21%, respectively.

Figure 4 shows the dose metrics of OARs including the D_max of small intestine, the V_{15 Gy (RBE)} of small intestine, the D_max of duodenum and V₃₆ of the normal issue. V^’₃₆ referred to the volume of normal tissue exposed to 80% of the prescription dose. To standardize evaluation criteria, this parameter was expressed as that of the proportion of the 10phase plan. In the five plans (2phase, 3phase, 6Exphase, 6Inphase and 3D), the average values of 6Exphase and 6Inphase plans were closer to the 10phase plan. The more breathing phases selected, the larger the normal tissue volume subjected to 36Gy. Four 4D plans (2phase, 3phase, 6Exphase, 6Inphase plans) showed statistically significant differences compared to the 10phase plan (p < 0.001). The average value of the V^’₃₆ for 3D plan was lower than that of the 10phase plan. The difference was statistically significant (p < 0.05). The average values of 2phase, 3phase, 6Exphase, 6Inphase and 3D plans were 0.89 ± 0.09%, 0.90 ± 0.09%, 0.95 ± 0.05%, 0.95 ± 0.07% and 0.93 ± 0.12%, respectively.

As for the maximum dose (D₂) received by the small intestine, it can be seen that the average value increased with the increase of selected respiratory phases in the five plans of 10phase, 2phase, 3phase, 6Exphase and 6Inphase. The differences between 2phase, 3phase and 10phase plans were statistically significant (p < 0.05). There was a slightly decrease of the average value for 3D plan compared to the 10phase plan. The difference was not statistically significant (p > 0.05). The average values of 10phase, 2phase, 3phase, 6Exphase, 6Inphase and 3D plans were 38.87 ± 5.19, 37.82 ± 6.08, 38.17 ± 5.75, 38.86 ± 5.25, 38.50 ± 6.00 and 38.31 ± 5.71 Gy(RBE), respectively.

For small intestine V₁₅, the mean of the six plans increased with the number of selected respiratory phases. There was no statistical significance between the 3D plan and the 10phase plan (p > 0.05), while there were statistical significances between the other four plans and the 10phase plan (p < 0.05). The average values of 10phase, 2phase, 3phase, 6Exphase, 6Inphase and 3D plans were 23.97 ± 16.26%, 22.62 ± 15.28%, 22.97 ± 15.77%, 23.34 ± 15.65%, 23.30 ± 16.11% and 22.55 ± 14.46%, respectively.

For the maximum dose (D₂) received by the duodenum, there were little differences in the average values of the five plans (10phase, 2phase, 3phase, 6Exphase and 6Inphase plans), the difference were all below 0.5Gy(RBE). Except for 3phase plan, there were no significant differences in other plans (p > 0.05). The average value of 3D plan was higher than that of 10phase plan, and the difference was not statistically significant (p > 0.05). The average values of 10phase, 2phase, 3phase, 6Exphase, 6Inphase and 3D plans were 35.29 ± 18.17, 34.97 ± 18.21, 34.77 ± 18.21, 34.78 ± 18.48, 35.11 ± 18.48 and 36.03 ± 18.04 Gy(RBE), respectively.

Figure 5 shows the dose distributions for one representative example, calculated from the 10phase, 2phase, 3phase, 6Exphase, 6Inphase and 3D plans. The CT images shown in the figure were taken from the reference phase (0%Ex). The pink and yellow lines indicated the outlines of the CTVs. It can be seen that the uniformity of the target dose from all plans was reduced due to the interplay effect.

4D robust optimization considers all respiratory phases to account for tumor deformation during movement. However, selecting more phases increases optimization time. Multiple sets of 4D CT images are needed for precise anatomical movement analysis^[21]. Therefore, minimizing calculation load and optimization time is crucial. This study analyzed 15 cases with varied tumor size, location, and motion amplitude, which had certain credibility.

Optimizing the number of phases selected for the target improves dose coverage and uniformity significantly (p < 0.05). Conversely, an increase in the number of phases selected for the target leads to poor conformality (CI). This could be attributed to the inclusion of a wider range of tumor movement scenarios with varying amplitude and density changes. However, as tumor anatomical changes are not entirely predictable, this complexity can hinder optimization efforts. Further research is needed to explore the integration of tumor movement management and 4D optimization. Reduction in selected respiratory phases had minimal impact on dose distribution in OARs. In cases of pancreatic cancer, the tumor location and size significantly influenced the dose to OARs, making organ protection a challenge in proton therapy^[22].

To alleviate interplay effect, various methods have been suggested, including respiratory gating, tumor tracking, and breath holding^{[8, 23]}. In addition to using 4D robust optimization in the study, it is also a good method to use iso-energy layer repeated scanning technology. The scanning technology performed multiple repeated scans on each energy layer^[24]. Reasonable selection of the number of repeated scans based on the case situation can also alleviate the interplay effect^[25]. The combination of iso-energy layer repeated scanning technology and 4D robust optimization will also be applied to subsequent studies.

This study focused on optimizing the treatment planning time by incorporating 4D robust optimization alongside 3D robust optimization. Patient setup uncertainties were simulated by shifting the patient iso-center in the antero–posterior (A–P), superior–inferior (S–I), and right-left (R–L) directions by 5 mm, range uncertainties were simulated by ± 3.5%. The results obtained were based on the 10phase plan. The average time of this optimization method was 7971.8s. It was observed that full-time phase optimization can be time-consuming in clinical planning, as highlighted in a previous study by Buti et al^[26]. Therefore, reducing optimization time is crucial for practical clinical applications. However, the study had limitations. The small number of cases (15) could not fully represent all patients. Because of the irregular changes in respiratory cycle, the inability of 4D CT images cannot capture all respiratory movements^{[21, 27]}. Tumor movement also caused the irregular phase distribution. The study also noted that the correlation between tumor motion amplitude and optimization results required further investigation. Additionally, the simulation in the study was simplified with regular beam delivery and fixed respiratory cycle initiation. Future research should carefully consider the combination of respiratory movement and beam delivery logfile for a more comprehensive analysis.

In this study, a comprehensive evaluation of five 4D robust treatment planning strategies and one 3D treatment planning strategy for pancreatic cancer patients receiving IMPT was performed. The results showed in this work highlighted that the dosimetric performance of the 6Exphase and 6Inphase plans closely aligned with that of the 10phase plan. These plans offered a feasible alternative to 10phase optimization by reducing optimization time while maintaining dose coverage of the target and protection of OARs. This research provides guidelines to reduce optimization time and improve clinical efficiency for pancreatic cancer IMPT.

IMPT

intensity modulated proton therapy

4DDD

4D dynamic dose

Computed Tomography

GTV

gross target volume

CTV

clinical tumor volume

ICTV

internal clinical target volume

OARs

organs at risk

conformability index

heterogeneity index

Monte Carlo

RBE

relative biologic effectiveness

HFS

Head First Supine

Ethics approval and consent to participate

This study was approved by the Research Ethics Board of the Shandong Cancer Hospital. Written informed consent was waived by the Institutional Review Board.

Informed consent

Not applicable.

Competing interests

The authors have no relevant conflicts of interest to disclose.

Funding

This work was jointly funded by projects 12105160, 82072094 and 12275162 supported by National Natural Science Foundation of China; projects ZR2019LZL017 and ZR2021QA099 supported by Shandong Provincial Natural Science Foundation; project ts201712098 supported by Taishan Scholars Project of Shandong Province; project 2022B03019-5 supported by Xinjiang Uygur Autonomous Region key research and development project; and project 2021HZ81 supported by Tumor precision radiotherapy peak plan.

Author Contribution

XYF participated in the design of the study, data collection and the main manuscript writing. STW, WJL and TXL involved in the acquisition of data and revising the manuscript. YY and TYD participated in the revising of the manuscript critically for important intellectual content. All authors reviewed and approved the final manuscript.

Acknowledgement

No Acknowledgement.

Data availability

All data included in this study are available upon lquest by contact with the

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No competing interests reported.

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Effect of Breathing Phase Number on the 4D Robust Optimization for Pancreatic Cancer Intensity Modulated Proton Therapy

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