Abstract
To evaluate the plan quality and robustness of volumetric modulated arc therapy (VMAT) and intensity modulated radiation therapy (IMRT) for breast cancer, 50 patients, including 25 patients who received radiotherapy after breast-conserving surgery (BCR) and 25 patients who received postmastectomy radiotherapy (PRT), were selected for this study. Nominal VMAT and IMRT plans were generated for each patient on Eclipse treatment planning system (version 15.6). The dosimetric metrics, dose distribution, gamma passing rate, and delivery time were compared. In addition, 12 uncertainty plans with plan isocenter uncertainty and CT density uncertainty were recalculated based on the nominal plans for each patient. The dose volume histogram (DVH) band width (DVHBW) was adopted to quantify the plan robustness of the nominal plans for the perturbed scenarios in this study. For BCR, the dosimetric metrics except planning target volume (PTV) conformal index (CI) and ipsilateral lung V 5 were not statistically different for IMRT and VMAT plans. PTV CI of VMAT plans was better than that of IMRT plans (VMAT: 0.923 ± 0.024, IMRT: 0.855 ± 0.032, p = 0.003). The ipsilateral lung V 5 of VMAT plan was higher than that of IMRT plan (VMAT: 42.4% ± 2.8%, IMRT: 40.5% ± 4.0%, p = 0.045). The VMAT plans save more than 1.20 min compared to the IMRT plans (VMAT: 0.87 min, IMRT: 2.08 min, p < 0.001). The gamma passing rates of VMAT plans were better than those of IMRT plans (3 mm/3%, VMAT: 99.7% ± 0.2%, IMRT: 99.4% ± 0.4%, p < 0.001; 2 mm/2%, VMAT: 97.2% ± 1.0%, IMRT: 96.9% ± 0.6%, p = 0.108). For PRT, the dosimetric metrics of VMAT plans, including PTV D mean, homogeneity index (HI), CI, and D max of spinal cord, were significantly better than those of IMRT plans. The VMAT plans save more than 45% time compared with IMRT plans (VMAT: 1.54 min, IMRT: 2.81 min, p < 0.001). The difference in gamma passing rates between VMAT plans and IMRT plans was not statistically significant. For the plan robustness, the DVHBW of VMAT plans and IMRT plans for BCR were 2.09% ± 0.23% and 2.98% ± 0.40%, respectively (p < 0.05). For PRT, the DVHBW of VMAT plans was significantly better than those of IMRT plans (VMAT: 3.05% ± 0.26%, IMRT: 3.57% ± 0.27%, p < 0.05). The results show that the dosimetric metrics of VMAT plans were comparable to those of IMRT plans. More importantly, the VMAT plans had excited dose distribution and fast execution efficiency. The plan robustness of VMAT plans were superior.
1 Introduction
There were 19.3 million new cancer cases and about 9.96 million new deaths worldwide in 2020 [1], says the World Health Organization. The severity of cancer treatment has brought major challenges to global public health. In 2020, 2.3 million women worldwide were diagnosed with breast cancer, and 685,000 women died from breast cancer. Breast cancer has become one of the most important factors threatening women’s health [2].
Radiation therapy (RT) plays a very important role in the treatment of breast cancer. For early-stage breast cancer, RT can prevent women from having to undergo mastectomy. For late-stage cancer, RT can reduce the risk of cancer recurrence, even if a mastectomy has been performed. For advanced breast cancer, RT can reduce the likelihood of dying from the disease in some cases [3]. Both intensity modulated radiation therapy (IMRT) [4,5] and volumetric modulated arc therapy (VMAT) [6,7,8] are the main radiotherapy techniques for breast cancer. Different radiation techniques have a great impact on the dose distribution of the target volume and the organs at risk (OARs). There are also some differences in treatment time due to different radiation techniques. Whether using IMRT or VMAT technology, the ultimate goal is to give the target as high a dose as possible and protect the adjacent OARs as much as possible.
Previous studies have demonstrated that IMRT is beneficial in reducing the volume of the affected lung that is irradiated at low dose, which can reduce the chance of radiation pneumonitis caused by RT [9,10]. In addition, the mean dose of the heart is reduced. VMAT is conducive in improving the uniformity and dose conformity of the target volume [6], reducing the number of monitor units (MUs) in the radiotherapy plan, and shortening the treatment time of patients.
The Halcyon accelerator is a new generation of smart radiotherapy system of Varian, equipped with a double-layer multi-leaf collimator (MLC) that greatly improves radiation leakage and has a high level of safety [11,12]. The misaligned design of the double-layer MLC can better conform the target and provide better protection of the OARs. In addition, the dose rate of Halcyon accelerator reaches 800 MU/min, which can greatly improve the efficiency of treatment.
The present study will explore the clinical application of IMRT and VMAT in breast cancer radiotherapy based on the Eclipse treatment planning system and the Halcyon V2.0 linear accelerator. Several tools will be introduced to assess the plan quality and plan robustness for breast cancer.
2 Materials and methods
2.1 Patients selection
This retrospective study included 50 patients with breast cancer who have undergone radiotherapy. 25 of them were treated with radiotherapy after breast-conserving surgery (BCR), named as group BCR, and the other 25 were treated with postmastectomy radiation therapy (PRT), named as group PRT.
2.2 CT scanning
CT scans were performed using Somatom Confidence CT (Siemens, Germany). The upper boundary was the mandible, lower boundary was the lower border of the liver, and the slice thickness was 3 mm. The scanning current and voltage were 400 mAs and 120 kV, respectively. Field of View was 300 mm.
2.3 Contouring
Clinical target volume (CTV) and OARs were defined according to the Guideline of target delineation and treatment planning of adjuvant radiotherapy for breast cancer issued by the National Cancer Center & National Cancer Quality Control Center, where the prescription dose has been standardized [13]. CTV included breast/chest wall, supraclavicular, internal mammary, and axillary lymph nodes (CTV of group BCR only included breast/chest wall). Planning target volume (PTV) included CTV and a 5 mm margin based on CTV. OARs, including ipsilateral lung, heart, spinal cord, and contralateral lung, were delineated.
2.4 Treatment planning
Plans based on IMRT or VMAT were created for all patients using the Eclipse treatment planning system (Version 15.6). The calculation algorithm is anisotropic analytical algorithm (AAA) and the calculation grid is 2.5 mm. The IMRT plans used six fields with the gantry angle of 300°, 315°, 330°, 100°, 115°,and 130° for the left-sided BCR and 215°, 230°, 245°, 45°, 60°, and 75° for the right-sided BCR. For the group PRT based on IMRT, seven fields were used with the gantry angle of 300°, 315°, 330°, 10°, 100°, 115°, and 130° for the left-sided PRT and 215°, 230°, 245°, 350°, 45°, 60°, and 75° for the right-sided PRT. All the VMAT plans used two semi-arcs for all patients. For the left-sided BCR or PRT, the gantry was rotated from 300° to 130° clockwise and then from 130° to 300° counterclockwise. For the right-sided BCR or PRT, the gantry was rotated from 215° to 75° clockwise and then from 75° to 215° counterclockwise. The total prescribed dose was 50 Gy in 25 fractions for all patients.
During the planning design process, in order to limit the range of motion of the MLC and protect the affected lung and heart, an auxiliary structure will be delineated. The range of the auxiliary structure is shown in Figure 1, the left-right directions and the head-feet directions of the auxiliary structure do not exceed the range of the affected lung, the anterior and posterior directions are bounded by 3 cm from the target volume, and the posterior boundary does not exceed the range of the affected lung. OARs around the target volume are protected by limiting the beam fluence through auxiliary structure. In addition, for the BCR patients, the target volume is located on the chest wall, close to the heart. The target volume will move with breathing during the treatment process. In order to avoid missed radiation in the target caused by breathing, the out-diffusion of the fluence along the chest wall will be carried out, and the range of the external expansion is 1 cm. The out-diffusion of the fluence is shown in Figure 2.

Schematic diagram of the auxiliary structure.

Out-diffusion of fluence.
All treatment plans should meet the following optimization objectives: the volume that PTV received the prescription dose more than 95% of PTV (PTV V 50Gy ≥ 95%) and at most 5% of PTV received a maximum of 107% of the prescription dose (PTV V 53.5Gy ≤ 5%). For the OARs, the specific optimization objectives are shown in Table 1. The maximum dose rate of Halcyon accelerator is 800 MUs per minute.
Optimization objectives of OARs in the plans
| Optimization objectives | Group BCR | Group PRT |
|---|---|---|
| Ipsilateral lung | ||
| V 5Gy | ≤45% | ≤50–55% |
| V 20Gy | ≤20% | ≤25% |
| D mean | ≤900 cGy | ≤1,200 cGy |
| Heart | ||
| V 5Gy | ≤20%(*R) ≤30%(*L) | ≤25%(*R) ≤35%(*L) |
| D mean | ≤400 cGy(*R) ≤600 cGy(*L) | ≤500 cGy(*R) ≤800 cGy(*L) |
| Spinal cord | ||
| D max | ≤1,500 cGy | ≤3,000 cGy |
| Contralateral lung | ||
| V 5Gy | ≤20% | ≤25% |
Abbreviation: BCR: radiotherapy after breast-conserving surgery; PRT: postmastectomy RT; V xGy: the volume that a structure received xGy as a percentage of the volume of the structure; D mean: mean dose; *R: right-sided breast cancer; *L: left-sided breast cancer.
2.5 Evaluation
2.5.1 Dose volume histogram (DVH) curves
DVH curves for all regions of interest were calculated on the same coordinate. The nominal doses and perturbed doses are displayed in this study.
2.5.2 Dosimetric parameters
The comparison between IMRT and VMAT plans on dosimetric parameters was performed when the endpoint in this study was plan quality. The primary evaluation indices are shown in Table 2. In addition to the parameters mentioned in Table 2, the PTV conformal index (CI) and homogeneity index (HI) recommended by ICRU report 83 [14] was introduced in this study.
Details of the evaluation indices in the plans
| Structure | Evaluation metrics |
|---|---|
| PTV | V 50Gy/D 98%/D 50%/D 2%/D mean |
| Ipsilateral lung | V 5Gy/V 20Gy/D mean |
| Heart | D mean/V 5Gy |
| Spinal cord | D max |
| Contralateral lung | V 5Gy |
The PTV CI is defined as formula (1).
where
The PTV HI is defined as formula (2).
where D 2%, D 98%, and D 50% is the dose received by 2, 98, and 50% volume of PTV, respectively. The lower HI means the better uniformity for PTV.
2.5.3 Delivery time
The quality assurance mode based on the Halcyon accelerator was used to simulate the irradiation of two plans for each case to obtain the delivery time of the patient during radiotherapy when the end point of the study was the delivery time.
2.5.4 Gamma passing rate
All plans were tested with the gamma passing rate using the ArcCheck 3D matrix verification system based on the SNC Patient gamma passing rate analysis software of SUN NUCLEAR corporation. The evaluation metrics were gamma passing rate under the conditions of 3 mm/3% and 2 mm/2%, respectively.
2.6 Plan robustness
According to the previous study, the crucial factors causing the difference between the actual dose distribution and the planned dose distribution are plan isocenter shift and CT density uncertainty [15,16,17]. Paganetti [18] suggested setting a plan isocenter shift of 5 mm and CT density uncertainties of ±2% to calculate the perturbed dose. Liu et al. [19] set a value of 3 mm isocenter uncertainty and ±3% CT density uncertainty for the treatment of distal esophageal carcinoma.
114 patients who had finished radiotherapy for breast cancer in our center were retrospectively selected; the data about plan isocenter shift of 2,352 treatments for these patients are shown in Figure 3. 95% confidence interval for the anterior-posterior (AP), superior-inferior (SI), and left-right (LR) directions are (−0.09, 0.31), (−0.11, 0.44), and (−0.10, 0.43), respectively. Thus, the plan isocenter shifts were set to 0.31 cm for AP direction, 0.44 cm for SI direction, and 0.43 cm for LR direction in this study. Finally, all perturbed doses were calculated with 12 scenarios. The details of these 12 scenarios taken into account are shown in Table 3.

Plan isocenter shift distances in the anterior-posterior, superior-inferior, and left-right directions of 2,352 treatments of the 114 breast cancer patients.
Plan isocenter uncertainty and CT density uncertainty with 12 scenarios
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| AP, cm | 0.31 | 0.31 | −0.31 | −0.31 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| SI, cm | 0 | 0 | 0 | 0 | 0.44 | 0.44 | −0.44 | −0.44 | 0 | 0 | 0 | 0 |
| LR, cm | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.43 | 0.43 | −0.43 | −0.43 |
| CT, % | 2 | −2 | 2 | −2 | 2 | −2 | 2 | −2 | 2 | −2 | 2 | −2 |
DVH band width (DVHBW) was adopted to quantify the plan robustness in this study, the difference between the perturbed scenario and nominal scenario were calculated. The DVHBW can be defined as formula (3) [20,21].
where
2.7 Statistical analysis
The paired t test was performed using SPSS Statistics version 21 software. The p value of less than 0.05 (p < 0.05) was considered statistically significant.
3 Results
3.1 DVH curves
Figure 4 shows the results obtained using two typical cases. As can be seen in Figure 4a (BCR), the V 50Gy of PTV for both IMRT and VMAT are 98%, but the homogeneity of the VMAT plan is better than that of the IMRT plan. For the ipsilateral lung, V 20Gy, V 30Gy, and mean dose of VMAT plan are better than those of IMRT plan, and V 5Gy is slightly higher. The doses to heart and contralateral lung of the VMAT plan are higher than those of the IMRT plan, but they are far less than the dose limitation. As can be seen in Figure 4b (PRT), the V 50Gy of PTV for VMAT plan and IMRT plan are 99.1 and 99.0%, respectively. The homogeneity of the VMAT plan is better than that of the IMRT plan. For the ipsilateral lung, the volume of VMAT plan is higher than that of IMRT plan when the dose is less than 1,000 cGy. However, the opposite result is found when the dose is between 1,000 and 3,000 cGy. In the high-dose region (>3,000 cGy), the DVH curves of the two plans almost overlapped. The doses to heart, contralateral lung, and spinal cord in VMAT plan are higher than those in IMRT plan, but they are lower than their dose limitations.

Dose Volume histogram curves for (a) BCR plan and (b) PRT plan. (Note: * is VMAT plan, Ip is the abbreviation of ipsilateral, and Co is the abbreviation of contralateral).
3.2 Dosimetric parameters
As can be seen from Table 4, the major parameters of PTV, including PTV, D95%, D mean, and HI, are not statistically different for IMRT plan and VMAT plan (p > 0.05). PTV CI of VMAT plan is better than that of IMRT plan, and the difference is statistically significant (p < 0.05). For OARs, the ipsilateral lung V 20 and D mean, and heart D mean and V 5 of VMAT plan are slightly higher than those of IMRT plan, the difference is not statistically significant (p > 0.05). The V 5 of ipsilateral lung and contralateral lung in IMRT plan are about 1.9 and 4.9% lower than those in VMAT plan, respectively (p < 0.05).
Parameter statistics of the radiotherapy plan after BCR
| Group | Structure | Parameter/unit | IMRT | VMAT | p-value |
|---|---|---|---|---|---|
| BCR | PTV | D95%/cGy | 5054.7 ± 19.3 | 5051.5 ± 19.5 | 0.704 |
| D mean/cGy | 5187.7 ± 17.7 | 5187.9 ± 24.2 | 0.979 | ||
| HI/– | 0.062 ± 0.010 | 0.058 ± 0.009 | 0.280 | ||
| CI/– | 0.855 ± 0.032 | 0.923 ± 0.024 | 0.003 | ||
| Ipsilateral lung | V 20/% | 15.0 ± 2.9% | 15.6 ± 2.6% | 0.208 | |
| V 5/% | 40.5 ± 4.0% | 42.4 ± 2.8% | 0.045 | ||
| D mean/cGy | 922.6 ± 110.7 | 934.5 ± 93.6 | 0.453 | ||
| Heart | D mean/cGy | 224.3 ± 117.8 | 252.8 ± 102.7 | 0.349 | |
| V 5/% | 9.1 ± 8.4% | 10.1 ± 4.8% | 0.597 | ||
| Contralateral lung | V 5/% | 2.5 ± 4.6% | 7.4 ± 5.6% | 0.015 |
As can be seen from Table 5, PTV D95% is not statistically different for IMRT plan and VMAT plan (p = 0.151). However, PTV CI and PTV HI of VMAT plan are better than those of IMRT plan, and the difference is statistically significant (p < 0.001). For OARs, the ipsilateral lung V 20, V 5, and D mean and heart D mean and V 5 are not statistically different. The D max of spinal cord of VMAT plan is lower than that of IMRT plan (p < 0.05).
Parameter statistics of the PRT plan
| Group | Structure | Parameter/unit | IMRT | VMAT | p-value |
|---|---|---|---|---|---|
| PRT | PTV | D95%/cGy | 5029.4 ± 20.6 | 5034.1 ± 21.0 | 0.151 |
| D mean/cGy | 5190.4 ± 15.3 | 5204.0 ± 25.3 | <0.001 | ||
| HI/– | 0.072 ± 0.010 | 0.067 ± 0.010 | <0.001 | ||
| CI/– | 0.763 ± 0.046 | 0.799 ± 0.055 | <0.001 | ||
| Ipsilateral lung | V 20/% | 18.5% ± 2.4% | 18.3% ± 2.1% | 0.327 | |
| V 5/% | 49.5% ± 3.7% | 49.6% ± 4.3% | 0.606 | ||
| D mean/cGy | 1107.6 ± 108.8 | 1115.6 ± 109.6 | 0.052 | ||
| Heart | D mean/cGy | 371.5 ± 161.9 | 374.7 ± 153.3 | 0.523 | |
| V 5/% | 15.0% ± 6.8% | 14.2% ± 5.4% | 0.263 | ||
| Spinal cord | D max | 2580.9 ± 829.5 | 2502.2 ± 804.4 | 0.047 | |
| Contralateral lung | V 5/% | 3.5% ± 3.3% | 4.0% ± 3.5% | 0.130 |
3.3 Delivery time
As can be seen in Figure 5, the average delivery time of all VMAT plans is obviously lower than that of IMRT plans, the difference is statistically significant (VMAT: 1.20 min, IMRT: 2.45 min, p < 0.001). For the BCR plans, 1.15 min are saved using VMAT compared with using IMRT, and the difference is statistically significant (VMAT: 0.87 min, IMRT: 2.08 min, p < 0.001). For the PRT plans, the VMAT plans save more than 45% time compared with IMRT plans (VMAT: 1.54 min, IMRT: 2.81 min, p < 0.001).

The delivery time of all plans on Halcyon accelerator.
3.4 Gamma passing rate
Figure 6 illustrates the gamma passing rate using ArcCheck three-dimensional verification system and SNC Patient gamma analysis software under the condition of 3 mm/3% or 2 mm/2%. On the whole, all gamma passing rates are better than 95.4%, the lowest data of 3 mm/3% is 97.9 in PRT plans using IMRT. Under the condition of 3 mm/3%, gamma passing rate for all plans is 99.5 ± 0.4%, ranging from 97.9% to 100%. Under the condition of 2 mm/2%, gamma passing rate for all plans is 97.2 ± 0.9%, ranging from 95.4 to 99.2%. Specifically, for BCR plans, gamma passing rate of VMAT plans is 99.7 ± 0.2 and 99.4 ± 0.4% for IMRT plans with the condition of 3 mm/3%, the difference between VMAT and IMRT is statistically significant (p < 0.001). 97.2 ± 1.0 and 96.9 ± 0.6% are the data for VMAT plans and IMRT plans under the condition of 2 mm/2%, respectively (p = 0.108). For PRT plans, VMAT plans and IMRT plans with 3 mm/3% are 99.6 ± 0.3 and 99.4 ± 0.6%, respectively, the difference is not statistically significant (p = 0.287). 97.3 ± 1.0 and 97.2 ± 0.8% are the data for VMAT plans and IMRT plans under the condition of 2 mm/2%, respectively. The difference is not statistically significant (p = 0.704).

Statistics of gamma passing rate for all plans.
3.5 Plan robustness
Previous study had demonstrated that the plan isocenter shift and CT density uncertainty will cause the difference between the actual dose distribution and the planned dose distribution [14,15,16,17,18]. In this study, plan robustness was evaluated in both IMRT plans and VMAT plans with 12 scenarios. The plan robustness quantification parameter λ was applied, and λ is displayed in Figures 7 and 8.

DVHBW (λ) of IMRT and VMAT plans for BCR.

DVHBW (λ) of IMRT and VMAT plans for PRT.
As shown in Figure 7, the λ of VMAT plans is significantly better than those of IMRT plans in BCR group (p < 0.05). Specifically, the λ of VMAT plans is 2.09 ± 0.23%, ranging from 1.67 to 2.56%. And the λ of IMRT plans is 2.98 ± 0.40%, ranging from 2.18 to 3.98%.
As shown in Figure 8, the λ of VMAT plans is significantly better than those of IMRT plans in BCR group (p < 0.05). Specifically, the λ of VMAT plans is 3.05 ± 0.26%, ranging from 2.63 to 3.66%. And the λ of IMRT plans is 3.57 ± 0.27%, ranging from 3.08 to 4.13%.
4 Discussion
Radiotherapy is one of the important methods of tumor treatment, about 70% of tumor patients receive radiotherapy during the treatment process, about 40% of malignant tumors can be cured by radiotherapy [22,23,24]. According to the statistics, breast cancer has become the first major cancer disease, and it is the main factor that threatens women’s health in the world [1,2]. In order to compare the plan robustness, plan quality, delivery time, and 3-Dimensional gamma passing rate between VMAT plans and IMRT plans for breast cancer, 25 patients, who received BCR, and another 25 patients, who received PRT, were selected for this study.
The same patient setup uncertainties and CT density uncertainty were applied for both VMAT and IMRT in this study. DVHBW was used to compare the plan robustness of VMAT plans and IMRT plans. The DVHBW of VMAT plans are 2.09% for BCR and 3.05% for PRT, which are statistically better than those of IMRT plans (BCR: 2.09% for VMAT vs 2.98% for IMRT, p < 0.05; PRT: 3.05% for VMAT vs 3.57% for IMRT, p < 0.05). Our results provide compelling evidence that VMAT is more capable of dealing with uncertainties. The perturbed dose distribution is closer to the nominal dose distribution.
When focusing on the plan quality, the traditional DVH metric methods is a convenient method for quantitatively evaluating the plan quality. Our results show that the PTV coverage differences between IMRT and VMAT are negligible. The CI is more elevated in VMAT plans than in IMRT plans (BCR: 0.923 vs 0.855, p < 0.05; PRT: 0.799 vs 0.763, p < 0.05). Most notably, there are no significant dose differences for most OARs between two beam delivery modalities. VMAT plans are more elevated than IMRT plans for both BCR and PRT when the plan quality is the endpoint of this study. Previous studies have demonstrated that effective protection of the heart and both lungs is beneficial to reduce the side effects such as ischemic heart disease and radiation pneumonitis caused by radiotherapy [25,26,27,28].
In terms of treatment efficiency, the VMAT plans provide more quick treatment than IMRT plans (VMAT: 1.20 min, IMRT: 2.45 min, p < 0.001). The gamma passing rates under the condition of 3 mm/3% or 2 mm/2% were introduced to evaluate the difference between the planned dose distribution and the actual dose distribution. On the whole, the gamma passing rates of all plans is 97.2 ± 0.9% with 2 mm/2% criteria and 99.5 ± 0.4% with 3 mm/3% criteria. The gamma passing rates of all plans are better than the recommended value of AAPM TG-119 report [29] and AAPM TG-218 report [30]. VMAT plans have a higher gamma passing rates than IMRT plans (VMAT: 98.4 ± 1.4%, IMRT: 98.2 ± 1.3%, p = 0.015).
Some limitations are worth focusing, the positional variation and anatomical variation caused by breathing are needed to be considered. In addition, the CT density uncertainty and plan isocenter shift data used in this study were based on the clinical data from our department. In the following study, further research is needed for optimizing the plan robustness to improve the robustness in the scenarios of the CT density uncertainty and plan isocenter shift. Another point to note is that the dose calculation inaccuracy of the target volume was around 3%, and the dose calculation error of the OARs was mostly within 5% when using the AAA algorithm in other published studies [31,32]. In clinical work, the deviation of AAA algorithm in dose calculation in inhomogeneous media should be fully considered to provide a more realistic and reasonable treatment plan.
5 Conclusion
In our study, the robustness, the plan quality, the treatment time, and the gamma passing rate were investigated by comparing VMAT and IMRT for breast cancer. Our results showed that VMAT generated a more robust plan in target volume. Furthermore, VMAT provides a more efficient and more accurate plan without compromising the plan quality. In the following work, the robustness optimization of the treatment plan is our focus direction. The robust optimization considers the range deviation, setup error, and CT value uncertainty. Theoretically, robust optimization will improve the robustness of the plan to better cope with setup errors and CT value uncertainty. In addition, robust optimization would reduce the dose to normal tissues and improve the HI of the target volume.
Acknowledgments
The authors sincerely thank all teachers who helped in the process of this article.
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Funding information: This research was supported by the Special Support for Postdoctoral Research Projects in Sichuan Province, No TB2022072; and Special project of Chengdu University of Traditional Chinese Medicine, No XJ2023000101.
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Author contributions: Chuou Yin: conceptualization, methodology, validation, data curation, data analysis, visualization, writing – original draft, and writing – review and editing; Juan Deng: design treatment plans; Guojian Mei: review treatment plans; Hao Cheng: delineation and review treatment plans; Yingying He: delineation and review treat-ment plans; and Jiang Liu: supervision. All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
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Conflict of interest: The authors state no conflict of interest.
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Ethical approval: The research related to human use has been complied with all the relevant national regulations, institutional policies and in accordance the tenets of the Helsinki Declaration, and has been approved by the authors' institutional review board or equivalent committee.
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Data availability statement: The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.
References
[1] Sung H, Ferlay J, Siegel RL, Laversanne M, Soerjomataram I, Jemal A, et al. Global Cancer Statistics 2020: GLOBOCAN estimates of incidence and mortality worldwide for 36 cancers in 185 countries. CA: A Cancer J Clin. 2021;71(3):209–49.10.3322/caac.21660Search in Google Scholar PubMed
[2] Rositch AF, Unger-Saldaña K, DeBoer RJ, Ng'ang'a A, Weiner BJ. The role of dissemination and implementation science in global breast cancer control programs: Frameworks, methods, and examples. Cancer. 2020;126(Suppl 10):2394–404.10.1002/cncr.32877Search in Google Scholar PubMed
[3] Fozza A, De Rose F, De Santis MC, Meattini I, Meduri B, D'angelo E, et al. Technological advancements and future perspectives in breast cancer radiation therapy. Expert Rev Anticancer Ther. 2023;23(4):407–19. 10.1080/14737140.2023.2195167.Search in Google Scholar PubMed
[4] Lee HH, Chen CH, Luo KH, Chuang HY, Huang CJ, Cheng YK, et al. Five-year survival outcomes of intensity-modulated radiotherapy with simultaneous integrated boost (IMRT-SIB) using forward IMRT or tomotherapy for breast cancer. Sci Rep. 2020;10:4342.10.1038/s41598-020-61403-6Search in Google Scholar PubMed PubMed Central
[5] Torres MA, Gogineni K, Howard DH. Intensity-modulated radiation therapy in breast cancer patients following the release of a choosing wisely recommendation. J Natl Cancer Inst. 2020;112(3):314–7. 10.1093/jnci/djz198.Search in Google Scholar PubMed PubMed Central
[6] Kuo L, Ballangrud ÅM, Ho AY, Mechalakos JG, Li G, Hong L. A VMAT planning technique for locally advanced breast cancer patients with expander or implant reconstructions requiring comprehensive postmastectomy radiation therapy. Med Dosim: Off J Am Assoc Med Dosim. 2019;44(2):150–4. 10.1016/j.meddos.2018.04.006.Search in Google Scholar PubMed PubMed Central
[7] Rossi M, Virén T, Heikkilä J, Seppälä J, Boman E. The robustness of VMAT radiotherapy for breast cancer with tissue deformations. Med Dosim: Off J Am Assoc Med Dosim. 2021;46(1):86–93. 10.1016/j.meddos.2020.09.005.Search in Google Scholar PubMed
[8] Zhang Y, Huang Y, Ding S, Yuan X, Shu Y, Liang J, et al. A dosimetric and radiobiological evaluation of VMAT following mastectomy for patients with left-sided breast cancer. Radiat Oncol. 2021;16:171.10.1186/s13014-021-01895-2Search in Google Scholar PubMed PubMed Central
[9] Du L, Qu B, Ma N, Huang X, Yu W, Xu S, et al. P1.17-03 Potential Associated SNPs by GWAS with radiation pneumonitis (RP) in patients with lung cancer treated with radiotherapy. J Thorac Oncol. 2018;13(10):S655–6. 10.1016/j.jtho.2018.08.1036 ISSN 1556-0864.Search in Google Scholar
[10] Zhang X, Lv B, Rui L, Cai L, Liu F. Regression analysis of factors based on cluster analysis of acute radiation pneumonia due to radiation therapy for lung cancer. J Healthc Eng. Oct. 2021;2021:3727794. 10.1155/2021/3727794.Search in Google Scholar PubMed PubMed Central
[11] Kim MM, Bollinger D, Kennedy C, Zou W, Scheuermann R, Teo BK, et al. Dosimetric characterization of the dual layer MLC system for an O-ring linear accelerator. Technol Cancer Res Treat. 2019;18:1533033819883641. 10.1177/1533033819883641.Search in Google Scholar PubMed PubMed Central
[12] Pawlicki T, Atwood T, McConnell K, Kim GY. Clinical safety assessment of the Halcyon system. Med Phys. 2019;46(10):4340–5. 10.1002/mp.13736.Search in Google Scholar PubMed
[13] National Cancer Center/National Cancer Quality Control Center. Guideline of target delineation and treatment planning of adjuvant radiotherapy for breast cancer. Chin J Radiat Oncol. 2022;31(10):863–78. 10.3760/cma.j.cn113030-20220627-00226.Search in Google Scholar
[14] Grégoire V, Mackie TR. State of the art on dose prescription, reporting and recording in intensity-modulated radiation therapy (ICRU report No. 83). Cancer Radiother. 2011;15(6–7):555–9. 10.1016/j.canrad.2011.04.003.Search in Google Scholar PubMed
[15] Shang H, Pu Y, Wang W, Dai Z, Jin F. Evaluation of plan quality and robustness of IMPT and helical IMRT for cervical cancer. Radiat Oncol. 2020 Feb;15(1):34. 10.1186/s13014-020-1483-x. PMID: 32054496. PMCID: PMC7020599.Search in Google Scholar
[16] Ding Z, Xiang X, Zeng Q, Ma J, Dai Z, Kang K, et al. Evaluation of plan robustness on the dosimetry of volumetric arc radiotherapy (VMAT) with set-up uncertainty in nasopharyngeal carcinoma (NPC) radiotherapy. Radiat Oncol. 2022;17:1. 10.1186/s13014-021-01970-8.Search in Google Scholar PubMed PubMed Central
[17] Kaplan LP, Placidi L, Bäck A, Canters R, Hussein M, Vaniqui A, et al. Plan quality assessment in clinical practice: Results of the 2020 ESTRO survey on plan complexity and robustness. Radiother Oncol. 2022 Aug;173:254–61. 10.1016/j.radonc.2022.06.005. Epub 2022 Jun 14. PMID: 35714808.Search in Google Scholar PubMed
[18] Paganetti H Range uncertainties in proton therapy and the role of Monte Carlo simulations. Phys Med Biol. 2012 Jun;57(11):R99–117. 10.1088/0031-9155/57/11/R99. Epub 2012 May 9 PMID: 22571913. PMCID: PMC3374500.Search in Google Scholar PubMed PubMed Central
[19] Liu C, Bhangoo RS, Sio TT, Yu NY, Shan J, Chiang JS, et al. Dosimetric comparison of distal esophageal carcinoma plans for patients treated with small-spot intensity-modulated proton versus volumetric-modulated arc therapies. J Appl Clin Med Phys. 2019 Jul;20(7):15–27. 10.1002/acm2.12623. Epub 2019 May 21 PMID: 31112371. PMCID: PMC6612702.Search in Google Scholar
[20] Liu C, Bhangoo RS, Sio TT, Yu NY, Shan J, Chiang JS, et al. Dosimetric comparison of distal esophageal carcinoma plans for patients treated with small-spot intensity-modulated proton versus volumetric-modulated arc therapies. J Appl Clin Med Phys. 2019;20:15–27. 10.1002/acm2.12623.Search in Google Scholar PubMed PubMed Central
[21] Ding Z, Zeng Q, Kang K, Xu M, Xiang X, Liu C. Evaluation of plan robustness using hybrid intensity-modulated radiotherapy (IMRT) and Volumetric arc modulation radiotherapy (VMAT) for left-sided breast cancer. Bioengineering. 2022 Mar;9(4):131. 10.3390/bioengineering9040131. PMID: 35447691; PMCID: PMC9028731.Search in Google Scholar PubMed PubMed Central
[22] Ferlay J, Ervik M, Lam F, Colombet M, Mery L, Piñeros M, et al. Global Cancer Observatory: Cancer Today. Lyon: International Agency for Research on Cancer; 2020. https://gco.iarc.fr/todayaccessed February 2021).Search in Google Scholar
[23] de Martel C, Georges D, Bray F, Ferlay J, Clifford GM. Global burden of cancer attributable to infections in 2018: a worldwide incidence analysis. Lancet Glob Health. 2020;8(2):e180–90.10.1016/S2214-109X(19)30488-7Search in Google Scholar PubMed
[24] Assessing National Capacity for the Prevention and Control of Noncommunicable Diseases: Report of the. Global survey. Geneva: World Health Organization; 2019. p. 2020.Search in Google Scholar
[25] Ellahham S, Khalouf A, Elkhazendar M, et al. An overview of radiation-induced heart disease. Radiat Oncol J. 2022Jun;40(2):89–102. 10.3857/roj.2021.00766. Epub 2022 Jun 21 PMID: 35796112; PMCID: PMC9262704.Search in Google Scholar PubMed PubMed Central
[26] Wadsten C, Wennstig AK, Garmo H, Nilsson G, Blomqvist C, Holmberg L, et al. Risk of ischemic heart disease after radiotherapy for ductal carcinoma in situ. Breast Cancer Res Treat. 2018;171(1):95–101. 10.1007/s10549-018-4803-1.Search in Google Scholar PubMed
[27] Arroyo-Hernández M, Maldonado F, Lozano-Ruiz F, Muñoz-Montaño W, Nuñez-Baez M, Arrieta O. Radiation-induced lung injury: current evidence. BMC Pulm Med. 2021;21:9. 10.1186/s12890-020-01376-4.Search in Google Scholar PubMed PubMed Central
[28] Hanania AN, Mainwaring W, Ghebre YT, Hanania NA, Ludwig M. Radiation-induced lung injury: assessment and management. Chest. 2019;156(1):150–62. 10.1016/j.chest.2019.03.033.Search in Google Scholar PubMed PubMed Central
[29] Ezzell GA, Burmeister JW, Dogan N, LoSasso TJ, Mechalakos JG, Mihailidis D, et al. IMRT commissioning: multiple institution planning and dosimetry comparisons, a report from AAPM Task Group 119. Med Phys. 2009 Nov;36:5359–73.10.1118/1.3238104Search in Google Scholar PubMed
[30] Miften M, Olch A, Mihailidis D, Moran J, Pawlicki T, Molineu A, et al. Tolerance limits and methodologies for IMRT measurement-based verification QA: recommendations of AAPM Task Group No. 218. J Med Phys. 2018;45(4):e53–83.10.1002/mp.12810Search in Google Scholar PubMed
[31] Bosse C, Narayanasamy G, Saenz D, Myers P, Kirby N, Rasmussen K, et al. Dose calculation comparisons between three modern treatment planning systems, J Med Phys. 2020 Jul–Sep;45(3):143–7. 10.4103/jmp.JMP_111_19. Epub 2020 Oct 13 PMID: 33487926. PMCID: PMC7810148.Search in Google Scholar
[32] Bragg CM, Conway J. Dosimetric verification of the anisotropic analytical algorithm for radiotherapy treatment planning. Radiother Oncol. 2006 Dec;81(3):315–23. 10.1016/j.radonc.2006.10.020, Epub 2006 Nov 27. PMID: 17125862.Search in Google Scholar PubMed
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Articles in the same Issue
- Regular Articles
- Numerical study of flow and heat transfer in the channel of panel-type radiator with semi-detached inclined trapezoidal wing vortex generators
- Homogeneous–heterogeneous reactions in the colloidal investigation of Casson fluid
- High-speed mid-infrared Mach–Zehnder electro-optical modulators in lithium niobate thin film on sapphire
- Numerical analysis of dengue transmission model using Caputo–Fabrizio fractional derivative
- Mononuclear nanofluids undergoing convective heating across a stretching sheet and undergoing MHD flow in three dimensions: Potential industrial applications
- Heat transfer characteristics of cobalt ferrite nanoparticles scattered in sodium alginate-based non-Newtonian nanofluid over a stretching/shrinking horizontal plane surface
- The electrically conducting water-based nanofluid flow containing titanium and aluminum alloys over a rotating disk surface with nonlinear thermal radiation: A numerical analysis
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- A numerical analysis of the blood-based Casson hybrid nanofluid flow past a convectively heated surface embedded in a porous medium
- Optoelectronic–thermomagnetic effect of a microelongated non-local rotating semiconductor heated by pulsed laser with varying thermal conductivity
- Thermal proficiency of magnetized and radiative cross-ternary hybrid nanofluid flow induced by a vertical cylinder
- Enhanced heat transfer and fluid motion in 3D nanofluid with anisotropic slip and magnetic field
- Numerical analysis of thermophoretic particle deposition on 3D Casson nanofluid: Artificial neural networks-based Levenberg–Marquardt algorithm
- Analyzing fuzzy fractional Degasperis–Procesi and Camassa–Holm equations with the Atangana–Baleanu operator
- Bayesian estimation of equipment reliability with normal-type life distribution based on multiple batch tests
- Chaotic control problem of BEC system based on Hartree–Fock mean field theory
- Optimized framework numerical solution for swirling hybrid nanofluid flow with silver/gold nanoparticles on a stretching cylinder with heat source/sink and reactive agents
- Stability analysis and numerical results for some schemes discretising 2D nonconstant coefficient advection–diffusion equations
- Convective flow of a magnetohydrodynamic second-grade fluid past a stretching surface with Cattaneo–Christov heat and mass flux model
- Analysis of the heat transfer enhancement in water-based micropolar hybrid nanofluid flow over a vertical flat surface
- Microscopic seepage simulation of gas and water in shale pores and slits based on VOF
- Model of conversion of flow from confined to unconfined aquifers with stochastic approach
- Study of fractional variable-order lymphatic filariasis infection model
- Soliton, quasi-soliton, and their interaction solutions of a nonlinear (2 + 1)-dimensional ZK–mZK–BBM equation for gravity waves
- Application of conserved quantities using the formal Lagrangian of a nonlinear integro partial differential equation through optimal system of one-dimensional subalgebras in physics and engineering
- Nonlinear fractional-order differential equations: New closed-form traveling-wave solutions
- Sixth-kind Chebyshev polynomials technique to numerically treat the dissipative viscoelastic fluid flow in the rheology of Cattaneo–Christov model
- Some transforms, Riemann–Liouville fractional operators, and applications of newly extended M–L (p, s, k) function
- Magnetohydrodynamic water-based hybrid nanofluid flow comprising diamond and copper nanoparticles on a stretching sheet with slips constraints
- Super-resolution reconstruction method of the optical synthetic aperture image using generative adversarial network
- A two-stage framework for predicting the remaining useful life of bearings
- Influence of variable fluid properties on mixed convective Darcy–Forchheimer flow relation over a surface with Soret and Dufour spectacle
- Inclined surface mixed convection flow of viscous fluid with porous medium and Soret effects
- Exact solutions to vorticity of the fractional nonuniform Poiseuille flows
- In silico modified UV spectrophotometric approaches to resolve overlapped spectra for quality control of rosuvastatin and teneligliptin formulation
- Numerical simulations for fractional Hirota–Satsuma coupled Korteweg–de Vries systems
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- A comparative analysis of shielding effectiveness in glass and concrete containers
- Numerical analysis of the MHD Williamson nanofluid flow over a nonlinear stretching sheet through a Darcy porous medium: Modeling and simulation
- Analytical and numerical investigation for viscoelastic fluid with heat transfer analysis during rollover-web coating phenomena
- Influence of variable viscosity on existing sheet thickness in the calendering of non-isothermal viscoelastic materials
- Analysis of nonlinear fractional-order Fisher equation using two reliable techniques
- Comparison of plan quality and robustness using VMAT and IMRT for breast cancer
- Radiative nanofluid flow over a slender stretching Riga plate under the impact of exponential heat source/sink
- Numerical investigation of acoustic streaming vortices in cylindrical tube arrays
- Numerical study of blood-based MHD tangent hyperbolic hybrid nanofluid flow over a permeable stretching sheet with variable thermal conductivity and cross-diffusion
- Fractional view analytical analysis of generalized regularized long wave equation
- Dynamic simulation of non-Newtonian boundary layer flow: An enhanced exponential time integrator approach with spatially and temporally variable heat sources
- Inclined magnetized infinite shear rate viscosity of non-Newtonian tetra hybrid nanofluid in stenosed artery with non-uniform heat sink/source
- Estimation of monotone α-quantile of past lifetime function with application
- Numerical simulation for the slip impacts on the radiative nanofluid flow over a stretched surface with nonuniform heat generation and viscous dissipation
- Study of fractional telegraph equation via Shehu homotopy perturbation method
- An investigation into the impact of thermal radiation and chemical reactions on the flow through porous media of a Casson hybrid nanofluid including unstable mixed convection with stretched sheet in the presence of thermophoresis and Brownian motion
- Establishing breather and N-soliton solutions for conformable Klein–Gordon equation
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- Study on cavitation and pulsation characteristics of a novel rotor-radial groove hydrodynamic cavitation reactor
- Optimizing heat transport in a permeable cavity with an isothermal solid block: Influence of nanoparticles volume fraction and wall velocity ratio
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- Effect of electron temperature and concentration on production of hydroxyl radical and nitric oxide in atmospheric pressure low-temperature helium plasma jet: Swarm analysis and global model investigation
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- Fourier spectral method for the fractional-in-space coupled Whitham–Broer–Kaup equations on unbounded domain
- The chaotic behavior and traveling wave solutions of the conformable extended Korteweg–de-Vries model
- Research on optimization of combustor liner structure based on arc-shaped slot hole
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Articles in the same Issue
- Regular Articles
- Numerical study of flow and heat transfer in the channel of panel-type radiator with semi-detached inclined trapezoidal wing vortex generators
- Homogeneous–heterogeneous reactions in the colloidal investigation of Casson fluid
- High-speed mid-infrared Mach–Zehnder electro-optical modulators in lithium niobate thin film on sapphire
- Numerical analysis of dengue transmission model using Caputo–Fabrizio fractional derivative
- Mononuclear nanofluids undergoing convective heating across a stretching sheet and undergoing MHD flow in three dimensions: Potential industrial applications
- Heat transfer characteristics of cobalt ferrite nanoparticles scattered in sodium alginate-based non-Newtonian nanofluid over a stretching/shrinking horizontal plane surface
- The electrically conducting water-based nanofluid flow containing titanium and aluminum alloys over a rotating disk surface with nonlinear thermal radiation: A numerical analysis
- Growth, characterization, and anti-bacterial activity of l-methionine supplemented with sulphamic acid single crystals
- A numerical analysis of the blood-based Casson hybrid nanofluid flow past a convectively heated surface embedded in a porous medium
- Optoelectronic–thermomagnetic effect of a microelongated non-local rotating semiconductor heated by pulsed laser with varying thermal conductivity
- Thermal proficiency of magnetized and radiative cross-ternary hybrid nanofluid flow induced by a vertical cylinder
- Enhanced heat transfer and fluid motion in 3D nanofluid with anisotropic slip and magnetic field
- Numerical analysis of thermophoretic particle deposition on 3D Casson nanofluid: Artificial neural networks-based Levenberg–Marquardt algorithm
- Analyzing fuzzy fractional Degasperis–Procesi and Camassa–Holm equations with the Atangana–Baleanu operator
- Bayesian estimation of equipment reliability with normal-type life distribution based on multiple batch tests
- Chaotic control problem of BEC system based on Hartree–Fock mean field theory
- Optimized framework numerical solution for swirling hybrid nanofluid flow with silver/gold nanoparticles on a stretching cylinder with heat source/sink and reactive agents
- Stability analysis and numerical results for some schemes discretising 2D nonconstant coefficient advection–diffusion equations
- Convective flow of a magnetohydrodynamic second-grade fluid past a stretching surface with Cattaneo–Christov heat and mass flux model
- Analysis of the heat transfer enhancement in water-based micropolar hybrid nanofluid flow over a vertical flat surface
- Microscopic seepage simulation of gas and water in shale pores and slits based on VOF
- Model of conversion of flow from confined to unconfined aquifers with stochastic approach
- Study of fractional variable-order lymphatic filariasis infection model
- Soliton, quasi-soliton, and their interaction solutions of a nonlinear (2 + 1)-dimensional ZK–mZK–BBM equation for gravity waves
- Application of conserved quantities using the formal Lagrangian of a nonlinear integro partial differential equation through optimal system of one-dimensional subalgebras in physics and engineering
- Nonlinear fractional-order differential equations: New closed-form traveling-wave solutions
- Sixth-kind Chebyshev polynomials technique to numerically treat the dissipative viscoelastic fluid flow in the rheology of Cattaneo–Christov model
- Some transforms, Riemann–Liouville fractional operators, and applications of newly extended M–L (p, s, k) function
- Magnetohydrodynamic water-based hybrid nanofluid flow comprising diamond and copper nanoparticles on a stretching sheet with slips constraints
- Super-resolution reconstruction method of the optical synthetic aperture image using generative adversarial network
- A two-stage framework for predicting the remaining useful life of bearings
- Influence of variable fluid properties on mixed convective Darcy–Forchheimer flow relation over a surface with Soret and Dufour spectacle
- Inclined surface mixed convection flow of viscous fluid with porous medium and Soret effects
- Exact solutions to vorticity of the fractional nonuniform Poiseuille flows
- In silico modified UV spectrophotometric approaches to resolve overlapped spectra for quality control of rosuvastatin and teneligliptin formulation
- Numerical simulations for fractional Hirota–Satsuma coupled Korteweg–de Vries systems
- Substituent effect on the electronic and optical properties of newly designed pyrrole derivatives using density functional theory
- A comparative analysis of shielding effectiveness in glass and concrete containers
- Numerical analysis of the MHD Williamson nanofluid flow over a nonlinear stretching sheet through a Darcy porous medium: Modeling and simulation
- Analytical and numerical investigation for viscoelastic fluid with heat transfer analysis during rollover-web coating phenomena
- Influence of variable viscosity on existing sheet thickness in the calendering of non-isothermal viscoelastic materials
- Analysis of nonlinear fractional-order Fisher equation using two reliable techniques
- Comparison of plan quality and robustness using VMAT and IMRT for breast cancer
- Radiative nanofluid flow over a slender stretching Riga plate under the impact of exponential heat source/sink
- Numerical investigation of acoustic streaming vortices in cylindrical tube arrays
- Numerical study of blood-based MHD tangent hyperbolic hybrid nanofluid flow over a permeable stretching sheet with variable thermal conductivity and cross-diffusion
- Fractional view analytical analysis of generalized regularized long wave equation
- Dynamic simulation of non-Newtonian boundary layer flow: An enhanced exponential time integrator approach with spatially and temporally variable heat sources
- Inclined magnetized infinite shear rate viscosity of non-Newtonian tetra hybrid nanofluid in stenosed artery with non-uniform heat sink/source
- Estimation of monotone α-quantile of past lifetime function with application
- Numerical simulation for the slip impacts on the radiative nanofluid flow over a stretched surface with nonuniform heat generation and viscous dissipation
- Study of fractional telegraph equation via Shehu homotopy perturbation method
- An investigation into the impact of thermal radiation and chemical reactions on the flow through porous media of a Casson hybrid nanofluid including unstable mixed convection with stretched sheet in the presence of thermophoresis and Brownian motion
- Establishing breather and N-soliton solutions for conformable Klein–Gordon equation
- An electro-optic half subtractor from a silicon-based hybrid surface plasmon polariton waveguide
- CFD analysis of particle shape and Reynolds number on heat transfer characteristics of nanofluid in heated tube
- Abundant exact traveling wave solutions and modulation instability analysis to the generalized Hirota–Satsuma–Ito equation
- A short report on a probability-based interpretation of quantum mechanics
- Study on cavitation and pulsation characteristics of a novel rotor-radial groove hydrodynamic cavitation reactor
- Optimizing heat transport in a permeable cavity with an isothermal solid block: Influence of nanoparticles volume fraction and wall velocity ratio
- Linear instability of the vertical throughflow in a porous layer saturated by a power-law fluid with variable gravity effect
- Thermal analysis of generalized Cattaneo–Christov theories in Burgers nanofluid in the presence of thermo-diffusion effects and variable thermal conductivity
- A new benchmark for camouflaged object detection: RGB-D camouflaged object detection dataset
- Effect of electron temperature and concentration on production of hydroxyl radical and nitric oxide in atmospheric pressure low-temperature helium plasma jet: Swarm analysis and global model investigation
- Double diffusion convection of Maxwell–Cattaneo fluids in a vertical slot
- Thermal analysis of extended surfaces using deep neural networks
- Steady-state thermodynamic process in multilayered heterogeneous cylinder
- Multiresponse optimisation and process capability analysis of chemical vapour jet machining for the acrylonitrile butadiene styrene polymer: Unveiling the morphology
- Modeling monkeypox virus transmission: Stability analysis and comparison of analytical techniques
- Fourier spectral method for the fractional-in-space coupled Whitham–Broer–Kaup equations on unbounded domain
- The chaotic behavior and traveling wave solutions of the conformable extended Korteweg–de-Vries model
- Research on optimization of combustor liner structure based on arc-shaped slot hole
- Construction of M-shaped solitons for a modified regularized long-wave equation via Hirota's bilinear method
- Effectiveness of microwave ablation using two simultaneous antennas for liver malignancy treatment
- Discussion on optical solitons, sensitivity and qualitative analysis to a fractional model of ion sound and Langmuir waves with Atangana Baleanu derivatives
- Reliability of two-dimensional steady magnetized Jeffery fluid over shrinking sheet with chemical effect
- Generalized model of thermoelasticity associated with fractional time-derivative operators and its applications to non-simple elastic materials
- Migration of two rigid spheres translating within an infinite couple stress fluid under the impact of magnetic field
- A comparative investigation of neutron and gamma radiation interaction properties of zircaloy-2 and zircaloy-4 with consideration of mechanical properties
- New optical stochastic solutions for the Schrödinger equation with multiplicative Wiener process/random variable coefficients using two different methods
- Physical aspects of quantile residual lifetime sequence
- Synthesis, structure, I–V characteristics, and optical properties of chromium oxide thin films for optoelectronic applications
- Smart mathematically filtered UV spectroscopic methods for quality assurance of rosuvastatin and valsartan from formulation
- A novel investigation into time-fractional multi-dimensional Navier–Stokes equations within Aboodh transform
- Homotopic dynamic solution of hydrodynamic nonlinear natural convection containing superhydrophobicity and isothermally heated parallel plate with hybrid nanoparticles
- A novel tetra hybrid bio-nanofluid model with stenosed artery
- Propagation of traveling wave solution of the strain wave equation in microcrystalline materials
- Innovative analysis to the time-fractional q-deformed tanh-Gordon equation via modified double Laplace transform method
- A new investigation of the extended Sakovich equation for abundant soliton solution in industrial engineering via two efficient techniques
- New soliton solutions of the conformable time fractional Drinfel'd–Sokolov–Wilson equation based on the complete discriminant system method
- Irradiation of hydrophilic acrylic intraocular lenses by a 365 nm UV lamp
- Inflation and the principle of equivalence
- The use of a supercontinuum light source for the characterization of passive fiber optic components
- Optical solitons to the fractional Kundu–Mukherjee–Naskar equation with time-dependent coefficients
- A promising photocathode for green hydrogen generation from sanitation water without external sacrificing agent: silver-silver oxide/poly(1H-pyrrole) dendritic nanocomposite seeded on poly-1H pyrrole film
- Photon balance in the fiber laser model
- Propagation of optical spatial solitons in nematic liquid crystals with quadruple power law of nonlinearity appears in fluid mechanics
- Theoretical investigation and sensitivity analysis of non-Newtonian fluid during roll coating process by response surface methodology
- Utilizing slip conditions on transport phenomena of heat energy with dust and tiny nanoparticles over a wedge
- Bismuthyl chloride/poly(m-toluidine) nanocomposite seeded on poly-1H pyrrole: Photocathode for green hydrogen generation
- Infrared thermography based fault diagnosis of diesel engines using convolutional neural network and image enhancement
- On some solitary wave solutions of the Estevez--Mansfield--Clarkson equation with conformable fractional derivatives in time
- Impact of permeability and fluid parameters in couple stress media on rotating eccentric spheres
- Review Article
- Transformer-based intelligent fault diagnosis methods of mechanical equipment: A survey
- Special Issue on Predicting pattern alterations in nature - Part II
- A comparative study of Bagley–Torvik equation under nonsingular kernel derivatives using Weeks method
- On the existence and numerical simulation of Cholera epidemic model
- Numerical solutions of generalized Atangana–Baleanu time-fractional FitzHugh–Nagumo equation using cubic B-spline functions
- Dynamic properties of the multimalware attacks in wireless sensor networks: Fractional derivative analysis of wireless sensor networks
- Prediction of COVID-19 spread with models in different patterns: A case study of Russia
- Study of chronic myeloid leukemia with T-cell under fractal-fractional order model
- Accumulation process in the environment for a generalized mass transport system
- Analysis of a generalized proportional fractional stochastic differential equation incorporating Carathéodory's approximation and applications
- Special Issue on Nanomaterial utilization and structural optimization - Part II
- Numerical study on flow and heat transfer performance of a spiral-wound heat exchanger for natural gas
- Study of ultrasonic influence on heat transfer and resistance performance of round tube with twisted belt
- Numerical study on bionic airfoil fins used in printed circuit plate heat exchanger
- Improving heat transfer efficiency via optimization and sensitivity assessment in hybrid nanofluid flow with variable magnetism using the Yamada–Ota model
- Special Issue on Nanofluids: Synthesis, Characterization, and Applications
- Exact solutions of a class of generalized nanofluidic models
- Stability enhancement of Al2O3, ZnO, and TiO2 binary nanofluids for heat transfer applications
- Thermal transport energy performance on tangent hyperbolic hybrid nanofluids and their implementation in concentrated solar aircraft wings
- Studying nonlinear vibration analysis of nanoelectro-mechanical resonators via analytical computational method
- Numerical analysis of non-linear radiative Casson fluids containing CNTs having length and radius over permeable moving plate
- Two-phase numerical simulation of thermal and solutal transport exploration of a non-Newtonian nanomaterial flow past a stretching surface with chemical reaction
- Natural convection and flow patterns of Cu–water nanofluids in hexagonal cavity: A novel thermal case study
- Solitonic solutions and study of nonlinear wave dynamics in a Murnaghan hyperelastic circular pipe
- Comparative study of couple stress fluid flow using OHAM and NIM
- Utilization of OHAM to investigate entropy generation with a temperature-dependent thermal conductivity model in hybrid nanofluid using the radiation phenomenon
- Slip effects on magnetized radiatively hybridized ferrofluid flow with acute magnetic force over shrinking/stretching surface
- Significance of 3D rectangular closed domain filled with charged particles and nanoparticles engaging finite element methodology
- Robustness and dynamical features of fractional difference spacecraft model with Mittag–Leffler stability
- Characterizing magnetohydrodynamic effects on developed nanofluid flow in an obstructed vertical duct under constant pressure gradient
- Study on dynamic and static tensile and puncture-resistant mechanical properties of impregnated STF multi-dimensional structure Kevlar fiber reinforced composites
- Thermosolutal Marangoni convective flow of MHD tangent hyperbolic hybrid nanofluids with elastic deformation and heat source
- Investigation of convective heat transport in a Carreau hybrid nanofluid between two stretchable rotatory disks
- Single-channel cooling system design by using perforated porous insert and modeling with POD for double conductive panel
- Special Issue on Fundamental Physics from Atoms to Cosmos - Part I
- Pulsed excitation of a quantum oscillator: A model accounting for damping
- Review of recent analytical advances in the spectroscopy of hydrogenic lines in plasmas
- Heavy mesons mass spectroscopy under a spin-dependent Cornell potential within the framework of the spinless Salpeter equation
- Coherent manipulation of bright and dark solitons of reflection and transmission pulses through sodium atomic medium
- Effect of the gravitational field strength on the rate of chemical reactions
- The kinetic relativity theory – hiding in plain sight
- Special Issue on Advanced Energy Materials - Part III
- Eco-friendly graphitic carbon nitride–poly(1H pyrrole) nanocomposite: A photocathode for green hydrogen production, paving the way for commercial applications