Effect of MU‐weighted multi‐leaf collimator position error on dose distribution of SBRT radiotherapy in peripheral non‐small cell lung cancer

Abstract Purpose Position accuracy of the multi‐leaf collimator (MLC) is essential in stereotactic body radiotherapy (SBRT). This study is aimed to investigate the dosimetric impacts of the MU‐weighted MLC positioning uncertainties of SBRT for patients with early stage peripheral non‐small cell lung cancer (NSCLC). Methods Three types of MLC position error were simulated: Type 1, random error; Type 2, system shift, in which both MLC banks shifted to the left or right direction; and Type 3, in which both MLC banks moved with same magnitudes in the opposite directions. Two baseline plans were generated: an automatic plan (AP) and a manually optimized plan (MP). Multi‐leaf collimator position errors were introduced to generate simulated plans with the preset MLC leaf position errors, which were then reimported into the Pinnacle system to generate simulated plans, respectively. The dosimetric parameters (CI, nCI, GI, etc.) and gEUD values of PTV and OARs were calculated. Linear regression between MU‐weighted/unweighted MLC position error and gEUD was performed to obtain dose sensitivity. Results The dose sensitivities of the PTVs were −4.93, −38.94, −41.70, −55.55, and 30.33 Gy/mm for random, left shift, right shift, system close, and system open MLC errors, respectively. There were significant differences between the MU‐weighted and the unweighted dose sensitivity, which was −38.94 Gy/mm vs −3.42 Gy/mm (left shift), −41.70 Gy/mm vs −3.56 Gy/mm (right shift), −55.55 Gy/mm vs −4.84 Gy/mm (system close), and 30.33 vs 2.64 Gy/mm (system open). For the system open/close MLC errors, as the PTV volume became larger, the dose sensitivity decreased. APs provided smaller dose sensitivity for the system shift and system close MLC errors compared to the conventional MPs. Conclusions There was significant difference in dose sensitivity between MU‐weighted and unweighted MLC position error of SBRT radiotherapy in peripheral NSCLC. MU is suggested to be included in the dosimetric evaluation of the MLC misalignments, since it is much closer to clinical radiotherapy.


| INTRODUCTION
Lung cancer is one of the major malignant tumors with high morbidity and mortality in China and worldwide. The incidence rate of lung cancer is steadily increasing. 1 With the advancement of radiotherapy, stereotactic body radiotherapy (SBRT) has become an increasingly common treatment option for patients with non-small cell lung cancer (NSCLC), with comparable clinical outcomes to surgery. [2][3][4] For patients with inoperable NSCLC, SBRT is often the critical alternative therapy.
Stereotactic body radiotherapy demands much more stringent dose constraints to both the target volumes and critical normal tissues, which in turn requires a high-quality treatment plan, and efficient treatment planning process and technologies. In order to improve quality, efficiency, and consistency in treatment planning, automated treatment planning systems (ATPs) have gained wide interest in the radiation oncology and medical physics communities. [5][6][7] The automatic planning systems can in principle achieve highly consistent treatment automatic plans (APs) in which the target coverage can be significantly improved at the little expense of planning time compared to manual plans (MPs). 8 However, APs automatically generate many artificial dose limiting structures and corresponding dose parameters, [9][10][11] which might increase the complexity of the plan.
In our center, step-and-shoot IMRT is routinely used for SBRT treatments. In the treatment delivery of IMRT, the multi-leaf collimator (MLC) leaves are divided into many subfields, and the position accuracy of the MLC leaves can directly cause dose deviations from the desired for both the target volumes and organs at risk (OARs). By analyzing the MLC log files of IMRT delivery treatments, Olasoloalonso et al. 12  This study was based on prior work on MLC error during IMRT delivery. Oliver et al. 13 reported that for systematic MLC gap open errors, the dose sensitivity was 8.2% per mm and for MLC gap close errors the dose sensitivity was −7.2% per mm.
We found that MU, one of the complexity levels, has an impact on dose distribution. For example, if the MU of a single beam is large, though the MLC error of this beam is small, it still has quite a large effect on dose distribution. Furthermore, the dosimetric impact of MLC positional errors is important when it comes to SBRT since the delivery requirements can be more stringent. In addition, the previous studies were all conducted on treatment deliveries designed with manual plans and did not involve fast-growing automatic plans.
Hence, there is a need to investigate the dosimetric impacts of MUweighted MLC position errors not only on the MPs but also on APs for SBRT treatments.
The aim of this study is to explore the effects of MU-weighted MLC position error on dose distributions of SBRT in APs for NSCLC, and compare with MPs. We explored the differences in dose sensitivity between APs and MPs for three types of MLC errors, and tried to find out whether MU-weighted is necessary for dosimetric evaluation of the MLC misalignments.

2.A | Patient selection and contouring
A total of ten patients were selected for this study. All patients were diagnosed with clinically stage I-IIA peripheral NSCLC and underwent CT simulation scans using a SOMATOM Definition AS (Siemens Healthcare Gmbh, Erlangen, Bayern, Germany). The slice thickness of CT images was 3 mm. Four-dimensional CT images were acquired to allow delineation of internal target volume (ITV) for lung SBRT. PTV included the entire delineated ITV plus a 5-mm margin. All the patients received SBRT on a linear accelerator equipped with CBCT using online IGRT (Varian, Palo Alto, CA) for each treatment fraction.

2.B | Treatment planning of SBRT
Two SBRT IMRT plans, an automatic plan and a manual plan, were generated for each of the ten patients, respectively. The plans were generated using Pinnacle 3TM treatment planning system (TPS, v9.10, Philips Medical Systems, Cleveland, USA) for an Edge linear accelerator (Varian, Palo Alto, CA) equipped with 120 MLC leaves (Millennium MLC) and 6 MV photon beam. The autoplanning module of Pinnacle 3TM TPS is based on progressive automatic algorithm, [14][15][16] which is a fully integrated module, similar to the manual inverse optimizer module. During AP module, individual optimization goals, constraints, and weights are automatically added and adjusted. In addition, the optimizer is automatically run multiple times with adjustments being made during and between optimization processes. 8 APs and MPs were created using the same set of 10 coplanar beams and other basic beam parameters. For each plan, optimizations were performed with a direct machine parameter optimization (DMPO) algorithm and dose distributions were calculated using the collapsed cone convolution algorithm (CCC) with a calculation grid of 2 mm. The prescribed dose for lung SBRT was 50 Gy (10 Gy/fraction) to PTV; the dose limits of OARs are defined according to RTOG 0813 protocol. 17 Minor deviations were allowed only if it is necessary to achieve the dose constraints for the OARs and if the maximum dose remained within the ITV.

2.C | Simulation of MLC position error in SBRT plans
Three types of MLC position errors were investigated in this study. As an example, Fig. 1(a) shows the leaf positions in a plan.
Type 1 errors were random errors that were simulated and introduced by sampling a Gaussian function with error magnitude equal to the standard derivation. In simulated plans, the moving leaf banks were made to randomly deviate from the planned positions, either extending over or retracting back as shown in Fig. 1(b).  was the ratio of the volume covered by 50% of the prescription dose to the volume covered by the prescription dose. In this study, the GI was computed as: GI ¼ R50% R100% , where R 50% is the ratio of 50% prescription isodose volume to the PTV and R 100% is the ratio of 100% prescription isodose volume to the PTV, which is mathematically equivalent to the previous definition. The gEUD was calculated as:gEUD with the parameter a set to 1 and 20, respectively, according to the study of Mihailidis et al. 19 and Rangel et al. 20 The percentage change [Eq. (1)] was used to estimate the relative error between a simulated plan and the corresponding baseline plan.
where X represents a parameter used in the evaluations, X Error is the parameter of a simulation plan, while X Base is the parameter of the corresponding baseline plan. The second fit took MU of a single beam into account and normalized it to the total MU of the patient. The fitting formula was expressed as:

2.E | Dose sensitivity study of MLC position error
where k ij represents the dose sensitivity of jth beam of ith patient, MU ij represents the jth subfield MU of the ith patient, n represents the total number of subfields of the ith patient, ∑ j¼n j¼1 MU ij represents the total MU of ith patient,MLCPE ij represents the position error of the jth subfield of the ith patient, b ij represent the intercept of jth beam of ith patient.
Secondly, the dose sensitivity of ith patient was calculated as: Finally, we calculated the dose sensitivity of each patient and then took the mean value to get the mean dose sensitivity of ten performed for two kinds of linear regressions and different planning methods, and P < 0.05 was considered to be statistically significant.
The linear regression fits were analyzed by using Software package Origin (version 9.0).  As is observed in Fig. 3(a)    The highest dose sensitivity of spinal cord and total lung both appeared for Type 3b error, which was 9.62 and 2.88 Gy/mm, respectively. The dose sensitivity of OARs was relatively small compared to the PTV.

3.C | Preliminary study of the linear relationship between PTV volume and Type 3 dose sensitivity on APs
We conducted a preliminary investigation of the linear relationship between PTV volume and dose sensitivity of MU-weighted Type 3 MLC error on APs.
The PTV volume of the different patients and the corresponding dose sensitivity of the PTVs were listed in

3.D | Comparison of dose sensitivity between AP and MP
The results of this study showed that the random error had negligible dosimetric effects on the PTV and OARs. Therefore, the comparisons between the AP and MP were focused on Type 2 and Type 3 MLC position errors.  T A B L E 2 A list shows the volume of PTV, the corresponding dose sensitivity, and the total MU/per patient for ten patients. Oliver et al. 13 reported that there was a linear relationship between different types of MLC errors and PTV gEUD in VMAT plans of prostate cancer. Sen et al. 21 reported that when the magnitude of MLC random error in nasopharyngeal carcinoma reaches 2 mm, it has few effects on target and OARs. Blake et al. 22 reported that there was less patient-to-patient variation occurred from MLC delivery uncertainties in VMAT than step-and-shoot IMRT.

| CONCLUSION
This study investigated the effects of MU-weighted MLC positional error on dose distribution of SBRT radiotherapy for peripheral NSCLC patients. There is significant difference in dose sensitivity between MU-weighted and unweighted MLC position errors on APs.
Therefore, it is necessary to include MU in the dosimetric evaluation.

ACKNOWLEDG MENTS
This study was supported by grants from the Interdisciplinary Program of Shanghai Jiao Tong University (No. YG2019ZDB07).

AUTHOR CONTRI BUTIONS
AiHui Feng was involved in conceptualization, investigation, methodology, software, data curation, and writing original draft preparation and review/editing; Hua Chen was involved in conceptualization, methodology, and software; Hao Wang was involved in software and writing review and editing; HengLe Gu was involved in data curation and writing review and editing; Yan Shao was involved in data curation and visualization; YanHua Duan was involved in methodology and visualization; YanChen Ying was involved in software; Ning Jeff Yue was involved in writing review and editing; ZhiYong Xu was involved in conceptualization, methodology, project administration, supervision, and writing original draft preparation and review/editing. All authors read and approved the final manuscript.