Optimization of collimator angles in dual-arc volumetric modulated arc therapy planning for whole-brain radiotherapy with hippocampus and inner ear sparing

To optimize the collimator angles in dual-arc volumetric modulated arc therapy (VMAT) plans for whole-brain radiotherapy with hippocampus and inner ear sparing (HIS-WBRT). Two sets of dual-arc VMAT plans were generated for 13 small-cell lung cancer patients: (1) The collimator angles of arcs 1 and 2 (θ1/θ2) were 350°/10°, 350°/30°, 350°/45°, 350°/60°, and 350°/80°, i.e., the intersection angle of θ1 and θ2 (Δθ) increased. (2) θ1/θ2 were 280°/10°, 300°/30°, 315°/45°, 330°/60°, and 350°/80°, i.e., Δθ = 90°. The conformity index (CI), homogeneity index (HI), monitor units (MUs), and dosimetric parameters of organs-at-risk were analyzed. Quality assurance for Δθ = 90° plans was performed. With Δθ increasing towards 90°, a significant improvement was observed for most parameters. In 350°/80° plans compared with 350°/10° ones, CI and HI were improved by 1.1% and 25.2%, respectively; MUs were reduced by 16.2%; minimum, maximum, and mean doses (D100%, Dmax, and Dmean, respectively) to the hippocampus were reduced by 5.5%, 6.3%, and 5.4%, respectively; Dmean to the inner ear and eye were reduced by 0.7% and 5.1%, respectively. With Δθ kept at 90°, the plan quality was not significantly affected by θ1/θ2 combinations. The gamma-index passing rates in 280°/10° and 350°/80° plans were relatively lower compared with the other Δθ = 90° plans. Δθ showed a significant effect on dual-arc VMAT plans for HIS-WBRT. With Δθ approaching 90°, the plan quality exhibited a nearly continuous improvement, whereas with Δθ = 90°, the effect of θ1/θ2 combination was insignificant.

Treatment planning. VMAT plans were optimized on Eclipse version 13.5 for 6 MV X-ray beams of a Varian TrueBeam linear accelerator equipped with a Millennium MLC-120 MLC (Varian Medical Systems, Palo Alto, CA). The maximum dose rate was 600 MUs/min. The dose distributions were calculated using the anisotropic analytic algorithm with a grid of 2.5 mm. The jaw tracking was enabled, and the maximum field size (X × Y) was 15 cm × 40 cm to adequately cover the whole brain.
For each patient, all plans were optimized with identical dosimetric constraints and normalized to 92% of the PTV receiving 30 Gy, while there were certain adjustments in the optimization methods for different patients to assure that all plans complied with the dose criteria.  26,27 and where TV is the target volume, PIV is the prescription isodose volume, TV PIV is the target volume within the prescription isodose volume, and D n% represents the dose delivered to n% of the target volume. CI closer to 1 indicates better dose conformity. HI closer to 0 indicates better dose homogeneity. The evaluated dosimetric parameters of OAR included the minimum, maximum, and mean doses (D 100% , D max , and D mean , respectively) of the hippocampus; the D mean of the inner ear and eye; and the D max of the optical nerve and lens. Quality assurance. QA was performed for Δθ = 90° plans by using local gamma-index analysis with 3%/3, 3%/2, and 2%/2 mm criteria 28 , using an a-Si 1200 Electronic Portal Imaging Device with an active area of 40 cm × 40 cm and a pixel number of 1190 × 1190. Dose images were acquired for each arc with a source-todetector distance of 100 cm and later retrieved to the Portal Dosimetry module of the Eclipse TPS. The Portal Dose Image Prediction version 13.6.23 algorithm was used to calculate the predicted dose images.
Statistical analysis. Friedman test was first carried out for the above parameters within each set of plans, i.e., with different Δθ and same Δθ (= 90°), to investigate if Δθ and the specific angle of each arc could affect the plan quality of dual-arc VMAT. Wilcoxon signed-rank test was performed for multiple comparisons between the Δθ = 90° and Δθ < 90° plans. The comparisons were conducted in two groups, that is, (A) between plans with same θ 1 but different θ 2 and (B) between those with same θ 2 but different θ 1 . The obtained p-values were evaluated with Bonferroni correction.
The above two tests were also used for the gamma-index passing rate evaluation in the plan QA for Δθ = 90° plans. All statistical analyses were performed using IBM SPSS Statistics version 26.0 software (IBM Corporation, Armonk, NY). p < 0.05 was defined as statistically significant.
Ethics approval and consent to participate. All experimental protocols were approved by the Ethics Committee of the First Hospital of Jilin University. The Ethics Committee of the First Hospital of Jilin University waived the need for informed consent. All research was performed in accordance with relevant guidelines and regulations. Table 2 shows the evaluated parameters and their corresponding Friedman test results for the VMAT plans with increasing Δθ. Figure 1 presents the predicted dose distribution of each arc in these plans for a typical patient. The results for plans with the same Δθ (= 90°) are shown in Table 3. Supplementary Fig. S1 presents the calculated dose distribution in one 350°/80° plan for a typical patient and the corresponding DVH compared with that in Δθ < 90° plans. www.nature.com/scientificreports/ Plan quality with increasing Δθ. As shown in Table 2, Δθ showed a significant effect on the CI, HI, MUs, and dosimetric parameters of the hippocampus (D 100% , D max , and D mean ), inner ear (D mean ), and eye (D mean ), whereas no significance was found in the D max of lens and optical nerve. Among the five collimator settings, the 350°/80° (Δθ = 90°) plans exhibited the best HI, MUs, and dosimetric parameters of the hippocampus, inner ear, and eye and the second-best CI. In the 350°/80° plans compared with the 350°/10° ones, the CI and HI were improved by 1.1% (p = 0.007) and 25.2% (p < 0.001), respectively; MUs were reduced by 16.2% (p < 0.001); the D 100% , D max , and D mean to the hippocampus were reduced by 5.5% (p < 0.001), 6.3% (p < 0.001), and 5.4% (p < 0.001), respectively; the D mean to the inner ear was reduced by 0.7% (p = 0.039); and the D mean to the eye was reduced by 5.1% (p < 0.001).

Results
For further investigation of the relation between the plan quality and Δθ, the parameter values in the Δθ = 90° plans minus those in the Δθ < 90° plans are shown in Fig. 2 in two groups: group A, plans with the same θ 1 indicated by the solid lines; and group B, plans with the same θ 2 indicated by the dashed lines. The difference in the plan Δθ was denoted by δθ = 90° − Δθ (< 90°).
With decreasing δθ, i.e., Δθ increasing towards 90°, improvements were clearly demonstrated for the CI, HI, MUs, and dosimetric parameters of the hippocampus and eye. A high degree of similarity was observed between groups A and B. One-tailed Wilcoxon signed-rank tests were performed for the comparisons within groups A and B, and the results are shown in Supplementary Tables S1 and S2, respectively. Compared with the Δθ < 90° plans, the Δθ = 90° plans generally showed significantly better or similar results depending on δθ.
Quality assurance for Δθ = 90° plans. The QA results for the Δθ = 90° plans are displayed in Table 4.

Discussion
Considering the positive results demonstrated in the RTOG 0933 trail, HIS-WBRT has gradually become a common practice for the treatment of brain metastases and prophylactic cranial irradiation [7][8][9][29][30][31] . The plan quality is especially important, and choosing the collimator angle is a vital part of the plan optimization to achieve an ideal dose distribution due to the complexity of HIS-WBRT. In the present study, the collimator  www.nature.com/scientificreports/ angle had a significant effect on the dose distribution quality and MUs, in agreement with the previous studies. Zhang et al. 32 developed a collimator trajectory selection method for VMAT, and an enhanced dose distribution could be achieved by aligning the collimator with the target shape. Several studies showed that the VMAT optimization involving sectional optimization of collimator angle could provide delivery efficiency and dosimetric improvements 33,34 . Recent studies on the dynamic collimator rotation approach have shown positive results on improving the plan quality 24,[35][36][37] . Table 2 shows that among the five sets of plans with different Δθ, the 350°/80° (Δθ = 90°) plans had the best overall dosimetric performance and MUs. Figure 2 demonstrates the differences between the Δθ = 90° and Δθ < 90° plans with respect to δθ. A visible similarity was present between groups A and B in the improvement of CI, HI, MUs, and doses to the hippocampus and eye with decreasing δθ, indicating that with Δθ increasing towards 90°, the plan quality could be gradually improved.
The five sets of Δθ = 90° plans were compared to investigate the possible effect from the θ 1 /θ 2 combination with the same Δθ, and the results are shown in Table 3. Thus, when the intersection Δθ was the same, most parameters showed no significant correlation with θ 1 /θ 2 combinations, except the MUs and maximum doses to lens and optical nerve. Considering the behavior of all parameters, the effect of Δθ was much greater than that of the specific angle of each arc.
The collimator angle should allow the MLC aperture to encompass the PTV while avoiding the sparing region. For the near-spherical target volume in HIS-WBRT, with the avoidance of two hippocampi, which exist bilaterally in the middle of the brain, the plan complexity could be considerably increased compared with conventional WBRT. Many studies proposed that high plan complexity could affect the accuracy of dose calculation and beam delivery [38][39][40] . The predicted dose distribution shown in Fig. 1 indicated that regardless of the collimator setting, the plan optimization tended to form mutually orthogonal dose distributions in two arcs, and the integrated dose distribution could then conform with the complex-shape target volume of HIS-WBRT. With the Δθ = 90° plans, i.e., the MLC orientations of two arcs perpendicular to each other, the motion complexity of MLC could be potentially reduced compared with the Δθ < 90° plans, which could be part of the reason for the improved dose distribution quality of Δθ = 90° plans.
Previous studies on the effect of collimator angle on VMAT plan quality proposed various optimal settings depending on the tumor site and shape 12,17,41 . For vertebrae metastases, Mancosu et al. suggested a collimator angle of around 90° to align the MLC leaf motion with the spinal cord 41 . For prostate cancer, Li et al. suggested an angle of 45° for the optimal dose distribution plan complexity 17 . For nasopharynx cancer, Otto found that 45° was preferable in most cases 12 . In the present study, the optimal collimator setting is affected by the complex-shaped target of HIS-WBRT and thus different from the above findings. For the dual-arc VMAT technique adopted for HIS-WBRT, the optimal plan quality was acquired with Δθ = 90°, while the effect from the specific setting of each arc was relatively insignificant.
For the Δθ = 90° plans with different collimator angle combinations, the gamma-index analysis results shown in Tables 4 and 5 indicated that the passing rates could be affected by the specific angle of each arc. Although the passing rate with the collimator closer to 0° showed preferable results in this study, it should be noted that the QA result could be associated with many factors, such as the dosimetric leaf gap, tongue-and-groove effect, interleaf leakage, and intra-and inter-leaf transmission settings of MLC [42][43][44][45] . For the PDIP algorithm in the Eclipse TPS, these MLC configuration parameters are constant for all collimator and gantry angles, but in practice, they may vary for different situations. The leaf position accuracy could be affected by the gantry rotation with different collimator angles due to gravitational effects imposed on the leaf carriage system 45 . The varying MLC parameters could yield a significant dose error, especially for highly modulated plans. Therefore, with regard to the plan QA for other institutions, the preferable result may vary.

Conclusions
This study demonstrated the role of collimator settings in dual-arc VMAT planning for HIS-WBRT. The intersection angle between two collimator settings, Δθ, showed a significant influence on the plan quality. With Δθ approaching 90°, a nearly continuous improvement was observed in the dose distributions and MUs. However, with the same Δθ = 90°, the effect of specific collimator angle of each arc was relatively trivial. The QA results indicated that the 300°/30°, 315°/45°, and 330°/60° plans had a better delivery accuracy than the 280°/10° and 350°/80° plans.

Data availability
Research data analyzed in this study are included as supplementary materials. Other data that support the findings of this study are available from the corresponding author upon reasonable request.