Efficacy of robust optimization plan with partial‐arc VMAT for photon volumetric‐modulated arc therapy: A phantom study

Abstract This study investigated position dependence in planning target volume (PTV)‐based and robust optimization plans using full‐arc and partial‐arc volumetric modulated arc therapy (VMAT). The gantry angles at the periphery, intermediate, and center CTV positions were 181°–180° (full‐arc VMAT) and 181°–360° (partial‐arc VMAT). A PTV‐based optimization plan was defined by 5 mm margin expansion of the CTV to a PTV volume, on which the dose constraints were applied. The robust optimization plan consisted of a directly optimized dose to the CTV under a maximum‐uncertainties setup of 5 mm. The prescription dose was normalized to the CTV D99% (the minimum relative dose that covers 99% of the volume of the CTV) as an original plan. The isocenter was rigidly shifted at 1 mm intervals in the anterior‐posterior (A‐P), superior‐inferior (S‐I), and right‐left (R‐L) directions from the original position to the maximum‐uncertainties setup of 5 mm in the original plan, yielding recalculated dose distributions. It was found that for the intermediate and center positions, the uncertainties in the D99% doses to the CTV for all directions did not significantly differ when comparing the PTV‐based and robust optimization plans (P > 0.05). For the periphery position, uncertainties in the D99% doses to the CTV in the R‐L direction for the robust optimization plan were found to be lower than those in the PTV‐based optimization plan (P < 0.05). Our study demonstrated that a robust optimization plan's efficacy using partial‐arc VMAT depends on the periphery CTV position.

Intensity Modulated Proton Therapy (IMPT) dose distributions are sensitive to both high stopping-power dependency and steep beam-dose gradients. The Bragg peak positions are highly affected by the densities and materials of the volume traversed by the incident protons. In proton therapy, setup errors, density errors, and organ motion can lead to differences in dose distributions when comparing the planned and delivered doses. Several authors have previously reported that stochastic programming and robust optimization in IMPT have minimized this problem. [5][6][7][8][9][10][11][12] Presently, RayStation (RaySearch Medical Laboratories AB, Stockholm, Sweden) offers one of the robust optimization methods used to address these demands. RayStation's robust optimization has been applied mainly to treatment planning for IMPT.
There are limited reports of robust optimization plans for photon treatment planning systems (TPSs). 13 tions were set at 181°-360°(partial-arc VMAT) and 181°-180°(fullarc VMAT) clockwise arcs. The collimator angle was fixed at 10°. A PTV-based optimization plan was defined by 5 mm margin expansion of the CTV to a PTV volume, on which the dose constraints were applied. The robust optimization plan entailed administering a directly optimized dose to the CTV under a maximum-uncertainties setup of 5 mm. A PTV was not necessary for the robust optimization plan, but was used for an evaluative region of interest (ROI). We compared the PTV-based optimization plan and the robust optimization plan to investigate the position dependence between full-arc and partial-arc VMAT. All the plans were created with a single fraction and a prescription dose of 1000 cGy.
The RayStation system offers minimax optimization, in which the optimization functions selected to be robust are considered under the worst-case scenario. 8 The interfractional patient-setup uncertainties are considered to be random; they are incorporated by shifting the isocen- RayStation robust optimization has an accurately model on the surface and at shallow depths using scintillator and film measurements. 15 For quantitative comparisons based on the DVH, the dose distribution for each plan was normalized to that of a CTV D 99% (the minimum relative dose that covers 99% of the volume of the CTV) as an original plan. For the PTV, a homogeneity index (HI) was calculated using the following formula: 16 where D 2% , D 98% , and D 50% are doses that covered 2%, 98%, and 50% of the PTV, respectively. The following method was used to investigate the variation in dose indices caused by setup errors. For setup uncertainties, the isocenter of the patient was rigidly shifted in the A-P, S-I, and R-L directions, yielding six dose distributions.
The isocenter was rigidly shifted from the original position to the maximum-uncertainties setup of 5 mm at 1 mm intervals in the original plan. D 99% was used to evaluate the plan's quality, where the relative dose was the ratio of the received dose to the prescribed dose. The obtained data were analyzed using the analysis of variance (ANOVA) method, with the statistical significance set at P < 0.05.

| RESULTS
In the original plan, Table 1 compares the HI to the PTV for PTVbased and robust optimization plans using the full-arc and partial-arc  Figure 4 shows the DVH for the effect of the setup uncertainty on the dose distribution for the periphery position in the R-L direction for PTV-based and the robust optimization plans using full-arc and partial-arc VMAT. The uncertainty in the dose to the CTV using the partial-arc VMAT plan was dependent on the target's location. doses to the CTV in the S-I direction were higher for the robust optimization plans than for the PTV-based plan (P < 0.05). Table 3 compares the D 99% doses to the CTV obtained from the rigidly shifted plan between the PTV-based and the robust optimization plans using full-arc VMAT, with data shown as averages and standard deviations, with ranges in parentheses. All positions and directions were no statistically significant differences (P > 0.05). Table 4 compares the HI of CTV obtained from the rigidly shifted plan between the PTV-based and the robust optimization plans using partial-arc VMAT, with data shown as averages and standard deviations, with ranges in parentheses. For the periphery position, uncertainties for the HI of CTV in the S-I direction were higher for the robust optimization plans than for the PTV-based plan (P < 0.05).   The analysis of variance (ANOVA) resulted in a statistically significant variance to the R-L and S-I directions in the periphery position (P < 0.05).
T A B L E 3 D 99% doses to the CTV for full-arc VMAT using PTV-based and robust optimization for three positions. Averages and standard deviations, with ranges in parentheses, are shown.  Because day-to-day setup variations were random, it was necessary to use a mathematical calculation of the probability distribution that considers the number of fractions. 18 The dose distribution within the PTV on the periphery location was more inhomogeneous in the robust optimization plan than in the PTV-based optimization plan. A more homogeneous plan within the PTV is usually preferred and approved by the physician. If the plan's quality under the robust optimization plan is acceptable, the actual dose to the target can lead to more accuracy. The International Commission on Radiation Units and Measurements (ICRU) noted in Report 24 that the available evidence for certain types of tumors points to the need for 5% accuracy in the delivery of an absorbed dose to a target volume to achieve local control. 19 The OAR objectives were not constrained in this study. One of the clinical goals depended on the dose to the OAR. The most important goal was that the dose to the tumor was premeditatedly received.
An evaluation of the robust optimization plan is thus necessary for preventing large discrepancies between the planned and delivered doses and because robust optimization is a novel method in commercial TPS. Even if PTV-based optimization is used, we recommend robust evaluation to confirm the uncertainty of doses to the target on the periphery of the body when using partial-arc VMAT. Plan evaluations should be provided not only for certain-situation DVHs but also for the several-situation DVHs to ensure secure therapy. 20 Another limitation of this study is that it was performed under a phantom study. Further studies are needed to account for nonrigid variations in anatomy and intra-fractional motion because of the deformations and changes in the positions of anatomical structures daily.

| CONCLUSION
In conclusion, this study demonstrated that the efficacy of the robust optimization plan was dependent on the CTV position. We T A B L E 4 Homogeneity index of CTV for partial-arc VMAT using PTV-based and robust optimization for three positions. Averages and standard deviations, with ranges in parentheses, are shown.  focused on peripheral cancer, which may benefit from a robust optimization plan due to its location. This study supports the acceptability of robust photon treatment planning based on the dose prescription defined to the CTV.

CONF LICT OF I NTEREST
The authors declare no conflict of interest.