Robust optimization in lung treatment plans accounting for geometric uncertainty

Abstract Robust optimization generates scenario‐based plans by a minimax optimization method to find optimal scenario for the trade‐off between target coverage robustness and organ‐at‐risk (OAR) sparing. In this study, 20 lung cancer patients with tumors located at various anatomical regions within the lungs were selected and robust optimization photon treatment plans including intensity modulated radiotherapy (IMRT) and volumetric modulated arc therapy (VMAT) plans were generated. The plan robustness was analyzed using perturbed doses with setup error boundary of ±3 mm in anterior/posterior (AP), ±3 mm in left/right (LR), and ±5 mm in inferior/superior (IS) directions from isocenter. Perturbed doses for D99, D98, and D95 were computed from six shifted isocenter plans to evaluate plan robustness. Dosimetric study was performed to compare the internal target volume‐based robust optimization plans (ITV‐IMRT and ITV‐VMAT) and conventional PTV margin‐based plans (PTV‐IMRT and PTV‐VMAT). The dosimetric comparison parameters were: ITV target mean dose (Dmean), R95(D95/Dprescription), Paddick's conformity index (CI), homogeneity index (HI), monitor unit (MU), and OAR doses including lung (Dmean, V20 Gy and V15 Gy), chest wall, heart, esophagus, and maximum cord doses. A comparison of optimization results showed the robust optimization plan had better ITV dose coverage, better CI, worse HI, and lower OAR doses than conventional PTV margin‐based plans. Plan robustness evaluation showed that the perturbed doses of D99, D98, and D95 were all satisfied at least 99% of the ITV to received 95% of prescription doses. It was also observed that PTV margin‐based plans had higher MU than robust optimization plans. The results also showed robust optimization can generate plans that offer increased OAR sparing, especially for normal lungs and OARs near or abutting the target. Weak correlation was found between normal lung dose and target size, and no other correlation was observed in this study.


| INTRODUCTION
Robust optimization is primarily used to plan intensity modulated proton therapy (IMPT) 1 and it was not until recently that robust optimization techniques have been available for x-ray beam in radiation therapy treatment planning system. 2 Robust optimization methods have been used in radiation therapy to account for position uncertainties relative to the target volume during treatment delivery.
Position uncertainties come from two sources: tumor motion and variations in tumor shapes, and patient setup uncertainties. One way to approach these uncertainties is to use minimax optimization. 3 Instead of expanding the internal target volume (ITV) with a fixed margin to create the planning target volume (PTV), robust optimization allows entering the setup uncertainties into the planning computer and discretizes them into multiple scenarios (shifts within the margin bounds). The minimax optimization method minimizes the objective function such that the prescription holds true even in the worst case scenario. That is, robust optimization method generates scenario-based plans that have plan quality considered at least equivalent to static PTV margin-based plans. [4][5][6] This method has the potential to reduce the doses to healthy tissues, especially for tumors with substantially larger intrafraction motions in which there could be overlap between PTV and organ at risk (OAR).
The purpose of this study was to investigate the use of RayStation (v.5.4, RaySearch Laboratories, Sweden) photon robust optimization method for planning lung cancer patients. Both robustoptimized intensity modulated radiotherapy plans (ITV-IMRT) and robust-optimized volumetric modulated arc therapy plans (ITV-VMAT) were evaluated. A dosimetric study was performed to compare robust optimization plans with the corresponding traditional PTV margin-based plans (PTV-IMRT and PTV-VMAT). A correlation study was also performed to investigate the relationship between the target mean dose and the tumor size or tumor motion and the relationship between normal lung dose and tumor size or tumor motion.

2.A | Patient characteristics
Twenty lung cancer patients who were previously treated in our clinic were selected. Tumors located at various anatomical regions within the lungs were selected (11 in upper lobe, 8 in lower lobe, and 1 in middle lobe). Among these, 4 were centrally located and 16 were peripherally located according to the definition of peripheral or central tumor location defined in RTOG 0915. 7 The median ITV volume was 10.39 cc (3.29-107.23 cc) and the median PTV volume was 38.57 cc (19.12-210.23 cc). The tumor motion was determined by measuring the largest shifted distance from the center of tumor mass in the inferior-superior (IS), left-right (LR), and anterior-posterior (AP) directions. The isocenter was placed automatically at the center of tumor mass during treatment planning and the tumor motion was measured based on 4D-CT volume image set. The median maximum tumor motion within 3D mobility vectors was 1.45 cm (0.54-3.4 cm). The patient characteristic details are listed in Table 1.

2.B | ITV and PTV contour generation
To account for potential lung tumor motion for each patient, fourdimensional CT (4DCT) images with ten respiratory phases (0% to 90%) were acquired on a CT-simulator (Brilliance CT Big Bore, Philips, Cleveland, OH, USA) for each patient and imported to the RayStation treatment planning system (TPS). Ten gross tumor volumes (GTV) corresponding to different phase image datasets (GTV 0% to GTV 90%) were identified and manually delineated by the treating radiation oncologist. A single planning ITV contour was then created by encompassing all ten-phases of GTVs. The PTV contour was generated by extending the ITV contour to 0.5 cm in LR and AP direction and 1.0 cm along IS direction.
The robust treatment plans were generated based on all ten respiratory phases of the CT image datasets to evaluate the plan robustness caused by the tumor motion. Plan comparison between robust optimization and PTV margin-based optimization was performed using treatment plans generated based on the 20% phase of the CT image dataset. 2.C | ITV robust optimization plan and PTV marginbased plan ITV robust optimization plans were generated using minimax optimization method by minimizing the penalty of the worst case scenario. The minimax method does not minimize the worst of all possible scenarios, but the worst scenario within some predefined range. It considers only scenarios that are physically reliable; with unnecessary conservative case scenarios being avoided. 3,4 The range of patient setup error specified by the user was 0.5 cm in LR, 1.0 cm in IS, and 0.5 cm in AP direction for this study. This range of uncertainty was selected based on RTOG 0236 and 0915 protocols. 8,9 The total numbers of scenarios considered in the minimax optimization are related to the size of the uncertainty range specified in the TPS. In this study, a total of seventeen scenarios were generated based on the selected uncertainty.
Four treatment plans were generated per patient, among them two plans were robust optimization plans (ITV-IMRT and ITV-VMAT) and two plans were PTV margin-based plans (PTV-IMRT and PTV-VMAT). For comparison purposes, the planning and optimization parameters were kept identical for all plans except those in ITV optimization-based plans where the robust optimization function was used. The prescription dose (D p ) was such that at least 95% of the ITV or PTV receives 60 Gy in eight fractions. The lung doses were constrained as V 20 Gy <20% and V 15 Gy <37%. 10

2.D | Plan evaluation
Where TV is the target volume, TV PIV is the target volume covered by the prescription isodose volume (PIV), and V PIV is the total prescription isodose volume. The homogeneity index (HI) is calculated based on the following equation: Where D p is the prescription dose.

2.E | Statistics
A multivariate ANOVA statistical test 11

3.A | Target dose evaluation
The median and ranges of target mean doses (D mean ), target coverage (R 95 ), HI, CI, and MU from robust optimization and PTV marginbased plans using both IMRT and VMAT treatment techniques are shown in Table 2. Table 2 shows that the ITV target dose coverage satisfied the prescription requirement for both robust optimization and PTV margin-based plans. In addition, the robust optimization plans showed better CI and worse HI compared to PTV margin-based plans. The differences between the IMRT and VMAT technique using robust optimization method were compared and the results are shown in Table 3 and Fig. 1

3.B | OAR doses
The median mean doses and ranges for lung, heart, esophagus, and median maximum doses and ranges for spinal cord from robust optimization and PTV margin-based plans using IMRT and VMAT treatment techniques are shown in Table 7. Results showed statistically significant differences between robust optimization and PTV marginbased plans. The robust optimization plans showed lower OARs doses compared to PTV margin-based plans.

Similar results of OAR doses for robust optimization (ITV-IMRT
and ITV-VMAT) plans are shown in Table 8 and results showed no statistically significant differences between robust optimization ITV-IMRT and ITV-VMAT plans.

| DISCUSSION
The main goal of this study was to investigate the photon robust optimization method for lung cancer patient and to evaluate the plan robustness with perturbed doses shifted from isocenter. In addition, robust optimization plans were compared with traditional PTV  There are several important factors that can contribute to the deviation between planned and delivered dose. These factors include organ motion, geometrical uncertainties during target delineation and random/systematic errors during positioning and treatment. 13 Organ motion and geometrical uncertainties will directly affect the definition of ITVs. Generally there are two methods to generate ITV; one is to manually contour GTV using ten selected phases of 4DCT datasets; the other is to generate an ITV contour based on the maximum intensity projections (MIP) that was automatically generated from 4DCT simulation. The former method is time consuming and requires more physician time. However, the latter was reported to produce smaller ITV volumes compared to the ten-phase manually contouring method. 14 Therefore in this study, we decided to use the former method to define ITV, with the additional benefit of obtaining dose distributions in each phase of the respiratory cycle. The ten-phase manually contouring method is not very practical for the routine clinic performance. The simplified ITV contouring method needs to be developed such as using MIP plus two more image datasets (the full inspiration and expiration phases of the respiratory cycle). However, this proposed method need to be verified and it is beyond the scope of this study. For each patient, ten robust optimization treatment plans were generated corresponding to each of the ten-phase image datasets. Differences were found in ITV dose distributions for both IMRT and VMAT treatment plans. Figs. 2 and 3 show an example of two patients' ITV DVHs, whereas Fig. 2 shows the ten-phase DVHs for one patient with the largest tumor motion among all 20 patients in this study. Figure 3 shows ten-phases DVHs for the patient with the smallest target motion. It was noticed that the tenphase ITV dose distributions were more widely spatially distributed for the patients with larger tumor motions, while they almost overlapped with each other for patients with smaller tumor motions.
In comparing robust and nonrobust optimization plans, robust optimization plans had better ITV dose coverage, better CI, and worse HI compared to corresponding PTV margin-based plans (  In robust optimization, a minimal margin is applied to the target. 15  Robust optimization plans spared more of the OAR doses including lung, chest wall, heart, esophagus, and maximum cord doses compared to PTV margin-based plans ( Table 7). The robust optimization plans have the advantage of finding the best scenario for the trade-off between target coverage robustness and OAR sparing. This is important for those critical organs located near the target. For example, it was observed that 8 of 20 patients for PTV margin-based plans, the chest wall doses were above the constraint dose (at most 5 cc of the chest wall volume received 5 Gy) 10 in this study, whereas all the chest wall doses calculated from robust optimization plans were within this dose-volume limit. Figure 4 shows an example of isodose distribution from a robust optimization plan (a) and from a PTV margin-based plan (b) for one of the selected patients whose tumor target was located near the chest wall.

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