Implementation and validation of an in‐house geometry optimization software for SRS VMAT planning of multiple cranial metastases

Abstract Purpose The implementation and evaluation of an in‐house developed geometry optimization (GO) software are described. The GO script provides optimal lesion clustering, isocenter placement, and collimator angle of each arc for cranial multi‐lesion stereotactic radiosurgery (SRS) volumetric modulated arc therapy (VMAT) planning. Materials and methods An Eclipse‐plugin program was developed to facilitate automatic plan geometry generation for multiple metastases SRS VMAT plans. A mixed, semi‐supervised exhaustive and k‐means clustering method is used to group lesions and place isocenters. The sum of squared euclidean distance (SSED) and the boundaries of lesions’ projection from beams’ eye view are used as supervised parameters to determine the optimal isocenter numbers. The collimator angle is optimized by minimizing the sum of the MLC opening area from all gantry angles for each arc. In all, 10 clinical cases treated during 2016–2017 were compared to plan quality of GO script generated plans. Paddick gradient index (GI), conformity index (CI), and local brain volume receiving 12 Gy (local V12 Gy) around each lesion were compared. Result For four cases, the number of isocenters was reduced in the GO plans. For four other cases, the GO plans had the same number of isocenters as their corresponding clinical plans but with different lesion grouping. The GO plans had significantly lower GI (4.1 ± 1.0 vs 4.4 ± 0.9, P < 0.0001) and local V12 Gy (5.1 ± 4.2 vs 5.5 ± 4.3 in cm3, P < 0.0001), but not significantly different mean normal brain dose or CI. The volume of normal brain receiving ≥6 Gy was significantly lower in the GO plans. The total time to run the GO script for each case was <2 min. Conclusion The GO software automates lesion grouping, isocenter placement, and the collimator angles for SRS VMAT planning. When tested on 10 cases, the GO script resulted in improved plan quality and shorter planning time when compared to the clinical SRS VMAT plans.


| INTRODUCTION
Radiation treatment of multiple metastatic cranial lesions with volumetric modulated arc therapy (VMAT) has become one of many radiation treatment options in the past years. [1][2][3][4][5] Compared to conventional techniques such as Gamma Knife (Elekta, Crawley, UK), CyberKnife (Accuray Inc, Sunnyvale, CA, USA), and conventional C-arm linear accelerators (Linacs) employing cones or conformally shaped multi-leaf collimator (MLC) patterns, all targeting one lesion at a time; VMAT techniques improve the treatment delivery efficiency using one isocenter to target multiple lesions. These VMAT plans can achieve highly conformal dose distributions similar to Gamma Knife plans. [4][5][6][7] Although most of these studies were based on using a single isocenter VMAT plan to treat multiple cranial lesions, [1][2][3][4][5][6][7][8] other studies indicate that VMAT plans with multiple isocenters may be required to improve the plan quality, reduce the risk of comprised coverage for lesions far from isocenter, [9][10][11] and account for the MLC model inaccuracy in the dose calculation algorithms. [12][13] Grouping the targets into multiple plans and isocenters results in increased treatment planning complexity and long planning times. It is challenging and time-consuming for planners to determine the best grouping of lesions into separate isocenters, to select the best arcs for each isocenter, and finally choose the optimal collimator angles for each arc. Each planner may choose different solutions for the same patient, resulting in plans with variable plan quality and posing a challenge for institutional quality assurance.
Previous studies propose different methods to solve lesion grouping and optimal collimator geometry separately. 8,[14][15] However, none of them have presented the results from combining both methods. In this study, we present a tool for optimizing lesion grouping and finding the optimal collimator angle for each arc so that SRS VMAT treatment plans are generated in shorter time and with more consistent plan quality. We prototyped a geometry optimization (GO) script in Matlab (Mathworks, Natick, MA, USA), subsequently implemented it using the Eclipse Scripting Application Programming interface (ESAPI, Varian Medical Systems, Palo Alto, CA), and eventually integrated it into the production Eclipse system for routine clinical operations. The overall goal of this script is to reduce planning time while creating plan geometries that can produce plans that at least match or improve on manually created plans. In this study, we present a thorough description of this script and the script-generated plans are validated against a set of high-quality, manually created clinical plans.

2.A | Automatic lesion grouping algorithm
In this study, we developed a mixed, semi-supervised exhaustive and k-means clustering method to group lesions and place isocenters. For total lesion numbers less or equal to 7 and isocenter numbers less or equal to 3, the script uses the exhaustive search method, and for more than 7 lesions the k-means method is used. We choose to combine both methods in this study since the exhaustive method is not very efficient compared to the k-means method when the number of lesions is large. Both methods use the squared Euclidean distance as the optimization metric, theoretically they should give the same clustering results. The flowchart for both methods is shown in Fig. 1.
For the exhaustive search method, the search starts with one isocenter (one cluster), and lesions are grouped based on exhaustive combination lists predefined for up to n = 3 isocenters, which for a single isocenter is the trivial single combination of all lesions being in the same cluster. In every possible combination, an isocenter location is placed for each of n clusters based on the lesions' centroid in that cluster. A projection distance check is performed to determine if all lesions fall within a preset distance criteria from the assigned isocenter. If none of the possible combinations meet the criteria, the number of isocenters is increased by one, and the process is repeated, with all the possible combinations of grouping lesions into n + 1 clusters with n + 1 isocenters being tested again, until one or more combinations are found where all clusters meet the geometric distance criteria. If multiple different combinations of clusters meet the criteria, the Sum of squared euclidean distance (SSED) from the isocenter to all grouped lesions is calculated for each group and the combination with the smallest SSED is selected as the optimal clustering result. Details of the isocenter placement and geometric distance check method will be described in the following sections.
If the total number of lesions is larger than 7 and the resulting number of isocenters is large than 3, a k-means ++ clustering algorithm is used to group the lesions instead of the exhaustive method, running repeats equal to the total number of lesions to avoid suboptimal clustering results. We select squared Euclidean distance as the distance metric in the k-means ++ algorithm to minimize the withincluster variance which is equivalent to the SSED. Each search starts with one isocenter per cluster and checks if each cluster generated from the k-means method meets the distance criteria. If none of the clusters meet the criteria, the number of isocenters is increased by one as input for the next k-means clustering until all clusters meet the set distance criteria.

2.B | Isocenter placement
There are different methods to place isocenter for multiple lesions and a previous study compared the plan quality difference between these methods. 11 These methods include volume centroid, centroid of equally weighted points, centroid of points weighted by inverse of volume, and treatment planning system built-in method. In terms of dose fall-off outside the target, there is no significant difference between these methods except for the inverse volume centroid method which was found to result in slightly inferior plan quality. 11 The optimizer described in this study is placing the isocenter at the  angle. The optimal collimator angle has the smallest summed total MLC opening area (Fig. 3). The final jaw positions are fit to clustered lesions with optimal collimator angle for each manually selected arc using the method provided in the ESAPI. Maximum jaw positions in each Y direction are set to 4 cm for the Varian TrueBeam STx with HD120 to ensure that only the 2.5 mm MLC are used.
2.E | Implementation in Varian Eclipse API 15.5 The software was originally developed in Matlab and rewritten in C#

2.F | Pre-clinical validation and release
Before releasing the plugin clinically, two tests were performed to validate that the GO script worked correctly and as intended. The were selected for testing of the GO software. Both the clinical and the GO plans were generated in Varian Eclipse V13.6 with a specific analytical anisotropic algorithm (AAA) dose calculation model tuned for small targets. 12 The dose calculation grid was 1.25 mm. For cases where the GO software created identical lesion grouping and isocenter location to the actual clinical plan, the same couch angles and gantry angles used in the clinical plan were used for the GO plan but the GO plan used the optimal collimator angles as determined by the GO software. If the GO software created different lesion grouping than the clinical plan, four default arcs with couch angles at 0°(full arc), 90°,45°, and 315°(180°range partial arcs) with the optimal collimator angles as determined by the GO software were used to generate the GO plan.
The plan quality of the GO plans was compared to the clinical plans by evaluating the Paddick gradient index (GI), 16 RTOG GI, 17 conformity index (CI), 18 local brain volume receiving 12 Gy (local V12Gy) around each lesion, normal brain mean dose, and volumes of normal brain receiving 4 Gy-16 Gy in 1 Gy increments (V4Gy, V5Gy⋯V16Gy). In addition, total MU and calculation time for isocenter and collimator optimization were recorded for each case. A paired T-test was used for statistical analysis.

| RESULTS
The isocenter and collimator optimization algorithms were successfully translated into the GO script and gave the same results as the original Matlab code on grouping lesions and isocenter placement.
Because the MLC fitting method in the Matlab code does not take the MLC travel motion limitation into account, for some arcs, the optimal collimator angle found by the GO script could be up to 15°d ifferent than in Matlab, but the final plan quality was almost identical (data are not shown).
For 4 out of the total 10 cases, the number of isocenters was reduced in the GO plans as compared to the clinical plans. For these cases, the total MUs were also reduced. For four other cases, the GO plans had the same number of isocenters as the clinical plans but with different lesion grouping (Table 1). For each of the 10 cases, the total geometry optimization time was <2 min. The time it takes for a planner to manually group the targets and select isocenter depends on the distribution and the number of lesions, and ranges from 20 to 60 min. The GO script will significantly shorten the treatment planning time for multi-lesion SRS VMAT cases. 13 The Paddick-GI, the RTOG-GI, the CI, and the volume included in the local 12 Gy isodose line around each PTV are shown in Table 2, along with the dose to normal brain. The mean and range are listed for each parameter. A paired T-test is used to compare the clinical plan to the GO plan for each parameter and the P value is shown in the last column. The GO plans had significantly lower GI, CI, and local V12Gy values than the clinical plans. The GO plans had slightly higher mean normal brain dose, but the difference was not statistically significant. The volume of normal brain receiving 6 Gy and higher was lower in the GO plans than in the clinical plans (Table 2 and Fig. 4). As an example, Fig. 5  found that due to dose modeling limitations by the treatment planning system, the AAA model does not provide accurate dose calculation for both the 2.5 mm and the 5 mm MLC on the TrueBeam STx and we chose to fit the model to the small MLC only and limit the treatment delivery to these leaves. 12 For these reasons, there may be a rationale for using multiple isocenters, depending on the spatial distribution of the cranial metastases. The GO software provides fast grouping of lesions, optimal collimator angles for each arc, and the outcome is more standardized plan quality than is provided manually by a group of treatment planners. Since the release of the GO script in February 2019, it has been used for planning of more than 70 multi-lesion SRS VMAT cases with three or more lesions at our institution.
Several prior studies present clustering solutions. 9,15 Morrison et al. 9 manually assigned targets to one of the isocenters iteratively until the distance between the centroid of each target to the respective isocenter was less than 5 cm and overall distance was minimized. Yock et al. 15 were the first group who applied a data clustering algorithm to solve lesion grouping and isocenter placement for multiple intracranial metastases by utilizing the k-means clustering algorithm. In their study, SSED and target coverage metric were used as quantitative optimization objectives. However, they ran k- However, based on our experience with a few cases (data not shown), none of these methods can perfectly solve all possible distributions of lesions. Therefore, a hybrid method to provide multiple optimal cluster selections for the planners may be beneficial for very complex lesion distributions.
Finding the optimal collimator angle for each arc is critical to reduce dose to normal brain and critical organs resulting from the "island blocking problem" and larger than necessary jaw openings. 8,14 Kang, et al. 14  In a few prior studies, the collimator optimization objectives have been used to also optimize couch angles. 8,14,15,23 In this study, we found that the objectives' value in the collimator optimization was very similar for different couch angles and therefore decided it was not realistic to use the same algorithm for collimator optimization to also select best couch angles (data not shown). Furthermore, using only one simple objective may be not enough to optimize couch angle, and other objectives or optimization methods should be considered.
Regardless, in 8 out of 10 test cases, 4 standard arc angles were used and produced slightly better plans than the clinical plans. This may indicate that for VMAT plans with multiple isocenters, optimal couch angles may not have a significant impact on the plan quality.
For cases with a large number of lesions, complex lesion distribution, and proximation between lesions and organs at risk, different human dosimetrists typically generate plans with very different lesion groupings, arc geometries, and collimator angles. The solution depends on the dosimetrists' experience level. It is not trivial to determine the optimal grouping of lesions. Some dosimetrists would create more isocenters and that would significantly increase both planning and delivery time but not necessarily create a better plan quality than a solution with fewer isocenters. Our goal was to automate the planning processes and significantly reduce the planning time while maintaining similar or better plan quality.

| CONCLUSION
The GO script was implemented in the clinic in February 2019, and since then it has been used in the planning of more than 70 cases.
Using the GO software to group PTVs, set isocenter, and optimize the collimator angles for all arcs resulted in similar or slightly improved plan quality as compared to the manually created clinical plans while significantly shortening planning time and providing more consistent plan quality among different planners.

ACKNOWLEDGMENTS
This study was presented in part at the 2019 AAPM 61th Annual

Meeting in Austin, TX. This research is funded by the MSK Cancer
Center Support Grant/Core Grant (P30 CA008748).

CONF LICT OF I NTEREST
There is no conflict of interest related to this study.