iCONE‐SRS: Development of inverse treatment planning for cone‐based stereotactic radiosurgery

Abstract Purpose At present, commercially available treatment planning systems (TPS) only offer manual planning functionality for cone‐based stereotactic radiosurgery (SRS) leading to labor intensive treatment planning. Our objective was to reduce treatment planning time through development of a simple inverse TPS for cone‐based SRS. Methods The iCONE TPS was developed using MATLAB (R2015a, The MathWorks Inc.) and serves as an inverse planning adjunct to a commercially available TPS. Simulated annealing is used to determine optimal table angle, gantry start and stop angles, and cone sizes for a user‐defined number of non‐coplanar arcs relative to user‐defined dose objectives. iCONE and clinically generated plans were compared through a retrospective planning study of 60 patients treated for 1–3 brain metastases (total of 100 lesions). Results Planning target volume (PTV) coverage was enforced for all plans through normalization. PTV maximum dose was constrained to be within 120%–135% of the prescription dose. The median conformity index for iCONE plans was 1.35, 1.33, and 1.32 for 1, 2, and 3‐target cases respectively corresponding to a median increase of 0.05 (range = −0.1 to 0.5, P < 0.05), 0.06 (range = −0.83 to 0.53, P < 0.05), and 0.03 (range = −1.21 to 0.74, P > 0.05) relative to the clinical plans. No clinically significant differences were found with respect to the dose to organs‐at‐risk. Median iCONE planning times were approximately a factor of five lower than consensus estimates for manual planning provided by local experienced SRS planners. Conclusions A simple inverse TPS for cone‐based SRS was developed. Plan quality was found to be similar to manually generated plans; however, degradation was observed in some cases highlighting the need for continued oversight and manual adjustment by experienced planners if implemented in the clinic. A factor of five reduction in treatment planning time was estimated.


| INTRODUCTION
Stereotactic radiosurgery (SRS) has been shown to be an effective treatment for brain metastases 1,2 leading to an increase in demand and pressure on clinical resources. Effective treatment can be delivered using standard linear accelerators equipped with a set of small conical collimators; 3,4 however, both treatment planning and delivery can be labor intensive. Accordingly, there has been a push toward multi-leaf collimator (MLC) based SRS which improves efficiency through the use of dedicated inverse planning tools and single isocenter deliveries (e.g. Varian HyperArc™, Brainlab Elements™ -Automatic Brain Metastases Planning). 5,6 Nonetheless, cone-based SRS is still commonly employed and offers several attractive features such as a sharp penumbra, low transmission, and the reliability of a simple two-part collimation system which does not move during treatment (e.g. simplified beam modeling, low delivery uncertainty, few device failure modes).
Unfortunately, unlike MLC-based SRS, commercially available treatment planning systems (TPS) only offer forward planning functionality for cone-based deliveries and so treatment planners must manually optimize several dozen parameters per treated target. This manual approach leads to prolonged treatment planning times particularly within the context of treating non-spherical lesions. In addition, a significant learning curve is associated with becoming proficient with this type of planning. Meeks et al 7 have previously reported a manual optimization algorithm to facilitate cone-based SRS planning; however, their primary goal was to improve dose conformity for irregularly shaped lesions rather than to reduce treatment planning time.
Our objective was to address the challenge of prolonged treatment planning times for cone-based SRS through the development of a simple inverse TPS which we refer to as iCONE. The iCONE algorithm is described and efficacy is demonstrated through retrospective application to data from patients previously treated for brain metastases. which serves as an inverse planning adjunct to a commercially available TPS. The iCONE workflow is summarized in Fig. 1 and a screenshot of the iCONE interface is shown in Fig. 2.
First, the user must delineate all targets, organs at risk (OARs), and an external or body contour in their respective commercial TPS and then export these structures in DICOM RT format. iCONE subsequently imports the DICOM RT file and the user identifies the target that they would like to generate a plan for (i.e. select planning target volume).
In iCONE, the user defines desired plan parameters including the number of non-coplanar arcs and the maximum number of unique cone sizes to appear in the final plan (Fig. 2, "Optimization" panel).
Default values were set to five arcs and a maximum of two unique cone sizes. iCONE automatically estimates the most relevant cone sizes to be considered for a given target; however, cone sizes can also be manually specified if desired. Relevant cone sizes are estimated by computing the diameter of a sphere with a volume equal to the target volume. The nearest-diameter cone is identified and then the range of considered cone sizes is equal to this cone size plus or minus two cone sizes.
Next, the user defines optimization parameters which include the number of optimizer iterations and optimization objectives. For the selected target, the conformity index (CI), gradient index (GI), and maximum dose can be constrained.
CI is defined in iCONE as the ratio of the treated volume to the planning target volume (PTV) where the treated volume is equal to the total volume receiving the dose that must cover the PTV (D cov ).
The coverage dose D cov has a default value of 95% of the prescribed dose but can also be specified by the user. Hereafter, CI 95 will be used to denote the CI as computed using D cov = 95%. The GI isH: \journals\W3G\ACM2\12609\ACM2_12609.3d defined as the ratio of the volume receiving 50% of the prescribed dose to the volume which receives 100% of the prescribed dose. The desired CI, GI, and maximum dose (D max ) values can be specified along with optimization weights. For OARs, the maximum dose can be constrained to a specified value. The maximum dose to targets that are not being treated by the current plan can also be constrained in order to limit the interaction between plans generated for multi-target cases. iCONE then uses simulated annealing 8 to search for a set of arc parameters which produces an optimal dose distribution with respect to the optimization objectives. During optimization, the CI, GI as well the maximum dose to all structures is displayed for the most optimal solution found at the time of the current iteration ( Fig. 2, "Plan Evaluation" panel). Once optimization is complete, iCONE outputs the table angle, gantry start and stop angles, cone size, and weighting for each arc along with the isocenter coordinates ( Fig. 2, "Plan Parameters" panel). A visualization of the arc geometry relative to the target and OAR structures is also provided (Fig. 2, "Arc Geometry" panel). The current plan can be reoptimized using different objectives or alternatively a new plan can be created.
Creating a new plan "locks" the previous plan and generates a new plan tab which appears at the top of the window. Each locked plan can be reviewed for comparison purposes at any time by selecting its associated plan tab. Once a desirable plan has been found, arc parameters must then be manually transcribed into the commercial TPS by the user.

2.A.2 | Dose calculation
A simple correction-based dose algorithm was implemented in iCONE. For simplicity and to reduce computation time, no heterogeneity correction was applied. Each arc is discretized into a series of beamlets for which the isocenter is defined as the PTV centroid. LAUSCH ET AL.

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Beamlets are defined every 10°. The relative dose contribution of beamlet b at calculation pointx is described by

2.A.3 | Optimization
The iCONE optimization parameter space corresponds to the set of all unique combinations of table angle, gantry start position, gantry stop position, and cone size for the user-specified number of arcs.
The range of considered Simulated annealing coupled with a coarse-to-fine optimization scheme was used to search the parameter space for an optimal solution. The starting solution for each optimization was defined to be a set of equally spaced 180°non-coplanar arcs each with the same cone size. This initial cone size was chosen to be the median size in the iCONE-or user-specified range of cone sizes to be considered by the optimizer.
In the first or "coarse" level, a neighbor solution is generated by incrementing the table and gantry angle parameters of the current solution by 20°. In the second or "fine" level, angle parameters are incremented by 10°. The cone size increment is set to an increase or decrease in one size for both optimization levels. All plan parameters have an equal probability of changing or remaining the same when a neighbor solution is generated. The best plan found during the coarse optimization is then used to seed the fine optimization.
A weighted sum-of-squares objective function of the form was used to inform the optimizer whereÕ ι is the objective for i-th parameter and O i is the value of that parameter for the plan considered in the current iteration. The {w i } are the user-specified optimization priorities for each objective and are normalized by iCONE prior to optimization such that ∑ i w i ¼ 1.
The acceptance probability for less optimal solutions was defined to be Optimization was subject to several additional constraints. First, the minimum table angle separation between arcs was limited to 20°. Second, the minimum arc length was constrained to be 60°.
Third, the sum of all arc lengths was constrained to be greater than or equal to 340°. These constraints were related to local planning procedures and so were hardcoded in iCONE; however, they can be changed to assume any value.

2.B.1 | Dataset
Treatment planning data from 60 patients previously treated with cone-based SRS for brain metastases were used for this retrospective study. Thirty cases were treated for a single metastasis, 20 cases were treated for two metastases, and 10 cases were treated for three metastases for a total of 100 treated targets. Cases were selected at random with a preference for more recently treated patients since the local SRS program was initiated in 2014 and planning expertise was assumed to have increased over time. Table 1 summarizes the location of the 100 lesions. | 73 Organs at risk and gross tumor volumes (GTVs) were previously delineated by experienced treatment planners and radiation oncologists respectively. A 2 mm PTV margin was used to account for known setup uncertainty. The median PTV volume was 1.6 cc (range = 0.3-10.9 cc). The median prescription dose was 15 Gy (range = 11-21 Gy) with lower doses associated with OAR-target proximity, larger target volumes, and multi-target cases.

2.B.2 | Treatment planning
The clinically delivered treatment plans were originally generated using the iPlan TPS (version 4.5.6, Brainlab) which employed a correction-based dose model with heterogeneity correction. The planning constraints that were used during generation of the clinical plans are summarized in Table 2 and represent the minimum requirements for an acceptable plan. Brain dose constraints are not listed in Table 2

2.B.3 | Analyses
The primary analyses made were with respect to plan quality, plan complexity, and treatment planning time. For plan quality, the

3.A | Plan quality
Stereotactic radiosurgery plans were generated using iCONE for the N = 60 cases (100 targets) and compared to the clinically delivered plans (CLIN). Relative dose distributions are shown for three different lesions in Fig. 3. Examples are provided where iCONE decreased the CI (i.e. improved conformity, Fig. 3a), maintained similar CI (Fig. 3 b), and increased the CI (i.e. reduced conformity, Fig. 3c   The differences between iCONE and CLIN values from Fig. 4 were computed and are displayed in Table 3. A small increase in CI 95 was observed for iCONE generated plans which was found to be statistically significant for 1-and 2-target cases (P < 0.05) but not for 3-target cases. A statistically significant increase in the PTV maximum dose was observed for 1, 2, and 3-target cases planned using iCONE while no significant differences were observed with respect to the gradient index.    Table 2.
For the healthy brain, the median V12 values for clinical and iCONE plans were 4.7 cc (range = 0-17.9 cc) and 4.5 cc (range = 0-21.3 cc) respectively. The median difference was −0.2 cc (range = −7.5 to 6.8 cc) which corresponded to a small but statistically significant decrease in the iCONE plans (P < 0.05).

| DISCUSSION
A simple inverse-treatment planning system called iCONE was developed to address the challenge of prolonged treatment planning times for cone-based SRS. To our knowledge, this is the first study to report the application of inverse optimization techniques to conebased SRS planning. The new tool was applied retrospectively to data from 60 patients previously treated for 1-3 brain metastases.
Performance was assessed with respect to plan quality, complexity, and planning time relative to the clinically delivered treatments.
iCONE plan quality was found to be comparable to clinically generated plans with the exception of a median increase in CI 95 of between 0.03 and 0.06 depending on the number of treated targets (Table 3).
PTV maximum dose values were higher than clinical plans; however, the distribution of values was better centered within the clinically desirable range (Fig. 4b) While iCONE plan quality was similar to clinical plans, plan complexity was found to be higher. Increased plan complexity was typically due the addition of an extra arc. The number of arcs and unique cone sizes used by the optimizer is defined by the user a-priori so that they can directly control plan complexity. Within this study, an extra arc was primarily added to ensure that no more than 999 monitor units were delivered at a single couch angle due to a local planning constraint rather than to further improve dose metrics.
An alternative approach could have involved using fewer arcs followed by incrementally decreasing the weight of the offending arc once the plan was transferred into the commercial TPS.
The primary objective of this study was to reduce cone-based SRS treatment planning times through development of inverse planning. Median iCONE planning times were found to be approximately a factor of five lower than consensus estimates for manual planning (Table 5) suggesting potential for significant planning time reduction.
Furthermore, the number of optimizer iterations used in this study (N = 4000) was not determined a-priori to offer the best trade-off between optimization time and solution quality. Subsequent testing has suggested that similar quality plans could be generated using half as many iterations which could lead to a further factor of two reduction in iCONE planning time.
There are several important limitations to consider when interpreting the results of this study. Principal among these is the potential for discrepancies between iCONE and commercial TPS derived estimates of plan quality metrics. In practice, the user will rely on iCONE-estimated metrics to decide when they have arrived at a suitable solution and should transcribe the plan to a commercial TPS.
However, due to differences between the geometry representation and dose calculation methods employed by iCONE and the commercial TPS, the value of these metrics can change upon final evaluation in the commercial TPS. For example, Brainlab iPlan employs an adaptive resolution scheme that uses a finer dose grid near steep gradients whereas iCONE uses a uniform grid in order to enable the use of pre-computed dose kernels and rapid dose calculation.
In view of this limitation, we only report commercial TPS-derived quality metrics for iCONE plans and also did not permit re-optimization in the event that reduced quality was observed in the commer- was a statistically significant increase in CI 95 values (P ≪ 0.01, median = +0.05, IQR = 0-0.10). Similarly for the maximum dose to the target, the iCONE estimated median was 125% (IQR = 123%-127%) but there was a statistically significant increase upon re-evaluation in Brainlab iPlan (P ≪ 0.01, median = +0.1%, IQR = 0-4%).
This result has several implications. First and foremost, the possibility for quality degradation underscores the importance of the evaluation step in the Fig. 1 workflow. Continued oversight by experienced planners is essential to ensure that the plan in the commercial TPS realizes the plan quality as estimated by iCONE. This may necessitate manual adjustment and increase planning time. Second, iCONE-estimated plan quality appears to be equal to the plan quality attainable via current manual methods and so iCONE estimates can provide guidance on the quality that is possible for a given case. Third, increased knowledge and incorporation of commercial TPS methodologies or direct integration into a commercial TPS could improve utility via increased concordance in quality metric estimation.
Other current iCONE limitations include no split-arc support, no isocenter position or beam weighting optimization, serial optimization of multiple targets, and no computation of absolute dose.
Despite these limitations, favorable results were still found in this study and so supervised iCONE-use will begin to be investigated in our local workflows with functionality to be expanded in future versions if desired by the clinic.

| CONCLUSION
A simple inverse treatment planning system for cone-based SRS called iCONE was developed. Plan quality was found to be similar to manually generated plans in a retrospective analysis of patients treated for 1-3 brain metastases, however, quality degradation was observed in some cases highlighting the need for continued oversight and manual adjustment by experienced planners. A factor of five reduction in treatment planning time was estimated if iCONE were to be integrated into the local clinical workflow.