Characteristics and limitations of a secondary dose check software for VMAT plan calculation

Abstract Purpose To assess the implementation, accuracy, and validity of the dosimetric leaf gap correction (DLGC) in Mobius3D VMAT plan calculations. Methods The optimal Mobius3D DLGC was determined for both a TrueBeam with a Millennium multi‐leaf collimator and a TrueBeamSTx with a high‐definition multi‐leaf collimator. By analyzing a broad series of seven VMAT plans and comparing the calculated to the measured dose delivered to a cylindrical phantom, optimal DLGC values were determined by minimizing the dose difference for both the collection of all plans, as well as for each plan individually. The effects of plan removal from the optimization of the collective DLGC value, as well as plan‐specific DLGC values, were explored to determine the impact of plan suite design on the final DLGC determination. Results Optimal collective DLGC values across all energies were between −0.71 and 0.89 mm for the TrueBeam, and between 0.35 and 1.85 mm for the TrueBeamSTx. The dose differences ranged between −6.1% and 2.6% across all plans when the optimal collective DLGC values were used. On a per‐plan basis, the plan‐specific optimal DLGC values ranged from −4.36 to 2.35 mm for the TrueBeam, and between −1.83 and 2.62 mm for the TrueBeamSTx. Comparing the plan‐specific optimal DLGC to the average absolute leaf position from the central axis for each plan, a negative correlation was observed. Conclusions The optimal DLGC determination depends on the plans investigated, making it essential for users to utilize a suite of test plans that encompasses the full range of expected clinical plans when determining the optimal DLGC value. Validation of the secondary dose calculation should always be based on measurements, and not a comparison with the primary TPS. Varying disagreement with measurements across plans for a single DLGC value indicates potential limitations in the Mobius3D MLC model.


| INTRODUCTION
Secondary dose calculations are utilized to serve as an independent verification of the primary treatment planning system (TPS). This independence is enhanced when the secondary check arrives in a pre-configured state with a standard beam model for a given machine/energy class. In this case, it is recommended that the user makes minimal, if any, modifications to the software's model configuration. When changes are made, it is essential to have an understanding of the modifiable factors and their impact on dose calculations, as well as how parameter value variation relates to a measurement scenario.
Mobius3D (Varian Medical Systems Inc., Palo Alto, CA) is a secondary check software that provides quality assurance calculations for a full range of clinical photon and electron plans. For photon beams, Mobius3D utilizes a CT dataset along with plan and structure information (exported from the primary TPS) to perform an independent convolution-superposition dose calculation for comparison with the dose calculated by the primary treatment planning system. 1 Vendor-specific beam models which contain a set of default values are provided. Outside of the necessary linac calibration conditions, it is recommended that the beam model is maintained as provided unless large variations are observed between the reference and measured percent depth dose (PDD) and off-axis ratios (OAR).
Customization of the beam-model may be facilitated with an auto-modeling feature at the expense of reducing the independence of the beam model. 2 In addition to built-in parameters, there is a series of machine configuration parameters whose values the user can adjust, including those related to the determination of treatment times (dose rate), deliverability (max MU/field), clearance (distance between isocenter and collimator surface; collimator radius), and dose (dosimetric leaf gap correction). Of these parameters, the dosimetric leaf gap correction (DLGC) is the only one that will directly affect the dose calculation for MLC-based plans, and subsequently the dose calculation accuracy of the system. The Mobius DLG parameter contains two parts, an internal value (DLGI), which is not exposed to the user and is determined by automodeling routines executed by the vendor, and a correction (DLGC) which the user can vary. Prior to calculation, each MLC leaf position value in Mobius is moved by an amount of DLG/2 = (DLGI + DLGC)/2. There are specific DLGI and DLGC values for each machine and energy combination. According to Varian documentation, the DLGC in Mobius3D is modifiable by the user on a per-machine, per-energy basis to help account for differences between real-world dosimetry and the inherent Mobius MLC transmission model. 2 Making the DLGC more positive increases the calculated dose, while making it more negative decreases the calculated dose. Essentially, the Mobius3D DLG can be interpreted as a single entry to a leaf offset table within the software, where the DLGC is used to tune the internal DLGI to the institution's preference.
An important distinction when considering the Mobius3D DLG is that it is not defined in the same manner as the DLG in the Eclipse treatment planning system (DLG E ). In Eclipse, the DLG E is an inherent part of the step-wise transmission function utilized to model the rounded leaf tip of the MLC. There is no consideration of leaf height and no leaf offset table. Alternatively, Mobius3D utilizes a full rounded leaf-tip calculation using ray-tracing and considering the leaf height to define the transmission function, which results in a smooth falloff of the fluence through the rounded leaf end. 3 There have been investigations reported in the literature regarding the commissioning, validity and implementation of Mobius3D for use as a secondary dose calculation tool. [4][5][6][7][8] On average, prior works saw typical agreement relative to ion chamber measurements in a phantom of <2%, 4,6-8 though differences as large as 5.5% were reported. 8

2.A | Collective DLGC optimization
The optimal DLGC value was determined for a TrueBeam with an MMLC and energies of flattened 6, 10, and 15 MV, as well as unflattened 6 and 10 MV. It was also determined for a TrueBeamSTx with an HDMLC and the same energies except 15 MV flattened. The DLGC was determined for each energy on each machine independently following an optimization process that was a variation of that recommended by Mobius3D, 2 where our approach utilized multiple ion chamber measurements (in target, both on-and off-axis). The optimal collective DLGC value for each energy was determined by comparing the Mobius3D calculated dose at several DLGC values to the measured ion chamber dose for a series of test plans.
Seven VMAT test plans were utilized throughout the optimization: four geometrically based, and three anatomically based. The four geometrically based plans were based on recommendations made in TG-119 and contained either a central cylinder, lateral cylinder, large cylinder, or c-shape target structure. 11 The anatomically based plans consisted of a representative head and neck, lung SBRT, and chest wall targets. The plans were chosen to cover a range of SHEPARD AND FRIGO | 217 the clinical scenarios expected at our institution. An overview of each plan and the corresponding target structure is provided in Table 1.
All plans were delivered to a cylindrical TomoTherapy "cheese" phantom (diameter = 30 cm, length = 18 cm; Accuray Inc., Sunnyvale, CA), which allowed for the placement of six A1SL ion chambers (r cav = 2.00 mm; collecting volume = 0.053 cm 3 ; Standard Imaging Inc., Middleton, WI) laterally along the central slice of the phantom.
The ion chambers were positioned such that measurements were acquired at representative target (high-dose) locations for each of the plans investigated. An example of the setup used for measurement acquisition is shown in Fig. 1 The decision to use the cheese phantom with multiple A1SL ion chambers was made based on the availability of equipment in our clinic, the desire to acquire multiple measurements for each plan at a variety of positions, and the utilization of smaller ion chamber measurement volumes.
For each plan, the ion chambers were placed in high-level, lowgradient dose regions corresponding to the treatment target volume.
The charge was measured and converted to absolute dose using appropriate chamber correction and calibration factors. Absolute dose uncertainty for the A1SL was estimated to be 1%. 12 The percent difference between the calculated and measured dose was calculated for each chamber location, defined as This formulation considers the measurement as the reference and produces a result that gives a direct indication of whether the calculation is higher or lower than the measurement. Chambers were only considered if they had a measured dose of >80% of the maximum calculated dose.  to be the optimal value for the specific energy and machine.

2.B | Individual plan DLGC optimization
In addition to determining the optimal collective DLGC, the optimal DLGC for each individual plan was also calculated in an identical manner, as an investigation into the variability of the DLGC based on plan characteristics. As opposed to the collective DLGC, the planspecific values will be referred to in this work as the plan-specific DLGC.
The plan-specific values were calculated for each machine and energy independently based on the line of best-fit for each individual plan. It was observed that some of the optimal plan-specific DLGC values fell outside of the initial values set for the collective DLGC optimization, so spot-check calculations were performed for those plans which required extrapolation. This was in order to verify the validity of the best-fit curve. In the scenario that the extrapolated value still resulted in a dose difference of >1% (estimate of absolute dose determination uncertainty for A1SL 12 ), the new data point was added to the analysis, and a new best-fit for that specific plan was determined.
The importance of each plan to the determination of the collective DLGC was assessed by performing a collective DLGC optimization while excluding single plans from the analysis, in order to assess the potential impact of test plan selection.

2.C | Plan-specific DLGC correlation to plan complexity metrics
The optimal values for the plan-specific DLGC were assessed relative to several plan metrics to assess whether any relevant correlation between DLGC values and plan metrics was present. These metrics

3.A | Collective DLGC optimization
The average dose difference between the calculated and measured dose across all plans investigated is presented in Fig. 2  on a per-plan basis. This calculation was performed for each machine and energy combination, and an example of the analysis for the 6 MV beam on the TrueBeam model is provided in Fig. 4.
All extrapolated values were spot-checked, and the percent difference was within AE0.6% at the extrapolated DLGC value. Considering each plan and energy individually resulted in DLGC values between −5.38 and 4.59 mm. The optimal plan-specific DLGC averaged over all energies is shown in Fig. 5, with values ranging from −4.36 to 2.62 mm. By presenting these data as an average across all energies, it helps isolate the plan-specific variability in the values observed.

3.C | Plan-specific DLGC correlation to plan complexity metrics
To assess the potential dependence of the DLGC on plan characteris-  Fig. 6 are representative of a AE1% uncertainty in the dose measurement.
Note that plans with a lower DLGC sensitivity, as demonstrated by a lower slope in Fig. 4, correspondingly had a larger optimal DLGC uncertainty for a constant AE1% dose uncertainty.

3.D | Effects of plan exclusion from optimization
To assess the potential impact that plan selection can have on the optimal collective DLGC determination, the same analysis was repeated after removing a single plan and the change in the collective DLGC was noted. This was performed independently for an exclusion of both the lung SBRT plan and the lateral cylinder plan F I G . 3. Plan Specific Dose Deviation at Optimal Collective DLGC. The dose deviation between Mobius3D calculated dose and measurement at the optimal collective DLGC for each plan and energy on the (a) TrueBeam with MMLC and (b) TrueBeamSTx with HDMLC is presented. Measurements for the lateral cylinder plan was noted to be consistently lower than calculations, while measurements for the lung SBRT plan was consistently higher than calculations; others show mixed agreement. (representative of the plans exhibiting the largest dose differences when the optimal collective DLGC value was used).
With plan removal, the change in the optimal collective DLGC value ranged from −0.63 to 0.86 mm. The results for all energies are presented in Fig. 7(a) Fig. 7(b).

3.E | Comparison with RayStation calculations
Dose calculations were also performed with the RayStation treat-  4,5,7 Mobius3D is often used with relatively large gamma parameter tolerances of 5%/3 mm, providing an effective means for detecting gross errors and differences with the treatment planning system. As clinics look to potentially implement tighter action criteria, it is essential that they do so keeping current limitations in mind. If the goal is to focus the scope on a small number of plans, and the DLGC has been optimized specifically for the given plan characteristics, it may be reasonable to decrease the tolerance values, as in general, relatively good agreement between Mobius3D and measurements was observed. However, when considering a wide range of potential plans as was investigated in this work, a tightening of the action criteria could unduly raise flags due to plan disagreement from calculation inaccuracy. In this scenario, it may be difficult to truly determine whether disagreement between Mobius3D and the primary calculation is due to a problem with the plan, the primary TPS, plans whose slope (sensitivity) is higher.
Using plans that are representative of the full range of expected clinical plans is essential to the proper selection of the collective DLGC parameter value to be used. For instance, Fig. 7 This work focused on the implementation of the DLGC for VMAT deliveries; however, it is important to consider the potential impact on conformal arc deliveries as well. This is particularly relevant at target edges and for small-field conformal arc plans where the DLG will consti-

| CONCLUSION
A Mobius3D DLGC optimization procedure was implemented on both a TrueBeam with an MMLC and a TrueBeamSTx with an HDMLC. Optimal DLGC parameter values based on all test plans investigated were able to be determined through the comparisons of calculated and measured dose. While the DLGC was able to be optimized for the collective dose difference of the plans, the optimal collective DLGC was not the same as the optimal DLGC for each plan individually. Ultimately, the DLGC value determined from the optimization procedure will be dependent on the test plan spectrum, making it essential for users to consider how the software will be used and the shortcomings that may result from a given test plan suite. In order to achieve an increased accuracy across a full spectrum of plans, it would likely be necessary for the MLC model to be improved. Based on these results, MLC model limitations in the second check software could have the possibility of raising a false positive. Lastly, a comparison between the primary TPS, secondary TPS, and measurement, points out that one must validate their secondary TPS against measurement, and not use agreement with the primary TPS for this purpose.

ACKNOWLEDG MENTS
The authors would like to thank Dr. Adam Bayliss, Dr. Jessie Huang-Vredevoogd, and Stephanie Olson for assistance with plan creation, as well as Dr. Jon Hansen and Maxwell Belanger for assistance with data acquisition.

CONFLI CT OF INTEREST
The authors have no conflict of interest to report.