Commissioning and performance evaluation of RadCalc for the Elekta unity MRI‐linac

Abstract Recent availability of MRI‐guided linear accelerators has introduced a number of clinical challenges, particularly in the context of online plan adaptation. Paramount among these is verification of plan quality prior to patient treatment. Currently, there are no commercial products available for monitor unit verification that fully support the newly FDA cleared Elekta Unity 1.5 T MRI‐linac. In this work, we investigate the accuracy and precision of RadCalc for this purpose, which is a software package that uses a Clarkson integration algorithm for point dose calculation. To this end, 18 IMRT patient plans (186 individual beams) were created and used for RadCalc point dose calculations. In comparison with the primary treatment planning system (Monaco), mean point dose deviations of 0.0 ± 1.0% (n = 18) and 1.7 ± 12.4% (n = 186) were obtained on a per‐plan and per‐beam basis, respectively. The dose plane comparison functionality within RadCalc was found to be highly inaccurate, however, modest improvements could be made by artificially shifting jaws and multi leaf collimator positions to account for the dosimetric shift due to the magnetic field (67.3% vs 96.5% mean 5%/5 mm gamma pass rate).


| INTRODUCTION
Image-guidance in radiotherapy has significantly advanced the achievable conformality of treatment plans due to the improved ability to localize the target during each treatment fraction. 1,2 The availability of commercial technologies such as kV planar imaging, kV cone beam computed tomography (CBCT), CT-on-rails, online fourdimensional-CT/CBCT, stereotactic ultrasound, surface monitoring, and stereoscopic fiducial localization have significantly improved the clinician's ability to localize target and nontarget tissues. More recently, investment in MRI-guided radiotherapy has grown rapidly due to the superior soft-tissue contrast of the magnetic resonance imaging (MRI), the ability to perform repeated imaging without additional radiation dose, and the ability for continuous near realtime intra-fraction imaging. [3][4][5] These advancements have created a number of paths for improved patient care including online adaptive planning, target tracking, and sophisticated gating techniques. 4,6,7 It is expected that these developments will likely lead to margin reductions and related changes in practice patterns such as dose escalation and hypofractionation. used for quality assurance must be MRI-safe or MRI-conditional, including daily quality assurance (QA) devices, IMRT QA devices, water tanks, and detectors used for output and beam scanning measurements. From a treatment planning perspective, conventional dose calculation algorithms are not suitable for the transport of charged particles in a magnetic field, so sophisticated algorithms that solve the linear Boltzmann transport equation must be utilized such as the stochastic Monte Carlo method or a deterministic grid-based Boltzmann solver. [8][9][10] Although these challenges have largely been addressed for primary treatment planning purposes, the need for independent dose verification prior to patient treatment remains.
The need for an efficient and accurate secondary monitor unit calculation is especially critical in the setting of online adaptive planning as a new treatment plan is generated for each fraction. Although a commercially available secondary dose calculator exists for the 0.35 T ViewRay MRIdian (ViewRay Inc., Oakwood, USA), 11 there are currently only preliminary reports of purpose-built software for the Elekta Unity. 12 In this work, we explore the utility and performance of Rad-Calc software (Lifeline Software Inc., Tyler, USA), a widely used secondary point dose calculator, in conjunction with a newly commissioned Elekta Unity MRI-linac. To our knowledge, there are no other reports in literature describing the commissioning and evaluation of this commercial product for use with the Elekta Unity MRI-linac.

2.A | Unity overview
The Elekta Unity MRI-Linac is comprised of a Philips Marlin 1.5 T MRI (Philips Healthcare) and a standing-wave linear accelerator. The linear accelerator produces a single 7-MV flattening filter-free photon energy with a maximum field-size in the isocenter plane of 57.4 cm (crossplane) by 22.0 cm (inplane). Beam collimation consists of jaws (crossplane) and a 160-leaf multi leaf collimator (MLC) (inplane), which has a leaf width of 7.175 mm in the isocenter plane. The Unity has a source to isocenter distance of 143.5 cm and an inner bore diameter of 70 cm. The gantry rotates with a speed of up to six rotations per minute and the collimator cannot be rotated. Currently, the system is only capable of delivering step-and-shoot intensity-modulated radiation theraphy (IMRT) and three-dimensional (3D) conformal treatments, however, no hardware limitations exist that would prevent future implementation of volumetric-modulated arc therapy (VMAT) capabilities.
The University of Iowa Elekta Unity was calibrated to 1 cGy per MU in water at isocenter at a depth of 10 cm (133.5 cm SSD). This depth was chosen over the more conventional depth of d max due to the fixed maximum dose rate of 425 MU/min for the Unity, regardless of calibration depth. Absolute output calibration of the Elekta Unity is complicated by nonstandard reference conditions, including but not limited to the presence of a magnetic field and a nonstandard sourceto-axis distance. As such, orientation-dependent correction factors for the ion chamber were required, 13 and the TPR 20,10 beam quality specifier was converted to PDD(10) x for k Q determination. 14

2.B | Relative beam data
Beam data were collected during commissioning of the Unity MRI-Linac in accordance with recommendations by Elekta and the requirements for beam modeling within the Monaco treatment planning system. As there is no commercially available 3D tank that is compatible with the Unity at the time of this writing, all depth dose and profile scans were acquired using a proprietary tank that is owned and provided by Elekta. Due to spatial constraints within the bore (and therefore within the 3D tank), the maximum scan depth was 12 cm when the gantry was set to 0 o (G0). With the gantry oriented to 90°or 270°(G90, G270), the maximum scan depth was 38 cm, however, the field size was limited to a maximum of 16 cm (crossplane) by 22 cm (inplane) in this orientation. As such, profile data for the field sizes of field for the largest field size (57. 4 × 22), as this field-size is prohibited in Monaco at G0 due to presence of the MRI cryostat pipe at the field periphery. All dose was computed with a specified Monte Carlo statistical uncertainty of 0.5% using a 2-mm dose grid. A Python program was written to extract depth dose and profile data from these dose plane files. Extracted data was smoothed using Savitzky-Golay filtering to reduce noise from the Monaco Monte Carlo dose calculation and formatted for import into RadCalc. Percent depth dose (PDD) data were manually converted to tissue phantom ratio (TPR) data for RadCalc modeling, as the use of PDD data was found to lead to errors in phantom scatter factor lookup for nonreference condition SSDs due to inappropriate use of field-size scaling.
Asymmetric field-sizes are not permitted in RadCalc beam modeling, so artificial inplane profiles for field-sizes larger than 22 × 22 cm 2 were generated from the corresponding crossplane profile.
Crossplane profiles for the Elekta Unity exhibit significant asymmetry due to the influence of the magnetic field on secondary electrons generated within the media. This effect has previously been described in literature, 18,19 and an example profile is shown in Fig. 1.
RadCalc does not utilize user-entered crossplane profiles unless a GRAVES ET AL. | 55 wedge is active, so this asymmetry cannot be accounted for. Even adding a wedge to the model and labeling the crossplane profiles as wedged fields does not achieve the desired result since the RadCalc fluence model assumes that the profiles should be centered about the central axis, and therefore the model's fit to the data is inappropriate. For this reason, the method of enabling wedge profiles was not used in the RadCalc model generation.

2.D | Model configuration
Following creation of a treatment machine in RadCalc, dosimetry data were imported and a number of machine-specific settings were configured. These settings are summarized in Table 1, and a schematic representation of the overall machine geometry is shown in  Table 1.
In addition to dosimetric tests in the patient geometry, tests out-  were performed using a rectangular prism phantom of water with beams entering at orthogonal and oblique angles. For a detailed description of these tests, the reader is referred to MPPG5a. Changes to the radiation leaf offset were also investigated as a means to improve dose plane comparison performance.

3.A | Point dose validation and refinement
The average per-plan point dose deviation between RadCalc and Monaco was found to be 0.0 ± 1.0% (n = 18). The maximum, median, and minimum per-plan deviations were 1.8%, −0.1%, and −1.7% respectively. The per-beam deviation between RadCalc and Monaco was less precise, with an average of 1.7 ± 12.4% (n = 186). The maximum, median, and minimum per-beam deviations were 131.7%, 0.1%, and −9.9% respectively. Point dose results for specific test cases are listed in Table 2. Point dose agreement distributions shown in Fig. 4 reveal an approximately normal underlying distribution for per-beam comparisons. The distribution of per-plan deviations is centered at about 0% and appears to be compactly supported in the domain of approximately −2% to +2%. Beams where the calculation point was Results from MPPG5a dosimetric evaluation are summarized in Table 3. All tests met the performance levels described in MPPG5a with the exception of crossplane profile agreement between RadCalc and commissioning data (Fig. 5), and point dose agreement for the large MLC-shaped field with extensive blocking (MPPG5a test 5.5).
Disagreement between crossplane profiles is expected due to magnetic field effects. Disagreement for the large MLC-shaped field (e.g., "Mantle"-shaped) may be due to uncertainty in the Monaco Monte Carlo calculation in addition to the modified Clarkson integral calculation methodology employed by RadCalc.

3.B | Dose plane comparisons
Comparison of dose planes calculated in Monaco and RadCalc revealed significant discrepancies. An average 5%/5 mm gamma pass-rate of approximately 80% was observed in beams examined (n = 136), which motivated investigation into methods for improving dose plane comparison performance. As shown in Fig. 6(a)  verification. 24 We have described a number of model parameters, many obtained directly from Elekta, that may be useful to other investigators and clinicians in commissioning their own secondary dose calculator for the Elekta Unity.
The RadCalc algorithm utilizes a modified Clarkson integration technique for IMRT dose calculation. Several assumptions are made T A B L E 2 List of treatment plans evaluated in RadCalc, and their associated point dose deviations from Monaco. Percent differences are calculated as (D RC − D RTP )/D RTP . Parentheses indicate the global percent deviation, obtained by multiplying the per-beam percent difference by the fractional contribution of the individual beam against the sum of beams for the given plan. This demonstrates that beams with large percentage deviation represent a relatively minor portion of the overall point dose calculation.  | 59 with this approach, namely flat patient entrance surface, homogeneous tissue surrounding the calculation point, and no magnetic field present. The modified Clarkson integration method relies on azimuthal symmetry of beam scattering, which is an assumption that does not hold true for the presence a magnetic field that is nonparallel to the central beam axis. For this reason, it was expected that significant deviations from the primary treatment planning system would be observed during the RadCalc commissioning and validation process. A number of improvements could potentially be made to the modified Clarkson integration method to improve its applicability to the MRI-linac, as exemplified by the recent work of Chen et al. 12 In their work, they describe implementation of a modified Clarkson integration method for the Elekta Unity whereby an angle-and depth-dependent positional correction factor is applied for each integration sector. Although this approach ignores changes to the profile shape, the first-order magnetic field effect is mitigated.
Comparison of RadCalc-modeled profiles against baseline Monaco data that were used for commissioning of RadCalc. All inplane profiles were found to meet the MPPG5a-specified deviation tolerance of 2%, however, crossplane profiles failed to meet this standard due to magnetic field effects. For larger field sizes (10 × 10 cm 2 and 22 × 22 cm 2 ) within the central 80% of the field, crossplane agreement was found to be within 2%.
near the field periphery, or outside the field entirely, no corrective action is warranted. These tolerances may be made tighter as additional clinical experience is gained. To achieve this level of agreement, a search radius of 5 mm was implemented in RadCalc, which will likely reduce the overall sensitivity to error detection. F I G . 6. Dose plane comparison using the nominal RadCalc model (a); after applying a 2-mm shift to the multi leaf collimator (MLC) and jaw positions and increasing leaf offset to +2 mm (b); and after applying a 2-mm shift to the MLC and jaw positions, increasing the leaf offset to +2 mm, and moving the jaws outward by 1.5 mm each (c).
T A B L E 4 Dose plane comparison gamma analysis (5%/5 mm) before and after implementation of the dose plane specific model. Significant improvement using the dose plane specific model is seen over the standard model for all normalization options (calculation point, maximum, or average). netic field effects will likely improve upon these results.

ACKNOWLEDGMENTS
We gratefully acknowledge assistance from collaborators at the MD Anderson Cancer Center, who shared values for several modeling parameters.

CONF LICT OF I NTEREST
No conflict of interest.