Monte Carlo simulation of 6‐MV dynamic wave VMAT deliveries by Vero4DRT linear accelerator using EGSnrc moving sources

Abstract The commissioning and benchmark of a Monte Carlo (MC) model of the 6‐MV Brainlab‐Mitsubishi Vero4DRT linear accelerator for the purpose of quality assurance of clinical dynamic wave arc (DWA) treatment plans is reported. Open‐source MC applications based on EGSnrc particle transport codes are used to simulate the medical linear accelerator head components. Complex radiotherapy irradiations can be simulated in a single MC run using a shared library format combined with BEAMnrc “source20.” Electron energy tuning is achieved by comparing measured vs simulated percentage depth doses (PDDs) for MLC‐defined field sizes in a water phantom. Electron spot size tuning is achieved by comparing measured and simulated inplane and crossplane beam profiles. DWA treatment plans generated from RayStation (RaySearch) treatment planning system (TPS) are simulated on voxelized (2.5 mm3) patient CT datasets. Planning target volume (PTV) and organs at risk (OAR) dose–volume histograms (DVHs) are compared to TPS‐calculated doses for clinically deliverable dynamic volumetric modulated arc therapy (VMAT) trajectories. MC simulations with an electron beam energy of 5.9 MeV and spot size FWHM of 1.9 mm had the closest agreement with measurement. DWA beam deliveries simulated on patient CT datasets results in DVH agreement with TPS‐calculated doses. PTV coverage agreed within 0.1% and OAR max doses (to 0.035 cc volume) agreed within 1 Gy. This MC model can be used as an independent dose calculation from the TPS and as a quality assurance tool for complex, dynamic radiotherapy treatment deliveries. Full patient CT treatment simulations are performed in a single Monte Carlo run in 23 min. Simulations are run in parallel using the Condor High‐Throughput Computing software1 on a cluster of eight servers. Each server has two physical processors (Intel Xeon CPU E5‐2650 0 @2.00 GHz), with 8 cores per CPU and two threads per core for 256 calculation nodes.

Unlike conventional linear accelerators, noncoplanar beam angles are achieved without moving the patient couch (the unit moves around a stationary patient). The Vero4DRT is a dedicated stereotactic ablative radiotherapy (SABR) unit capable of delivering conventional three-dimensional conformal radiation therapy (3DCRT) beams, conformal arcs, static field intensity-modulated radiotherapy (IMRT) beams, and VMAT arcs. In addition, the Vero4DRT has a unique clinical delivery mode called dynamic wave arc (DWA) which employs noncoplanar VMAT trajectories created by enabling simultaneous motion of the gantry and floor ring about the two axes of rotation. [5][6][7] The unit is equipped with integrated, dual-orthogonal kV image guidance systems (ExacTrac, Brainlab, Munich, Germany) and is cone-beam CT (CBCT) capable. The entire waveguide and collimation assembly is mounted on a 2D-gimbal which provides real-time, respiratory motion-correlated dynamic tumor tracking (DTT) capability.
The unit only has one static secondary collimator (jaw) field size which is set to 15 × 15 cm 2 at source to axis distance (SAD) of 100 cm. All beam shaping is achieved with a low transmission (~0.11-0.13%) 4,8 multileaf collimator (MLC). This MLC has 30 pairs of 5 mm width (at isocenter) tungsten leaves. 8 The Vero4DRT has been applied to various clinical scenarios including lung, liver, pancreas, breast, prostate, bone, and brain. [9][10][11][12][13] Monte Carlo modeling is a useful option for providing secondary dose calculation verification and has the added benefit of providing "gold standard" dose calculations in inhomogeneous materials. 14 It has been shown that MC models can provide useful information on dose calculation algorithm accuracy for smaller treatment fields (e.g., SABR or stereotactic radiosurgery type beam deliveries). [15][16][17] Ishihara et al. report on a Monte Carlo model for the Vero4DRT and its low-transmission MLC using the EGSnrc "VARMLC" component module. 18 This model was reported for static-field beam geometries.
With "moving" sources available (e.g., EGSnrc "source 20 and 21"), Monte Carlo can efficiently model complex, noncoplanar dynamic beam trajectories. 19 In addition, there is potential to model the dynamic tumor tracking respiratory-correlated motions on 4DCT datasets. 20   ter, ionization chambers, secondary collimator jaws, and MLC were modeled in a Monte Carlo environment (BEAMnrc) based on manufacturer specifications. 8,18 The composition of the materials and alloys, mass densities, position, dimensions, and shape of defining surfaces of the components, plus the properties of motion are all defined in detail within these modules.
In this study, a phase space plane (file describing particle type, energy, directional vectors, and location of last interaction) is defined just above the MLC and below the static secondary collimator (jaw) at a distance of 35.2 cm from the target. It is important to note that the Vero4DRT only has one static secondary collimator field size which is set to 15 × 15 cm 2 at source to axis distance (SAD) of 100 cm. This phase space represents the nonpatient-specific geometry of the linear accelerator. The phase space file is generated using By capturing a phase space file below the static components, the user can reuse it to transport particles through the moving (patientspecific) parts of the linac (i.e., MLC).
Radiation beams generated by BEAMnrc can be directed onto a voxelized phantom of CT patient data from patient-specific gantry and ring angles and radiation doses are scored using DOSXYZnrc codes. 24 In this study "source 20" was used 19 which allows the user to simulate dynamic motion of the virtual phase space source relative to the patient geometry or phantom.
The goal is to simulate enough histories to achieve <2% uncertainty in the patient or phantom voxel dose value. Simulations are run in parallel using the Condor High-Throughput Computing software 25 on a cluster of eight servers, under the Red Hat Enterprise Linux (release 6.4) operating system. Each server has two physical processors (Intel Xeon CPU E5-2650 0 @ 2.00 GHz), with 8 cores per CPU and two threads per core for a total of 256 calculation nodes.

2.B | MLC modeling
All dynamic beam shaping is achieved with a low-transmission (0.11-0.13% average) 4,8 60-leaf, tungsten MLC. The MLC Monte Carlo physical model parameters were the same as those used by Ishihara et al. 18 The MLC has 30 pairs of 5 mm width (at isocenter) tungsten leaves with a maximum field size of 15 × 15 cm 2 . Leaf height and length are 11 and 26 cm, respectively. Each leaf has a circular end, F I G . 2. Geometric schematic of the xray head and multileaf collimator for Vero4DRT. Note: the entire system is mounted on a movable two-dimensional gimbal for dynamic tumor tracking. The secondary collimator (jaws) is fixed at one 15 × 15 cm 2 field size.
with a radius of curvature of 37 cm and tongue-groove design (5.5 cm groove height). 8   Using this method, the electron energy was determined to be 5.9 MeV. The best match (found by minimizing the percent difference between the descending part of the PDD) determined the optimum energy of electron beam. Local percent differences between simulation and measurements results are reported. The electron beam FWHM gaussian width was varied from 1.5 to 2.2 mm in steps of 0.1 mm and simulated beam profiles were compared to measurement (normalized to 100% at central axis dose). The electron beam gaussian width was optimized for a 10 × 10 cm 2 field size at depth of d = 10 cm (found by minimizing the percent difference in low dose gradient regions of the profiles).
Once the beam energies and electron FWHM gaussian width were optimized, PDDs and beam profiles for field sizes ranging from 1 × 1 to 15 × 15 cm 2 were compared and assessed for agreement.

2.C.2 | Absolute dose conversion
The calibration conditions on the clinical Vero4DRT is such that 1 MU will deliver 1 cGy to the patient at depth of 1.5 cm for a 10 × 10 cm 2 field size at SAD of 100 cm. The radiation beam is directed onto a water phantom and dose distribution calculated using DOSXYZnrc. The calibration geometry for the virtual linac is a 10 × 10 cm 2 field, SAD of 100 cm and an isocenter depth of 10 cm.
The raw dose from the DOSXYZnrc Monte Carlo simulation is in units of "dose per particle incident on the target." The Monte Carlo "dose  A complex liver stereotactic ablative radiotherapy (SABR) VMAT treatment plan using dynamic, noncoplanar trajectories (DWA) was simulated (Fig. 4). Doses were prescribed to cover 95% of the planning target volume (PTV) with a prescription dose of 54 Gy, delivered in three fractions.
The entire Monte Carlo simulation is scripted 28 such that the user only has to provide the initial DICOM files for the plan parameters, dose matrix, CT and structure set from RayStation.
The script automatically generates the patient-geometry MC phantom (using ctcreate), creates all input files required by the BEAMnrc and DOSXYZnrc simulations, and launches the distributed simulation. Once a Monte Carlo 3D dose distribution is created on the patient geometry, additional processing is optionally applied such as a 3D denoising filter (based on Savitzky-Golay formalism). 29,30 The conversion to absolute dose is applied and a TPS-compatible DICOM dose matrix containing the Monte Carlo dose is generated (for import back into the TPS to provide dose/ DVH comparisons).
The DICOM CT datasets were converted to a Monte Carlo phantom using a voxel size of 2.5 mm 3 . DOSXYZnrc simulation parameters were set to achieve statistical uncertainty <2% in the dose calculation, (~9 × 10 8 histories). The MC calculated doses are imported into the TPS for dose distribution comparison purposes.
On the patient CT datasets, target coverage (PTV) and organ-at-risk dose volume constraints are compared. F I G . 3. Multileaf collimator (MLC) field setup for inplane and crossplane profile measurement. MLC leaf width is 5 mm at isocentre, 100 cm from the photon source.
F I G . 4. Liver stereotactic ablative radiotherapy treatment plan using dynamic, non-coplanar volumetric modulated arc theraphy trajectories (dynamic wave arc).
The DWA plan was also calculated on an in-house, cylindrical, uniform density quality assurance phantom (26.  T A B L E 1 Comparison of measured and calculated distances to the field edges (X50% and Y50%) and beam penumbras (X20%−X80%) and (Y20%−Y80%) for field size 1 × 1, 5 × 5 and 10 × 10 cm 2 at depth of 10 cm and SSD 90 cm.  minimized with an incident electron energy of 5.9 MeV. Monte Carlo simulated PDD curves for the Vero4DRT 6 MV beam are compared to measured doses, as shown in Fig. 5(a). Three field sizes of 5 × 5 cm 2 , 10 × 10 cm 2 , and 15 × 15 cm 2 are shown. Doses are normalized relative to the d max dose. The statistical uncertainty is less than 2% in the PDD calculation and error bars are equal or smaller than symbol sizes. The differences between measurement and Monte Carlo simulations are smaller than 2.15% for the descending part of PDDs [ Fig. 5(b)].

3.A.2 | Beam profiles
The beam profiles for a 1 ×  Table 1. The differences between nominal and MC calculated field sizes were within 1.5 mm. The differences between measured and MC calculated field sizes were within 0.4 mm. The differences between measured and MC calculated penumbra size were within 1 mm.
Monte Carlo simulated inplane and crossplane beam profile curves for field sizes of 1 × 1, 5 × 5 and 10 × 10 cm 2 of the Ver-o4DRT 6MV beam are compared to measured doses, as shown in

3.B | Dynamic Wave Arc (DWA) verification
The RayStation TPS dose distribution for the DWA Liver SABR plan delivered to the cylindrical uniform QA phantom is compared to Monte Carlo simulations in Fig. 10. The 3D gamma comparison for 3% dose difference relative to max dose ((MC dose − TPS dose)/max dose in TPS) and 3 mm distance to agreement with 30% max dose threshold is 99.3% (Fig. 11). This model has been implemented clini-   simulation. This will be an invaluable quality assurance tool when combined with a rigorous general machine quality assurance program. This will relieve the need to perform on-linac patient-specific phantom measurements for these complex wave arc plans prior to starting treatment. This model can be easily transition to patientspecific dose reconstructions on a per-fraction basis using machine delivery log files. Currently, using 256 CPU, a multiarc, noncoplanar simulation on patient geometries takes approximately 23 min.

| CONCLUSIONS
The authors have presented an efficient and accurate Monte Carlo model of the Vero4DRT radiotherapy linac. This model has been implemented clinically as a quality assurance tool for the RayStation TPS and has been applied to over 72 patient plan verifications to date.

ACKNOWLEDG MENTS
Two of the authors' research contributions were supported in part by JSPS KAKENHI (Grant No. 18KK0240).

CONFLI CT OF INTEREST
The authors have no relevant conflict of interest to disclose.
T A B L E 2 Comparison of dosimetry metrics for (a) PTV and (b) OAR calculated by MC and RayStation for a liver SABR treatment plan using dynamic, non-coplanar trajectories (dynamic wave VMAT arc). Chest-wall/D 0.035cc 66.9 67.9