Secondary monitor unit calculations for VMAT using parallelized Monte Carlo simulations

Abstract We have developed a fast and accurate in‐house Monte Carlo (MC) secondary monitor unit (MU) check method, based on the EGSnrc system, for independent verification of volumetric modulated arc therapy (VMAT) treatment planning system dose calculations, in accordance with TG‐114 recommendations. For a VMAT treatment plan created for a Varian Trilogy linac, DICOM information was exported from Eclipse. An open‐source platform was used to generate input files for dose calculations using the EGSnrc framework. The full VMAT plan simulation employed 107 histories, and was parallelized to run on a computer cluster. The resulting 3ddose matrices were converted to the DICOM format using CERR and imported into Eclipse. The method was evaluated using 35 clinical VMAT plans of various treatment sites. For each plan, the doses calculated with the MC approach at four three‐dimensional reference points were compared to the corresponding Eclipse calculations, as well as calculations performed using the clinical software package, MUCheck. Each MC arc simulation of 107 particles required 13–25 min of total time, including processing and calculation. The average discrepancies in calculated dose values between the MC method and Eclipse were 2.03% (compared to 3.43% for MUCheck) for prostate cases, 2.45% (3.22% for MUCheck) for head and neck cases, 1.7% (5.51% for MUCheck) for brain cases, and 2.84% (5.64% for MUCheck) for miscellaneous cases. Of 276 comparisons, 201 showed greater agreement between the treatment planning system and MC vs MUCheck. The largest discrepancies between MC and MUCheck were found in regions of high dose gradients and heterogeneous densities. By parallelizing the calculations, point‐dose accuracies of 2‐7%, sufficient for clinical secondary checks, can be achieved in a reasonable amount of time. As computer clusters and/or cloud computing become more widespread, this method will be useful in most clinical setups.


| INTRODUCTION
Treating patients with therapeutic radiation is a dynamic process with little room for error and potentially fatal consequences in cases of misadministration. As such, the process is accompanied by chart reviews and independent monitor unit (MU) calculations. 1 In the past, separate independent hand calculations were the primary method of verification. However, sophisticated linac hardware, coupled with advanced treatment planning algorithms, has made possible complex treatment delivery modalities. This is especially true in the case of volumetric modulated arc therapy (VMAT), which involves the computation and optimization of hundreds of multivariable control points across multiple treatment arcs. 2 Given the stringent demands on a physicist's time at a radiotherapy practice, sophisticated computer algorithms should be employed as part of the secondary MU verification process, as per TG-114 guidelines. 1 In addition, secondary MU verification also serves a diagnostic purpose. Standard treatment planning system (TPS) commissioning tests are not capable of evaluating system responses over the entire range of possible treatment scenarios that may be designed. Any bugs in the system code or erroneous module performances may be discovered through the secondary MU verification process. 3,4 As such, it is important that the verification system works independently of the hospital's commissioned TPS software. Our center uses Varian's Eclipse Ver. 13 Treatment Planning System (Varian Medical Systems, Palo Alto, CA) for all external-beam patient plans.
Monte Carlo (MC) algorithms provide the most accurate models of radiation transport by accounting for all relevant physical processes involved in each particle's interaction history. 5 The MC calculations also do not require approximations of the source to surface distance (SSD) or calculation depth for each control point. As a result of this comprehensive approach, a VMAT MC calculation requires significant computing resources to produce accurate results in a reasonable amount of time, and is not commonly employed for VMAT secondary MU checks. However, with cloud and cluster computing becoming more widespread, clinical use of MC calculations may be feasible. For this work, the computational resources of an academic supercomputer cluster were used.
Commercial software used for performing secondary MU checks vary in sophistication and dose calculation algorithms, but most use some form of modified Clarkson integration, as is the case for Rad-Calc (Lifeline Software Inc., Austin, TX), Diamond (PTW, Freiburg, Germany), and IMSure (Standard Imaging Inc., Middleton, WI). 6 One study 6 evaluated the performance of these software packages in comparison to the Pinnacle3 TPS (Philips Medical Systems, Bothell WA). The study found that for 59 VMAT arcs, IMSure, and Diamond produced the most outlying results, with the greatest variance in accuracies compared to the TPS, while RadCalc was found to be the most consistent and most accurate of these software packages.
Heterogeneity corrections are often a concern when using VMAT secondary check software. Most secondary check software employs simplistic heterogeneity corrections using density approximations and incorporating tissue only in the immediate area of the point of interest. [7][8][9][10]   provides GUI-based functionality for changing different parameters of the accelerator (mlc shapes and jaw position generation for specific patient plans) and was used to generate patient-specific simulation files.

2.A | Calibration factor
The EGSnrc calculation produces a 3ddose matrix, which assigns a floating-point value to each voxel in the phantom, in units of Gy/particle. In order to convert these values to Gy, a calibration factor must be determined. The calibration factor was obtained by performing an BHAGROO ET AL. DOSXYZnrc. An identical plan was created in Eclipse using 100 MUs. The energy used in both plans was 6 MV. In order to obtain the most accurate results possible within a reasonable time frame, the MC calculation was set to simulate 10 10 particles.
The results were compared to the Eclipse plan, as shown in

Avg. Disagreement (%)
Comparison with Eclipse for Brain Plans F I G . 5. Disagreement in Eclipse vs Monte Carlo calculations (yellow) and Eclipse vs MUCheck (red) for brain plans, evaluated at one reference point. There were a total of 20 arcs and 10 plans for the brain cases.

3.B | Calculated dose visualization
As a visual comparison of the MC and Eclipse dose calculations,    13 There were 15 out of 276 cases that exceeded 5% agreement. In general, these were the results of calculations performed for small fields or where inhomogeneities were present. In some cases, using more particles such as 10 8 or 10 9 at the same reference point did lower percent deviations for that point, though the agreement with Eclipse actually decreased for some reference points using 10 9 particles. This is potentially a result of the MC algorithm modeling the physics of radiation transport more accurately than Eclipse, which uses the Analytical Anisotropic Algorithm (AAA) to calculate dose. 9 The limitations of type-b, kernel-based algorithms such as AAA are well known. 9,14,15 Future work will involve dose calculated in Eclipse by a more sophisticated, type-c algorithm, such as Acuros XB. 16 Through the application of parallel processing, calculation times Agreements between MUCheck and Eclipse for brain cases were among the worst presented in this study. Though the density and composition of brain matter is relatively homogeneous and should not present any significant dose calculation challenges, MUCheck assumes that the patient surface at the area of beam incidence is flat. This approximation may lead to large dose calculation errors, but is not an issue for the MC method. VMAT plans are among the most complex radiotherapy treatments to design and deliver. As a result, a sophisticated secondary check algorithm should be employed to ensure the integrity of each treatment plan. The EGSnrc-based MC approach used in this study is significantly more accurate than algorithms commonly used in third-party commercial software, which often includes simplifications of geometry and particle interactions. Overall, given the constant progression of computing power and the integration and expansion of cloud comput-

| CONCLUSION
ing, this open-source approach could become a widely available tool for radiation medicine centers that employ VMAT treatment.

ACKNOWLEDG MENTS
Support provided by the Center for Computational Research at the University at Buffalo.

CONFLI CTS OF INTEREST
No conflicts of interest.