A superposition/convolution GPU-accelerated dose computation algorithm (the Calculator) has been recently incorporated into commercial software. The algorithm requires validation prior to clinical use. Three photon energies were examined: conventional 6 MV and 15 MV, and 10 MV flattening filter free (10 MVFFF). For a set of IMRT and VMAT plans based on four of the five AAPM Practice Guideline 5a downloadable datasets, ion chamber (IC) measurements were performed on the water-equivalent phantoms. The average difference between the Calculator and IC was -0.3 ± 0.8% (1SD). The same plans were projected on a phantom containing a biplanar diode array. We used the forthcoming criteria for routine gamma analysis, 3% dose-error (global (G) normalization, 2 mm distance to agreement, and 10% low dose cutoff). The γ (3%G/2 mm) average passing rate was 98.9 ± 2.1%. Measurement-guided three-dimensional dose reconstruction on the patient CT dataset (excluding the Lung) resulted in a similar average agreement rate with the Calculator: 98.2 ± 2.0%. The mean γ (3%G/2 mm) passing rate comparing the Calculator to the TPS (again excluding the Lung) was 99.0 ± 1.0%. Because of the significant inhomogeneity, the Lung case was investigated separately. The calculator has an alternate heterogeneity correction mode that can change the results in the thorax for higher-energy beams (15 MV). As this correction is nonphysical and was optimized for simple slab geometries, its application leads to mixed results when compared to the TPS and independent Monte Carlo calculations, depending on the CT dataset and the plan. The Calculator vs. TPS 15 MV Guideline 5a IMRT and VMAT plans demonstrate 96.3% and 93.4% γ (3%G/2 mm) passing rates respectively. For the lower energies, which should be predominantly used in the thoracic region, the passing rates for the same plans and criteria range from 98.6 to 100%. Overall, the Calculator accuracy is sufficient for the intended use.

Monte Carlo methods are a central component of radiotherapy treatment planning, shielding design, detector modeling, and other applications. Long calculation times, however, can limit the usefulness of these purely stochastic methods. The coarse mesh method for photon and electron transport (COMET-PE) provides an attractive alternative. By combining stochastic pre-computation with a deterministic solver, COMET-PE achieves accuracy comparable to Monte Carlo methods in only a fraction of the time. The method’s implementation has been extended to 3D, and in this work, it is validated by comparison to DOSXYZnrc using a photon radiotherapy benchmark. The comparison demonstrates excellent agreement; of the voxels that received more than 10% of the maximum dose, over 97.3% pass a 2% / 2mm acceptance test and over 99.7% pass a 3% / 3mm test. Furthermore, the method is over an order of magnitude faster than DOSXYZnrc and is able to take advantage of both distributed-memory and shared-memory parallel architectures for increased performance.

Purpose: To develop a hybrid stochastic‐deterministic method, COMET‐PE, for dose calculation in external beam photon radiotherapy. Methods: To calculate dose, COMET‐PE solves the coupled Boltzmann Transport Equations for photons and electrons. The method uses a deterministic iteration to compose response functions that are pre‐computed using Monte Carlo. Thus, COMET‐PE takes advantage of Monte Carlo physics without incurring the computational costs typically required for statistical convergence. Dose distributions are calculated for a heterogeneous benchmark problem using both COMET‐PE and DOSXYZnrc (Monte Carlo) methods. The benchmark consists of a CT‐based lung phantom, composed of air, lung, soft tissue, and bone, irradiated by a 2 cm × 2 cm photon field. The 6 MV source spectrum comes from Monte Carlo simulation of a Varian Clinac 2100. The COMET‐PE solution is computed at resolution of 1 mm (27,648,000 voxels) before being reduced to a resolution of 5 mm (221,184 voxels) for compatibility with the DOSXYZnrc reference solution. Results: The agreement between dose distributions calculated with COMET‐PE and Monte Carlo is excellent. Of voxels receiving greater than 10% of the maximum dose, 98.73% pass the 2% (point‐wise relative difference) or 2 mm (distance‐to‐agreement) criterion and 99.38% pass the 3% / 3 mm criterion. Localized discrepancies are observed at the beam corners; these are caused by the difficulty of using a continuous representation for the discontinuous primary fluence. Most of the failures, however, occur where the beam exits the phantom and where Monte Carlo uncertainties are the highest. The COMET‐PE calculation is over 10 times faster than the Monte Carlo reference solution. Conclusion: The COMET‐PE method calculates dose with accuracy comparable to Monte Carlo while using only a fraction of the time and providing a solution with orders of magnitude more detail.

A new hybrid stochastic–deterministic transport theory method, which is designed to couple with diffusion theory, is presented. The new method is an extension of the incident flux response expansion method, and it combines the speed of diffusion theory with the accuracy of transport theory. With ease of use in mind, the new method is derived in such a way that it can be implemented with only minimal modifications to an existing diffusion theory method. A new angular expansion, which is necessary for the diffusion theory coupling, is developed in 2D and 3D. The method is implemented in 2D hexagonal geometry, and an HTTR benchmark problem is used to test its accuracy in a standalone configuration. It is found that the new method produces excellent results (with average relative error in partial current less than 0.033%) when compared with Monte Carlo reference solutions. Furthermore, the method is fast, solving all test cases in less than 12s.

Accurate dose calculation is a central component of radiotherapy treatment planning. A new method of dose calculation has been developed based on transport theory and validated by comparison to Monte Carlo methods. The coarse mesh transport method has been extended to allow coupled photon-electron transport in 3D. The method combines stochastic pre-computation with a deterministic solver to achieve high accuracy and precision. To enhance the method for radiotherapy calculations, a new angular basis was derived, and an analytical source treatment was developed. Validation was performed by comparison to DOSXYZnrc using a heterogeneous interface phantom composed of water, aluminum, and lung. Calculations of both kinetic energy released per unit mass and dose were compared. Good agreement was found with a maximum error and root mean square relative error of less than 1.5% for all cases. The results show that the new method achieves an accuracy comparable to Monte Carlo.

Purpose: To develop and test a novel, transport‐based method for calculating the energy deposition of a photon beam in tissue. Method and Materials: The new method is based on a hybrid Monte Carlo‐Deterministic Coarse Mesh Transport Method COMET. COMET is a method for solving the linear Boltzmann Transport Equation based on an incident angular current expansion. It has been shown to perform well for 2D coupled photon‐electron transport calculations aimed at determining the energy deposition of a photon beam. The COMET method uses pre‐computed Monte Carlo‐based response expansion coefficients to achieve accuracy comparable to Monte Carlo methods in a fraction of the time. The current work extends the photon transport capability of the COMET method to handle 3D geometry and to simulate realistic photon sources. The method is tested with a simple benchmark problem consisting of a 20×20×20cm water phantom irradiated by a collimated, polyenergetic photon source at a source‐to‐surface distance (SSD) of 80cm. Although the COMET mesh size is arbitrary, the phantom is divided into 1×1×1cm voxels for convenience. The accuracy of the method is evaluated by comparison to a reference calculation performed with EGSnrc. Results: The distribution of energy deposition was examined voxel by voxel. The largest error for any voxel is found to be less than 3.3% of the maximum energy deposition value from the reference solution. The relative standard error for each voxel in the reference solution is less than 0.5%. The COMET solution took 0.27 core‐hours to compute compared with 84 core‐hours for the reference solution. Conclusion: The work indicates that the COMET method holds promise for fast and accurate 3D photon and electron dose calculations. Furthermore, sources of error are identified and suggestions are made to improve the accuracy of the new method during future development.