Todd A. Wareing

Report of the Task Group 186 on model-based dose calculation methods in brachytherapy beyond the TG-43 formalism: Current status and recommendations for clinical implementation

The charge of Task Group 186 (TG-186) is to provide guidance for early adopters of model-based dose calculation algorithms (MBDCAs) for brachytherapy (BT) dose calculations to ensure practice uniformity. Contrary to external beam radiotherapy, heterogeneity correction algorithms have only recently been made available to the BT community. Yet, BT dose calculation accuracy is highly dependent on scatter conditions and photoelectric effect cross-sections relative to water. In specific situations, differences between the current water-based BT dose calculation formalism (TG-43) and MBDCAs can lead to differences in calculated doses exceeding a factor of 10. MBDCAs raise three major issues that are not addressed by current guidance documents: (1) MBDCA calculated doses are sensitive to the dose specification medium, resulting in energy-dependent differences between dose calculated to water in a homogeneous water geometry (TG-43), dose calculated to the local medium in the heterogeneous medium, and the intermediate scenario of dose calculated to a small volume of water in the heterogeneous medium. (2) MBDCA doses are sensitive to voxel-by-voxel interaction cross sections. Neither conventional single-energy CT nor ICRU∕ICRP tissue composition compilations provide useful guidance for the task of assigning interaction cross sections to each voxel. (3) Since each patient-source-applicator combination is unique, having reference data for each possible combination to benchmark MBDCAs is an impractical strategy. Hence, a new commissioning process is required. TG-186 addresses in detail the above issues through the literature review and provides explicit recommendations based on the current state of knowledge. TG-43-based dose prescription and dose calculation remain in effect, with MBDCA dose reporting performed in parallel when available. In using MBDCAs, it is recommended that the radiation transport should be performed in the heterogeneous medium and, at minimum, the dose to the local medium be reported along with the TG-43 calculated doses. Assignments of voxel-by-voxel cross sections represent a particular challenge. Electron density information is readily extracted from CT imaging, but cannot be used to distinguish between different materials having the same density. Therefore, a recommendation is made to use a number of standardized materials to maintain uniformity across institutions. Sensitivity analysis shows that this recommendation offers increased accuracy over TG-43. MBDCA commissioning will share commonalities with current TG-43-based systems, but in addition there will be algorithm-specific tasks. Two levels of commissioning are recommended: reproducing TG-43 dose parameters and testing the advanced capabilities of MBDCAs. For validation of heterogeneity and scatter conditions, MBDCAs should mimic the 3D dose distributions from reference virtual geometries. Potential changes in BT dose prescriptions and MBDCA limitations are discussed. When data required for full MBDCA implementation are insufficient, interim recommendations are made and potential areas of research are identified. Application of TG-186 guidance should retain practice uniformity in transitioning from the TG-43 to the MBDCA approach.

Validation of a new grid-based Boltzmann equation solver for dose calculation in radiotherapy with photon beams

A new grid-based Boltzmann equation solver, Acuros, was developed specifically for performing accurate and rapid radiotherapy dose calculations. In this study we benchmarked its performance against Monte Carlo for 6 and 18 MV photon beams in heterogeneous media. Acuros solves the coupled Boltzmann transport equations for neutral and charged particles on a locally adaptive Cartesian grid. The Acuros solver is an optimized rewrite of the general purpose Attila software, and for comparable accuracy levels, it is roughly an order of magnitude faster than Attila. Comparisons were made between Monte Carlo (EGSnrc) and Acuros for 6 and 18 MV photon beams impinging on a slab phantom comprising tissue, bone and lung materials. To provide an accurate reference solution, Monte Carlo simulations were run to a tight statistical uncertainty (sigma approximately 0.1%) and fine resolution (1-2 mm). Acuros results were output on a 2 mm cubic voxel grid encompassing the entire phantom. Comparisons were also made for a breast treatment plan on an anthropomorphic phantom. For the slab phantom in regions where the dose exceeded 10% of the maximum dose, agreement between Acuros and Monte Carlo was within 2% of the local dose or 1 mm distance to agreement. For the breast case, agreement was within 2% of local dose or 2 mm distance to agreement in 99.9% of voxels where the dose exceeded 10% of the prescription dose. Elsewhere, in low dose regions, agreement for all cases was within 1% of the maximum dose. Since all Acuros calculations required less than 5 min on a dual-core two-processor workstation, it is efficient enough for routine clinical use. Additionally, since Acuros calculation times are only weakly dependent on the number of beams, Acuros may ideally be suited to arc therapies, where current clinical algorithms may incur long calculation times.

Discontinuous finite element SN methods on three-dimensional unstructured grids

Abstract Discontinuous finite element methods for the SN equations on three-dimensional unstructured tetrahedral and hexahedral meshes are presented. Solution techniques including source iteration and diffusion-synthetic acceleration are described. Numerical results are presented that demonstrate the accuracy and efficiency of these methods.

Comparison of a finite-element multigroup discrete-ordinates code with Monte Carlo for radiotherapy calculations

Radiotherapy calculations often involve complex geometries such as interfaces between materials of vastly differing atomic number, such as lung, bone and/or air interfaces. Monte Carlo methods have been used to calculate accurately the perturbation effects of the interfaces. However, these methods can be computationally expensive for routine clinical calculations. An alternative approach is to solve the Boltzmann equation deterministically. We present one such deterministic code, Attila. Further, we computed a brachytherapy example and an external beam benchmark to compare the results with data previously calculated by MCNPX and EGS4. Our data suggest that the presented deterministic code is as accurate as EGS4 and MCNPX for the transport geometries examined in this study.

Krylov iterative methods and the degraded effectiveness of diffusion synthetic acceleration for multidimensional SN calculations in problems with material discontinuities

Abstract A loss in the effectiveness of diffusion synthetic acceleration (DSA) schemes has been observed with certain SN discretizations on two-dimensional Cartesian grids in the presence of material discontinuities. We will present more evidence supporting the conjecture that DSA effectiveness will degrade for multidimensional problems with discontinuous total cross sections, regardless of the particular physical configuration or spatial discretization. Fourier analysis and numerical experiments help us identify a set of representative problems for which established DSA schemes are ineffective, focusing on diffusive problems for which DSA is most needed. We consider a lumped, linear discontinuous spatial discretization of the SN transport equation on three-dimensional, unstructured tetrahedral meshes and look at a fully consistent and a “partially consistent” DSA method for this discretization. The effectiveness of both methods is shown to degrade significantly. A Fourier analysis of the fully consistent DSA scheme in the limit of decreasing cell optical thickness supports the view that the DSA itself is failing when material discontinuities are present in a problem. We show that a Krylov iterative method, preconditioned with DSA, is an effective remedy that can be used to efficiently compute solutions for this class of problems. We show that as a preconditioner to the Krylov method, a partially consistent DSA method is more than adequate. In fact, it is preferable to a fully consistent method because the partially consistent method is based on a continuous finite element discretization of the diffusion equation that can be solved relatively easily. The Krylov method can be implemented in terms of the original SN source iteration coding with only slight modification. Results from numerical experiments show that replacing source iteration with a preconditioned Krylov method can efficiently solve problems that are virtually intractable with accelerated source iteration.

Radiative transport-based frequency-domain fluorescence tomography

We report the development of radiative transport model-based fluorescence optical tomography from frequency-domain boundary measurements. The coupled radiative transport model for describing NIR fluorescence propagation in tissue is solved by a novel software based on the established Attila particle transport simulation platform. The proposed scheme enables the prediction of fluorescence measurements with non-contact sources and detectors at a minimal computational cost. An adjoint transport solution-based fluorescence tomography algorithm is implemented on dual grids to efficiently assemble the measurement sensitivity Jacobian matrix. Finally, we demonstrate fluorescence tomography on a realistic computational mouse model to locate nM to microM fluorophore concentration distributions in simulated mouse organs.

Optimization of deterministic transport parameters for the calculation of the dose distribution around a high dose-rate 192Ir brachytherapy source

The goal of this work was to calculate the dose distribution around a high dose-rate 192Ir brachytherapy source using a multi-group discrete ordinates code and then to compare the results with a Monte Carlo calculated dose distribution. The unstructured tetrahedral mesh discrete ordinates code Attila version 6.1.1 was used to calculate the photon kerma rate distribution in water around the Nucletron microSelectron mHDRv2 source. MCNPX 2.5.c was used to compute the Monte Carlo water photon kerma rate distribution. Two hundred million histories were simulated, resulting in standard errors of the mean of less than 3% overall. The number of energy groups, S(n) (angular order), P(n) (scattering order), and mesh elements were varied in addition to the method of analytic ray tracing to assess their effects on the deterministic solution. Water photon kerma rate matrices were exported from both codes into an in-house data analysis software. This software quantified the percent dose difference distribution, the number of points within +/- 3% and +/- 5%, and the mean percent difference between the two codes. The data demonstrated that a 5 energy-group cross-section set calculated results to within 0.5% of a 15 group cross-section set. S12 was sufficient to resolve the solution in angle. P2 expansion of the scattering cross-section was necessary to compute accurate distributions. A computational mesh with 55 064 tetrahedral elements in a 30 cm diameter phantom resolved the solution spatially. An efficiency factor of 110 with the above parameters was realized in comparison to MC methods. The Attila code provided an accurate and efficient solution of the Boltzmann transport equation for the mHDRv2 source.

FEASIBILITY OF A MULTIGROUP DETERMINISTIC SOLUTION METHOD FOR THREE-DIMENSIONAL RADIOTHERAPY DOSE CALCULATIONS

PURPOSE To investigate the potential of a novel deterministic solver, Attila, for external photon beam radiotherapy dose calculations. METHODS AND MATERIALS Two hypothetical cases for prostate and head-and-neck cancer photon beam treatment plans were calculated using Attila and EGSnrc Monte Carlo simulations. Open beams were modeled as isotropic photon point sources collimated to specified field sizes. The sources had a realistic energy spectrum calculated by Monte Carlo for a Varian Clinac 2100 operated in a 6-MV photon mode. The Attila computational grids consisted of 106,000 elements, or 424,000 spatial degrees of freedom, for the prostate case, and 123,000 tetrahedral elements, or 492,000 spatial degrees of freedom, for the head-and-neck cases. RESULTS For both cases, results demonstrate excellent agreement between Attila and EGSnrc in all areas, including the build-up regions, near heterogeneities, and at the beam penumbra. Dose agreement for 99% of the voxels was within the 3% (relative point-wise difference) or 3-mm distance-to-agreement criterion. Localized differences between the Attila and EGSnrc results were observed at bone and soft-tissue interfaces and are attributable to the effect of voxel material homogenization in calculating dose-to-medium in EGSnrc. For both cases, Attila calculation times were <20 central processing unit minutes on a single 2.2-GHz AMD Opteron processor. CONCLUSIONS The methods in Attila have the potential to be the basis for an efficient dose engine for patient-specific treatment planning, providing accuracy similar to that obtained by Monte Carlo.

Fully Consistent Diffusion Synthetic Acceleration of Linear Discontinuous SN Transport Discretizations on Unstructured Tetrahedral Meshes

Abstract We recently presented a method for efficiently solving linear discontinuous discretizations of the two-dimensional P1 equations on rectangular meshes. The linear system was efficiently solved with Krylov iterative methods and a novel two-level preconditioner based on a linear continuous finite element discretization of the diffusion equation. Here, we extend the preconditioned solution method to three-dimensional, unstructured tetrahedral meshes. Solution of the P1 equations forms the basis of a diffusion synthetic acceleration (DSA) scheme for three-dimensional SN transport calculations with isotropic scattering. The P1 equations and the transport equation are both discretized with isoparametric linear discontinuous finite elements so that the DSA method is fully consistent. Fourier analysis in three dimensions and computational results show that this DSA scheme is stable and very effective. The fully consistent method is compared to other “partially consistent” DSA schemes. Results show that the effectiveness of the partially consistent schemes can degrade for skewed or optically thick mesh cells. In fact, one such scheme can degrade to the extent of being unstable even though it is both unconditionally stable and effective on rectangular grids. Results for a model application show that our fully consistent DSA method can outperform the partially consistent DSA schemes under certain circumstances.

Radiative transport in fluorescence-enhanced frequency domain photon migration

Small animal optical tomography has significant, but potential application for streamlining drug discovery and pre-clinical investigation of drug candidates. However, accurate modeling of photon propagation in small animal volumes is critical to quantitatively obtain accurate tomographic images. Herein we present solutions from a robust fluorescence-enhanced, frequency domain radiative transport equation (RTE) solver with unique attributes that facilitate its deployment within tomographic algorithms. Specifically, the coupled equations describing time-dependent excitation and emission light transport are solved using discrete ordinates (SN) angular differencing along with linear discontinuous finite-element spatial differencing on unstructured tetrahedral grids. Source iteration in conjunction with diffusion synthetic acceleration is used to iteratively solve the resulting system of equations. This RTE solver can accurately and efficiently predict ballistic as well as diffusion limited transport regimes which could simultaneously exist in small animals. Furthermore, the solver provides accurate solutions on unstructured, tetrahedral grids with relatively large element sizes as compared to commonly employed solvers that use step differencing. The predictions of the solver are validated by a series of frequency-domain, phantom measurements with optical properties ranging from diffusion limited to transport limited propagation. Our results demonstrate that the RTE solution consistently matches measurements made under both diffusion and transport-limited conditions. This work demonstrates the use of an appropriate RTE solver for deployment in small animal optical tomography.