Linear Boltzmann equation solver for voxel-level dosimetry in radiopharmaceutical therapy: Comparison with Monte Carlo and kernel convolution.

BACKGROUND: With recent interest in patient-specific dosimetry for radiopharmaceutical therapy (RPT) and selective internal radiation therapy (SIRT), an increasing number of voxel-based algorithms are being evaluated. Monte Carlo (MC) radiation transport, generally considered to be the most accurate among different methods for voxel-level absorbed dose estimation, can be computationally inefficient for routine clinical use. PURPOSE: This work demonstrates a recently implemented grid-based linear Boltzmann transport equation (LBTE) solver for fast and accurate voxel-based dosimetry in RPT and SIRT and benchmarks it against MC. METHODS: A deterministic LBTE solver (Acuros MRT) was implemented within a commercial RPT dosimetry package (Velocity 4.1). The LBTE is directly discretized using an adaptive mesh refined grid and then the coupled photon-electron radiation transport is iteratively solved inside specified volumes to estimate radiation doses from both photons and charged particles in heterogeneous media. To evaluate the performance of the LBTE solver for RPT and SIRT applications, 177 Lu SPECT/CT, 90 Y PET/CT, and 131 I SPECT/CT images of phantoms and patients were used. Multiple lesions (2-1052 mL) and normal organs were delineated for each study. Voxel dosimetry was performed with the LBTE solver, dose voxel kernel (DVK) convolution with density correction, and a validated in-house MC code using the same time-integrated activity and density maps as input to the different dose engines. The resulting dose maps, difference maps, and dose-volume-histogram (DVH) metrics were compared, to assess the voxel-level agreement. Evaluation of mean absorbed dose included comparison with structure-level estimates from OLINDA. RESULTS: In the phantom inserts/compartments, the LBTE solver versus MC and DVK convolution demonstrated good agreement with mean absorbed dose and DVH metrics agreeing to within 5% except for the D90 and D70 metrics of a very low activity concentration insert of 90 Y where the agreement was within 15%. In the patient studies (five patients imaged after 177 Lu DOTATATE RPT, five after 90 Y SIRT, and two after 131 I radioimmunotherapy), in general, there was better agreement between the LBTE solver and MC than between LBTE solver and DVK convolution for mean absorbed dose and voxel-level evaluations. Across all patients for all three radionuclides, for soft tissue structures (kidney, liver, lesions), the mean absorbed dose estimates from the LBTE solver were in good agreement with those from MC (median difference < 1%, maximum 9%) and those from DVK (median difference < 5%, maximum 9%). The LBTE and OLINDA estimates for mean absorbed dose in kidneys and liver agreed to within 10%, but differences for lesions were larger with a maximum 14% for 177 Lu, 23% for 90 Y, and 26% for 131 I. For bone regions, the agreement in mean absorbed doses between LBTE and both MC and DVK were similar (median < 11%, max 11%) while for lung the agreement between LBTE and MC (median < 1%, max 8%) was substantially better than between LBTE and DVK (median < 16%, max 33%). Voxel level estimates for soft tissue structures also showed good agreement between the LBTE solver and both MC and DVK with a median difference < 5% (maximum < 13%) for the DVH metrics with all three radionuclides. The largest difference in DVH metrics was for the D90 and D70 metric in lung and bone where the uptake was low. Here, the difference between LBTE and MC had a median value < 14% (maximum 23%) for bone and < 4% (maximum 37%) for lung, while the corresponding differences between LBTE and DVK were < 23% (maximum 31%) and < 67% (maximum 313%), respectively. For a typical patient with a matrix size of 166 × 166 × 129 (voxel size 3 × 3 × 3 mm3 ), voxel dosimetry using the LBTE solver was as fast as ∼2 min on a desktop computer. CONCLUSION: Having established good agreement between the LBTE solver and MC for RPT and SIRT applications, the LBTE solver is a viable option for voxel dosimetry that can be faster than MC. Further analysis is being performed to encompass the broad range of radionuclides and conditions encountered clinically.

Validation of a deterministic linear Boltzmann transport equation solver for rapid CT dose computation using physical dose measurements in pediatric phantoms.

PURPOSE: The risk of inducing cancer to patients undergoing CT examinations has motivated efforts for CT dose estimation, monitoring, and reduction, especially among pediatric population. The method investigated in this study is Acuros CTD (Varian Medical Systems, Palo Alto, CA), a deterministic linear Boltzmann transport equation (LBTE) solver aimed at generating rapid and reliable dose maps of CT exams. By applying organ contours, organ doses can also be obtained, thus patient-specific organ dose estimates can be provided. This study experimentally validated Acuros against measurements performed on a clinical CT system using a range of physical pediatric anthropomorphic phantoms and acquisition protocols. METHODS: The study consisted of (1) the acquisition of dose measurements on a clinical CT scanner through thermoluminescent dosimeters (TLDs), and (2) the modeling in the Acuros platform of the measurement set up, which includes the modeling of the CT scanner and of the anthropomorphic phantoms. For the measurements, 1-year-old, 5-year-old, and 10-year-old anthropomorphic phantoms of the CIRS ATOM family were used. TLDs were placed in selected organ locations such as stomach, liver, lungs, and heart. The pediatric phantoms were scanned helically with the GE Discovery 750 HD clinical scanner for several examination protocols. For the simulations in Acuros, scanner-specific input, such as bowtie filters, overrange collimation, and tube current modulation schemes, were modeled. These scanner complexities were implemented by defining discretized X-ray beams whose spectral distribution, defined in Acuros by only six energy bins, varied across fan angle, cone angle, and slice position. The images generated during the CT acquisitions were used to create the geometrical models, by applying thresholding algorithms and assigning materials to the HU values. The TLDs were contoured in the phantom models as sensitive cylindrical volumes at the locations selected for dosimeters placement, to provide dose estimates, in terms of dose per unit photon. To compare measured doses with dose estimates, a calibration factor was derived from the CTDIvol displayed by the scanner, to account for the number of photons emitted by the X-ray tube during the procedure. RESULTS: The differences of the measured and estimated doses, in terms of absolute % errors, were within 13% for 153 TLD locations, with an error of 17% at the stomach for one study with the 10-year-old phantom. Root-mean-squared-errors (RMSE) across all TLD locations for all configurations were in the range of 3%-8%, with Acuros providing dose estimates in a time range of a few seconds up to 2 min. CONCLUSIONS: An overall good agreement between measurements and simulations was achieved, with average RMSE of 6% across all cases. The results demonstrate that Acuros can model a specific clinical scanner despite the required discretization in spatial and energy domains. The proposed deterministic tool has the potential to be part of a near real-time individualized dosimetry monitoring system for CT applications, providing patient-specific organ dose estimates.

Deterministic linear Boltzmann transport equation solver for patient-specific CT dose estimation: Comparison against a Monte Carlo benchmark for realistic scanner configurations and patient models.

PURPOSE: Epidemiological evidence suggests an increased risk of cancer related to computed tomography (CT) scans, with children exposed to greater risk. The purpose of this work is to test the reliability of a linear Boltzmann transport equation (LBTE) solver for rapid and patient-specific CT dose estimation. This includes building a flexible LBTE framework for modeling modern clinical CT scanners and to validate the resulting dose maps across a range of realistic scanner configurations and patient models. METHODS: In this study, computational tools were developed for modeling CT scanners, including a bowtie filter, overrange collimation, and tube current modulation. The LBTE solver requires discretization in the spatial, angular, and spectral dimensions, which may affect the accuracy of scanner modeling. To investigate these effects, this study evaluated the LBTE dose accuracy for different discretization parameters, scanner configurations, and patient models (male, female, adults, pediatric). The method used to validate the LBTE dose maps was the Monte Carlo code Geant4, which provided ground truth dose maps. LBTE simulations were implemented on a GeForce GTX 1080 graphic unit, while Geant4 was implemented on a distributed cluster of CPUs. RESULTS: The agreement between Geant4 and the LBTE solver quantifies the accuracy of the LBTE, which was similar across the different protocols and phantoms. The results suggest that 18 views per rotation provides sufficient accuracy, as no significant improvement in the accuracy was observed by increasing the number of projection views. Considering this discretization, the LBTE solver average simulation time was approximately 30 s. However, in the LBTE solver the phantom model was implemented with a lower voxel resolution with respect to Geant4, as it is limited by the memory of the GPU. Despite this discretization, the results showed a good agreement between the LBTE and Geant4, with root mean square error of the dose in organs of approximately 3.5% for most of the studied configurations. CONCLUSIONS: The LBTE solver is proposed as an alternative to Monte Carlo for patient-specific organ dose estimation. This study demonstrated accurate organ dose estimates for the rapid LBTE solver when considering realistic aspects of CT scanners and a range of phantom models. Future plans will combine the LBTE framework with deep learning autosegmentation algorithms to provide near real-time patient-specific organ dose estimation.

A fast, linear Boltzmann transport equation solver for computed tomography dose calculation (Acuros CTD).

PURPOSE: To improve dose reporting of CT scans, patient-specific organ doses are highly desired. However, estimating the dose distribution in a fast and accurate manner remains challenging, despite advances in Monte Carlo methods. In this work, we present an alternative method that deterministically solves the linear Boltzmann transport equation (LBTE), which governs the behavior of x-ray photon transport through an object. METHODS: Our deterministic solver for CT dose (Acuros CTD) is based on the same approach used to estimate scatter in projection images of a CT scan (Acuros CTS). A deterministic method is used to compute photon fluence within the object, which is then converted to deposited energy by multiplying by known, material-specific conversion factors. To benchmark Acuros CTD, we used the AAPM Task Group 195 test for CT dose, which models an axial, fan beam scan (10 mm thick beam) and calculates energy deposited in each organ of an anthropomorphic phantom. We also validated our own Monte Carlo implementation of Geant4 to use as a reference to compare Acuros against for other common geometries like an axial, cone beam scan (160 mm thick beam) and a helical scan (40 mm thick beam with table motion for a pitch of 1). RESULTS: For the fan beam scan, Acuros CTD accurately estimated organ dose, with a maximum error of 2.7% and RMSE of 1.4% when excluding organs with <0.1% of the total energy deposited. The cone beam and helical scans yielded similar levels of accuracy compared to Geant4. Increasing the number of source positions beyond 18 or decreasing the voxel size below 5 × 5 × 5 mm3 provided marginal improvement to the accuracy for the cone beam scan but came at the expense of increased run time. Across the different scan geometries, run time of Acuros CTD ranged from 8 to 23 s. CONCLUSIONS: In this digital phantom study, a deterministic LBTE solver was capable of fast and accurate organ dose estimates.

Acuros CTS: A fast, linear Boltzmann transport equation solver for computed tomography scatter - Part I: Core algorithms and validation.

PURPOSE: To describe Acuros® CTS, a new software tool for rapidly and accurately estimating scatter in x-ray projection images by deterministically solving the linear Boltzmann transport equation (LBTE). METHODS: The LBTE describes the behavior of particles as they interact with an object across spatial, energy, and directional (propagation) domains. Acuros CTS deterministically solves the LBTE by modeling photon transport associated with an x-ray projection in three main steps: (a) Ray tracing photons from the x-ray source into the object where they experience their first scattering event and form scattering sources. (b) Propagating photons from their first scattering sources across the object in all directions to form second scattering sources, then repeating this process until all high-order scattering sources are computed using the source iteration method. (c) Ray-tracing photons from scattering sources within the object to the detector, accounting for the detector's energy and anti-scatter grid responses. To make this process computationally tractable, a combination of analytical and discrete methods is applied. The three domains are discretized using the Linear Discontinuous Finite Elements, Multigroup, and Discrete Ordinates methods, respectively, which confer the ability to maintain the accuracy of a continuous solution. Furthermore, through the implementation in CUDA, we sought to exploit the parallel computing capabilities of graphics processing units (GPUs) to achieve the speeds required for clinical utilization. Acuros CTS was validated against Geant4 Monte Carlo simulations using two digital phantoms: (a) a water phantom containing lung, air, and bone inserts (WLAB phantom) and (b) a pelvis phantom derived from a clinical CT dataset. For these studies, we modeled the TrueBeam® (Varian Medical Systems, Palo Alto, CA) kV imaging system with a source energy of 125 kVp. The imager comprised a 600 µm-thick Cesium Iodide (CsI) scintillator and a 10:1 one-dimensional anti-scatter grid. For the WLAB studies, the full-fan geometry without a bowtie filter was used (with and without the anti-scatter grid). For the pelvis phantom studies, a half-fan geometry with bowtie was used (with the anti-scatter grid). Scattered and primary photon fluences and energies deposited in the detector were recorded. RESULTS: The Acuros CTS and Monte Carlo results demonstrated excellent agreement. For the WLAB studies, the average percent difference between the Monte Carlo- and Acuros-generated scattered photon fluences at the face of the detector was -0.7%. After including the detector response, the average percent differences between the Monte Carlo- and Acuros-generated scatter fractions (SF) were -0.1% without the grid and 0.6% with the grid. For the digital pelvis simulation, the Monte Carlo- and Acuros-generated SFs agreed to within 0.1% on average, despite the scatter-to-primary ratios (SPRs) being as high as 5.5. The Acuros CTS computation time for each scatter image was ~1 s using a single GPU. CONCLUSIONS: Acuros CTS enables a fast and accurate calculation of scatter images by deterministically solving the LBTE thus offering a computationally attractive alternative to Monte Carlo methods. Part II describes the application of Acuros CTS to scatter correction of CBCT scans on the TrueBeam system.

A benchmarking method to evaluate the accuracy of a commercial proton monte carlo pencil beam scanning treatment planning system.

AcurosPT is a Monte Carlo algorithm in the Eclipse 13.7 treatment planning system, which is designed to provide rapid and accurate dose calculations for proton therapy. Computational run-time in minimized by simplifying or eliminating less significant physics processes. In this article, the accuracy of AcurosPT was benchmarked against both measurement and an independent MC calculation, TOPAS. Such a method can be applied to any new MC calculation for the detection of potential inaccuracies. To validate multiple Coulomb scattering (MCS) which affects primary beam broadening, single spot profiles in a Solidwater® phantom were compared for beams of five selected proton energies between AcurosPT, measurement and TOPAS. The spot Gaussian sigma in AcurosPT was found to increase faster with depth than both measurement and TOPAS, suggesting that the MCS algorithm in AcurosPT overestimates the scattering effect. To validate AcurosPT modeling of the halo component beyond primary beam broadening, field size factors (FSF) were compared for multi-spot profiles measured in a water phantom. The FSF for small field sizes were found to disagree with measurement, with the disagreement increasing with depth. Conversely, TOPAS simulations of the same FSF consistently agreed with measurement to within 1.5%. The disagreement in absolute dose between AcurosPT and measurement was smaller than 2% at the mid-range depth of multi-energy beams. While AcurosPT calculates acceptable dose distributions for typical clinical beams, users are cautioned of potentially larger errors at distal depths due to overestimated MCS and halo implementation.

Evaluation of a deterministic grid-based Boltzmann solver (GBBS) for voxel-level absorbed dose calculations in nuclear medicine.

To evaluate the 3D Grid-based Boltzmann Solver (GBBS) code ATTILA (®) for coupled electron and photon transport in the nuclear medicine energy regime for electron (beta, Auger and internal conversion electrons) and photon (gamma, x-ray) sources. Codes rewritten based on ATTILA are used clinically for both high-energy photon teletherapy and (192)Ir sealed source brachytherapy; little information exists for using the GBBS to calculate voxel-level absorbed doses in nuclear medicine. We compared DOSXYZnrc Monte Carlo (MC) with published voxel-S-values to establish MC as truth. GBBS was investigated for mono-energetic 1.0, 0.1, and 0.01 MeV electron and photon sources as well as (131)I and (90)Y radionuclides. We investigated convergence of GBBS by analyzing different meshes ([Formula: see text]), energy group structures ([Formula: see text]) for each radionuclide component, angular quadrature orders ([Formula: see text], and scattering order expansions ([Formula: see text]-[Formula: see text]); higher indices imply finer discretization. We compared GBBS to MC in (1) voxel-S-value geometry for soft tissue, lung, and bone, and (2) a source at the interface between combinations of lung, soft tissue, and bone. Excluding Auger and conversion electrons, MC agreed within ≈5% of published source voxel absorbed doses. For the finest discretization, most GBBS absorbed doses in the source voxel changed by less than 1% compared to the next finest discretization along each phase space variable indicating sufficient convergence. For the finest discretization, agreement with MC in the source voxel ranged from -3% to -20% with larger differences at lower energies (-3% for 1 MeV electron in lung to -20% for 0.01 MeV photon in bone); similar agreement was found for the interface geometries. Differences between GBBS and MC in the source voxel for (90)Y and (131)I were -6%. The GBBS ATTILA was benchmarked against MC in the nuclear medicine regime. GBBS can be a viable alternative to MC for voxel-level absorbed doses in nuclear medicine. However, reconciliation of the differences between GBBS and MC at lower energies requires further investigation of energy deposition cross-sections.

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.

Comparison of a 3-D multi-group SN particle transport code with Monte Carlo for intracavitary brachytherapy of the cervix uteri.

A patient dose distribution was calculated by a 3D multi-group S N particle transport code for intracavitary brachytherapy of the cervix uteri and compared to previously published Monte Carlo results. A Cs-137 LDR intracavitary brachytherapy CT data set was chosen from our clinical database. MCNPX version 2.5.c, was used to calculate the dose distribution. A 3D multi-group S N particle transport code, Attila version 6.1.1 was used to simulate the same patient. Each patient applicator was built in SolidWorks, a mechanical design package, and then assembled with a coordinate transformation and rotation for the patient. The SolidWorks exported applicator geometry was imported into Attila for calculation. Dose matrices were overlaid on the patient CT data set. Dose volume histograms and point doses were compared. The MCNPX calculation required 14.8 hours, whereas the Attila calculation required 22.2 minutes on a 1.8 GHz AMD Opteron CPU. Agreement between Attila and MCNPX dose calculations at the ICRU 38 points was within +/- 3%. Calculated doses to the 2 cc and 5 cc volumes of highest dose differed by not more than +/- 1.1% between the two codes. Dose and DVH overlays agreed well qualitatively. Attila can calculate dose accurately and efficiently for this Cs-137 CT-based patient geometry. Our data showed that a three-group cross-section set is adequate for Cs-137 computations. Future work is aimed at implementing an optimized version of Attila for radiotherapy calculations.

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.

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.

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.

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.

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.