Linear Boltzmann Transport Equation Solver Research Articles

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

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. 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. 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 (2-1052mL) 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. 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. 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.

Reduced Chest Computed Tomography Scan Length for Patients Positive for Coronavirus Disease 2019: Dose Reduction and Impact on Diagnostic Utility.

This study used the Personalized Rapid Estimation of Dose in CT (PREDICT) tool to estimate patient-specific organ doses from CT image data. The PREDICT is a research tool that combines a linear Boltzmann transport equation solver for radiation dose map generation with deep learning algorithms for organ contouring. Computed tomography images from 74 subjects in the Medical Imaging Data Resource Center-RSNA International COVID-19 Open Radiology Database data set (chest CT of adult patients positive for COVID-19), which included expert annotations including "infectious opacities," were analyzed. First, the full z-scan length of the CT image data set was evaluated. Next, the z-scan length was reduced from the left hemidiaphragm to the top of the aortic arch. Generic dose reduction based on dose length product (DLP) and patient-specific organ dose reductions were calculated. The percentage of infectious opacities excluded from the reduced z-scan length was used to quantify the effect on diagnostic utility. Generic dose reduction, based on DLP, was 69%. The organ dose reduction ranged from approximately equal to 18% (breasts) to approximately equal to 64% (bone surface and bone marrow). On average, 12.4% of the infectious opacities were not included in the reduced z-coverage, per patient, of which 5.1% were above the top of the arch and 7.5% below the left hemidiaphragm. Limiting z-scan length of chest CTs reduced radiation dose without significantly compromising diagnostic utility in COVID-19 patients. The PREDICT demonstrated that patient-specific organ dose reductions varied from generic dose reduction based on DLP.

The Effect of Various Dose Normalization Strategies When Implementing Linear Boltzmann Transport Equation Dose Calculation for Lung Stereotactic Body Radiation Therapy Planning

PurposeTo explore implications of various plan normalizations when implementing a linear Boltzmann transport equation solver dose calculation algorithm (LBTE) for lung stereotactic body radiation therapy (SBRT). Methods and MaterialsEighty-seven plans originally calculated with a convolution-superposition algorithm (CS) were recalculated with LBTE and normalized in 3 ways: prescription covering 95% of planning target volume (PTV), 99% of internal target volume (ITV), and keeping the original planned PTV coverage. Effect on delivered dose after implementing the new algorithm was quantified using change in total monitor units for each renormalization strategy. Treatment planning system–reported changes in PTV, ITV, and organ at risk (OAR) doses were also quantified, along with the feasibility of LBTE plans to meet institutional OAR planning objectives. ResultsLBTE renormalization resulted in monitor unit increases of 7.0 ± 8.8%, 0.31 ± 5.8%, and 7.9 ± 8.6% when normalizing to the PTV D95%, ITV D99%, and planned coverage, respectively. When normalizing to PTV D95%, the LBTE reported increased PTV and ITV D1% (Gy) relative to CS (median, 3.4% and 3.2%, respectively), and normalizing to ITV D99% showed a median 1.9% decrease. For LBTE plans, reported OAR doses were increased when normalizing to PTV D95% or planned coverage (median chest wall V30 Gy [cc] increase of 0.85 and 1.7 cc, respectively) and normalizing to ITV D99% resulted in decreased dose (median chest wall V30 Gy [cc] decrease of 1.8 cc). LBTE plans normalized to PTV D95% showed inferior ability to meet the OAR objectives, but reoptimizing kept the objectives manageable while maintaining PTV coverage. ConclusionsWhen transitioning from CS to LBTE dose calculation for lung SBRT, maintaining a PTV coverage-based normalization generally results in increased dose delivered relative to CS and increased reported target and OAR dose. In cases where PTV normalization results in unacceptably high doses to targets or OARs, normalizing based on ITV coverage can be considered to maintain similar target dose as CS.

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

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. 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. 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. 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.

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. 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. 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 30s. 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. 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.

Scatter Correction for Industrial Cone-Beam Computed Tomography (CBCT) Using VSHARP, a fast GPU-Based Linear Boltzmann Transport Equation Solver

The use of cone-beam computed tomography (CBCT) to inspect objects containing aluminum, Inconel and other metals is a challenge due to high amounts of scattered radiation in the projection data. Following in the footsteps of VSHARP, our kernel-based two-dimensional (2D) software scatter correction algorithm that operates on x-ray projection data, we introduce three-dimensional (3D) VSHARP designed to offer improved accuracy and flexibility. The core of 3D VSHARP is fast finite element Linear Boltzmann Transport Equation (LBTE) solver that models photon transport within the object-of-interest and computes the scatter component of the projection data with Monte Carlo-like accuracy but greatly reduced computation times. 3D VSHARP utilizes an object model consisting of 3D material density maps based on a first pass reconstruction, and an imaging chain model describing the system geometry, the x-ray source components (polychromatic spectrum, beam filtration, and collimation hardware), and the x-ray detector components (flat-panel imager in this case). The 3D material density maps making up the object model may be further informed by Computer Aided Design (CAD) files. Validation against Monte Carlo (MC) simulations of overlapping metal blocks showed that 3D VSHARP- and MC-computed scatter fractions agreed to within 3% RMS. The 3D VSHARP execution time was less than 1 sec per projection using a single NVidia TitanXp GPU (NVidia Inc., Santa Clara CA) while the MC simulations took 1566 CPU-hours using two Intel-Silver-Xenon, 2.2 GHz, 10x core CPU (Intel Inc., Santa Clara CA), in a Dell 7920 workstation (Dell Inc., Austin TX). Experimental CBCT scans were taken of an aluminum motorcycle cylinder head and Inconel turbine blade at 450kVp. Results showed that high quality reconstructions and volume renderings were obtained which may open up the possibility of in-line CBCT applications.

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

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. 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 (10mm 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 (160mm thick beam) and a helical scan (40mm thick beam with table motion for a pitch of 1). 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 × 5mm3 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 23s. 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.

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). 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 125kVp. The imager comprised a 600μm-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. 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 ~1s using a single GPU. 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.

Acuros CTS: A fast, linear Boltzmann transport equation solver for computed tomography scatter - Part II: System modeling, scatter correction, and optimization.

To correct for scatter in kV cone-beam CT (CBCT) projection data on a clinical system using a new tool, Acuros® CTS, that estimates scatter images rapidly and accurately by deterministically solving the linear Boltzmann transport equation. Phantom and patient CBCT scans were acquired on TrueBeam® radiotherapy machines. A first-pass reconstruction was used to create water and bone density maps of the imaged object, which was updated to include a more accurate representation of the patient couch. The imaging system model accounted for the TrueBeam x-ray source (polychromatic spectrum, beam filtration, bowtie filter, and collimation hardware) and x-ray detection system (antiscatter grid, flat-panel imager). Acuros CTS then used the system and object models to estimate the scatter component of each projection image, which was subtracted from the measured projections. The corrected projections were then reconstructed to produce the final result. We examined the tradeoff between run time and accuracy using a Pareto optimization of key parameters, including the voxel size of the down-sampled object model, the number of pixels in the down-sampled detector, and the number of scatter images (angular down-sampling). All computations and reconstructions were performed on a research workstation containing two graphics processing units (GPUs). In addition, we established a method for selecting a subset of projections for which scatter images were calculated. The projections were selected to minimize interpolation errors in the remaining projections. Image quality improvement was assessed by measuring the accuracy of the reconstructed phantom and patient images. The Pareto optimization yielded a set of parameters with an average run time of 26 seconds for scatter correction while maintaining high accuracy of scatter estimation. This was achieved in part by means of optimizing the projection angles that were processed, thus favoring the use of more angles in the lateral (i.e., horizontal) direction and fewer angles in the AP direction. In a 40 cm solid water phantom reconstruction, nonuniformities were decreased from 217 HU without scatter correction to 51 HU with conventional (kernel-based) scatter correction to 17 HU with Acuros CTS-based scatter correction. In clinical pelvis scans, nonuniformities in the bladder were reduced from 85 HU with conventional scatter correction to 14 HU with Acuros CTS. Acuros CTS is a promising new tool for fast and accurate scatter correction for CBCT imaging. By carefully modeling the imaging chain and optimizing several parameters, we achieved high correction accuracies with computation times compatible with the clinical workflow. The improvement in image quality enables better soft-tissue visualization and potentially enables applications such as adaptive radiotherapy.

Assessment of leakage dose in vivo in patients undergoing radiotherapy for breast cancer.

Background and purposeAccurate quantification of the relatively small radiation doses delivered to untargeted regions during breast irradiation in patients with breast cancer is of increasing clinical interest for the purpose of estimating long-term radiation-related risks. Out-of-field dose calculations from commercial planning systems however may be inaccurate which can impact estimates for long-term risks associated with treatment. This work compares calculated and measured dose out-of-field and explores the application of a correction for leakage radiation.Materials and methodsDose calculations of a Boltzmann transport equation solver, pencil beam-type, and superposition-type algorithms from a commercial treatment planning system (TPS) were compared with in vivo thermoluminescent dosimetry (TLD) measurements conducted out-of-field on the contralateral chest at points corresponding to the thyroid, axilla and contralateral breast of eleven patients undergoing tangential beam radiotherapy for breast cancer.ResultsOverall, the TPS was found to under-estimate doses at points distal to the radiation field edge with a modern linear Boltzmann transport equation solver providing the best estimates. Application of an additive correction for leakage (0.04% of central axis dose) improved correlation between the measured and calculated doses at points greater than 15 cm from the field edge.ConclusionsApplication of a correction for leakage doses within peripheral regions is feasible and could improve accuracy of TPS in estimating out-of-field doses in breast radiotherapy.

A medical image-based graphical platform—Features, applications and relevance for brachytherapy

Brachytherapy dose calculation is commonly performed using the Task Group-No 43 Report-Updated protocol (TG-43U1) formalism. Recently, a more accurate approach has been proposed that can handle tissue composition, tissue density, body shape, applicator geometry, and dose reporting either in media or water. Some model-based dose calculation algorithms are based on Monte Carlo (MC) simulations. This work presents a software platform capable of processing medical images and treatment plans, and preparing the required input data for MC simulations. The A Medical Image-based Graphical platfOrm-Brachytherapy module (AMIGOBrachy) is a user interface, coupled to the MCNP6 MC code, for absorbed dosecalculations. The AMIGOBrachy was first validated in water for a high-dose-rate (192)Ir source. Next, dose distributions were validated in uniform phantoms consisting of different materials. Finally, dose distributions were obtained in patient geometries. Results were compared against a treatment planning system including a linear Boltzmann transport equation (LBTE) solver capable of handling nonwater heterogeneities. The TG-43U1 source parameters are in good agreement with literature with more than 90% of anisotropy values within 1%. No significant dependence on the tissue composition was observed comparing MC results against an LBTE solver. Clinical cases showed differences up to 25%, when comparing MC results against TG-43U1. About 92% of the voxels exhibited dose differences lower than 2% when comparing MC results against an LBTE solver. The AMIGOBrachy can improve the accuracy of the TG-43U1 dose calculation by using a more accurate MC dose calculation algorithm. The AMIGOBrachy can be incorporated in clinical practice via a user-friendly graphical interface.

TH‐E‐BRE‐01: A 3D Solver of Linear Boltzmann Transport Equation Based On a New Angular Discretization Method with Positivity for Photon Dose Calculation Benchmarked with Geant4

Purpose:The Linear Boltzmann Transport Equation (LBTE) solved through statistical Monte Carlo (MC) method provides the accurate dose calculation in radiotherapy. This work is to investigate the alternative way for accurately solving LBTE using deterministic numerical method due to its possible advantage in computational speed from MC.Methods:Instead of using traditional spherical harmonics to approximate angular scattering kernel, our deterministic numerical method directly computes angular scattering weights, based on a new angular discretization method that utilizes linear finite element method on the local triangulation of unit angular sphere. As a Result, our angular discretization method has the unique advantage in positivity, i.e., to maintain all scattering weights nonnegative all the time, which is physically correct. Moreover, our method is local in angular space, and therefore handles the anisotropic scattering well, such as the forward‐peaking scattering. To be compatible with image‐guided radiotherapy, the spatial variables are discretized on the structured grid with the standard diamond scheme. After discretization, the improved sourceiteration method is utilized for solving the linear system without saving the linear system to memory. The accuracy of our 3D solver is validated using analytic solutions and benchmarked with Geant4, a popular MC solver.Results:The differences between Geant4 solutions and our solutions were less than 1.5% for various testing cases that mimic the practical cases. More details are available in the supporting document.Conclusion:We have developed a 3D LBTE solver based on a new angular discretization method that guarantees the positivity of scattering weights for physical correctness, and it has been benchmarked with Geant4 for photon dose calculation.

Evaluation of an analytic linear Boltzmann transport equation solver for high‐density inhomogeneities

Acuros external beam (Acuros XB) is a novel dose calculation algorithm implemented through the ECLIPSE treatment planning system. The algorithm finds a deterministic solution to the linear Boltzmann transport equation, the same equation commonly solved stochastically by Monte Carlo methods. This work is an evaluation of Acuros XB, by comparison with Monte Carlo, for dose calculation applications involving high-density materials. Existing non-Monte Carlo clinical dose calculation algorithms, such as the analytic anisotropic algorithm (AAA), do not accurately model dose perturbations due to increased electron scatter within high-density volumes. Acuros XB, AAA, and EGSnrc based Monte Carlo are used to calculate dose distributions from 18 MV and 6 MV photon beams delivered to a cubic water phantom containing a rectangular high density (4.0-8.0 g/cm(3)) volume at its center. The algorithms are also used to recalculate a clinical prostate treatment plan involving a unilateral hip prosthesis, originally evaluated using AAA. These results are compared graphically and numerically using gamma-index analysis. Radio-chromic film measurements are presented to augment Monte Carlo and Acuros XB dose perturbation data. Using a 2% and 1 mm gamma-analysis, between 91.3% and 96.8% of Acuros XB dose voxels containing greater than 50% the normalized dose were in agreement with Monte Carlo data for virtual phantoms involving 18 MV and 6 MV photons, stainless steel and titanium alloy implants and for on-axis and oblique field delivery. A similar gamma-analysis of AAA against Monte Carlo data showed between 80.8% and 87.3% agreement. Comparing Acuros XB and AAA evaluations of a clinical prostate patient plan involving a unilateral hip prosthesis, Acuros XB showed good overall agreement with Monte Carlo while AAA underestimated dose on the upstream medial surface of the prosthesis due to electron scatter from the high-density material. Film measurements support the dose perturbations demonstrated by Monte Carlo and Acuros XB data. Acuros XB is shown to perform as well as Monte Carlo methods and better than existing clinical algorithms for dose calculations involving high-density volumes.

Clinical validation of the Acuros XB photon dose calculation algorithm, a grid-based Boltzmann equation solver

Introduction. A new algorithm that uses a grid-based technique to solve the linear Boltzmann transport equation (LBTE) has been developed to improve the accuracy and speed of external photon beam treatment planning calculations. The aim of this study was to test the accuracy of this algorithm in both heterogeneous and homogeneous media. Material and methods. Output factors, depth dose curves and profiles for symmetric fields were measured in water using diamond and ionization chamber detectors. Furthermore, asymmetric fields, fields collimated with the multi-leaf collimator, enhanced dynamic wedge fields as well as fields with different source-skin distances were measured. Various test plans were created on a CIRS thorax phantom including tissue-equivalent inserts and corresponding dose distributions within the phantom were measured with radiochromic films. The new grid-based LBTE solver, Acuros XB (Eclipse version 10.0, Varian Medical Systems, CA, USA) was used to calculate dose distributions for all field configurations and plans, for both 6 MV and 15 MV photons. Calculations were also performed with AAA, a standard convolution algorithm. Results. Compared to measurements, the output factors were within 1% for Acuros XB. For the depth doses, the average deviations were within 1% in dose and 1 mm in distance to agreement (DTA). For the profiles, the deviations were within 2%/1 mm except near the penumbra. Similar results were obtained for the other field configurations. Good agreement with AAA was also found. For the plans calculated on the CIRS phantom, the number of points meeting the gamma criterion of 3% in dose and 3 mm in DTA was higher with Acuros XB (98% for 6 MV; 100% for 15 MV) than with AAA (94% for 6 MV; 96% for 15 MV). Conclusion. Dose calculations with the Acuros XB algorithm in homogeneous media are in good agreement with both measurements and the AAA algorithm. In heterogeneous media, the Acuros XB algorithm is superior to AAA in both lung and bony material.

SU-E-T-734: Evaluation of a New, Grid-Based Linear Boltzmann Transport Equation Solver for Dose Calculation in the Presence of High-Density Materials

Purpose: To evaluate the accuracy of a new, deterministic linear Boltzmann transport equation solver, AcurosXB, for radiotherapydose calculations in the presence of high‐density materials by comparison with Monte Carlo.Methods: AcurosXB, EGSnrc‐based Monte Carlo and Analytic Anisotropic Algorithm (AAA) were used to model 6MV and 18MV photon beams incident on phantom and patient geometries containing stainless steel and titanium high‐density objects. Monte Carlo was used as the evaluation benchmark while AAA was included as a representative of the convolution‐based clinical modeling algorithms currently used for radiotherapy treatment planning. Calculation geometries include a virtual cubic phantom created in MatLab, a cubic water phantom containing stainless steel rods and prosthetic hips and patient CT images with associated clinical treatment plans. Dose distributions were processed and analyzed in MatLab.Results: Agreement between AcurosXB and Monte Carlo is within 5% and 2mm. There is a backscatter peak position offset of up to one pixel (2mm) between AcurosXB and Monte Carlo which can be accounted for by differences in voxel coordinate definition, contour definition and interpolation effects. Additional differences between AcurosXB and Monte Carlo fall within statistical variance associated with Monte Carlo. Disagreement between AAA and Monte Carlo was far more dramatic; AAA was unable to model the sharp backscatter peak associated with photon transport across low‐ to high‐density boundaries resulting in inaccurate dose distribution through and past high density regions Conclusions: AcurosXB has shown to be an improvement on existing algorithms for calculating dose distribution in the presence of high‐density regions, nearly matching the current gold standard Monte Carlo method. Discrepancies between AcurosXB and Monte Carlo do not translate into clinically significant dose differences, while AAA has shown to under‐ or over‐estimate dose by as much as 20%. Varian Medical Systems has provided AcurosXB hardware and software for research activities.