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All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

SU-E-T-175: Clinical Evaluations of Monte Carlo-Based Inverse Treatment Plan Optimization for Intensity Modulated Radiotherapy

Purpose: Pencil-beam or superposition-convolution type dose calculation algorithms are routinely used in inverse plan optimization for intensity modulated radiation therapy (IMRT). However, due to their limited accuracy in some challenging cases, e.g. lung, the resulting dose may lose its optimality after being recomputed using an accurate algorithm, e.g. Monte Carlo (MC). It is the objective of this study to evaluate the feasibility and advantages of a new method to include MC in the treatment planning process. Methods: We developed a scheme to iteratively perform MC-based beamlet dose calculations and plan optimization. In the MC stage, a GPU-based dose engine was used and the particle number sampled from a beamlet was proportional to its optimized fluence from the previous step. We tested this scheme in four lung cancer IMRT cases. For each case, the original plan dose, plan dose re-computed by MC, and dose optimized by our scheme were obtained. Clinically relevant dosimetric quantities in these three plans were compared. Results: Although the original plan achieved a satisfactory PDV dose coverage, after re-computing doses using MC method, it was found that the PTV D95% were reduced by 4.60%–6.67%. After re-optimizing these cases with our scheme, the PTV coverage was improved to the same level as in the original plan, while the critical OAR coverages were maintained to clinically acceptable levels. Regarding the computation time, it took on average 144 sec per case using only one GPU card, including both MC-based beamlet dose calculation and treatment plan optimization. Conclusion: The achieved dosimetric gains and high computational efficiency indicate the feasibility and advantages of the proposed MC-based IMRT optimization method. Comprehensive validations in more patient cases are in progress.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2012

Domain decomposition for the SPN solver MINOS

In this article we present a domain decomposition method for the mixed SPN equations, discretized with Raviart-Thomas-Nedelec finite elements. This domain decomposition is based on the iterative Schwarz algorithm with Robin interface conditions to handle communications. After having described this method, we give details on how to optimize the convergence. Finally, we give some numerical results computed in a realistic 3D domain. The computations are done with the MINOS solver of the APOLLO3 (R) code. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

WE-AB-207A-03: A CBCT Head Scanner for Point-Of-Care Imaging of Intracranial Hemorrhage

Purpose: This work reports the design, development, and first technical assessment of a cone-beam CT (CBCT) scanner developed specifically for imaging of acute intracranial hemorrhage (ICH) at the point of care, with target applications in diagnosis and monitoring of traumatic brain injury, stroke, and postsurgical hemorrhage. Methods: System design employed a task-based image quality model to quantify the influence of factors such as additive noise and high-gain (HG) detector readout on ICH detectability. Three bowtie filters with varying bare-beam attenuation strength and curvature were designed to enable HG readout without detector saturation, and a polyenergetic gain correction was developed to minimize artifacts from bowtie flood-field calibration. Image reconstruction used an iterative penalized weighted least squares (PWLS) method with artifact correction including Monte Carlo scatter estimation, Joseph-Spital beam hardening correction, and spatiotemporal deconvolution of detector glare and lag. Radiation dose was characterized for half-scan and full-scan protocols at various kV, and imaging performance was assessed in a head phantom presenting simulated ICH with diameter ranging 2–12 mm. Results: The image quality model guided system design and was validated by measurements on a CBCT imaging bench. Compared to low-gain readout without a bowtie filter, the combination of HG readout and a modest bowtie improved the contrast-to-noise ratio (CNR per unit square-root dose) by 20% in the center of the image but degraded noise performance near the periphery (20% reduction in CNR). Low-frequency bowtie artifacts (∼100 HU magnitude) were corrected by the polyenergetic gain correction. Image reconstructions on the prototype scanner demonstrate clear visibility of the smallest ICH insert (2 mm diameter) in both HG readout (with a bowtie) and dual-gain readout (without bowtie). Conclusion: Technical assessment of the prototype scanner suggests the capability for reliable visualization of small (2 mm), low-contrast (50 HU) ICH at <20 mGy dose and motivates translation to clinical studies, now underway. Xiaohui Wang and David Foos (co-authors) are employees of Carestream Health. Research funding support from Carestream Health.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Parallel Dynamics Simulation Using a Krylov-Schwarz Linear Solution Scheme

Fast dynamics simulation of large-scale power systems is a computational challenge because of the need to solve a large set of stiff, nonlinear differential-algebraic equations at every time step. The main bottleneck in dynamic simulations is the solution of a linear system during each nonlinear iteration of Newton’s method. In this paper, we present a parallel Krylov- Schwarz linear solution scheme that uses the Krylov subspacebased iterative linear solver GMRES with an overlapping restricted additive Schwarz preconditioner. As a result, performance tests of the proposed Krylov-Schwarz scheme for several large test cases ranging from 2,000 to 20,000 buses, including a real utility network, show good scalability on different computing architectures.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2013

A New 2D-Transport, 1D-Diffusion Approximation of the Boltzmann Transport equation

The work performed in this project consisted of the derivation, implementation, and testing of a new, computationally advantageous approximation to the 3D Boltzmann transport equation. The solution of the Boltzmann equation is the neutron flux in nuclear reactor cores and shields, but solving this equation is difficult and costly. The new “2D/1D” approximation takes advantage of a special geometric feature of typical 3D reactors to approximate the neutron transport physics in a specific (ax- ial) direction, but not in the other two (radial) directions. The resulting equation is much less expensive to solve computationally, and its solutions are expected to be sufficiently accurate for many practical problems. In this project we formulated the new equation, discretized it using standard methods, developed a stable iteration scheme for solving the equation, implemented the new numerical scheme in the MPACT code, and tested the method on several realistic problems. All the hoped- for features of this new approximation were seen. For large, difficult problems, the resulting 2D/1D solution is highly accurate, and is calculated about 100 times faster than a 3D discrete ordinates simulation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Comprehensive analysis of disruption mitigation methods using gas and pellet-like injections in ITER-like Tokamaks

Abstract Inert-gas shielding could be an effective mechanism for protection of plasma facing surfaces (PFS) against plasma particles impact and photon radiation heat loads during transient events in fusion devices. Neutral gas injection is one promising way to mitigate erosion of tokamak components and contamination. The objective of this work is to study and optimize mitigation methods using neutral gas and pellet-like injections to decrease the heat load to the divertor surfaces and to prevent vaporization of the various internal surfaces due to transient events in ITER-like devices. The integrated self-consistent models implemented in the HEIGHTS package was used for detailed analysis of the potential secondary plasma generation from the injected inert gas, its radiative characteristics, and shielding effectiveness. We varied the density, size, and location of an argon gas cloud to minimize the disruption energy deposited into the divertor components. We also investigated innovative ways for minor changes in ITER-like internal design to mitigate disruptions. We found the optimum parameters to fully protect ITER tokamak surfaces from erosion and vaporization during plasma instabilities. This preliminary analysis showed that using Ar gas injection methods could lead to enhancement in components lifetime in ITER-like and future DEMO devices with minor design changes.

Science & Technology - Other Topics↗
DOE OSTI2016

Fourier Analysis of the Multilevel QD Method with {alpha}-Approximation For Time-Dependent Radiative Transfer Problems

Thermal radiation transfer (TRT) problems describe interaction of photon radiation with matter. They are defined by the time-dependent radiative transfer (RT) equation for the specific intensity I coupled with the energy balance (EB) equation. This class of problems is characterised by high dimensionality, multiple scales and strong nonlinearity. In this paper we analyze the multilevel quasi-diffusion (QD) method for solving TRT problems. This is a nonlinear method of moments with exact closures. The QD method enables one to reduce dimensionality of the original radiative transfer problem. It is formulated by a nonlinear system of equations consisting of (i) the high-order RT (HORT) equation for the intensity of photon radiation and (ii) low-order equations for the angular and energy moments of the intensity. The nonlinear closures are formulated by means of stable factors. The low-order problem brings the radiative transfer model to the level of multi-physics equations. The multilevel QD (MLQD) method possesses attractive features for efficient multi-physics coupling. To calculate the high-order RT solution we apply the {alpha}-approximation which assumes that the intensity changes exponentially in time over a time step. The {alpha}-approximation leads to the steady-state RT equation with a modified opacity and enables one to avoid storing the high-dimensional solution from the previous time step. The rate of change is evaluated by the solution of the time-dependent low-order QD (LOQD) equations for moments. We note that the HORT equation in the {alpha}-approximation contains an extra nonlinear term. It affects the iterative behaviour of the MLQD method. The obtained computational results indicated that the rate of convergence is slower compared to the rate when the time-dependent HORT is used to calculate the intensity. In this paper we perform an iterative stability analysis of the MLQD method in a discretized form and analyze convergence of outer (transport) iterations on a time step. We consider multigroup TRT problems in 1D slab geometry. The fully implicit scheme is used to discretize equations in time. The HORT equation is approximated with the method of step characteristics. A finite volume method is applied for spatial discretization of multigroup LOQD equations. The grey (one-group) LOQD equations are algebraically consistent with the multigroup LOQD equations. To perform Fourier analysis a model TRT problem in an infinite homogeneous medium is considered. The system of nonlinear equations of the MLQD method is linearized near an equilibrium solution at some given temperature. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

Effect of contrast enhancement prior to iteration procedure on image correction for soft x-ray projection microscopy

Soft X-ray microscopy is well recognized as a powerful tool of high-resolution imaging for hydrated biological specimens. Projection type of it has characteristics of easy zooming function, simple optical layout and so on. However the image is blurred by the diffraction of X-rays, leading the spatial resolution to be worse. In this study, the blurred images have been corrected by an iteration procedure, i.e., Fresnel and inverse Fresnel transformations repeated. This method was confirmed by earlier studies to be effective. Nevertheless it was not enough to some images showing too low contrast, especially at high magnification. In the present study, we tried a contrast enhancement method to make the diffraction fringes clearer prior to the iteration procedure. The method was effective to improve the images which were not successful by iteration procedure only.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Chord length sampling method for analyzing VHTR unit cells in continuous energy simulations

The chord length sampling method (CLS) is studied in the continuous energy simulations by applying it to analyzing two types of Very High Temperature Gas-cooled Reactor (VHTR) unit cells: the fuel compact cell in the prismatic type VHTR and the fuel pebble cell in the pebble-bed type VHTR. Infinite multiplication factors of the unit cells are calculated by the CLS and compared to the benchmark simulations at different volume packing fractions from 5% to 30%. It is shown that the accuracy of the CLS is affected by the boundary effect, which is induced by the CLS procedure itself and results in a reduction in the total volume packing fraction of the fuel particles. To mitigate the boundary effect, three correction schemes based on the research of 1) Murata et al. 2) Ji and Martin 3) Griesheimer et al. are used to improve the accuracy by applying a corrected value of the volume packing fraction to the CLS. These corrected values are calculated based on 1) a simple linear relationship, 2) an iterative self-consistent simulation correction method, and 3) a theoretically derived non-linear relationship, respectively. The CLS simulation using the corrected volume packing fraction shows excellent improvements in the infinite multiplication factors for the VHTR unit cells. Ji and Martin's self-consistent correction method shows the best improvement. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2019

Hybrid Fixed-Point Fixed-Stress Splitting Method for Linear Poroelasticity

Efficient and accurate poroelasticity models are critical in modeling geophysical problems such as oil exploration, gas-hydrate detection, and hydrogeology. We propose an efficient operator splitting method for Biot’s model of linear poroelasticity based on fixed-point iteration and constrained stress. In this method, we eliminate the constraint on time step via combining our fixed-point approach with a physics-based restraint between iterations. Three different cases are considered to demonstrate the stability and consistency of the method for constant and variable parameters. The results are validated against the results from the fully coupled approach. In case I, a single iteration is used for continuous coefficients. The relative error decreases with an increase in time. In case II, material coefficients are assumed to be linear. In the single iteration approach, the relative error grows significantly to 40% before rapidly decaying to zero. This is an artifact of the approximate solutions approaching the asymptotic solution. The error in the multiple iterations oscillates within 10 − 6 before decaying to the asymptotic solution. Nine iterations per time step are enough to achieve the relative error close to 10 − 7 . In the last case, the hybrid method with multiple iterations requires approximately 16 iterations to make the relative error 5 × 10 − 6 .

Delgado, Paul M.↗
DOE OSTI2022

Assessing the large-scale drivers of precipitation in the northeastern United States via linear orthogonal decomposition

This study examines the linear orthogonal modes associated with monthly precipitation in the northeastern United States, from CESM1 LENS (35 ensemble members, 1979–2005) and two reanalysis datasets (ERA5, 1950–2018 and NOAA-CIRES-DOE 20CRv3, 1950–2015). Calendar months are aggregated together, and any linear trends in data are removed. Using region-averaged precipitation anomaly time series and monthly anomalies for several global 2D atmospheric fields, a linear orthogonal decomposition method is implemented to iteratively extract time series (based on field and geographic location) of absolute maximum correlation. Linear modes associated with this method are then projected onto the full set of 2D fields to provide physical insight into the mechanisms involved in generating precipitation. In this region, the first mode is associated with vapor transport from the Atlantic seaboard, the second mode is characterized by westward vapor transport associated with extratropical cyclones, and the third mode captures vapor transport from the Gulf of Mexico during the fall and winter. However, the third mode is less robust in the spring and summer. Results are generally consistent across the datasets, and applying multiple linear regression with the linear modes to predict the precipitation anomalies produces R-squared values of around 0.54–0.65 for CESM1 LENS, and around 0.58–0.88 for reanalysis, with the lowest values generally in the spring and late summer. The influence of low-frequency climate variability on the modes is considered for CESM1 LENS, and the modes in late winter can be predicted with some success via a combination of several, prominent large-scale teleconnection patterns.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

MO-PIS-Exhibit Hall-01: Imaging: CT Dose Optimization Technologies I

Partners in Solutions is an exciting new program in which AAPM partners with our vendors to present practical “hands-on” information about the equipment and software systems that we use in our clinics. The imaging topic this year is CT scanner dose optimization capabilities. Note that the sessions are being held in a special purpose room built on the Exhibit Hall Floor, to encourage further interaction with the vendors. Dose Optimization Capabilities of GE Computed Tomography Scanners Presentation Time: 11:15 – 11:45 AM GE Healthcare is dedicated to the delivery of high quality clinical images through the development of technologies, which optimize the application of ionizing radiation. In computed tomography, dose management solutions fall into four categories: employs projection data and statistical modeling to decrease noise in the reconstructed image - creating an opportunity for mA reduction in the acquisition of diagnostic images. Veo represents true Model Based Iterative Reconstruction (MBiR). Using high-level algorithms in tandem with advanced computing power, Veo enables lower pixel noise standard deviation and improved spatial resolution within a single image. Advanced Adaptive Image Filters allow for maintenance of spatial resolution while reducing image noise. Examples of adaptive image space filters include Neuro 3-D filters and Cardiac Noise Reduction Filters. AutomA adjusts mA along the z-axis and is the CT equivalent of auto exposure control in conventional x-ray systems. Dynamic Z-axis Tracking offers an additional opportunity for dose reduction in helical acquisitions while SmartTrack Z-axis Tracking serves to ensure beam, collimator and detector alignment during tube rotation. SmartmA provides angular mA modulation. ECG Helical Modulation reduces mA during the systolic phase of the heart cycle. SmartBeam optimization uses bowtie beam-shaping hardware and software to filter off-axis x-rays - minimizing dose and reducing x-ray scatter. The DICOM Radiation Dose Structured Report (RDSR) generates a dose report at the conclusion of every examination. Dose Check preemptively notifies CT operators when scan parameters exceed user-defined dose thresholds. DoseWatch is an information technology application providing vendor-agnostic dose tracking and analysis for CT (and all other diagnostic x-ray modalities) SnapShot Pulse improves coronary CTA dose management. VolumeShuttle uses two acquisitions to increase coverage, decrease dose, and conserve on contrast administration. Color-Coding for Kids applies the Broselow-Luten Pediatric System to facilitate pediatric emergency care and reduce medical errors. FeatherLight achieves dose optimization through pediatric procedure-based protocols. Adventure Series scanners provide a child-friendly imaging environment promoting patient cooperation with resultant reduction in retakes and patient motion. Philips CT Dose Optimization Tools and Advanced Reconstruction Presentation Time: 11:45 ‘ 12:15 PM The first part of the talk will cover “Dose Reduction and Dose Optimization Technologies” present in Philips CT Scanners. The main Technologies to be presented include: DoseRight and tube current modulation (DoseRight, Z-DOM, 3D-DOM, DoseRight Cardiac) Special acquisition modes Beam filtration and beam shapers Eclipse collimator and ClearRay collimator NanoPanel detector DoseRight will cover automatic tube current selection that automatically adjusts the dose for the individual patient. The presentation will explore the modulation techniques currently employed in Philips CT scanners and will include the algorithmic concepts as well as illustrative examples. Modulation and current selection technologies to be covered include the Automatic Current Selection component of DoseRight, ZDOM longitudinal dose modulation, 3D-DOM (combination of longitudinal and rotational dose modulation), Cardiac Dose right (an ECG based dose modulation scheme), and the DoseRight Index (DRI) IQ index. The special acquisition modes covers acquisition techniques such as prospective gating that is designed to reduce exposure to the patient through the Cardiac Step and Shoot scan mode. This mode can substitute the much higher dose retrospective scan modes for certain types of cardiac imaging. The beam filtration and beam shaper portion will discuss the variety of filtration and beam shaping configurations available on Philips scanners. This topic includes the x-ray beam characteristics, tube filtration as well as dose compensator characteristics. The Eclipse collimator, ClearRay collimator and the NanoPanel detector portion will discuss additional technologies specific to wide coverage CT that address some of the unique challenges encountered and techniques employed to optimize image quality and optimize dose utilization. The Eclipse collimator reduces extraneous exposure by actively blocking the radiation tails at either end of helical scans that do not contribute to the image generation. The ClearRay collimator and the NanoPanel detector optimize the quality of the signal that reaches the detectors by addressing the increased scattered radiation present in wide coverage and the NanoPanel detector adds superior electronic noise characteristics valuable when imaging at a low dose level. The second part of the talk will present “Advanced Reconstruction Technologies” currently available on Philips CT Scanners. The talk will cover filtered back projection (FBP), iDose4 and Iterative Model Reconstruction (IMR). Each reconstruction method will include a discussion of the algorithm as well as similarities and differences between the algorithms. Examples illustrating the merits of each algorithm will be presented, and techniques and metrics to characterize the performance of each type of algorithm will be presented. The Filtered Back projection portion will discuss and provide a brief summary of relevant standard image reconstruction techniques in common use, and discuss the common tradeoffs when using the FBP algorithm. The iDose4 portion will present the algorithms used for iDose4 as well the different levels. The meaning of different levels of iDose4 available will be presented and quantified. Guidelines for selection iDose4 parameters based on the imaging need will be explained. The different image quality goals available with iDose4 and specifically how iDose4 enables noise reduction, spatial resolution improvement or both will be explained. The approaches to leveraging the benefits of iDose4 such as improved spatial resolution, decreased noise, and artifact prevention will be described and quantified; and measurements and metrics behind the improvements will be presented. The image quality benefits in specific imaging situations as well as how to best combine the technology with other dose reduction strategies to ensure the best image quality at a given dose level will be presented. Insight into the IMR algorithm as well as contrast to the iDose4 techniques and performance characteristics will be discussed. Metrics and techniques for characterizing this class of algorithm and IQ performance will be presented. The image quality benefits and the dose reduction capabilities of IMR will be explored. Illustrative examples of the noise reduction, spatial resolution improvement, and low contrast detectability improvements of the reconstruction method will be presented: clinical cases and phantom measurements demonstrating the benefits of IMR in the areas of low dose imaging, spatial resolution and low contrast resolution are discussed and the technical details behind the measurements will be presented compared to both iDose4 and traditional filtered back projection (FBP)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

SREMI: Super-resolution electromagnetic imaging with single-channel ground-penetrating radar

High-resolution near-surface imaging has important applications in civil engineering, infrastructure inspection, military threat detection, geological characterization, and lunar and planetary exploration. Zero-offset, singlechannel ground penetrating radar (GPR) imaging is an established technique for near-surface target imaging and sensing but often suffers from low spatial resolution and imaging artifacts, especially of deep structures. In response, we formulate the GPR imaging as a dual-sparsity optimization problem, and develop a super-resolution electromagnetic imaging method based on a fast iterative shrinkage-thresholding algorithm. We develop our GPR imaging method in the framework of electromagnetic exploding-reflectors simulation theory, therefore the imaging method is computationally efficient. In this work, we demonstrate through synthetic and field data examples that our method can produce sharper, more reliable images with fewer artifacts compared with single-pass reverse-time migration GPR method, thus leading to improved near-surface interpretation and object identification.

58 GEOSCIENCES↗
DOE OSTI2014

An efficient computational scheme for electronic excitation spectra of molecules in solution using the symmetry-adapted cluster–configuration interaction method: The accuracy of excitation energies and intuitive charge-transfer indices

Solvent effects on electronic excitation spectra are considerable in many situations; therefore, we propose an efficient and reliable computational scheme that is based on the symmetry-adapted cluster-configuration interaction (SAC-CI) method and the polarizable continuum model (PCM) for describing electronic excitations in solution. The new scheme combines the recently proposed first-order PCM SAC-CI method with the PTE (perturbation theory at the energy level) PCM SAC scheme. This is essentially equivalent to the usual SAC and SAC-CI computations with using the PCM Hartree-Fock orbital and integrals, except for the additional correction terms that represent solute-solvent interactions. The test calculations demonstrate that the present method is a very good approximation of the more costly iterative PCM SAC-CI method for excitation energies of closed-shell molecules in their equilibrium geometry. This method provides very accurate values of electric dipole moments but is insufficient for describing the charge-transfer (CT) indices in polar solvent. The present method accurately reproduces the absorption spectra and their solvatochromism of push-pull type 2,2{sup ′}-bithiophene molecules. Significant solvent and substituent effects on these molecules are intuitively visualized using the CT indices. The present method is the simplest and theoretically consistent extension of SAC-CI method for including PCM environment, and therefore, it is useful for theoretical and computational spectroscopy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Iterative HOMER with uncertainties

We present iHOMER, an iterative version of the HOMER method to extract Lund fragmentation functions from experimental data. Through iterations, we address the information gap between latent and observable phase spaces and systematically remove bias. To quantify uncertainties on the inferred weights, we use a combination of Bayesian neural networks and uncertainty-aware regression. We find that the combination of iterations and uncertainty quantification produces well-calibrated weights that accurately reproduce the data distribution. A parametric closure test shows that the iteratively learned fragmentation function is compatible with the true fragmentation function.

Butter, Anja [Heidelberg Univ. (Germany); Sorbonne↗
DOE OSTI2014

Analytic Evolution of Singular Distribution Amplitudes in QCD

We describe a method of analytic evolution of distribution amplitudes (DA) that have singularities, such as non-zero values at the end-points of the support region, jumps at some points inside the support region and cusps. We illustrate the method by applying it to the evolution of a flat (constant) DA, anti-symmetric at DA and then use it for evolution of the two-photon generalized distribution amplitude. Our approach has advantages over the standard method of expansion in Gegenbauer polynomials, which requires infinite number of terms in order to accurately reproduce functions in the vicinity of singular points, and over a straightforward iteration of an initial distribution with evolution kernel. The latter produces logarithmically divergent terms at each iteration, while in our method the logarithmic singularities are summed from the start, which immediately produces a continuous curve, with only one or two iterations needed afterwards in order to get rather precise results.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Comparison of multigrid algorithms for high‐order continuous finite element discretizations

Summary We present a comparison of different multigrid approaches for the solution of systems arising from high‐order continuous finite element discretizations of elliptic partial differential equations on complex geometries. We consider the pointwise Jacobi, the Chebyshev‐accelerated Jacobi, and the symmetric successive over‐relaxation smoothers, as well as elementwise block Jacobi smoothing. Three approaches for the multigrid hierarchy are compared: (1) high‐order h ‐multigrid, which uses high‐order interpolation and restriction between geometrically coarsened meshes; (2) p ‐multigrid, in which the polynomial order is reduced while the mesh remains unchanged, and the interpolation and restriction incorporate the different‐order basis functions; and (3) a first‐order approximation multigrid preconditioner constructed using the nodes of the high‐order discretization. This latter approach is often combined with algebraic multigrid for the low‐order operator and is attractive for high‐order discretizations on unstructured meshes, where geometric coarsening is difficult. Based on a simple performance model, we compare the computational cost of the different approaches. Using scalar test problems in two and three dimensions with constant and varying coefficients, we compare the performance of the different multigrid approaches for polynomial orders up to 16. Overall, both h ‐multigrid and p ‐multigrid work well; the first‐order approximation is less efficient. For constant coefficients, all smoothers work well. For variable coefficients, Chebyshev and symmetric successive over‐relaxation smoothing outperform Jacobi smoothing. While all of the tested methods converge in a mesh‐independent number of iterations, none of them behaves completely independent of the polynomial order. When multigrid is used as a preconditioner in a Krylov method, the iteration number decreases significantly compared with using multigrid as a solver. Copyright © 2015 John Wiley & Sons, Ltd.

Sundar, Hari↗
DOE OSTI2015

Multi-GPU implementation of a VMAT treatment plan optimization algorithm

Purpose: Volumetric modulated arc therapy (VMAT) optimization is a computationally challenging problem due to its large data size, high degrees of freedom, and many hardware constraints. High-performance graphics processing units (GPUs) have been used to speed up the computations. However, GPU’s relatively small memory size cannot handle cases with a large dose-deposition coefficient (DDC) matrix in cases of, e.g., those with a large target size, multiple targets, multiple arcs, and/or small beamlet size. The main purpose of this paper is to report an implementation of a column-generation-based VMAT algorithm, previously developed in the authors’ group, on a multi-GPU platform to solve the memory limitation problem. While the column-generation-based VMAT algorithm has been previously developed, the GPU implementation details have not been reported. Hence, another purpose is to present detailed techniques employed for GPU implementation. The authors also would like to utilize this particular problem as an example problem to study the feasibility of using a multi-GPU platform to solve large-scale problems in medical physics. Methods: The column-generation approach generates VMAT apertures sequentially by solving a pricing problem (PP) and a master problem (MP) iteratively. In the authors’ method, the sparse DDC matrix is first stored on a CPU in coordinate list format (COO). On the GPU side, this matrix is split into four submatrices according to beam angles, which are stored on four GPUs in compressed sparse row format. Computation of beamlet price, the first step in PP, is accomplished using multi-GPUs. A fast inter-GPU data transfer scheme is accomplished using peer-to-peer access. The remaining steps of PP and MP problems are implemented on CPU or a single GPU due to their modest problem scale and computational loads. Barzilai and Borwein algorithm with a subspace step scheme is adopted here to solve the MP problem. A head and neck (H and N) cancer case is then used to validate the authors’ method. The authors also compare their multi-GPU implementation with three different single GPU implementation strategies, i.e., truncating DDC matrix (S1), repeatedly transferring DDC matrix between CPU and GPU (S2), and porting computations involving DDC matrix to CPU (S3), in terms of both plan quality and computational efficiency. Two more H and N patient cases and three prostate cases are used to demonstrate the advantages of the authors’ method. Results: The authors’ multi-GPU implementation can finish the optimization process within ∼1 min for the H and N patient case. S1 leads to an inferior plan quality although its total time was 10 s shorter than the multi-GPU implementation due to the reduced matrix size. S2 and S3 yield the same plan quality as the multi-GPU implementation but take ∼4 and ∼6 min, respectively. High computational efficiency was consistently achieved for the other five patient cases tested, with VMAT plans of clinically acceptable quality obtained within 23–46 s. Conversely, to obtain clinically comparable or acceptable plans for all six of these VMAT cases that the authors have tested in this paper, the optimization time needed in a commercial TPS system on CPU was found to be in an order of several minutes. Conclusions: The results demonstrate that the multi-GPU implementation of the authors’ column-generation-based VMAT optimization can handle the large-scale VMAT optimization problem efficiently without sacrificing plan quality. The authors’ study may serve as an example to shed some light on other large-scale medical physics problems that require multi-GPU techniques.

60 APPLIED LIFE SCIENCES↗