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Optimal Bandwidth for Multitaper Spectrum Estimation

A systematic method for bandwidth parameter selection is desired for Thomson multitaper spectrum estimation. We give a method for determining the optimal bandwidth based on a mean squared error (MSE) criterion. When the true spectrum has a second-order Taylor series expansion, one can express quadratic local bias as a function of the curvature of the spectrum, which can be estimated by using a simple spline approximation. This is combined with a variance estimate, obtained by jackknifing over individual spectrum estimates, to produce an estimated MSE for the log spectrum estimate for each choice of time-bandwidth product. The bandwidth that minimizes the estimated MSE then gives the desired spectrum estimate. Additionally, the bandwidth obtained using our method is also optimal for cepstrum estimates. We give an example of a damped oscillatory (Lorentzian) process in which the approximate optimal bandwidth can be written as a function of the damping parameter. Furthermore, the true optimal bandwidth agrees well with that given by minimizing estimated the MSE in these examples.

97 MATHEMATICS AND COMPUTING↗

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 ↗

Principles of water oxidation and O2-based hydrocarbon transformation by multinuclear catalytic sites

Abstract The central thrust of this integrated experimental and computational research program was to obtain an atomistic-level understanding of the structural and dynamic factors underlying the design of catalysts for water oxidation and selective reductant-free O2-based transformations. The focus was on oxidatively robust polyoxometalate (POM) complexes in which a catalytic active site interacts with proximal metal centers in a synergistic manner. Thirty five publications in high-impact journals arose from this grant. I. Developing an oxidatively and hydrolytically stable and fast water oxidation catalyst (WOC), a central need in the production of green fuels using water as a reductant, has proven particularly challenging. During this grant period we have designed and investigated several carbon-free, molecular (homogenous), oxidatively and hydrolytically stable WOCs, including the Rb8K2[{Ru4O4(OH)2(H2O)4}(γ-SiW10O36)2]·25H2O (1) and [Co4(H2O)2(α-PW9O34)2]10- (2). Although complex 1 is fast, oxidatively and hydrolytically stable WOC, Ru is neither abundant nor inexpensive. Therefore, development of a stable and fast carbon-free homogenous WOC, based on earth-abundant elements became our highest priority. In 2010, we reported the first such catalyst, complex 2. This complex is substantially faster than 1 and stable under homogeneous conditions. Recently, we have extended our efforts and reported a V2-analog of the complex 2, i.e. [Co4(H2O)2(α-VW9O34)2]10- (3), which shows an even greater stability and reactivity. We succeeded in: (a) immobilizing catalysts 1 and 2 on the surface of various electrodes, and (b) elucidating the mechanism of O2 formation and release from complex 1, as well as the Mn4O4L6 “cubane” cluster. We have shown that the direct O-O bond formation is the most likely pathway for O2 formation during water oxidation catalyzed by 1. II. Oxo transfer catalysts that contain two proximal and synergistically interacting redox active metal centers in the active site form another part of considerable interest of our grant because species with such sites [including methane monooxygenase (MMO) and more] are some of the most effective oxygenase catalysts known. Our team conducted the following research on γ-M2-Keggin complexes: (a) investigated stability of the trimer [{Fe3(OH)3(H2O)2}3(γ-SiW10O36)3]15-, 4, in water, and developed the chemistry and catalysis of the di-iron centered POM, [γ(1,2)-SiW10{Fe(OH)}2O38]6-, 5, in organic solvents (Figure 2). We also study the thermodynamic and structural stability of γ-M2-Keggin in aqueous media for different M’s (d-electron metals). We have defined two structural classes of POMs with proximally bound d-electron metal centers. We refer to these structural isomers of the {γ-M2SiW10} family of POMs as “in-pocket” and “out-of pocket”. We have elucidated the factors controlling the structure and stability of the V, Fe, Ru, Tc, Mo and Rh derivatives of [(SiO4)M2(OH)2W10O32]4- using a range of computational tools. We have: (a) demonstrated that heteroatom X in these polyanions may function as an “internal switch” for defining the ground electronic states and, consequently, the reactivity of the γ-M2-Keggin POM complexes; (b) elucidated reactivity of divacant lacunary species and polyperoxotungstates (PPTs), {Xn+O4[WO(O2)2]4}n-, which could be degradation products of γ-M2-Keggin complexes in aqueous media; (c) elucidated the role of the POM ligand in stabilization of {Ru2} and {(Ru-oxo)2} fragments in the reactant and product of the reaction of {γ-[(Xn+O4)Ru2(OH)2W10O32]}(8-n)- (where X = Si4+, P5+ and S6+) with O2, and (d) the mechanisms of olefin epoxidation catalyzed by these di-d-transition metal substituted and divacant lacunary γ-M2-Keggin complexes. III. Complementing the efforts presented above was the development of less time-consuming but reasonably accurate computational methods allowing one to explore more deeply large catalytic systems. We developed Reactive Force Field (ReaxFF) to study interaction of the targeted POMs with water, proton and hydroxide ions in the liquid phase. We tested our ReaxFF parameters on the Lindqvist POMs, M6O19n-, where M = Nb and Ta. These parameters are made available as part of the ReaxFF code. In addition, we have developed parameters for Sc, Ti, Fe, Co and Ni in combination with H, C, N, O, as well as the same metal (M-M) for the spin-polarized self-consistent-charge density-functional tight-binding (DFTB) method. Test calculations showed that the DFTB method with the present parameters in most cases reproduces structural properties very well. These parameters are made available as part of the DFTB code. Thus, this DOE BES funded research project has clarified several key areas impacting (a) water oxidation and O2-based hydrocarbon transformation, (b) stabilization of key structures and catalytic intermediates in such processes, (c) immobilization of molecular catalysts on metal oxide surfaces, and (d) application of optimal computational methods to study reaction dynamics in large systems.

58 GEOSCIENCES↗

Adaptive Sampling-Based Bi-Fidelity Stochastic Trust Region Method for Stochastic Derivative-Free Optimization

Bi-fidelity stochastic optimization has gained increasing attention as an efficient approach to reduce computational costs by leveraging a low-fidelity (LF) model to optimize an expensive high-fidelity (HF) objective. In this paper, we propose ASTRO-BFDF, an adaptive sampling trust-region method specifically designed for unconstrained bi-fidelity stochastic derivative-free optimization problems. In ASTRO-BFDF, the LF function serves two purposes: (i) to identify better iterates for the HF function when the optimization process indicates a high correlation between them and (ii) to reduce the variance of the HF function estimates using bi-fidelity Monte Carlo (BFMC). The algorithm dynamically determines sample sizes while adaptively choosing between crude Monte Carlo and BFMC to balance the trade-off between optimization and sampling errors. We prove that the iterates generated by ASTRO-BFDF converge to a first-order stationary point almost surely. Additionally, we demonstrate the effectiveness of the proposed algorithm through numerical experiments on synthetic benchmarks and simulation optimization problems involving discrete event systems.

97 MATHEMATICS AND COMPUTING↗

A Method to Alleviate the Long History Problem Encountered in Monte Carlo Simulations via Weight Window Variance Reduction

When the weight window is implemented in large and complex models, streaming path and deep penetration could lead to a long history problem that takes a disproportionate amount of time for the accomplishment of Monte Carlo simulations and exerts a detrimental effect on the efficiency of parallel computing. An approach set the limitation of weight window splitting was proposed for the alleviation of long history problem. Tests were conducted on a streaming dog-leg geometry model and a 3D model of the Chinese Fusion Engineering Testing Reactor. The results show that a suitable parameter in the alleviation method could optimize both the performance of variance reduction and the efficiency of parallel calculation, which makes long history problem tractable.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Inclusion of trial functions in the Langevin equation path integral ground state method: Application to parahydrogen clusters and their isotopologues

We developed and studied the implementation of trial wavefunctions in the newly proposed Langevin equation Path Integral Ground State (LePIGS) method [S. Constable, M. Schmidt, C. Ing, T. Zeng, and P.-N. Roy, J. Phys. Chem. A 117, 7461 (2013)]. The LePIGS method is based on the Path Integral Ground State (PIGS) formalism combined with Path Integral Molecular Dynamics sampling using a Langevin equation based sampling of the canonical distribution. This LePIGS method originally incorporated a trivial trial wavefunction, ψ{sub T}, equal to unity. The present paper assesses the effectiveness of three different trial wavefunctions on three isotopes of hydrogen for cluster sizes N = 4, 8, and 13. The trial wavefunctions of interest are the unity trial wavefunction used in the original LePIGS work, a Jastrow trial wavefunction that includes correlations due to hard-core repulsions, and a normal mode trial wavefunction that includes information on the equilibrium geometry. Based on this analysis, we opt for the Jastrow wavefunction to calculate energetic and structural properties for parahydrogen, orthodeuterium, and paratritium clusters of size N = 4 − 19, 33. Energetic and structural properties are obtained and compared to earlier work based on Monte Carlo PIGS simulations to study the accuracy of the proposed approach. The new results for paratritium clusters will serve as benchmark for future studies. This paper provides a detailed, yet general method for optimizing the necessary parameters required for the study of the ground state of a large variety of systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Gray-Box Modeling for Distribution Systems With Inverter-Based Resources: Integrating Physics-Based and Data-Driven Approaches

Here, in this paper, we develop a novel gray-box modeling approach for distribution systems with inverter-based resources (IBRs). The proposed gray-box modeling method aims to improve estimation accuracy by taking advantages of both physics-based (white-box) and data-driven (black-box) modeling approaches. To this end, we utilize partial physical knowledge of the system, including the inverters’ structures and control diagrams, as well as the equivalent network model simplified through Kron reduction. The white-box model containing unknown parameters is then constructed with mathematical equations and an optimization-based method is subsequently employed to identify these unknown parameters within the white-box model. Next, the graybox modeling framework is then constructed by embedding the output variables of the white-box model into the input vector of a black-box model (represented using a neural network). Finally, the black-box section is trained using the collected input-output datasets and the gray-box model is then obtained. Furthermore, case studies demonstrate that our gray-box modeling approach effectively improves estimation accuracy compared to purely physics-based or data-driven methods.

42 ENGINEERING↗

Plan averaging for multicriteria navigation of sliding window IMRT and VMAT

Purpose: To describe a method for combining sliding window plans [intensity modulated radiation therapy (IMRT) or volumetric modulated arc therapy (VMAT)] for use in treatment plan averaging, which is needed for Pareto surface navigation based multicriteria treatment planning. Methods: The authors show that by taking an appropriately defined average of leaf trajectories of sliding window plans, the authors obtain a sliding window plan whose fluence map is the exact average of the fluence maps corresponding to the initial plans. In the case of static-beam IMRT, this also implies that the dose distribution of the averaged plan is the exact dosimetric average of the initial plans. In VMAT delivery, the dose distribution of the averaged plan is a close approximation of the dosimetric average of the initial plans. Results: The authors demonstrate the method on three Pareto optimal VMAT plans created for a demanding paraspinal case, where the tumor surrounds the spinal cord. The results show that the leaf averaged plans yield dose distributions that approximate the dosimetric averages of the precomputed Pareto optimal plans well. Conclusions: The proposed method enables the navigation of deliverable Pareto optimal plans directly, i.e., interactive multicriteria exploration of deliverable sliding window IMRT and VMAT plans, eliminating the need for a sequencing step after navigation and hence the dose degradation that is caused by such a sequencing step.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Multistage Stabilized Continuation for Indirect Optimal Control of Three-Dimensional Hypersonic Trajectories

This work presents the development of a multistaged stabilized continuation for the three-dimensional unpowered hypersonic trajectory planning problem using indirect optimal control methods. The stabilized continuation method is noniterative and guaranteed to terminate within a finite number of floating point operations, thereby making it well suited for onboard autonomous implementations. Here, we present a multistage formulation of the stabilized continuation scheme that involves starting with a “loose” integration tolerance during the first stage and ramping up toward a “strict” integration tolerance through subsequent stages. An important benefit of this approach is that even when the solution to the underlying optimal control problem is numerically unstable, such as with the hypersonic vehicle footprint generation problem, the stabilized continuation algorithm is shown to be successful in finding a solution while providing some additional insights into the underlying cause of the numerical instability.

33 ADVANCED PROPULSION SYSTEMS↗

SU-E-T-592: Relationship Between Dose of Distribution and Area of Segment Fields Among Different Intensity-Modulated Radiotherapy Planning in Cervix Cancer

Purpose: In premise of uninfluenced to dose distribution of tumor target and organ at risk(OAR) in cervical cancer,area of segment fields was changed to increase efficacy and optimize treatment method by designing different plan of intensity modulated radiotherapy(IMRT). Methods: 12 cases of cervical cancer were confirmed in pathology and treated with step and shoot IMRT. Dose of PTV was 50Gy/25fractions. Every patient was designed 9 treatment plans of IMRT by Pinnacle 8.0m planning system,each plan was used with 9 beams of uniform distribution and fixing incidence direction(200°,240°,280°,320°,0°,40°,80°,120°and 160°respectively),and designed for delivery on Elekta Synergy linear accelerator. All plans were optimized with the direct machine parameter optimization(DMPO) algorithm using the same set of optimization objectives. Number of maximum segment field was defined at 80 and minimum MU in each segment was 5MU,and minimal segment area was 2*1cm{sup 2},2*2cm{sup 2},3*3cm{sup 2},4*4cm{sup 2},5*5cm{sup 2},6*6cm{sup 2},7*7cm{sup 2},8*8cm{sup 2}and 9*9cm{sup 2},respectively.Coverage,homogeneity and conformity of PTV,sparing of OAR, MU and number of segment were compared. Results: In this group, mean volume of PTV was 916.8±228.7 cm{sup 3}. Compared with the area of minimal segment field increased from 2*1cm{sup 2} to 9*9 cm{sup 2},the number of mean MU was decreased from 1405±170 to 490±47 and the number of segment field was reduced from 76±4 to 39±7 respectively(p<0.05). When the limit of minimal segment area was increased from 2*1cm{sup 2} to 7*7 cm{sup 2},dose distribution of PTV,OAR,CI,HI and V{sub 2} {sub 3} were not different (p>0.05),but when the minimal segment area was 8*8 cm{sup 2} and 9*9 cm{sup 2},they were changed compared with 7*7 cm{sup 2} and below(p<0.05). Conclusion: The minimal segment field of IMRT plan designed by Pinnacle 8.0m planning system in cervical carcinoma should be enlarge reasonably and minimal segment area of 7*7 cm{sup 2} was recommend.

60 APPLIED LIFE SCIENCES↗

Extended Lagrangian Born-Oppenheimer molecular dynamics in the limit of vanishing self-consistent field optimization

We present an efficient general approach to first principles molecular dynamics simulations based on extended Lagrangian Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] in the limit of vanishing self-consistent field optimization. The reduction of the optimization requirement reduces the computational cost to a minimum, but without causing any significant loss of accuracy or long-term energy drift. The optimization-free first principles molecular dynamics requires only one single diagonalization per time step, but is still able to provide trajectories at the same level of accuracy as “exact,” fully converged, Born-Oppenheimer molecular dynamics simulations. The optimization-free limit of extended Lagrangian Born-Oppenheimer molecular dynamics therefore represents an ideal starting point for robust and efficient first principles quantum mechanical molecular dynamics simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Viscosity Meaurement Technique for Metal Fuels

Metallic fuels have exceptional transient behavior, excellent thermal conductivity, and a more straightforward reprocessing path, which does not separate out pure plutonium from the process stream. Fabrication of fuel containing minor actinides and rare earth (RE) elements for irradiation tests, for instance, U-20Pu-3Am-2Np-1.0RE-15Zr samples at the Idaho National Laboratory, is generally done by melt casting in an inert atmosphere. For the design of a casting system and further scale up development, computational modeling of the casting process is needed to provide information on melt flow and solidification for process optimization. Therefore, there is a need for melt viscosity data, the most important melt property that controls the melt flow. The goal of the project was to develop a measurement technique that uses fully sealed melt sample with no Americium vapor loss to determine the viscosity of metallic melts and at temperatures relevant to the casting process. The specific objectives of the project were to: develop mathematical models to establish the principle of the measurement method, design and build a viscosity measurement prototype system based on the established principle, and calibrate the system and quantify the uncertainty range. The result of the project indicates that the oscillation cup technique is applicable for melt viscosity measurement. Detailed mathematical models of innovative sample ampoule designs were developed to not only determine melt viscosity, but also melt density under certain designs. Measurement uncertainties were analyzed and quantified. The result of this project can be used as the initial step toward the eventual goal of establishing a viscosity measurement system for radioactive melts.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Optimal control to handle variations in moisture content and reactor in-feed rate

The variations in feedstock characteristics, such as moisture and particle size distribution, lead to an inconsistent flow of feedstock from the biomass pre-processing system to the reactor in-feed system. These inconsistencies result in low on-stream times at the reactor in-feed equipment. This research develops an optimal process control method for a biomass pre-processing system comprised of milling and densification operations to provide the consistent flow of feedstock to a reactor's throat. This method uses a mixed-integer optimization model to identify optimal bale sequencing, equipment in-feed rate, and buffer location and size in the biomass pre-processing system. This method, referred to as the hybrid process control (HPC), aims to maximize throughput over time. We compare HPC with a baseline feed forward process control. Our case study based on switchgrass finds that HPC reduces the variation of a reactor's feeding rate by up to 100% without increasing the operating cost of the biomass pre-processing system for biomass with moisture ranging from 10 to 25%. Additionally, HPC reduces the cost of processing biomass by 0.36%–2.22%, and reduces processing time by 0.35%-2.24%. Furthermore, a biorefinery can adapt HPC to achieve its design capacity.

09 BIOMASS FUELS↗

Adaptive Power Flow Approximations With Second-Order Sensitivity Insights

The power flow equations are fundamental to power system planning, analysis, and control. However, the inherent non-linearity and non-convexity of these equations present formidable obstacles in problem-solving processes. To mitigate these challenges, recent research has proposed adaptive power flow linearizations that aim to achieve accuracy over wide operating ranges. The accuracy of these approximations inherently depends on the curvature of the power flow equations within these ranges, which necessitates considering second-order sensitivities. In this paper, we leverage second-order sensitivities to both analyze and improve power flow approximations. We evaluate the curvature across broad operational ranges and subsequently utilize this information to inform the computation of various sample-based power flow approximation techniques. Additionally, we leverage second-order sensitivities to guide the development of rational approximations that yield linear constraints in optimization problems. In conclusion, this approach is extended to enhance accuracy beyond the limitations of linear functions across varied operational scenarios.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Intersection-distribution-based remapping between arbitrary meshes for staggered multi-material arbitrary Lagrangian-Eulerian hydrodynamics

In this paper, we present a new intersection-distribution-based remapping method between arbitrary polygonal meshes for indirect staggered multi-material arbitrary Lagrangian-Eulerian hydrodynamics. All cell-centered material quantities are conservatively remapped using intersections between the Lagrangian (old, source) mesh and the rezoned (new, target) mesh. The new nodal masses are obtained by conservative distribution of all material masses in each new cell to the cell's corners and then collecting those corner masses at new nodes. This distribution is done using a local constrained optimization approach for each cell in the new mesh. In order to remap nodal momentum we first define cell-centered momentum for each cell in the old mesh, conservatively remap this to the new mesh and then conservatively distribute the new zonal momentum to each cell's bounding nodes, again using local constrained optimization. Our method also conserves total energy by applying a new nodal kinetic energy correction that relies on a process similar to that used for remapping nodal mass and momentum. Cell-centered kinetic energy is computed, conservatively remapped and then distributed to nodes. The discrepancy between this conservatively remapped and actual nodal kinetic energy is then conservatively distributed to the internal energies of the materials in the cells surrounding each node. Unlike conventional cell-based corrections of this type, this new nodal kinetic energy correction has not been observed to drive material internal energy negative in any of our testing. Unlike flux based remapping, our new intersection-distribution method can be applied to remapping between source and target meshes that are arbitrarily different, which provides superior flexibility in the rezoning strategy. Our method is accurate, essentially conservative and essentially bounds preserving.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Optimization of an on-board imaging system for extremely rapid radiation therapy

Purpose: Next-generation extremely rapid radiation therapy systems could mitigate the need for motion management, improve patient comfort during the treatment, and increase patient throughput for cost effectiveness. Such systems require an on-board imaging system that is competitively priced, fast, and of sufficiently high quality to allow good registration between the image taken on the day of treatment and the image taken the day of treatment planning. In this study, three different detectors for a custom on-board CT system were investigated to select the best design for integration with an extremely rapid radiation therapy system. Methods: Three different CT detectors are proposed: low-resolution (all 4 × 4 mm pixels), medium-resolution (a combination of 4 × 4 mm pixels and 2 × 2 mm pixels), and high-resolution (all 1 × 1 mm pixels). An in-house program was used to generate projection images of a numerical anthropomorphic phantom and to reconstruct the projections into CT datasets, henceforth called “realistic” images. Scatter was calculated using a separate Monte Carlo simulation, and the model included an antiscatter grid and bowtie filter. Diagnostic-quality images of the phantom were generated to represent the patient scan at the time of treatment planning. Commercial deformable registration software was used to register the diagnostic-quality scan to images produced by the various on-board detector configurations. The deformation fields were compared against a “gold standard” deformation field generated by registering initial and deformed images of the numerical phantoms that were used to make the diagnostic and treatment-day images. Registrations of on-board imaging system data were judged by the amount their deformation fields differed from the corresponding gold standard deformation fields—the smaller the difference, the better the system. To evaluate the registrations, the pointwise distance between gold standard and realistic registration deformation fields was computed. Results: By most global metrics (e.g., mean, median, and maximum pointwise distance), the high-resolution detector had the best performance but the medium-resolution detector was comparable. For all medium- and high-resolution detector registrations, mean error between the realistic and gold standard deformation fields was less than 4 mm. By pointwise metrics (e.g., tracking a small lesion), the high- and medium-resolution detectors performed similarly. For these detectors, the smallest error between the realistic and gold standard registrations was 0.6 mm and the largest error was 3.6 mm. Conclusions: The medium-resolution CT detector was selected as the best for an extremely rapid radiation therapy system. In essentially all test cases, data from this detector produced a significantly better registration than data from the low-resolution detector and a comparable registration to data from the high-resolution detector. The medium-resolution detector provides an appropriate compromise between registration accuracy and system cost.

60 APPLIED LIFE SCIENCES↗

Binary optimal control by trust-region steepest descent

Abstract We present a trust-region steepest descent method for dynamic optimal control problems with binary-valued integrable control functions. Our method interprets the control function as an indicator function of a measurable set and makes set-valued adjustments derived from the sublevel sets of a topological gradient function. By combining this type of update with a trust-region framework, we are able to show by theoretical argument that our method achieves asymptotic stationarity despite possible discretization errors and truncation errors during step determination. To demonstrate the practical applicability of our method, we solve two optimal control problems constrained by ordinary and partial differential equations, respectively, and one topological optimization problem.

97 MATHEMATICS AND COMPUTING↗

SU-E-J-12: A New Stereological Method for Tumor Volume Evaluation for Esophageal Cancer

Purpose: Stereological method used to obtain three dimensional quantitative information from two dimensional images is a widely used tool in the study of cells and pathology. But the feasibility of the method for quantitative evaluation of volumes with 3D image data sets for radiotherapy clinical application has not been explored. On the other hand, a quick, easy-to-use and reliable method is highly desired in image-guided-radiotherapy(IGRT) for tumor volume measurement for the assessment of response to treatment. To meet this need, a stereological method for evaluating tumor volumes for esophageal cancer is presented in this abstract. Methods: The stereology method was optimized by selecting the appropriate grid point distances and sample types. 7 patients with esophageal cancer were selected retrospectively for this study, each having pre and post treatment computed tomography (CT) scans. Stereological measurements were performed for evaluating the gross tumor volume (GTV) changes after radiotherapy and the results was compared with the ones by planimetric measurements. Two independent observers evaluated the reproducibility for volume measurement using the new stereological technique. Results: The intraobserver variation in the GTV volume estimation was 3.42±1.68cm3 (the Wilcoxon matched-pairs test Resultwas Z=−1.726,P=0.084>0.05); the interobserver variation in the GTV volume estimation was 22.40±7.23 cm3 (Z=−3.296,P=0.083>0.05), which showed the consistency in GTV volume calculation with the new method for the same and different users. The agreement level between the results from the two techniques was also evaluated. Difference between the measured GTVs was 20.10±5.35 cm3 (Z=−3.101,P=0.089>0.05). Variation of the measurement results using the two techniques was low and clinically acceptable. Conclusion: The good agreement between stereological and planimetric techniques proves the reliability of the stereological tumor volume estimations. The optimized stereological technique described in this abstract may provide a quick, unbiased and reproducible tool for tumor volume estimation for treatment response assessment. Supported by NSFC (#81041107, #81171342 and #31000784)

60 APPLIED LIFE SCIENCES↗