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At least 1,675 records · Page 93
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DOE OSTI2016

Frame average optimization of cine-mode EPID images used for routine clinical in vivo patient dose verification of VMAT deliveries

Purpose: The in vivo 3D dose delivered to a patient during volumetric modulated arc therapy (VMAT) delivery can be calculated using electronic portal imaging device (EPID) images. These images must be acquired in cine-mode (i.e., “movie” mode) in order to capture the time-dependent delivery information. The angle subtended by each cine-mode EPID image during an arc can be changed via the frame averaging number selected within the image acquisition software. A large frame average number will decrease the EPID’s angular resolution and will result in a decrease in the accuracy of the dose information contained within each image. Alternatively, less EPID images acquired per delivery will decrease the overall 3D patient dose calculation time, which is appealing for large-scale clinical implementation. Therefore, the purpose of this study was to determine the optimal frame average value per EPID image, defined as the highest frame averaging that can be used without an appreciable loss in 3D dose reconstruction accuracy for VMAT treatments. Methods: Six different VMAT plans and six different SBRT-VMAT plans were delivered to an anthropomorphic phantom. Delivery was carried out on a Varian 2300ix model linear accelerator (Linac) equipped with an aS1000 EPID running at a frame acquisition rate of 7.5 Hz. An additional PC was set up at the Linac console area, equipped with specialized frame-grabber hardware and software packages allowing continuous acquisition of all EPID frames during delivery. Frames were averaged into “frame-averaged” EPID images using MATLAB. Each frame-averaged data set was used to calculate the in vivo dose to the patient and then compared to the single EPID frame in vivo dose calculation (the single frame calculation represents the highest possible angular resolution per EPID image). A mean percentage dose difference of low dose (<20% prescription dose) and high dose regions (>80% prescription dose) was calculated for each frame averaged scenario for each plan. The authors defined their unacceptable loss of accuracy as no more than a ±1% mean dose difference in the high dose region. Optimal frame average numbers were then determined as a function of the Linac’s average gantry speed and the dose per fraction. Results: The authors found that 9 and 11 frame averages were suitable for all VMAT and SBRT-VMAT treatments, respectively. This resulted in no more than a 1% loss to any of the dose region’s mean percentage difference when compared to the single frame reconstruction. The optimized number was dependent on the treatment’s dose per fraction and was determined to be as high as 14 for 12 Gy/fraction (fx), 15 for 8 Gy/fx, 11 for 6 Gy/fx, and 9 for 2 Gy/fx. Conclusions: The authors have determined an optimal EPID frame averaging number for multiple VMAT-type treatments. These are given as a function of the dose per fraction and average gantry speed. These optimized values are now used in the authors’ clinical, 3D, in vivo patient dosimetry program. This provides a reduction in calculation time while maintaining the authors’ required level of accuracy in the dose reconstruction.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2016

Cherenkov imaging method for rapid optimization of clinical treatment geometry in total skin electron beam therapy

Purpose: A method was developed utilizing Cherenkov imaging for rapid and thorough determination of the two gantry angles that produce the most uniform treatment plane during dual-field total skin electron beam therapy (TSET). Methods: Cherenkov imaging was implemented to gather 2D measurements of relative surface dose from 6 MeV electron beams on a white polyethylene sheet. An intensified charge-coupled device camera time-gated to the Linac was used for Cherenkov emission imaging at sixty-two different gantry angles (1° increments, from 239.5° to 300.5°). Following a modified Stanford TSET technique, which uses two fields per patient position for full body coverage, composite images were created as the sum of two beam images on the sheet; each angle pair was evaluated for minimum variation across the patient region of interest. Cherenkov versus dose correlation was verified with ionization chamber measurements. The process was repeated at source to surface distance (SSD) = 441, 370.5, and 300 cm to determine optimal angle spread for varying room geometries. In addition, three patients receiving TSET using a modified Stanford six-dual field technique with 6 MeV electron beams at SSD = 441 cm were imaged during treatment. Results: As in previous studies, Cherenkov intensity was shown to directly correlate with dose for homogenous flat phantoms (R{sup 2} = 0.93), making Cherenkov imaging an appropriate candidate to assess and optimize TSET setup geometry. This method provided dense 2D images allowing 1891 possible treatment geometries to be comprehensively analyzed from one data set of 62 single images. Gantry angles historically used for TSET at their institution were 255.5° and 284.5° at SSD = 441 cm; however, the angles optimized for maximum homogeneity were found to be 252.5° and 287.5° (+6° increase in angle spread). Ionization chamber measurements confirmed improvement in dose homogeneity across the treatment field from a range of 24.4% at the initial angles, to only 9.8% with the angles optimized. A linear relationship between angle spread and SSD was observed, ranging from 35° at 441 cm, to 39° at 300 cm, with no significant variation in percent-depth dose at midline (R{sup 2} = 0.998). For patient studies, factors influencing in vivo correlation between Cherenkov intensity and measured surface dose are still being investigated. Conclusions: Cherenkov intensity correlates to relative dose measured at depth of maximum dose in a uniform, flat phantom. Imaging of phantoms can thus be used to analyze and optimize TSET treatment geometry more extensively and rapidly than thermoluminescent dosimeters or ionization chambers. This work suggests that there could be an expanded role for Cherenkov imaging as a tool to efficiently improve treatment protocols and as a potential verification tool for routine monitoring of unique patient treatments.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2016

SU-F-J-105: Towards a Novel Treatment Planning Pipeline Delivering Pareto- Optimal Plans While Enabling Inter- and Intrafraction Plan Adaptation

Purpose: To develop a new IMRT treatment planning methodology suitable for the new generation of MR-linear accelerator machines. The pipeline is able to deliver Pareto-optimal plans and can be utilized for conventional treatments as well as for inter- and intrafraction plan adaptation based on real-time MR-data. Methods: A Pareto-optimal plan is generated using the automated multicriterial optimization approach Erasmus-iCycle. The resulting dose distribution is used as input to the second part of the pipeline, an iterative process which generates deliverable segments that target the latest anatomical state and gradually converges to the prescribed dose. This process continues until a certain percentage of the dose has been delivered. Under a conventional treatment, a Segment Weight Optimization (SWO) is then performed to ensure convergence to the prescribed dose. In the case of inter- and intrafraction adaptation, post-processing steps like SWO cannot be employed due to the changing anatomy. This is instead addressed by transferring the missing/excess dose to the input of the subsequent fraction. In this work, the resulting plans were delivered on a Delta4 phantom as a final Quality Assurance test. Results: A conventional static SWO IMRT plan was generated for two prostate cases. The sequencer faithfully reproduced the input dose for all volumes of interest. For the two cases the mean relative dose difference of the PTV between the ideal input and sequenced dose was 0.1% and −0.02% respectively. Both plans were delivered on a Delta4 phantom and passed the clinical Quality Assurance procedures by achieving 100% pass rate at a 3%/3mm gamma analysis. Conclusion: We have developed a new sequencing methodology capable of online plan adaptation. In this work, we extended the pipeline to support Pareto-optimal input and clinically validated that it can accurately achieve these ideal distributions, while its flexible design enables inter- and intrafraction plan adaptation. This research is financially supported by Elekta AB, Stockholm, Sweden.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

MO-DE-204-02: Optimization of the Patient CT Dose in Europe

The main topic of the session is to show how dose optimization is being implemented in various regions of the world, including Europe, Australia, North America and other regions. A multi-national study conducted under International Atomic Energy Agency (IAEA) across more than 50 less resourced countries gave insight into patient radiation doses and safety practices in CT, mammography, radiography and interventional procedures, both for children and adults. An important outcome was the capability development on dose assessment and management. An overview of recent European projects related to CT radiation dose and optimization both to adults and children will be presented. Existing data on DRLs together with a European methodology proposed on establishing and using DRLs for paediatric radiodiagnostic imaging and interventional radiology practices will be shown. Compared with much of Europe at least, many Australian imaging practices are relatively new to the task of diagnostic imaging dose optimisation. In 2008 the Australian Government prescribed a requirement to periodically compare patient radiation doses with diagnostic reference levels (DRLs), where DRLs have been established. Until recently, Australia had only established DRLs for computed tomography (CT). Regardless, both professional society and individual efforts to improved data collection and develop optimisation strategies across a range of modalities continues. Progress in this field, principally with respect to CT and interventional fluoroscopy will be presented. In the US, dose reduction and optimization efforts for computed tomography have been promoted and mandated by several organizations and accrediting entities. This presentation will cover the general motivation, implementation, and implications of such efforts. Learning Objectives: Understand importance of the dose optimization in Diagnostic Radiology. See how this goal is achieved in different regions of the World. Learn about the global trend in the dose optimization and future prospectives. M. Rehani, The work was a part of the work of IAEA where I was an employee and IAEA is a United Nations organization.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

MO-DE-204-04: Dose Optimization in CT: Trends and Motivation in the US

The main topic of the session is to show how dose optimization is being implemented in various regions of the world, including Europe, Australia, North America and other regions. A multi-national study conducted under International Atomic Energy Agency (IAEA) across more than 50 less resourced countries gave insight into patient radiation doses and safety practices in CT, mammography, radiography and interventional procedures, both for children and adults. An important outcome was the capability development on dose assessment and management. An overview of recent European projects related to CT radiation dose and optimization both to adults and children will be presented. Existing data on DRLs together with a European methodology proposed on establishing and using DRLs for paediatric radiodiagnostic imaging and interventional radiology practices will be shown. Compared with much of Europe at least, many Australian imaging practices are relatively new to the task of diagnostic imaging dose optimisation. In 2008 the Australian Government prescribed a requirement to periodically compare patient radiation doses with diagnostic reference levels (DRLs), where DRLs have been established. Until recently, Australia had only established DRLs for computed tomography (CT). Regardless, both professional society and individual efforts to improved data collection and develop optimisation strategies across a range of modalities continues. Progress in this field, principally with respect to CT and interventional fluoroscopy will be presented. In the US, dose reduction and optimization efforts for computed tomography have been promoted and mandated by several organizations and accrediting entities. This presentation will cover the general motivation, implementation, and implications of such efforts. Learning Objectives: Understand importance of the dose optimization in Diagnostic Radiology. See how this goal is achieved in different regions of the World. Learn about the global trend in the dose optimization and future prospectives. M. Rehani, The work was a part of the work of IAEA where I was an employee and IAEA is a United Nations organization.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

MO-FG-CAMPUS-TeP2-03: Multi-Criteria Optimization Using Taguchi Method for SRS of Multiple Lesions by Single Isocenter

Purpose: This study utilizes the Taguchi Method to evaluate the VMAT planning parameters of single isocenter treatment plans for multiple brain metastases. An optimization model based on Taguchi and utility concept is employed to optimize the planning parameters including: arc arrangement, calculation grid size, calculation model, and beam energy on multiple performance characteristics namely conformity index and dose to normal brain. Methods: Treatment plans, each with 4 metastatic brain lesions were planned using single isocenter technique. The collimator angles were optimized to avoid open areas. In this analysis four planning parameters (a–d) were considered: (a)-Arc arrangements: set1: Gantry 181cw179 couch0; gantry179ccw0, couch315; and gantry0ccw181, couch45. set2: set1 plus additional arc: Gantry 0cw179, couch270. (b)-Energy: 6-MV; 6MV-FFF (c)-Calculation grid size: 1mm; 1.5mm (d)-Calculation models: AAA; Acuros Treatment planning was performed in Varian Eclipse (ver.11.0.30). A suitable orthogonal array was selected (L8) to perform the experiments. After conducting the experiments with the combinations of planning parameters the conformity index (CI) and the normal brain dose S/N ratio for each parameter was calculated. Optimum levels for the multiple response optimizations were determined. Results: We determined that the factors most affecting the conformity index are arc arrangement and beam energy. These tests were also used to evaluate dose to normal brain. In these evaluations, the significant parameters were grid size and calculation model. Using the utility concept we determined the combination of each of the four factors tested in this study that most significantly influence quality of the resulting treatment plans: (a)-arc arrangement-set2, (b)-6MV, (c)-calc.grid 1mm, (d)-Acuros algorithm. Overall, the dominant significant influences on plan quality are (a)-arcarrangement, and (b)-beamenergy. Conclusion: Results were analyzed using ANOVA and were found to be within the confidence interval. Further investigation using this methodology. Such parameters might include: virtual OAR and optimization criterion such as normal tissue objective.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

MO-FG-CAMPUS-TeP2-04: Optimizing for a Specified Target Coverage Probability

Purpose: The purpose of this work is to develop a method for inverse planning of radiation therapy margins. When using this method the user specifies a desired target coverage probability and the system optimizes to meet the demand without any explicit specification of margins to handle setup uncertainty. Methods: The method determines which voxels to include in an optimization function promoting target coverage in order to achieve a specified target coverage probability. Voxels are selected in a way that retains the correlation between them: The target is displaced according to the setup errors and the voxels to include are selected as the union of the displaced target regions under the x% best scenarios according to some quality measure. The quality measure could depend on the dose to the considered structure alone or could depend on the dose to multiple structures in order to take into account correlation between structures. Results: A target coverage function was applied to the CTV of a prostate case with prescription 78 Gy and compared to conventional planning using a DVH function on the PTV. Planning was performed to achieve 90% probability of CTV coverage. The plan optimized using the coverage probability function had P(D98 > 77.95 Gy) = 0.97 for the CTV. The PTV plan using a constraint on minimum DVH 78 Gy at 90% had P(D98 > 77.95) = 0.44 for the CTV. To match the coverage probability optimization, the DVH volume parameter had to be increased to 97% which resulted in 0.5 Gy higher average dose to the rectum. Conclusion: Optimizing a target coverage probability is an easily used method to find a margin that achieves the desired coverage probability. It can lead to reduced OAR doses at the same coverage probability compared to planning with margins and DVH functions.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

MO-FG-CAMPUS-TeP2-05: Optimizing Stereotactic Radiosurgery Treatment of Multiple Brain Metastasis Lesions with Individualized Rotational Arc Trajectories

Purpose: Radiosurgery of multiple (n>4) brain metastasis lesions requires 3–4 noncoplanar VMAT arcs with excessively high monitor units and long delivery time. We investigated whether an improved optimization technique would decrease the needed arc numbers and increase the delivery efficiency, while improving or maintaining the plan quality. Methods: The proposed 4pi arc space optimization algorithm consists of two steps: automatic couch angle selection followed by aperture generation for each arc with optimized control points distribution. We use a greedy algorithm to select the couch angles. Starting from a single coplanar arc plan we search through the candidate noncoplanar arcs to pick a single noncoplanar arc that will bring the best plan quality when added into the existing treatment plan. Each time, only one additional noncoplanar arc is considered making the calculation time tractable. This process repeats itself until desired number of arc is reached. The technique is first evaluated in coplanar arc delivery scheme with testing cases and then applied to noncoplanar treatments of a case with 12 brain metastasis lesions. Results: Clinically acceptable plans are created within minutes. For the coplanar testing cases the algorithm yields singlearc plans with better dose distributions than that of two-arc VMAT, simultaneously with a 12–17% reduction in the delivery time and a 14–21% reduction in MUs. For the treatment of 12 brain mets while Paddick conformity indexes of the two plans were comparable the SCG-optimization with 2 arcs (1 noncoplanar and 1 coplanar) significantly improved the conventional VMAT with 3 arcs (2 noncoplanar and 1 coplanar). Specifically V16 V10 and V5 of the brain were reduced by 11%, 11% and 12% respectively. The beam delivery time was shortened by approximately 30%. Conclusion: The proposed 4pi arc space optimization technique promises to significantly reduce the brain toxicity while greatly improving the treatment efficiency.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

WE-AB-209-10: Optimizing the Delivery of Sequential Fluence Maps for Efficient VMAT Delivery

Purpose: To develop an optimization model and solution approach for computing MLC leaf trajectories and dose rates for high quality matching of a set of optimized fluence maps to be delivered sequentially around a patient in a VMAT treatment. Methods: We formulate the fluence map matching problem as a nonlinear optimization problem where time is discretized but dose rates and leaf positions are continuous variables. For a given allotted time, which is allocated across the fluence maps based on the complexity of each fluence map, the optimization problem searches for the best leaf trajectories and dose rates such that the original fluence maps are closely recreated. Constraints include maximum leaf speed, maximum dose rate, and leaf collision avoidance, as well as the constraint that the ending leaf positions for one map are the starting leaf positions for the next map. The resulting model is non-convex but smooth, and therefore we solve it by local searches from a variety of starting positions. We improve solution time by a custom decomposition approach which allows us to decouple the rows of the fluence maps and solve each leaf pair individually. This decomposition also makes the problem easily parallelized. Results: We demonstrate method on a prostate case and a head-and-neck case and show that one can recreate fluence maps to high degree of fidelity in modest total delivery time (minutes). Conclusion: We present a VMAT sequencing method that reproduces optimal fluence maps by searching over a vast number of possible leaf trajectories. By varying the total allotted time given, this approach is the first of its kind to allow users to produce VMAT solutions that span the range of wide-field coarse VMAT deliveries to narrow-field high-MU sliding window-like approaches.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

WE-DE-201-01: BEST IN PHYSICS (THERAPY): A Fast Multi-Target Inverse Treatment Planning Strategy Optimizing Dosimetric Measures for High-Dose-Rate (HDR) Brachytherapy

Purpose: Inverse treatment planning (ITP) for interstitial HDR brachytherapy of gynecologic cancers seeks to maximize coverage of the clinical target volumes (tumor and vagina) while respecting dose-volume-histogram related dosimetric measures (DMs) for organs at risk (OARs). Commercially available ITP tools do not support DM-based planning because it is computationally too expensive to solve. In this study we present a novel approach that allows fast ITP for gynecologic cancers based on DMs for the first time. Methods: This novel strategy is an optimization model based on a smooth DM-based objective function. The smooth approximation is achieved by utilizing a logistic function for the evaluation of DMs. The resulting nonconvex and constrained optimization problem is then optimized with a BFGS algorithm. The model was evaluated using the implant geometry extracted from 20 patient treatment plans under an IRB-approved retrospective study. For each plan, the final DMs were evaluated and compared to the original clinical plans. The CTVs were the contoured tumor volume and the contoured surface of the vagina. Statistical significance was evaluated with a one-sided paired Wilcoxon signed-rank test. Results: As did the clinical plans, all generated plans fulfilled the defined DMs for OARs. The proposed strategy showed a statistically significant improvement (p<0.001) in coverage of the tumor and vagina, with absolute improvements of related DMs of (6.9 +/− 7.9)% and (28.2 +/− 12.0)%, respectively. This was achieved with a statistically significant (p<0.01) decrease of the high-dose-related DM for the tumor. The runtime of the optimization was (2.3 +/− 2.0) seconds. Conclusion: We demonstrated using clinical data that our novel approach allows rapid DM-based optimization with improved coverage of CTVs with fewer hot spots. Being up to three orders of magnitude faster than the current clinical practice, the method dramatically shortens planning time.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

TH-CD-202-08: Feasibility Study of Planning Phase Optimization Using Patient Geometry-Driven Information for Better Dose Sparing of Organ at Risks

Purpose: To propose a simple and effective cost value function to search optimal planning phase (gating window) and demonstrated its feasibility for respiratory correlated radiation therapy. Methods: We acquired 4DCT of 10 phases for 10 lung patients who have tumor located near OARs such as esophagus, heart, and spinal cord (i.e., central lung cancer patients). A simplified mathematical optimization function was established by using overlap volume histogram (OVH) between the target and organ at risk (OAR) at each phase and the tolerance dose of selected OARs to achieve surrounding OARs dose-sparing. For all patients and all phases, delineation of the target volume and selected OARs (esophagus, heart, and spinal cord) was performed (by one observer to avoid inter-observer variation), then cost values were calculated for all phases. After the breathing phases were ranked according to cost value function, the relationship between score and dose distribution at highest and lowest cost value phases were evaluated by comparing the mean/max dose. Results: A simplified mathematical cost value function showed noticeable difference from phase to phase, implying it is possible to find optimal phases for gating window. The lowest cost value which may result in lower mean/max dose to OARs was distributed at various phases for all patients. The mean doses of the OARs significantly decreased about 10% with statistical significance for all 3 OARs at the phase with the lowest cost value. Also, the max doses of the OARs were decreased about 2∼5% at the phase with the lowest cost value compared to the phase with the highest cost value. Conclusion: It is demonstrated that optimal phases (in dose distribution perspective) for gating window could exist differently through each patient and the proposed cost value function can be a useful tool for determining such phases without performing dose optimization calculations. This research was supported by the Mid-career Researcher Program through NRF funded by the Ministry of Science, ICT & Future Planning of Korea (NRF-2014R1A2A1A10050270) and by the Radiation Technology R&D program through the National Research Foundation of Korea funded by the Ministry of Science, ICT & Future Planning (No. 2013M2A2A7038291)

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Sci-Thur AM: YIS – 07: Optimizing dual-energy x-ray parameters using a single filter for both high and low-energy images to enhance soft-tissue imaging

Objective: To optimize dual-energy parameters of ExacTrac stereoscopic x-ray imaging system for lung SBRT patients Methods: Simulated spectra and a lung phantom were used to optimize filter material, thickness, kVps, and weighting factors to obtain bone subtracted dual-energy images. Spektr simulations were used to identify material in the atomic number (Z) range [3–83] based on a metric defined to separate spectrums of high and low energies. Both energies used the same filter due to time constraints of image acquisition in lung SBRT imaging. A lung phantom containing bone, soft tissue, and a tumor mimicking material was imaged with filter thicknesses range [0–1] mm and kVp range [60–140]. A cost function based on contrast-to-noise-ratio of bone, soft tissue, and tumor, as well as image noise content, was defined to optimize filter thickness and kVp. Using the optimized parameters, dual-energy images of anthropomorphic Rando phantom were acquired and evaluated for bone subtraction. Imaging dose was measured with dual-energy technique using tin filtering. Results: Tin was the material of choice providing the best energy separation, non-toxicity, and non-reactiveness. The best soft-tissue-only image in the lung phantom was obtained using 0.3 mm tin and [140, 80] kVp pair. Dual-energy images of the Rando phantom had noticeable bone elimination when compared to no filtration. Dose was lower with tin filtering compared to no filtration. Conclusions: Dual-energy soft-tissue imaging is feasible using ExacTrac stereoscopic imaging system utilizing a single tin filter for both high and low energies and optimized acquisition parameters.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Optimal Multistage Algorithm for Adjoint Computation

We reexamine the work of Stumm and Walther on multistage algorithms for adjoint computation. We provide an optimal algorithm for this problem when there are two levels of checkpoints, in memory and on disk. Previously, optimal algorithms for adjoint computations were known only for a single level of checkpoints with no writing and reading costs; a well-known example is the binomial checkpointing algorithm of Griewank and Walther. Stumm and Walther extended that binomial checkpointing algorithm to the case of two levels of checkpoints, but they did not provide any optimality results. We bridge the gap by designing the first optimal algorithm in this context. We experimentally compare our optimal algorithm with that of Stumm and Walther to assess the difference in performance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

An Efficient Parallel-in-Time Method for Optimization with Parabolic PDEs

To solve optimization problems with parabolic PDE constraints, often methods working on the reduced objective functional are used. They are computationally expensive due to the necessity of solving both the state equation and a backward-in-time adjoint equation to evaluate the reduced gradient in each iteration of the optimization method. In this study, we investigate the use of the parallel-in-time method PFASST in the setting of PDE-constrained optimization. In order to develop an efficient fully time-parallel algorithm, we discuss different options for applying PFASST to adjoint gradient computation, including the possibility of doing PFASST iterations on both the state and the adjoint equations simultaneously. Here, we also explore the additional gains in efficiency from reusing information from previous optimization iterations when solving each equation. Numerical results for both a linear and a nonlinear reaction-diffusion optimal control problem demonstrate the parallel speedup and efficiency of different approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Domain Decomposition for Integer Optimal Control with Total Variation Regularization

Total variation integer optimal control problems admit solutions and necessary optimality conditions via geometric variational analysis. In spite of the existence of said solutions, algorithms which solve the discretized objective suffer from high numerical cost associated with the combinatorial nature of integer programming. Hence, such methods are often limited to small and medium-sized problems. We propose a globally convergent, coordinate descent–inspired algorithm that allows tractable subproblem solutions restricted to a partition of the domain. Our decomposition method solves relatively small trust-region subproblems that modify the control variable on a subdomain only. Given nontrivial subdomain overlap, we prove that a global first-order necessary optimality condition is equivalent to a first-order necessary optimality condition per subdomain. We additionally show that a sufficient decrease is achieved on a single subdomain by way of a trust-region subproblem solver using geometric measure–theoretic arguments, which we integrate with a greedy patch selection to prove convergence of our algorithm. In conclusion, we demonstrate the practicality of our algorithm on a benchmark large-scale, PDE-constrained integer optimal control problem and find that our method is faster than the state of the art.

domain decomposition↗
DOE OSTI2026

Optimized Tandem Catalyst Patterning for CO 2 Reduction Flow Reactors

Tandem catalysis involves two or more catalysts arranged in proximity within a single reaction vessel, with the aim of synergistically aligning the catalysts’ reaction pathways to maximize overall system performance. This study presents a proof of concept showing the integration of continuum transport modeling with design optimization in a simplified two-dimensional flow reactor setup for electrochemical CO 2 reduction. Ag catalysts provide the CO 2 ⟶ CO reaction capability, and Cu catalysts provide the CO ⟶ high-value products reaction capability. Given a set of input parameters, the optimization algorithm uses adjoint methods to modify the Ag/Cu surface patterning in order to maximize the current density toward high-value products, such as ethylene. The optimized designs yield significant performance enhancement especially at more negative applied voltages (i.e., stronger surface reactions) and for larger numbers of patterning sections. For an applied voltage of −1.7 V vs. SHE, the 12-section optimized design increases the current density toward ethylene by up to 65% compared to the unoptimized 2-section design. For the optimized cases, observed differences in the production and consumption of CO (the key intermediate species) and minimized zones of low CO reactant surface concentration on Cu sections explain the improved reactor performance.

CO2 reduction↗
DOE OSTI2017

Improving the FLORIS wind plant model for compatibility with gradient-based optimization

The FLORIS (FLOw Redirection and Induction in Steady-state) model, a parametric wind turbine wake model that predicts steady-state wake characteristics based on wind turbine position and yaw angle, was developed for optimization of control settings and turbine locations. This article provides details on changes made to the FLORIS model to make the model more suitable for gradient-based optimization. Changes to the FLORIS model were made to remove discontinuities and add curvature to regions of non-physical zero gradient. Exact gradients for the FLORIS model were obtained using algorithmic differentiation. A set of three case studies demonstrate that using exact gradients with gradient-based optimization reduces the number of function calls by several orders of magnitude. The case studies also show that adding curvature improves convergence behavior, allowing gradient-based optimization algorithms used with the FLORIS model to more reliably find better solutions to wind farm optimization problems.

17 WIND ENERGY↗
DOE OSTI2015

Optimal shielding design for minimum materials cost or mass

The mathematical underpinnings of cost optimal radiation shielding designs based on an extension of optimal control theory are presented, a heuristic algorithm to iteratively solve the resulting optimal design equations is suggested, and computational results for a simple test case are discussed. A typical radiation shielding design problem can have infinitely many solutions, all satisfying the problem's specified set of radiation attenuation requirements. Each such design has its own total materials cost. For a design to be optimal, no admissible change in its deployment of shielding materials can result in a lower cost. This applies in particular to very small changes, which can be restated using the calculus of variations as the Euler-Lagrange equations. Furthermore, the associated Hamiltonian function and application of Pontryagin's theorem lead to conditions for a shield to be optimal.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗