Topology optimization for inverse magnetostatics as sparse regression: Application to electromagnetic coils for stellarators
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Kaptanoglu, Alan A. (ORCID:0000000263372907)↗
SEARCH · Engineering Papers
Results for “Inverse Optimization”
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Inverse design optimization for efficient coupling of an electrically injected optical antenna-LED to a single-mode waveguide
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Andrade, Nicolas M.↗
Data-Driven Pricing Strategy for Demand-Side Resource Aggregators
We consider a utility who seeks to coordinate the energy consumption of multiple demand-side flexible resource aggregators. For the purpose of privacy protection, the utility has no access to the detailed information of loads of resource aggregators. Instead, we assume that the utility can directly observe each aggregator's aggregate energy consumption outcomes. Furthermore, the utility can leverage resource aggregator energy consumption via time-varying electricity price profiles. Based on inverse optimization technique, we propose an estimation method for the utility to infer the energy requirement information of aggregators. Subsequently, we design a data-driven pricing scheme to help the utility achieve system-level control objectives (e.g., minimizing peak demand) by combining hybrid particle swarm optimizer with mutation algorithm and an iterative algorithm. Case studies have demonstrated the effectiveness of the proposed approach against two benchmark pricing strategies-a flat-rate scheme and a time-of-use scheme.
data-driven optimization↗
Optimal beam margins in linac-based VMAT stereotactic ablative body radiotherapy: a Pareto front analysis for liver metastases
We explored the Pareto fronts mathematical strategy to determine the optimal block margin and prescription isodose for stereotactic body radiotherapy (SBRT) treatments of liver metastases using the volumetric-modulated arc therapy (VMAT) technique. Three targets (planning target volumes [PTVs] = 20, 55, and 101 cc) were selected. A single fraction dose of 26 Gy was prescribed (prescription dose [PD]). VMAT plans were generated for 3 different beam energies. Pareto fronts based on (1) different multileaf collimator (MLC) block margin around PTV and (2) different prescription isodose lines (IDL) were produced. For each block margin, the greatest IDL fulfilling the criteria (95% of PTV reached 100%) was considered as providing the optimal clinical plan for PTV coverage. Liver D{sub mean}, V7Gy, and V12Gy were used against the PTV coverage to generate the fronts. Gradient indexes (GI and mGI), homogeneity index (HI), and healthy liver irradiation in terms of D{sub mean}, V7Gy, and V12Gy were calculated to compare different plans. In addition, each target was also optimized with a full-inverse planning engine to obtain a direct comparison with anatomy-based treatment planning system (TPS) results. About 900 plans were calculated to generate the fronts. GI and mGI show a U-shaped behavior as a function of beam margin with minimal values obtained with a +1 mm MLC margin. For these plans, the IDL ranges from 74% to 86%. GI and mGI show also a V-shaped behavior with respect to HI index, with minimum values at 1 mm for all metrics, independent of tumor dimensions and beam energy. Full-inversed optimized plans reported worse results with respect to Pareto plans. In conclusion, Pareto fronts provide a rigorous strategy to choose clinical optimal plans in SBRT treatments. We show that a 1-mm MLC block margin provides the best results with regard to healthy liver tissue irradiation and steepness of dose fallout.
62 RADIOLOGY AND NUCLEAR MEDICINE↗
WE-DE-201-03: Combined Use of 192Ir, 60Co, and 169Yb Sources with the Novel Direction Modulated Brachytherapy Tandem Applicator for High Dose Rate Brachytherapy Planning of Cervical Cancer
Purpose: To evaluate the improvement in plan quality when various combinations of 192Ir, 60Co, and 169Yb sources are used in combination with a novel direction modulated brachytherapy (DMBT) tandem applicator for high dose rate brachytherapy of cervical cancer. Methods: The proposed DMBT tandem applicator is designed for image-guided adaptive brachytherapy (IGABT), especially MRI, of cervical cancer. It has 6 peripheral holes of 1.3-mm width, grooved along a 5.4-mm diameter nonmagnetic tungsten alloy rod of density 18.0 g/cc, capable of generating directional dose profiles - leading to enhanced dose sculpting capacity through inverse planning. Monte Carlo simulations of the three HDR sources individually inside the DMBT applicator were performed and imported into an in-house developed inverse optimization code. We then performed inverse planning with 14 cervical cancer patients enrolled in EMBRACE study. In all patients, 3D MRI-based planning was performed while utilizing 1) tandem-ring and needles attached-to-ring (7 patients) and 2) tandem-ring and needles both attached-to-ring and free-hand-loaded (7 patients), in accordance with the GEC-ESTRO recommendations. All plans were normalized to receive the same HRCTV D90 and DVH parameters were evaluated. Results: The DMBT tandem was used in all cases. Overall, the combined use of two sources (192Ir-60Co and 192Ir-169Yb, but not 60Co-169Yb) generally produced better quality plans than with the 192Ir source alone in terms of sparing OARs. For example, up to 3.5, 4.4, and 3.9% individual reductions in D2cc were observed for the bladder, rectum, and sigmoid, respectively, between 192Ir-60Co and 192Ir-only plans for patient cases in #1. While up to 5.5, 2.0, and 5.7% individual reductions were observed for patient cases in #2. Conclusion: We have demonstrated that, in addition to “directional modulation” of DMBT, use of multiple sources with sufficient differences in energy can be utilized to achieve additional improvement in plan quality for IGABT of cervical cancer.
60 APPLIED LIFE SCIENCES↗
Robust A-Optimal Experimental Design for Sensor Placement in Bayesian Linear Inverse Problems
Optimal design of experiments for Bayesian inverse problems has recently gained wide popularity and attracted much attention, especially in the computational science and Bayesian inversion communities. An optimal design maximizes a predefined utility function that is formulated in terms of the elements of an inverse problem, an example being optimal sensor placement for parameter identification. The state-of-the-art algorithmic approaches following this simple formulation generally overlook misspecification of the elements of the inverse problem, such as the prior or the measurement uncertainties. This work presents an efficient algorithmic approach for designing optimal experimental design schemes for Bayesian linear inverse problems such that the optimal design is robust to misspecification of elements of the inverse problem. Specifically, we consider a worst-case scenario approach for the uncertain or misspecified parameters, formulate robust objectives, and propose an algorithmic approach for optimizing such objectives. Furthermore, both relaxation and stochastic solution approaches are discussed with detailed analysis and insight into the interpretation of the problem and the proposed algorithmic approach. Extensive numerical experiments to validate and analyze the proposed approach are carried out for sensor placement in a parameter identification problem.
Bayesian inverse problems↗
The inverse problem of the optimal regulator.
The inverse problem of the optimal regulator is considered for a general class of multi-input systems with integral-type performance indices. A new phase variable canonical form is shown to be convenient for this analysis. The advantage of the canonical form is to separate the state variables into subvectors of directly controlled, indirectly controlled, and uncontrollable components. Necessary and sufficient conditions for optimized performance indices are given. With the nonlinearities of the system restricted to functions of the directly controlled state variables, additional results are developed about the nonnegative property of optimized loss functions.
Yokoyama, R.↗
SU-E-T-214: Intensity Modulated Proton Therapy (IMPT) Based On Passively Scattered Protons and Multi-Leaf Collimation: Prototype TPS and Dosimetry Study
Purpose. Intensity-modulated proton therapy is usually implemented with multi-field optimization of pencil-beam scanning (PBS) proton fields. However, at the view of the experience with photon-IMRT, proton facilities equipped with double-scattering (DS) delivery and multi-leaf collimation (MLC) could produce highly conformal dose distributions (and possibly eliminate the need for patient-specific compensators) with a clever use of their MLC field shaping, provided that an optimal inverse TPS is developed. Methods. A prototype TPS was developed in MATLAB. The dose calculation process was based on a fluence-dose algorithm on an adaptive divergent grid. A database of dose kernels was precalculated in order to allow for fast variations of the field range and modulation during optimization. The inverse planning process was based on the adaptive simulated annealing approach, with direct aperture optimization of the MLC leaves. A dosimetry study was performed on a phantom formed by three concentrical semicylinders separated by 5 mm, of which the inner-most and outer-most were regarded as organs at risk (OARs), and the middle one as the PTV. We chose a concave target (which is not treatable with conventional DS fields) to show the potential of our technique. The optimizer was configured to minimize the mean dose to the OARs while keeping a good coverage of the target. Results. The plan produced by the prototype TPS achieved a conformity index of 1.34, with the mean doses to the OARs below 78% of the prescribed dose. This Result is hardly achievable with traditional conformal DS technique with compensators, and it compares to what can be obtained with PBS. Conclusion. It is certainly feasible to produce IMPT fields with MLC passive scattering fields. With a fully developed treatment planning system, the produced plans can be superior to traditional DS plans in terms of plan conformity and dose to organs at risk.
60 APPLIED LIFE SCIENCES↗
SU-E-T-183: Feasibility of Extreme Dose Escalation for Glioblastoma Multiforme Using 4π Radiotherapy
Purpose: GBM recurrence primarily occurs inside or near the high-dose radiation field of original tumor site requiring greater than 100 Gy to significantly improve local control. We utilize 4π non-coplanar radiotherapy to test the feasibility of planning target volume (PTV) margin expansions or extreme dose escalations without incurring additional radiation toxicities. Methods: 11 GBM patients treated with VMAT to a prescription dose of 59.4 Gy or 60 Gy were replanned with 4π. Original VMAT plans were created with 2 to 4 coplanar or non-coplanar arcs using 3 mm hi-res MLC. The 4π optimization, using 5 mm MLC, selected and inverse optimized 30 beams from a candidate pool of 1162 beams evenly distributed through 4π steradians. 4π plans were first compared to clinical plans using the same prescription dose. Two more studies were then performed to respectively escalate the GTV and PTV doses to 100 Gy, followed by a fourth plan expanding the PTV by 5 mm and maintaining the prescription dose. Results: The standard 4π plan significantly reduced (p<0.01) max and mean doses to critical structures by a range of 47.0–98.4% and 61.0–99.2%, respectively. The high dose PTV/high dose GTV/expanded PTV studies showed a reduction (p<0.05) or unchanged* (p>0.05) maximum dose of 72.1%/86.7%/77.1% (chiasm), 7.2%*/27.7%*/30.7% (brainstem), 39.8%*/84.2%/51.9%* (spinal cord), 69.0%/87.0%/66.9% (L eye), 76.2%/88.1%/84.1% (R eye), 95.0%/98.6%/97.5% (L lens), 93.9%/98.8%/97.6% (R lens), 74.3%/88.5%/72.4% (L optical nerve), 80.4%/91.3%/75.7% (R optical nerve), 64.8%/84.2%/44.9%* (L cochlea), and 85.2%/93.0%/78.0% (R cochlea), respectively. V30 and V36 for both brain and (brain - PTV) were reduced for all cases except the high dose PTV plan. PTV dose coverage increased for all 4π plans. Conclusion: Extreme dose escalation or further margin expansion is achievable using 4π, maintaining or reducing OAR doses. This study indicates that clinical trials employing 4π delivery using prescription doses up to 100 Gy are feasible. Funding support partially contributed by Varian.
60 APPLIED LIFE SCIENCES↗
Deterministic direct aperture optimization using multiphase piecewise constant segmentation
Purpose Direct aperture optimization (DAO) attempts to incorporate machine constraints in the inverse optimization to eliminate the post‐processing steps in fluence map optimization (FMO) that degrade plan quality. Current commercial DAO methods utilize a stochastic or greedy approach to search a small aperture solution space. In this study, we propose a novel deterministic direct aperture optimization that integrates the segmentation of fluence map in the optimization problem using the multiphase piecewise constant Mumford‐Shah formulation. Methods The Mumford‐Shah based direct aperture optimization problem was formulated to include an L2‐norm dose fidelity term to penalize differences between the projected dose and the prescribed dose, an anisotropic total variation term to promote piecewise continuity in the fluence maps, and the multiphase piecewise constant Mumford‐Shah function to partition the fluence into pairwise discrete segments. A proximal‐class, first‐order primal‐dual solver was implemented to solve the large scale optimization problem, and an alternating module strategy was implemented to update fluence and delivery segments. Three patients of varying complexity—one glioblastoma multiforme (GBM) patient, one lung (LNG) patient, and one bilateral head and neck (H&N) patient with 3 PTVs—were selected to test the new DAO method. For each patient, 20 non‐coplanar beams were first selected using column generation, followed by the Mumford‐Shah based DAO (DAO MS ). For comparison, a popular and successful approach to DAO known as simulated annealing—a stochastic approach—was replicated. The simulated annealing DAO (DAO SA ) plans were then created using the same beam angles and maximum number of segments per beam. PTV coverage, PTV homogeneity , and OAR sparing were assessed for each plan. In addition, high dose spillage, defined as the 50% isodose volume divided by the tumor volume, as well as conformity, defined as the van't Riet conformation number, were evaluated. Results DAO MS achieved essentially the same OAR doses compared with the DAO SA plans for the GBM case. The average difference of OAR D max and D mean between the two plans were within 0.05% of the plan prescription dose. The lung case showed slightly improved critical structure sparing using the DAO MS approach, where the average OAR D max and D mean were reduced by 3.67% and 1.08%, respectively, of the prescription dose. The DAO MS plan substantially improved OAR dose sparing for the H&N patient, where the average OAR D max and D mean were reduced by over 10% of the prescription dose. The DAO MS and DAO SA plans were comparable for the GBM and LNG PTV coverage, while the DAO MS plan substantially improved the H&N PTV coverage, increasing D99 by 6.98% of the prescription dose. For the GBM and LNG patients, the DAO MS and DAO SA plans had comparable high dose spillage but slightly worse conformity with the DAO MS approach. For the H&N plan, DAO MS was considerably superior in high dose spillage and conformity to the DAO SA . The deterministic approach is able to solve the DAO problem substantially faster than the simulated annealing approach, with a 9.5‐ to 40‐fold decrease in total solve time, depending on the patient case. Conclusions A novel deterministic direct aperture optimization formulation was developed and evaluated. It combines fluence map optimization and the multiphase piecewise constant Mumford‐Shah segmentation into a unified framework, and the resulting optimization problem can be solved efficiently. Compared to the widely and commercially used simulated annealing DAO approach, it showed comparable dosimetry behavior for simple plans, and substantially improved OAR sparing, PTV coverage, PTV homogeneity, high dose spillage, and conformity for the more complex head and neck plan.
Nguyen, Dan↗
Research on inverse methods and optimization in Italy
The research activities in Italy on inverse design and optimization are reviewed. The review is focused on aerodynamic aspects in turbomachinery and wing section design. Inverse design of blade rows and ducts of turbomachinery in subsonic and transonic regime are illustrated by the Politecnico di Torino and turbomachinery industry (FIAT AVIO).
Larocca, Francesco↗
SU-E-T-567: A Three-Field Mono-Isocentric Inverse Treatment Planning Method for the Patients with Larger Breasts
Purpose: The purpose of this study is to develop a three-field monoisocentric inverse breast treatment planning technique without the use of half-beam block. Methods: Conventional three-field breast treatment with supraclavicular half-beam blocked requires two isocenters when the breast is too large to be contained within half-beam. The inferior border of the supraclavicular field and superior borders of the breast fields are matched on patient's skin with the light field. This method causes a large dose variation in the matching region due to daily setup uncertainties and requires a longer treatment setup time. We developed a three-field mono-isocentric planning method for the treatment of larger breasts. The three fields share the same isocenter located in the breast. Beam matching is achieved by rotating collimator, couch and gantry. Furthermore, we employed a mixed open-IMRT inverse optimization method to improve dose uniformity and coverage. Results: Perfect geometric beam matching was achieved by rotating couch, collimator and gantry together. Treatment setup time was significantly reduced without light-field matching during treatment deliveries. Inverse mixed open-IMRT optimization method achieved better dose uniformity and PTV coverage while keeping sufficient air flash to compensate setup and breast shape changes in daily treatments. Conclusion: By eliminating light field matching, the three-field mono-isocentric treatment method can significantly reduce setup time and uncertainty for large breast patients. Plan quality is further improved by inverse IMRT planning.
60 APPLIED LIFE SCIENCES↗
Lightweight Metal Stamping Optimization Enabled by Artificial Intelligence
Successfully manufacturing an automotive body structure made via the sheet metal stamping process depends upon simultaneous consideration of component design, tooling design, stamping process control, and material properties. In many cases, introducing lightweight sheet materials (e.g., aluminum alloys, magnesium alloys, advanced high strength steels) holds the potential to significantly reduce vehicle weight, but challenges the stamping process by introducing materials with inherently less ductility. Successful and repeatable applications require co-developing the stamping process controls with the varying material properties, including formability. During the stamping process, as soon as the forming limit of the sheet is exceeded, the material shows localized necking which quickly leads to splits. Controlling process variability to avoid these material splits will enable deployment of less formable, lighter, and stronger materials for stamped automotive components. A typical optimization procedure for manufacturing requires an iterative process involving parameter setting, execution of computational simulations, and modifying the parameters. The entire process demands substantial computational time, making it impractical for real-time feedback towards rapid corrective actions required for in-line control for running production processes. To overcome this challenge, artificial intelligence (AI) can be leveraged to determine optimal manufacturing parameters within a single manufacturing cycle time. This research proposes an in-line optimization framework incorporating a trained AI model to predict kidney-shaped die forming. Preliminary results indicate that the AI framework can accurately predict draw-in values based on a given parameter set, a process referred to as forward prediction. Furthermore, the AI framework can also predict the optimal parameter set that leads to the desired draw-in values, referred to as inverse optimization (or backward prediction). This research has been performed in collaborations with USCAR (US Council for Automotive Research) and AutoForm. The members of USCAR are Ford, GM, and Stellantis.
36 MATERIALS SCIENCE↗
SU-E-J-36: Combining CBCT Dose Into IMRT Treatment Planning
Purpose: Cone beam CT (CBCT) is increasingly used in patient setup for IMRT. Daily CBCT may provide effective localization, however, it introduces concern over excessive imaging dose. Previous studies investigated the calculation of excess CBCT dose, however, no study has yet treated this dose as a source of therapeutic radiation, optimized in consideration of PTV and OARs constrains. Here we present a novel combined MV+kV inverse optimization engine to weave the CBCT and MV dose together such that CBCT dose is used for both imaging and therapeutic purposes. This may mitigate some of the excess imaging dose effects of daily CBCT and allow complete evaluation of the CBCT dose prior to treatment. Methods: The EGSnrc Monte Carlo system was used to model a Varian Trilogy CBCT system and 6 MV treatment beam. Using the model, the dose to patient from treatment beam and imaging beam was calculated for ten patients. The standard IMRT objective function was modified to include CBCT dose. Treatment plan optimization using the MOSEK optimization tool was performed retrospectively with and without assuming kV radiation dose from CBCT, assuming one CBCT per fraction. Results: Across ten patients, the CBCT delivered peaks of between .4% and 3.0% of the prescription dose to the PTV, with average CBCT dose to the PTV between .3% and .8%. By including CBCT dose to skin as a constraint during optimization, peak skin dose is reduced by between 1.9% and 7.4%, and average skin dose is reduced by .2% to 3.3%. Conclusions: Pre-treatment CBCT may deliver a substantial amount of radiation dose to the target volume. By considering CBCT dose to skin at the point of treatment planning, it is possible to reduce patient skin dose from current clinical levels, and to provide patient treatment with the improved accuracy that daily CBCT provides.
60 APPLIED LIFE SCIENCES↗
Complex optimization for big computational and experimental neutron datasets
Here, we present a framework to use high performance computing to determine accurate solutions to the inverse optimization problem of big experimental data against computational models. We demonstrate how image processing, mathematical regularization, and hierarchical modeling can be used to solve complex optimization problems on big data. We also demonstrate how both model and data information can be used to further increase solution accuracy of optimization by providing confidence regions for the processing and regularization algorithms. Finally, we use the framework in conjunction with the software package SIMPHONIES to analyze results from neutron scattering experiments on silicon single crystals, and refine first principles calculations to better describe the experimental data.
36 MATERIALS SCIENCE↗
Retrieval of high time resolution growth factor probability density function from a humidity-controlled fast integrated mobility spectrometer
Hygroscopicity describes the tendency of aerosol particle to uptake water and is among the key parameters in determining the impact of atmospheric aerosols on global radiation and climate. A hygroscopicity tandem differential mobility analyzer (HTDMA) system is the most widely utilized instrument for determining the aerosol hygroscopic growth. Because of the time needed to scan the classifying voltage of the DMA, HTDMA measurement normally requires a minimum of 30 min to characterize the particle hygroscopic growth at a single relative humidity for five to six different sizes. This slow speed is often inadequate for measurements onboard mobile platforms or when aerosols evolve rapidly. Recently, a humidity-controlled fast integrated mobility spectrometer (HFIMS) was developed for measuring the hygroscopic growth of particles. The measurement speed of the HFIMS is about one order of magnitude faster than that of the conventional HTDMA. Here, a data inversion routine is developed to retrieve the growth factor probability density function (GF-PDF) of particles measured by the HFIMS. The inversion routine considers the transfer functions of the upstream DMA and the downstream water-based fast integrated mobility spectrometer (FIMS), and derives the GF-PDF that reproduces the measured responses of the HFIMS. The performance of the inversion routine is examined using ambient measurements with different assumptions for the spectral shape of the particle GF-PDF (multimodal lognormal or piecewise linear). The influences of the data inversion parameters and counting statistics on the inverted GF-PDFs were further investigated, and an approach to determine the optimized inversion parameters is presented.
47 OTHER INSTRUMENTATION↗
SU-F-BRD-01: A Logistic Regression Model to Predict Objective Function Weights in Prostate Cancer IMRT
Purpose: To develop a statistical model that predicts optimization objective function weights from patient geometry for intensity-modulation radiotherapy (IMRT) of prostate cancer. Methods: A previously developed inverse optimization method (IOM) is applied retrospectively to determine optimal weights for 51 treated patients. We use an overlap volume ratio (OVR) of bladder and rectum for different PTV expansions in order to quantify patient geometry in explanatory variables. Using the optimal weights as ground truth, we develop and train a logistic regression (LR) model to predict the rectum weight and thus the bladder weight. Post hoc, we fix the weights of the left femoral head, right femoral head, and an artificial structure that encourages conformity to the population average while normalizing the bladder and rectum weights accordingly. The population average of objective function weights is used for comparison. Results: The OVR at 0.7cm was found to be the most predictive of the rectum weights. The LR model performance is statistically significant when compared to the population average over a range of clinical metrics including bladder/rectum V53Gy, bladder/rectum V70Gy, and mean voxel dose to the bladder, rectum, CTV, and PTV. On average, the LR model predicted bladder and rectum weights that are both 63% closer to the optimal weights compared to the population average. The treatment plans resulting from the LR weights have, on average, a rectum V70Gy that is 35% closer to the clinical plan and a bladder V70Gy that is 43% closer. Similar results are seen for bladder V54Gy and rectum V54Gy. Conclusion: Statistical modelling from patient anatomy can be used to determine objective function weights in IMRT for prostate cancer. Our method allows the treatment planners to begin the personalization process from an informed starting point, which may lead to more consistent clinical plans and reduce overall planning time.
60 APPLIED LIFE SCIENCES↗