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Simultaneous motion estimation and image reconstruction (SMEIR) for 4D cone-beam CT

Purpose: Image reconstruction and motion model estimation in four-dimensional cone-beam CT (4D-CBCT) are conventionally handled as two sequential steps. Due to the limited number of projections at each phase, the image quality of 4D-CBCT is degraded by view aliasing artifacts, and the accuracy of subsequent motion modeling is decreased by the inferior 4D-CBCT. The objective of this work is to enhance both the image quality of 4D-CBCT and the accuracy of motion model estimation with a novel strategy enabling simultaneous motion estimation and image reconstruction (SMEIR).Methods: The proposed SMEIR algorithm consists of two alternating steps: (1) model-based iterative image reconstruction to obtain a motion-compensated primary CBCT (m-pCBCT) and (2) motion model estimation to obtain an optimal set of deformation vector fields (DVFs) between the m-pCBCT and other 4D-CBCT phases. The motion-compensated image reconstruction is based on the simultaneous algebraic reconstruction technique (SART) coupled with total variation minimization. During the forward- and backprojection of SART, measured projections from an entire set of 4D-CBCT are used for reconstruction of the m-pCBCT by utilizing the updated DVF. The DVF is estimated by matching the forward projection of the deformed m-pCBCT and measured projections of other phases of 4D-CBCT. The performance of the SMEIR algorithm is quantitatively evaluated on a 4D NCAT phantom. The quality of reconstructed 4D images and the accuracy of tumor motion trajectory are assessed by comparing with those resulting from conventional sequential 4D-CBCT reconstructions (FDK and total variation minimization) and motion estimation (demons algorithm). The performance of the SMEIR algorithm is further evaluated by reconstructing a lung cancer patient 4D-CBCT.Results: Image quality of 4D-CBCT is greatly improved by the SMEIR algorithm in both phantom and patient studies. When all projections are used to reconstruct a 3D-CBCT by FDK, motion-blurring artifacts are present, leading to a 24.4% relative reconstruction error in the NACT phantom. View aliasing artifacts are present in 4D-CBCT reconstructed by FDK from 20 projections, with a relative error of 32.1%. When total variation minimization is used to reconstruct 4D-CBCT, the relative error is 18.9%. Image quality of 4D-CBCT is substantially improved by using the SMEIR algorithm and relative error is reduced to 7.6%. The maximum error (MaxE) of tumor motion determined from the DVF obtained by demons registration on a FDK-reconstructed 4D-CBCT is 3.0, 2.3, and 7.1 mm along left–right (L-R), anterior–posterior (A-P), and superior–inferior (S-I) directions, respectively. From the DVF obtained by demons registration on 4D-CBCT reconstructed by total variation minimization, the MaxE of tumor motion is reduced to 1.5, 0.5, and 5.5 mm along L-R, A-P, and S-I directions. From the DVF estimated by SMEIR algorithm, the MaxE of tumor motion is further reduced to 0.8, 0.4, and 1.5 mm along L-R, A-P, and S-I directions, respectively.Conclusions: The proposed SMEIR algorithm is able to estimate a motion model and reconstruct motion-compensated 4D-CBCT. The SMEIR algorithm improves image reconstruction accuracy of 4D-CBCT and tumor motion trajectory estimation accuracy as compared to conventional sequential 4D-CBCT reconstruction and motion estimation.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Accelerating and stabilizing the convergence of vibrational self-consistent field calculations via the direct inversion of the iterative subspace (vDIIS) algorithm

The vibrational self-consistent field (VSCF) method yields anharmonic states and spectra for molecular vibrations, and it serves as the starting point for more sophisticated correlated-vibration methods. Convergence of the iterative, non-linear optimization in VSCF calculations can be erratic or altogether unsuccessful, particularly for chemical systems involving low-frequency motions. In this work, a vibrational formulation of the Direct Inversion of the Iterative Subspace method of Pulay is presented and investigated. This formulation accounts for distinct attributes of the vibrational and electronic cases, including the expansion of each single-mode vibrational wavefunction in its own basis set. The resulting Direct Inversion of the Iterative Subspace method is shown to substantially accelerate VSCF convergence in all convergent cases as well as rectify many cases where Roothaan-based methods fail. Performance across systems ranging from small, rigid molecules to weakly bound molecular clusters is investigated in this analysis.

Chemistry↗

PARETO: A novel evolutionary optimization approach to multiobjective IMRT planning

Purpose: In radiation therapy treatment planning, the clinical objectives of uniform high dose to the planning target volume (PTV) and low dose to the organs-at-risk (OARs) are invariably in conflict, often requiring compromises to be made between them when selecting the best treatment plan for a particular patient. In this work, the authors introduce Pareto-Aware Radiotherapy Evolutionary Treatment Optimization (pareto), a multiobjective optimization tool to solve for beam angles and fluence patterns in intensity-modulated radiation therapy (IMRT) treatment planning. Methods: pareto is built around a powerful multiobjective genetic algorithm (GA), which allows us to treat the problem of IMRT treatment plan optimization as a combined monolithic problem, where all beam fluence and angle parameters are treated equally during the optimization. We have employed a simple parameterized beam fluence representation with a realistic dose calculation approach, incorporating patient scatter effects, to demonstrate feasibility of the proposed approach on two phantoms. The first phantom is a simple cylindrical phantom containing a target surrounded by three OARs, while the second phantom is more complex and represents a paraspinal patient. Results: pareto results in a large database of Pareto nondominated solutions that represent the necessary trade-offs between objectives. The solution quality was examined for several PTV and OAR fitness functions. The combination of a conformity-based PTV fitness function and a dose-volume histogram (DVH) or equivalent uniform dose (EUD) -based fitness function for the OAR produced relatively uniform and conformal PTV doses, with well-spaced beams. A penalty function added to the fitness functions eliminates hotspots. Comparison of resulting DVHs to those from treatment plans developed with a single-objective fluence optimizer (from a commercial treatment planning system) showed good correlation. Results also indicated that pareto shows promise in optimizing the number of beams. Conclusions: This initial evaluation of the evolutionary optimization software tool pareto for IMRT treatment planning demonstrates feasibility and provides motivation for continued development. Advantages of this approach over current commercial methods for treatment planning are many, including: (1) fully automated optimization that avoids human controlled iterative optimization and potentially improves overall process efficiency, (2) formulation of the problem as a true multiobjective one, which provides an optimized set of Pareto nondominated solutions refined over hundreds of generations and compiled from thousands of parameter sets explored during the run, and (3) rapid exploration of the final nondominated set accomplished by a graphical interface used to select the best treatment option for the patient.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Application of the rectilinear impact pseudostate method to modeling of third-body effects on interplanetary trajectories

Interplanetary transfer trajectories, subject to the third-body gravitational attraction of the departure and arrival planets, noticeably deviate from the conic Lambert theorem solutions. The pseudostate method represents a useful improvement over conic theory by allowing the spacecraft motion about the sun and each terminal body to be superimposed, provided certain rules are followed. The new variant of the method requires iteration on time along the two planetocentric rectilinear impact trajectories. The operational equivalence of the method to the point-to-point Lambert formulation is an attractive feature, already used to advantage in the generation of mission design data

Sergeyevsky, A. B.↗

Schroedinger's radial equation - Solution by extrapolation

A high-accuracy numerical method for the solution of a 1D Schroedinger equation that is suitable for a diatomic molecule, obtained by combining a finite-difference method with iterative extrapolation to the limit, is presently shown to have several advantages over more conventional methods. Initial guesses for the term values are obviated, and implementation of the algorithm is straightforward. The method is both less sensitive to round-off error, and faster than conventional methods for equivalent accuracy. These advantages are illustrated through the solution of Schroedinger's equation for a Morse potential function suited for HCl and a numerically derived Rydberg-Klein-Rees potential function for the X 1Sigma(+) state of CO.

Goorvitch, D.↗

Mixed-Precision Spectral Deferred Correction: Preprint

Convergence of spectral deferred correction (SDC), where low-order time integration methods are used to construct higher-order methods through iterative refinement, can be accelerated in terms of computational effort by using mixed-precision methods. Using ideas from multi-level SDC (in turn based on FAS multigrid ideas), some of the SDC correction sweeps can use function values computed in reduced precision without adversely impacting the accuracy of the final solution. This is particularly beneficial for the performance of combustion solvers such as S3D [6] which require double precision accuracy but are performance limited by the cost of data motion.

97 MATHEMATICS AND COMPUTING↗

SU-E-J-170: Beyond Single-Cycle 4DCT: Maximum a Posteriori (MAP) Reconstruction-Based Binning-Free Multicycle 4DCT for Lung Radiotherapy

Purpose: Thoracic motion changes from cycle-to-cycle and day-to-day. Conventional 4DCT does not capture these cycle to cycle variations. We present initial results of a novel 4DCT reconstruction technique based on maximum a posteriori (MAP) reconstruction. The technique uses the same acquisition process (and therefore dose) as a conventional 4DCT in order to create a high spatiotemporal resolution cine CT that captures several breathing cycles. Methods: Raw 4DCT data were acquired from a lung cancer patient. The continuous 4DCT was reconstructed using MAP algorithm which uses the raw, time-stamped CT data to reconstruct images while simultaneously estimating deformation in the subject's anatomy. This framework incorporates physical effects such as hysteresis and is robust to detector noise and irregular breathing patterns. The 4D image is described in terms of a 3D reference image defined at one end of the hysteresis loop, and two deformation vector fields (DVFs) corresponding to inhale motion and exhale motion respectively. The MAP method uses all of the CT projection data and maximizes the log posterior in order to iteratively estimate a timevariant deformation vector field that describes the entire moving and deforming volume. Results: The MAP 4DCT yielded CT-quality images for multiple cycles corresponding to the entire duration of CT acquisition, unlike the conventional 4DCT, which only yielded a single cycle. Variations such as amplitude and frequency changes and baseline shifts were clearly captured by the MAP 4DC Conclusion: We have developed a novel, binning-free, parameterized 4DCT reconstruction technique that can capture cycle-to-cycle variations of respiratory motion. This technique provides an invaluable tool for respiratory motion management research. This work was supported by funding from the National Institutes of Health and VisionRT Ltd. Amit Sawant receives research funding from Varian Medical Systems, Vision RT and Elekta.

60 APPLIED LIFE SCIENCES↗

TU-EF-204-12: Quantitative Evaluation of Spectral Detector CT Using Virtual Monochromatic Images: Initial Results

Purpose To evaluate the image quality and spectral information of a spectral detector CT (SDCT) scanner using virtual monochromatic (VM) energy images. Methods The SDCT scanner (Philips Healthcare) was equipped with a dual-layer detector and spectral iterative reconstruction (IR), which generates conventional 80–140 kV polychromatic energy (PE) CT images using both detector layers, PE images from the low-energy (upper) and high-energy (lower) detector layers and VM images. A solid water phantom with iodine (2.0–20.0 mg I/ml) and calcium (50.0–600.0 mg Ca/ml) rod inserts was used to evaluate effective energy estimate (EEE) and iodine contrast to noise ratio (CNR). The EEE corresponding to an insert CT number in a PE image was calculated from a CT number fit to the VM image set. Since PE image is prone to beam-hardening artifact EEE may underestimate the actual energy separation from two layers of the detector. A 30-cm-diameter water phantom was used to evaluate noise power spectrum (NPS). The phantoms were scanned at 120 and 140 kV with the same CTDIvol. Results The CT number difference for contrast inserts in VM images (50–150 keV) was 1.3±6% between 120 and 140 kV scans. The difference of EEE calculated from low- and high-energy detector images was 11.5 and 16.7 keV for 120 and 140 kV scans, respectively. The differences calculated from 140 and 100 kV conventional PE images were 12.8, and 20.1 keV from 140 and 80 kV conventional PE images. The iodine CNR increased monotonically with decreased keV. Compared to conventional PE images, the peak of NPS curves from VM images were shifted to lower frequency. Conclusion The EEE results indicates that SDCT at 120 and 140 kV may have energy separation comparable to 100/140 kV and 80/140 kV dual-kV imaging. The effects of IR on CNR and NPS require further investigation for SDCT. Author YY and AD are Philips Healthcare employees.

60 APPLIED LIFE SCIENCES↗

Modifying PASVART to solve singular nonlinear 2-point boundary problems

To study the buckling and post-buckling behavior of shells and various other structures, one must solve a nonlinear 2-point boundary problem. Since closed-form analytic solutions for such problems are virtually nonexistent, numerical approximations are inevitable. This makes the availability of accurate and reliable software indispensable. In a series of papers Lentini and Pereyra, expanding on the work of Keller, developed PASVART: an adaptive finite difference solver for nonlinear 2-point boundary problems. While the program does produce extremely accurate solutions with great efficiency, it is hindered by a major limitation. PASVART will only locate isolated solutions of the problem. In buckling problems, the solution set is not unique. It will contain singular or bifurcation points, where different branches of the solution set may intersect. Thus, PASVART is useless precisely when the problem becomes interesting. To resolve this deficiency we propose a modification of PASVART that will enable the user to perform a more complete bifurcation analysis. PASVART would be combined with the Thurston bifurcation solution: as adaptation of Newton's method that was motivated by the work of Koiter 3 are reinterpreted in terms of an iterative computational method by Thurston.

Fulton, James P.↗

SU-E-I-34: Evaluating Use of AEC to Lower Dose for Lung Cancer Screening CT Protocols

Purpose: The National Lung Screening Trial mandated manual low dose CT technique factors, where up to a doubling of radiation output could be used over a regular to large patient size range. Recent guidance from the AAPM and ACR for lung cancer CT screening recommends radiation output adjustment for patient size either through AEC or a manual technique chart. This study evaluated the use of AEC for output control and dose reduction. Methods: The study was performed on a multidetector helical CT scanner (Aquillion ONE, Toshiba Medical) equipped with iterative reconstruction (ADIR-3D), AEC was adjusted with a standard deviation (SD) image quality noise index. The protocol SD parameter was incrementally increased to reduce patient population dose while image quality was evaluated by radiologist readers scoring the clinical utility of images on a Likert scale. Results: Plots of effective dose vs. body size (water cylinder diameter reported by the scanner) demonstrate monotonic increase in patient dose with increasing patient size. At the initial SD setting of 19 the average CTDIvol for a standard size patient was ∼ 2.0 mGy (1.2 mSv effective dose). This was reduced to ∼1.0 mGy (0.5 mSv) at an SD of 25 with no noticeable reduction in clinical utility of images as demonstrated by Likert scoring. Plots of effective patient diameter and BMI vs body size indicate that these metrics could also be used for manual technique charts. Conclusion: AEC offered consistent and reliable control of radiation output in this study. Dose for a standard size patient was reduced to one-third of the 3 mGy CTDIvol limit required for ACR accreditation of lung cancer CT screening. Gary Arbique: Research Grant, Toshiba America Medical Systems; Cecelia Brewington: Research Grant, Toshiba America Medical Systems; Di Zhang: Employee, Toshiba America Medical Systems.

60 APPLIED LIFE SCIENCES↗

TU-AB-303-12: Towards Inter and Intra Fraction Plan Adaptation for the MR-Linac

Purpose: To develop a new sequencer for IMRT that during treatment can account for anatomy changes provided by online and real-time MRI. This sequencer employs a novel inter and intra fraction scheme that converges to the prescribed dose without a final segment weight optimization (SWO) and enables immediate optimization and delivery of radiation adapted to the deformed anatomy. Methods: The sequencer is initially supplied with a voxel-based dose prescription and during the optimization iteratively generates segments that provide this prescribed dose. Every iteration selects the best segment for the current anatomy state, calculates the dose it will deliver, warps it back to the reference prescription grid and subtracts it from the remaining prescribed dose. This process continues until a certain percentage of dose or a number of segments has been delivered. The anatomy changes that occur during treatment require that convergence is achieved without a final SWO. This is resolved by adding the difference between the prescribed and delivered dose up to this fraction to the prescription of the subsequent fraction. This process is repeated for all fractions of the treatment. Results: Two breast cases were selected to stress test the pipeline by producing artificial inter and intra fraction anatomy deformations using a combination of incrementally applied rigid transformations. The dose convergence of the adaptive scheme over the entire treatment, relative to the prescribed dose, was on average 8.6% higher than the static plans delivered to the respective deformed anatomies and only 1.6% less than the static segment weighted plans on the static anatomy. Conclusion: This new adaptive sequencing strategy enables dose convergence without the need of SWO while adapting the plan to intermediate anatomies, which is a prerequisite for online plan adaptation. We are now testing our pipeline on prostate cases using clinical anatomy deformation data from our department. This work is financially supported by Elekta AB, Stockholm, Sweden.

60 APPLIED LIFE SCIENCES↗

The application of image processing to satellite navigation

Given the locations of several landmarks on a satellite acquired image and their true geographic coordinates, the position and orientation of the satellite can be determined. Two methods for automatically locating the image coordinates of specified landmarks are described. The first, a particularly fast sequential similarity detection algorithm for template matching was originally described by Nagel and Rosenfeld. The second method involves iteratively resampling the picture function in the vicinity of the anticipated landmark. A variety of other speedup methods is also described. An application to SMS imagery is envisioned.

Hord, R. M.↗

Testing of the method for water microleakage detection from OH hydroxyl spectral lines at the L-2M stellarator

Results are presented from L-2M stellarator experiments on testing a possible method for detection of water microleakages in the cooling system of the first wall and vacuum chamber of ITER. The method consists in the spectroscopic detection of spectral lines of the OH hydroxyl, which forms via the dissociation of water molecules in plasma. Emission in the spectral band of 305-310 nm can be detected even at water leakage rates less than 10{sup -4} Pa m{sup 3}/s. Chemical reactions between water and boron compounds on the vacuum chamber wall delay the detection of leakages up to {approx}2000 s. A similar phenomenon can be expected when a leakage will occur in ITER, where the materials suggested for the first wall (Be, Li) can also chemically react with water.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Invertible Neural Networks for Airfoil Design

We report the airfoil design problem, in which an engineer seeks a shape with desired performance characteristics, is fundamental to aerodynamics. Design workflows traditionally rely on iterative optimization methods using low-fidelity integral boundary-layer methods as higher-fidelity adjoint-based computational fluid dynamics methods are computationally expensive. Surrogate-based approaches can accelerate the design process but still rely on some iterative inverse design procedure. In this work, we leverage emerging invertible neural network (INN) tools to enable the rapid inverse design of airfoil shapes for wind turbines. INNs are specialized deep-learning models with well-defined inverse mappings. When trained appropriately, INN surrogate models are capable of forward prediction of aerodynamic and structural quantities for a given airfoil shape as well as inverse recovery of airfoil shapes with specified aerodynamic and structural characteristics. The INN approach offers a roughly 100 times speed-up compared to adjoint-based methods for inverse design. We demonstrate the INN tool for inverse design on three test cases of 100 airfoils each that satisfy the performance characteristics close to those of airfoils used in wind-turbine blades. All generated shapes satisfy the desired aerodynamic characteristics, demonstrating the success of the INN approach for inverse design of airfoils.

17 WIND ENERGY↗

Periodic Pulay method for robust and efficient convergence acceleration of self-consistent field iterations

Pulay's Direct Inversion in the Iterative Subspace (DIIS) method is one of the most widely used mixing schemes for accelerating the self-consistent solution of electronic structure problems. In this work, we propose a simple generalization of DIIS in which Pulay extrapolation is performed at periodic intervals rather than on every self-consistent field iteration, and linear mixing is performed on all other iterations. Lastly, we demonstrate through numerical tests on a wide variety of materials systems in the framework of density functional theory that the proposed generalization of Pulay's method significantly improves its robustness and efficiency.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

WE-G-207-05: Relationship Between CT Image Quality, Segmentation Performance, and Quantitative Image Feature Analysis

Purpose: Segmentation quality can affect quantitative image feature analysis. The objective of this study is to examine the relationship between computed tomography (CT) image quality, segmentation performance, and quantitative image feature analysis. Methods: A total of 90 pathology proven breast lesions in 87 dedicated breast CT images were considered. An iterative image reconstruction (IIR) algorithm was used to obtain CT images with different quality. With different combinations of 4 variables in the algorithm, this study obtained a total of 28 different qualities of CT images. Two imaging tasks/objectives were considered: 1) segmentation and 2) classification of the lesion as benign or malignant. Twenty-three image features were extracted after segmentation using a semi-automated algorithm and 5 of them were selected via a feature selection technique. Logistic regression was trained and tested using leave-one-out-cross-validation and its area under the ROC curve (AUC) was recorded. The standard deviation of a homogeneous portion and the gradient of a parenchymal portion of an example breast were used as an estimate of image noise and sharpness. The DICE coefficient was computed using a radiologist’s drawing on the lesion. Mean DICE and AUC were used as performance metrics for each of the 28 reconstructions. The relationship between segmentation and classification performance under different reconstructions were compared. Distributions (median, 95% confidence interval) of DICE and AUC for each reconstruction were also compared. Results: Moderate correlation (Pearson’s rho = 0.43, p-value = 0.02) between DICE and AUC values was found. However, the variation between DICE and AUC values for each reconstruction increased as the image sharpness increased. There was a combination of IIR parameters that resulted in the best segmentation with the worst classification performance. Conclusion: There are certain images that yield better segmentation or classification performance. The best segmentation Result does not necessarily lead to the best classification Result. This work has been supported in part by grants from the NIH R21-EB015053. R Nishikawa is receives royalties form Hologic, Inc.

60 APPLIED LIFE SCIENCES↗

SU-F-T-261: Reconstruction of Initial Photon Fluence Based On EPID Images

Purpose: Verifying an algorithm to reconstruct relative initial photon fluence for clinical use. Clinical EPID and CT images were acquired to reconstruct an external photon radiation treatment field. The reconstructed initial photon fluence could be used to verify the treatment or calculate the applied dose to the patient. Methods: The acquired EPID images were corrected for scatter caused by the patient and the EPID with an iterative reconstruction algorithm. The transmitted photon fluence behind the patient was calculated subsequently. Based on the transmitted fluence the initial photon fluence was calculated using a back-projection algorithm which takes the patient geometry and its energy dependent linear attenuation into account. This attenuation was gained from the acquired cone-beam CT or the planning CT by calculating a water-equivalent radiological thickness for each irradiation direction. To verify the algorithm an inhomogeneous phantom consisting of three inhomogeneities was irradiated by a static 6 MV photon field and compared to a reference flood field image. Results: The mean deviation between the reconstructed relative photon fluence for the inhomogeneous phantom and the flood field EPID image was 3% rising up to 7% for off-axis fluence. This was probably caused by the used clinical EPID calibration, which flattens the inhomogeneous fluence profile of the beam. Conclusion: In this clinical experiment the algorithm achieved good results in the center of the field while it showed high deviation of the lateral fluence. This could be reduced by optimizing the EPID calibration, considering the off-axis differential energy response. In further progress this and other aspects of the EPID, eg. field size dependency, CT and dose calibration have to be studied to realize a clinical acceptable accuracy of 2%.

60 APPLIED LIFE SCIENCES↗

Automated procedure for design of wing structures to satisfy strength and flutter requirements

A pilot computer program was developed for the design of minimum mass wing structures under flutter, strength, and minimum gage constraints. The wing structure is idealized by finite elements, and second-order piston theory aerodynamics is used in the flutter calculation. Mathematical programing methods are used for the optimization. Computation times during the design process are reduced by three techniques. First, iterative analysis methods used to reduce significantly reanalysis times. Second, the number of design variables is kept small by not using a one-to-one correspondence between finite elements and design variables. Third, a technique for using approximate second derivatives with Newton's method for the optimization is incorporated. The program output is compared witH previous published results. It is found that some flutter characteristics, such as the flutter speed, can display discontinous dependence on the design variables (which are the thicknesses of the structural elements). It is concluded that it is undesirable to use such quantities in the formulation of the flutter constraint.

Haftka, R. T.↗