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At least 55 records · Page 3

Evaluation of the cone beam CT for internal target volume localization in lung stereotactic radiotherapy in comparison with 4D MIP images

Purpose: To investigate whether the three-dimensional cone-beam CT (CBCT) is clinically equivalent to the four-dimensional computed tomography (4DCT) maximum intensity projection (MIP) reconstructed images for internal target volume (ITV) localization in image-guided lung stereotactic radiotherapy.Methods: A ball-shaped polystyrene phantom with built-in cube, sphere, and cone of known volumes was attached to a motor-driven platform, which simulates a sinusoidal movement with changeable motion amplitude and frequency. Target motion was simulated in the patient in a superior-inferior (S-I) direction with three motion periods and 2 cm peak-to-peak amplitudes. The Varian onboard Exact-Arms kV CBCT system and the GE LightSpeed four-slice CT integrated with the respiratory-position-management 4DCT scanner were used to scan the moving phantom. MIP images were generated from the 4DCT images. The clinical equivalence of the two sets of images was evaluated by comparing the extreme locations of the moving objects along the motion direction, the centroid position of the ITV, and the ITV volumes that were contoured automatically by Velocity or calculated with an imaging gradient method. The authors compared the ITV volumes determined by the above methods with those theoretically predicted by taking into account the physical object dimensions and the motion amplitudes. The extreme locations were determined by the gradient method along the S-I axis through the center of the object. The centroid positions were determined by autocenter functions. The effect of motion period on the volume sizes was also studied.Results: It was found that the extreme locations of the objects determined from the two image modalities agreed with each other satisfactorily. They were not affected by the motion period. The average difference between the two modalities in the extreme locations was 0.68% for the cube, 1.35% for the sphere, and 0.5% for the cone, respectively. The maximum difference in the centroid position of the cylinder, sphere, and cone was less than 1.4 mm between the two modalities for all motion periods studied. For the ITV volume evaluation, the authors found that both MIP-based and CBCT-based ITVs increased with increases of motion period. Furthermore, the MIP-based ITV volumes were generally larger than those determined from the CBCT images, with the difference in autocontoured volumes being 2.57%, 1.66%, and 1.82% for the sphere, cylinder, and cone, respectively, while these differences increased to 9.57%, 3.52%, 8.71% for the above objects when the gradient method was used. The authors found that the autocontour method was accurate enough to predict the actual ITV values with the absolute differences less than 2.4% comparing to the theoretically predicted values.Conclusions: The extreme location and the centroid position of the objects agree with each other between the two image modalities when the breathing motion is sinusoidal. Although the ITV volumes delineated from both image modalities changed with the motion period, the differences in ITV between the two modalities were minimal when an optimized window level was used. The authors’ results suggest that CBCT and MIP images are equivalent in determining an ITV's position in the conditions studied. The CBCT is adequate in providing imaging-guidance for lung cancer treatment.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Solid Phase Gradient Alloying Method via ShAPE

Alloying has been used to confer desirable properties to various metallic systems since the bronze age. For example, Ni, Mn, and Cr are alloyed into an Fe matrix to make steel, which has improved strength and corrosion resistance (as displayed in Fig. 1). In addition to the type of alloying elements, the amount of alloying elements added into a matrix is also very critical for a material’s mechanical property, physical property, machinability, and cost. Conventionally, new alloys are discovered by combining alloy precursors and elemental constituents into a mixture and melting them together. The solidified product or ingot represents a usually non-homogeneous combination of the chemistry with a microstructure dictated by the physics of solidification. It is time and energy intensive to optimize the alloying amounts via the casting process and hence, economically not conducive to rapid alloy discovery. In addition, the cast microstructure seen in the as-cast ingot is often not the ideal, nor even desired structure for optimized performance. Cast materials often need further processing such as homogenization, annealing, and deformation work put in through rolling, forging, extruding, etc. to have favorable microstructures and properties. A faster method to discover new alloy combinations and evaluate them in their worked or processed form is needed. Recently, Laser Engineered Net Shaping was applied to fabricate gradient compositional material for alloy designing. However, the mechanical properties of this gradient alloy were poor due to the existence of impurities, oxidation and cracks that are inherent in the melt-solidification process. Because of these limitations, we propose to use a solid-phase process (ShAPE) to create bulk materials (extrudates) that vary in composition from one end of the extruded solid to the other. Various manufacturing methods for alloy design including conventional casting method, laser based combinatorial method and current solid phase gradient alloying method are displayed and compared in Fig. 2. ShAPE machine and a schematic of ShAPE process are displayed in Fig. 3. Starting material is processed by a rotating and plunging die to form an extrudate. We are proposing through this methodology to invent a new, bulk-scale combinatorial technique. With this novel technique, alloying element can be dissolved into the matrix with a continued gradient without bulk melting. Formation of inter-metallics and defects originating from melt processing can be avoided. In addition, the ShAPE process creates the mixed alloy chemistry, and meanwhile subjects the material to severe plastic strain, which induces the favorable “worked” microstructure. Products from the ShAPE process can be tested in hardness directly providing a path to rapid evaluation of mechanical properties. The ability to create graded structures using friction stir processing (FSP) has been demonstrated, however using the ShAPE process we believe will lead to much faster and higher fidelity results. When combined with high throughput screening methods of physical, mechanical and microstructural property characterization, efficiency and accuracy of alloy design can be significantly improved.

36 MATERIALS SCIENCE↗

A benchmark of Gutzwiller conjugate gradient minimization method in ground state energy calculations of dimers

Herein we present numerical results of ground-state energies of 9 molecules in the well-established G2 molecule set given by the Gutzwiller conjugate gradient minimization (GCGM) method. The method, beyond the commonly used Gutzwiller approximation, was recently developed based on Gutzwiller variational wave functions. We find that compared to benchmark data given by full configuration interaction, GCGM total energies are reasonably well reproduced with the minimum basis set. To include the dynamical correlation beyond the minimal basis calculations, we adopt the local density approximation for the dynamical correlation energy $E_c$. By comparing the results with benchmark data given by experiments and large-basis configuration interaction, the GCGM total energies with $E_c$ are in general better reproduced, but discrepancies are still observed for some dimers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

SU-E-T-295: Simultaneous Beam Sampling and Aperture Shape Optimization for Station Parameter Optimized Radiation Therapy (SPORT)

Purpose: Station Parameter Optimized Radiation Therapy (SPORT) was recently proposed to fully utilize the technical capability of emerging digital LINACs, in which the station parameters of a delivery system, (such as aperture shape and weight, couch position/angle, gantry/collimator angle) are optimized altogether. SPORT promises to deliver unprecedented radiation dose distributions efficiently, yet there does not exist any optimization algorithm to implement it. The purpose of this work is to propose an optimization algorithm to simultaneously optimize the beam sampling and aperture shapes. Methods: We build a mathematical model whose variables are beam angles (including non-coplanar and/or even nonisocentric beams) and aperture shapes. To solve the resulting large scale optimization problem, we devise an exact, convergent and fast optimization algorithm by integrating three advanced optimization techniques named column generation, gradient method, and pattern search. Column generation is used to find a good set of aperture shapes as an initial solution by adding apertures sequentially. Then we apply the gradient method to iteratively improve the current solution by reshaping the aperture shapes and updating the beam angles toward the gradient. Algorithm continues by pattern search method to explore the part of the search space that cannot be reached by the gradient method. Results: The proposed technique is applied to a series of patient cases and significantly improves the plan quality. In a head-and-neck case, for example, the left parotid gland mean-dose, brainstem max-dose, spinal cord max-dose, and mandible mean-dose are reduced by 10%, 7%, 24% and 12% respectively, compared to the conventional VMAT plan while maintaining the same PTV coverage. Conclusion: Combined use of column generation, gradient search and pattern search algorithms provide an effective way to optimize simultaneously the large collection of station parameters and significantly improves quality of resultant treatment plans as compared with conventional VMAT or IMRT treatments.

07 ISOTOPE AND RADIATION SOURCES↗

SU-C-BRA-02: Gradient Based Method of Target Delineation On PET/MR Image of Head and Neck Cancer Patients

Purpose: Validate the consistency of a gradient-based segmentation tool to facilitate accurate delineation of PET/CT-based GTVs in head and neck cancers by comparing against hybrid PET/MR-derived GTV contours. Materials and Methods: A total of 18 head and neck target volumes (10 primary and 8 nodal) were retrospectively contoured using a gradient-based segmentation tool by two observers. Each observer independently contoured each target five times. Inter-observer variability was evaluated via absolute percent differences. Intra-observer variability was examined by percentage uncertainty. All target volumes were also contoured using the SUV percent threshold method. The thresholds were explored case by case so its derived volume matched with the gradient-based volume. Dice similarity coefficients (DSC) were calculated to determine overlap of PET/CT GTVs and PET/MR GTVs. Results: The Levene’s test showed there was no statistically significant difference of the variances between the observer’s gradient-derived contours. However, the absolute difference between the observer’s volumes was 10.83%, with a range from 0.39% up to 42.89%. PET-avid regions with qualitatively non-uniform shapes and intensity levels had a higher absolute percent difference near 25%, while regions with uniform shapes and intensity levels had an absolute percent difference of 2% between observers. The average percentage uncertainty between observers was 4.83% and 7%. As the volume of the gradient-derived contours increased, the SUV threshold percent needed to match the volume decreased. Dice coefficients showed good agreement of the PET/CT and PET/MR GTVs with an average DSC value across all volumes at 0.69. Conclusion: Gradient-based segmentation of PET volume showed good consistency in general but can vary considerably for non-uniform target shapes and intensity levels. PET/CT-derived GTV contours stemming from the gradient-based tool show good agreement with the anatomically and metabolically more accurate PET/MR-derived GTV contours, but tumor delineation accuracy can be further improved with the use PET/MR.

60 APPLIED LIFE SCIENCES↗

A posteriori superlinear convergence bounds for block conjugate gradient

In this paper, we extend to the block case the a posteriori bound showing superlinear convergence of the conjugate gradient method developed by van der Vorst and Vuik in [J. Comput. Applied Math., 48 (1993), pp. 327–341]. That is, we obtain similar bounds but now for the block conjugate gradient method. We also present a series of computational experiments, illustrating the validity of the bound developed here as well as the bound by Simoncini and Szyld from [SIAM Review, 47 (2005), pp. 247–272] using angles between subspaces. Using these bounds, we make some observations on the onset of superlinearity and how this onset depends on the eigenvalue distribution and the block size.

97 MATHEMATICS AND COMPUTING↗

Force field preconditioned ab initio structure relaxation method

We present a general method to accelerate ab initio atomic structural relaxations. In this method, the conjugate gradient ab initio relaxation is preconditioned by a force field relaxation. This force field is constructed on-the-flight with the information of the ab initio forces and the current atomic configuration. At each ab initio relaxation step, the so-constructed force field is used to prerelax the system, with the relaxation direction as the preconditioned direction for the ab initio conjugated gradient method. The force field model and its parameters are rather general making this method applicable for a wide range of systems commonly used in material simulations. We report more than 80 different systems have been tested representing different cases in material simulations. Across the board, we find accelerations mostly over a factor of 2 and for some large systems with a factor of 6 ~ 9 . There is no case where the relaxation becomes worse. The code and lib for this method are provided, which can be used as a plugin in a standard ab initio atomic relaxation code.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Approximate error conjugation gradient minimization methods

In one embodiment, a method includes selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, calculating an approximate error using the subset of rays, and calculating a minimum in a conjugate gradient direction based on the approximate error. In another embodiment, a system includes a processor for executing logic, logic for selecting a subset of rays from a set of all rays to use in an error calculation for a constrained conjugate gradient minimization problem, logic for calculating an approximate error using the subset of rays, and logic for calculating a minimum in a conjugate gradient direction based on the approximate error. In other embodiments, computer program products, methods, and systems are described capable of using approximate error in constrained conjugate gradient minimization problems.

97 MATHEMATICS AND COMPUTING↗

Distributed Energy Resources Coordination over Time-varying Directed Communication Networks

In this paper, we consider an optimal coordination problem for distributed energy resources (DERs) including distributed generators and energy storage devices. We first propose an algorithm based on the push-sum and gradient method to optimally coordinate storage devices and distributed generators in a distributed manner. In the proposed algorithm, each DER only maintains a set of variables and updates them through information exchange with a few neighboring DERs over a time-varying directed communication network. We show that the proposed distributed algorithm with appropriately chosen step-sizes solve the optimal DER coordination problem if the time-varying directed communication network is uniformly jointly strongly connected, which is a mild condition on the connectivity of communication topologies. The proposed distributed algorithm is illustrated and validated by numerical simulations.

Yang, Tao↗

A Scalable Gradient Free Method for Bayesian Experimental Design with Implicit Models

Bayesian experimental design (BED) is to answer the question that how to choose designs that maximize the information gathering. For implicit models, where the likelihood is intractable but sampling is possible, conventional BED methods have difficulties in efficiently estimating the posterior distribution and maximizing the mutual information (MI) between data and parameters. Recent work proposed the use of gradient ascent to maximize a lower bound on MI to deal with these issues. However, the approach requires a sampling path to compute the pathwise gradient of the MI lower bound with respect to the design variables, and such a pathwise gradient is usually inaccessible for implicit models. In this paper, we propose a novel approach that leverages recent advances in stochastic approximate gradient ascent incorporated with a smoothed variational MI estimator for efficient and robust BED. Without the necessity of pathwise gradients, our approach allows the design process to be achieved through a unified procedure with an approximate gradient for implicit models. Several experiments show that our approach outperforms baseline methods, and significantly improves the scalability of BED in high-dimensional problems.

Zhang, Jiaxin↗

A new accelerated algorithm for ill-conditioned ridge regression problems

In this work, we study the primal and dual formulations of the regularized least squares problem, in special norm L{sub 2}, named ridge regression. We state the Gradient method for the corresponding primal-dual problem through a fixed point approach. For this formulation, we present an original convergence analysis involving the spectral radius of a suitable iteration matrix. The main contribution of this work is to accelerate the studied method by means of a memory-like strategy. Some connections with the spectral properties of the associated iteration matrices were established to prove the convergence of the accelerated method. Preliminary experiments showed the good performance of the proposed algorithm when applied to solve ill-conditioned problems, providing better results than the conjugate gradient method for this class of problems.

97 MATHEMATICS AND COMPUTING↗

Nucleon-pair approximation for nuclei from spherical to deformed regions

Here we model low-lying states of atomic nuclei in the nucleon-pair approximation of the shell model, using three approaches to select collective nucleon pairs: the generalized seniority scheme, the conjugate gradient method, and the Hartree-Fock approach. We find the collective pairs obtained from the generalized seniority scheme provide a good description for nearly spherical nuclei, and those from the conjugate gradient method or the Hartree-Fock approach work well for transitional and deformed nuclei. Our NPA calculations using collective pairs with angular momenta 0, 2, and 4 (denoted by S D G pairs) reproduce the nuclear shape evolution in the N = 26 isotones, Ca 46 , Ti 48 , Cr 50 , and Fe 52 , and yield good agreement with full configuration-interaction calculations of low-lying states in medium-heavy transitional and deformed nuclei: Ti 44 – 48 , Cr 48 , Cr 50 , Fe 52 , Zn 60 – 64 , Ge 64 , 66 , Mo 84 , and Xe 108 – 112 . Finally, using the S D G I -pair approximation we describe low-lying states of Ba 112 , 114 , cases difficult to reach by conventional configuration-interaction methods.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Porous media properties of reticulated shape memory polymer foams and mock embolic coils for aneurysm treatment

Background: Shape memory polymer (SMP) foams are being investigated as an alternative aneurysm treatment method to embolic coils. The goal of both techniques is the reduction of blood flow into the aneurysm and the subsequent formation of a stable thrombus, which prevents future aneurysm rupture. The purpose of this study is to experimentally determine the parameters, permeability and form factor, which are related to the flow resistance imposed by both media when subjected to a pressure gradient. Methods: The porous media properties—permeability and form factor—of SMP foams and mock embolic coils (MECs) were measured with a pressure gradient method by means of an in vitro closed flow loop. We implemented the Forchheimer-Hazen-Dupuit-Darcy equation to calculate these properties. Mechanically-reticulated SMP foams were fabricated with average cell sizes of 0.7E-3 and 1.1E-3 m, while the MECs were arranged with volumetric packing densities of 11-28%. Results: The permeability of the SMP foams was an order of magnitude lower than that of the MECs. The form factor differed by up to two orders of magnitude and was higher for the SMP foams in all cases. The maximum flow rate of all samples tested was within the inertial laminar flow regime, with Reynolds numbers ranging between 1 and 35. Conclusions: The SMP foams impose a greater resistance to fluid flow compared to MECs, which is a result of increased viscous and inertial losses. These results suggest that aneurysms treated with SMP foam will have flow conditions more favorable for blood stasis than those treated with embolic coils having packing densities ≤ 28%.

36 MATERIALS SCIENCE↗

A gradient based method for modeling baryons and matter in halos of fast simulations

Fast N-body PM simulations with a small number of time steps such as FastPM or COLA have been remarkably successful in modeling the galaxy statistics, but their lack of small scale force resolution and long time steps cannot give accurate halo matter profiles or matter power spectrum. High resolution N-body simulations can improve on this, but lack baryonic effects, which can only be properly included in hydro simulations. Here we present a scheme to calibrate the fast simulations to mimic the precision of the hydrodynamic simulations or high resolution N-body simulations. The scheme is based on a gradient descent of either effective gravitational potential, which mimics the short range force, or of effective enthalpy, which mimics gas hydrodynamics and feedback. The scheme is fast and differentiable, and can be incorporated as a post-processing step into any simulation. It gives very good results for the matter power spectrum for several of the baryonic feedback and dark matter simulations, and also gives improved dark matter halo profiles. The scheme is even able to find the large subhalos, and increase the correlation coefficient between the fast simulations and the high resolution N-body or hydro simulations. It can also be used to add baryonic effects to the high resolution N-body simulations. While the method has free parameters that can be calibrated on various simulations, they can also be viewed as astrophysical nuisance parameters describing baryonic effects that can be marginalized over during the data analysis. In this view these parameters can be viewed as an efficient parametrization of baryonic effects.

79 ASTRONOMY AND ASTROPHYSICS↗

Field-gradient partitioning for fracture and frictional contact in the material point method: Field-gradient partitioning for fracture and frictional contact in the material point method [Fracture and frictional contact in material point method using damage-field gradients for velocity-field partitioning]

Contact and fracture in the material point method require grid-scale enrichment or partitioning of material into distinct velocity fields to allow for displacement or velocity discontinuities at a material interface. We present a new method which a kernel-based damage field is constructed from the particle data. The gradient of this field is used to dynamically repartition the material into contact pairs at each node. Our approach avoids the need to construct and evolve explicit cracks or contact surfaces and is therefore well suited to problems involving complex 3-D fracture with crack branching and coalescence. A straightforward extension of this approach permits frictional ‘self-contact’ between surfaces that are initially part of a single velocity field, enabling more accurate simulation of granular flow, porous compaction, fragmentation, and comminution of brittle materials. Finally, numerical simulations of self contact and dynamic crack propagation are presented to demonstrate the accuracy of the approach.

97 MATHEMATICS AND COMPUTING↗

QUANTIFYING THE SIGNIFICANCE OF THE MAGNETIC FIELD FROM LARGE-SCALE CLOUD TO COLLAPSING CORE: SELF-SIMILARITY, MASS-TO-FLUX RATIO, AND STAR FORMATION EFFICIENCY

Dust polarization observational results are analyzed for the high-mass star formation region W51 from the largest parent cloud ({approx}2 pc, James Clerk Maxwell Telescope) to the large-scale envelope ({approx}0.5 pc, BIMA array) down to the collapsing core e2 ({approx}60 mpc, Submillimeter Array). Magnetic field and dust emission gradient orientations reveal a correlation which becomes increasingly more tight with higher resolution. The previously developed polarization-intensity-gradient method is applied in order to quantify the magnetic field significance. This technique provides a way to estimate the local magnetic field force compared to gravity without the need of any mass or field strength measurements, solely making use of measured angles which reflect the geometrical imprint of the various forces. All three data sets clearly show regions with distinct features in the field-to-gravity force ratio. Azimuthally averaged radial profiles of this force ratio reveal a transition from a field dominance at larger distances to a gravity dominance closer to the emission peaks. Normalizing these profiles to a characteristic core scale points toward self-similarity. Furthermore, the polarization-intensity-gradient method is linked to the mass-to-flux ratio, providing a new approach to estimate the latter one without mass and field strength inputs. A transition from a magnetically supercritical to a subcritical state as a function of distance from the emission peak is found for the e2 core. Finally, based on the measured radius-dependent field-to-gravity force ratio we derive a modified star formation efficiency with a diluted gravity force. Compared to a standard (free-fall) efficiency, the observed field is capable of reducing the efficiency down to 10% or less.

79 ASTRONOMY AND ASTROPHYSICS↗

Prediction method of basic domain structure in Fe3%Si(110) single crystal with grooved surface

This paper proposes the method to accurately predict the 180° basic domain width (D{sub w}) in demagnetized states of the grooved Fe3%Si(110) single crystal with the tilt angle of [001] out of the sheet surface (β). The evaluation of D{sub w} enables the estimation of the anomalous eddy current losses. In this paper, D{sub w} is optimized to minimize the magnetic Gibbs free energy represented by vector potentials using the finite element method and the conjugate gradient method. The μ*-method is adopted to approximate the magnetization relaxation. The stray field energy generated by the magnetic charges occurring on both grooves cross section and sheet surfaces is considered in our proposed method. The validity of the proposed method was confirmed by comparison with the observed D{sub w}. As a result, we could reveal the β dependence of D{sub w} against the groove depth. Moreover, the theoretical threshold of the domain refinement due to the grooves has been suggested.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗