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All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Nozzle flow with vibrational nonequilibrium

This research concerns the modeling and numerical solutions of the coupled system of compressible Navier-Stokes equations in cylindrical coordinates under conditions of equilibrium and nonequilibrium thermodynamics. The problem considered was the modeling of a high temperature diatomic gas N2 flowing through a converging-diverging high expansion nozzle. The problem was modeled in two ways. The first model uses a single temperature with variable specific heats as functions of this temperature. For the second model we assume that the various degrees of freedom all have a Boltzmann distribution and that there is a continuous redistribution of energy among the various degrees of freedom as the gas passes through the nozzle. Each degree of freedom is assumed to have its own temperature and, consequently, each system state can be characterized by these temperatures. This suggests that formulation of a second model with a vibrational degree of freedom along with a rotational-translation degree of freedom, each degree of freedom having its own temperature. Initially the vibrational degree of freedom is excited by heating the gas to a high temperature. As the high temperature gas passes through the nozzle throat there is a sudden drop in temperature along with a relaxation time for the vibrational degree of freedom to achieve equilibrium with the rotational-translation degree of freedom. That is, we assume that the temperature change upon passing through the throat is so great that the changes in the vibrational degree of freedom occur at a much slower pace and consequently lags behind the rotational-translational energy changes. This lag results in a finite relaxation time. In this context the term nonequilibrium is used to denote the fact that the energy content of the various degrees of freedom are characterized by two temperatures. We neglect any chemical reactions which could also add nonequilibrium effects. We develop the energy equations for the nonequilibrium model from first principles. The resulting equations, which model the nozzle flow, can be expressed in various forms. In most forms the resulting equations are coupled systems of nonlinear partial differential equations subject to certain boundary conditions. To solve the resulting coupled system of nonlinear partial differential equations, several numerical techniques were investigated: (1) the explicit MacCormack method, (2) the explicit-implicit MacCormack method, (3) the method of operator splitting, (4) factorization schemes, and (5) the Steger-Warming scheme.

Heinbockel, J. H.↗
NASA NTRS1997

Efficient Gradient-Based Shape Optimization Methodology Using Inviscid/Viscous CFD

The formerly developed preconditioned-biconjugate-gradient (PBCG) solvers for the analysis and the sensitivity equations had resulted in very large error reductions per iteration; quadratic convergence was achieved whenever the solution entered the domain of attraction to the root. Its memory requirement was also lower as compared to a direct inversion solver. However, this memory requirement was high enough to preclude the realistic, high grid-density design of a practical 3D geometry. This limitation served as the impetus to the first-year activity (March 9, 1995 to March 8, 1996). Therefore, the major activity for this period was the development of the low-memory methodology for the discrete-sensitivity-based shape optimization. This was accomplished by solving all the resulting sets of equations using an alternating-direction-implicit (ADI) approach. The results indicated that shape optimization problems which required large numbers of grid points could be resolved with a gradient-based approach. Therefore, to better utilize the computational resources, it was recommended that a number of coarse grid cases, using the PBCG method, should initially be conducted to better define the optimization problem and the design space, and obtain an improved initial shape. Subsequently, a fine grid shape optimization, which necessitates using the ADI method, should be conducted to accurately obtain the final optimized shape. The other activity during this period was the interaction with the members of the Aerodynamic and Aeroacoustic Methods Branch of Langley Research Center during one stage of their investigation to develop an adjoint-variable sensitivity method using the viscous flow equations. This method had algorithmic similarities to the variational sensitivity methods and the control-theory approach. However, unlike the prior studies, it was considered for the three-dimensional, viscous flow equations. The major accomplishment in the second period of this project (March 9, 1996 to March 8, 1997) was the extension of the shape optimization methodology for the Thin-Layer Navier-Stokes equations. Both the Euler-based and the TLNS-based analyses compared with the analyses obtained using the CFL3D code. The sensitivities, again from both levels of the flow equations, also compared very well with the finite-differenced sensitivities. A fairly large set of shape optimization cases were conducted to study a number of issues previously not well understood. The testbed for these cases was the shaping of an arrow wing in Mach 2.4 flow. All the final shapes, obtained either from a coarse-grid-based or a fine-grid-based optimization, using either a Euler-based or a TLNS-based analysis, were all re-analyzed using a fine-grid, TLNS solution for their function evaluations. This allowed for a more fair comparison of their relative merits. From the aerodynamic performance standpoint, the fine-grid TLNS-based optimization produced the best shape, and the fine-grid Euler-based optimization produced the lowest cruise efficiency.

Baysal, Oktay↗
NASA NTRS1999

Sonic Boom Prediction and Minimization of the Douglas Reference OPT5 Configuration

Conventional CFD methods and grids do not yield adequate resolution of the complex shock flow pattern generated by a real aircraft geometry. As a result, a unique grid topology and supersonic flow solver was developed at Northrop Grumman based on the characteristic behavior of supersonic wave patterns emanating from the aircraft. Using this approach, it was possible to compute flow fields with adequate resolution several body lengths below the aircraft. In this region, three-dimensional effects are diminished and conventional two-dimensional modified linear theory (MLT) can be applied to estimate ground pressure signatures or sonic booms. To accommodate real aircraft geometries and alleviate the burdensome grid generation task, an implicit marching multi-block, multi-grid finite-volume Euler code was developed as the basis for the sonic boom prediction methodology. The Thomas two-dimensional extrapolation method is built into the Euler code so that ground signatures can be obtained quickly and efficiently with minimum computational effort suitable to the aircraft design environment. The loudness levels of these signatures can then be determined using a NASA generated noise code. Since the Euler code is a three-dimensional flow field solver, the complete circumferential region below the aircraft is computed. The extrapolation of all this field data from a cylinder of constant radius leads to the definition of the entire boom corridor occurring directly below and off to the side of the aircraft's flight path yielding an estimate for the entire noise "annoyance" corridor in miles as well as its magnitude. An automated multidisciplinary sonic boom design optimization software system was developed during the latter part of HSR Phase 1. Using this system, it was found that sonic boom signatures could be reduced through optimization of a variety of geometric aircraft parameters. This system uses a gradient based nonlinear optimizer as the driver in conjunction with a computationally efficient Euler CFD solver (NIIM3DSB) for computing the three-dimensional near-field characteristics of the aircraft. The intent of the design system is to identify and optimize geometric design variables that have a beneficial impact on the ground sonic boom. The system uses a simple wave drag data format to specify the aircraft geometry. The geometry is internally enhanced and analytic methods are used to generate marching grids suitable for the multi-block Euler solver. The Thomas extrapolation method is integrated into this system, and hence, the aircraft's centerline ground sonic boom signature is also automatically computed for a specified cruise altitude and yields the parameters necessary to evaluate the design function. The entire design system has been automated since the gradient based optimization software requires many flow analyses in order to obtain the required sensitivity derivatives for each design variable in order to converge on an optimal solution. Hence, once the problem is defined which includes defining the objective function and geometric and aerodynamic constraints, the system will automatically regenerate the perturbed geometry, the necessary grids, the Euler solution, and finally the ground sonic boom signature at the request of the optimizer.

Siclari, Michael J.↗
DOE OSTI2022

Pauling’s rules for oxide-based minerals: A re-examination based on quantum mechanical constraints and modern applications of bond-valence theory to Earth materials

Since their introduction in 1929, Pauling’s five rules have been used by scientists from many disciplines to rationalize and predict stable arrangements of atoms and coordination polyhedra in crystalline solids; amorphous materials such as silicate glasses and melts; nanomaterials, poorly crystalline solids; aqueous cation and anion complexes; and sorption complexes at mineral-aqueous solution interfaces. The predictive power of these simple yet powerful rules was challenged recently by George et al. (2020), who performed a statistical analysis of the performance of Pauling’s five rules for about 5000 oxide crystal structures. They concluded that only 13% of the oxides satisfy the last four rules simultaneously and that the second rule has the most exceptions. They also found that Pauling’s first rule is satisfied for only 66% of the coordination environments tested and concluded that no simple rule linking ionic radius to coordination environment will be predictive due to the variable quality of univalent radii. We address these concerns and discuss quantum mechanical calculations that complement Pauling’s rules, particularly his first (radius sum and radius ratio rule) and second (electrostatic valence rule) rules. We also present a more realistic view of the bonded radii of atoms, derived by determining the local minimum in the electron density distribution measured along trajectories between bonded atoms known as bond paths, i.e., the bond critical point (rc). Electron density at the bond critical point is a quantum mechanical observable that correlates well with Pauling bond strength. Moreover, a metal atom in a polyhedron has as many bonded radii as it has bonded interactions, resulting in metal and O atoms that may not be spherical. O atoms, for example, are not spherical in many oxide-based crystal structures. Instead, the electron density of a bonded oxygen is often highly distorted or polarized, with its bonded radius decreasing systematically from ~1.38 Å when bonded to highly electropositive atoms like sodium to 0.64 Å when bonded to highly electronegative atoms like nitrogen. Bonded radii determined for metal atoms match the Shannon (1976) radii for more electropositive atoms, but the match decreases systematically as the electronegativities of the M atoms increase. As a result, significant departures from the radius ratio rule in the analysis by George et al. (2020) is not surprising. We offer a modified, more fundamental version of Pauling’s first rule and demonstrate that the second rule has a one-to-one connection between the electron density accumulated between the bonded atoms at the bond critical point and the Pauling bond strength of the bonded interaction. Pauling’s second rule implicitly assumes that bond strength is invariant with bond length for a given pair of bonded atoms. Many studies have since shown that this is not the case, and Brown and Shannon (1973) developed an equation and a set of parameters to describe the relation between bond length and bond strength, now redefined as bond valence to avoid confusion with Pauling bond-strength. Brown (1980) used the valence-sum rule, together with the path rule and the valence-matching principle, as the three axioms of bond-valence theory (BVT), a powerful method for understanding many otherwise elusive aspects of crystals and also their participation in dynamic processes. We show how a priori bond-valence calculations can predict unstrained bond-lengths and how bond-valence mapping can locate low-Z atoms in a crystal structure (e.g., Li) or examine possible diffusion pathways for atoms through crystal structures. In addition, we briefly discuss Pauling’s third, fourth, and fifth rules, the first two of which concern the sharing of polyhedron elements (edges and faces) and the common instability associated with structures in which a polyhedron shares an edge or face with another polyhedron and contains high-valence cations. The olivine [α-(MgxFe1–x)2SiO4] crystal structure is used to illustrate the distortions from hexagonal close-packing of O atoms caused by metal-metal repulsion across shared polyhedron edges. We conclude by discussing several applications of BVT to Earth materials, including the use of BVT to: (1) locate H+ ions in crystal structures, including the location of protons in the crystal structures of nominally anhydrous minerals in Earth’s mantle; (2) determine how strongly bonded (usually anionic) structural units interact with weakly bonded (usually cationic) interstitial complexes in complex uranyl-oxide and uranyl-oxysalt minerals using the valence-matching principle; (3) calculate Lewis acid strengths of cations and Lewis base strengths of anions; (4) determine how (H2O) groups can function as bond-valence transformers by dividing one bond into two bonds of half the bond valence; (5) help characterize products of sorption reactions of aqueous cations (e.g., Co2+ and Pb2+) and oxyanions [e.g., selenate (Se6+O4)2- and selenite (Se4+O3)2-] at mineral-aqueous solution interfaces and the important role of protons in these reactions; and (6) help characterize the local coordination environments of highly charged cations (e.g., Zr4+, Ti4+, U4+, U5+, and U6+) in silicate glasses and melts.

Geochemistry & Geophysics↗
DOE OSTI2020

f-Orbital Mixing in the Octahedral f 2 Compounds UX 6 2– [X = F, Br, Cl, I] and PrCl 6 3–

Understanding how interactions between the f orbitals and ligand orbitals in lanthanide and actinide systems affect their physical properties is the central issue in f-element chemistry. A wide variety of approaches including both theoretical and experimental tools have been used to study these relationships. Among the most widely used tools has been crystal field theory (CFT), which bridges theory and experiment in that it is a model based largely on atomic theory that is parametrized using experimental data. Crystal field theory is quite accurate for the lanthanides, due in part to the highly contracted nature of the 4f orbitals. For actinides, crystal field theory is less accurate, potentially due to the treatment of orbital mixing. In CFT, orbital mixing is handled implicitly by allowing the electron repulsion parameters (Slater F k parameters) and the spin–orbit coupling constant to vary. As a result, orbital mixing in CFT is isotropic in that the F k parameters and the spin–orbit coupling constant affect all f orbitals equally. This approximation works well for the lanthanides due to the limited degree of orbital mixing in these complexes. In actinide complexes, the 5f orbitals have greater overlap with the ligand orbitals, and this approximation is less accurate than in the lanthanides. In this work, we report a modification of CFT that includes the effect of orbital mixing on electron repulsion and spin–orbit coupling for each f orbital. The model is applied to the tetravalent uranium hexahalide dianions and PrCl 6 3– for which the energies of many low-lying excited states are known. The new model generally fits the data as well the traditional CFT although with fewer parameters. However, the new model does not fit the data better than the more complex CFT models of Faucher and co-workers. The results of the model show in detail how changes in overlap and orbital energies influence the energies of the bonding and antibonding orbitals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Analog neutron transport for nuclear instrumentation applications with the Monte-Carlo code TRIPOLI-4 - Paper 3

Monte-Carlo codes simulating particle transport usually make use of well-known variance reduction techniques, leading to more efficient simulations. Even in configurations which do not deal with deep-penetration, some of these techniques, such as the implicit capture, are actually often used by default. The statistical weight of the simulated particles is then modified in order to take into account the modification of the sampling without introducing any bias in the estimation process. For instance, the implicit capture decreases the statistical weight of the particles at each collision, whereas the sampling of a single outgoing particle increases this statistical weight in case of scattering reactions producing multiple neutrons. In addition, Russian roulette and splitting operations, which are usually also played at each collision, lead to other modifications of the statistical weights. As a result, Monte-Carlo codes provide particle histories that are valid on average, but collect statistical weights which differ from 1, when tallying the estimation of the quantities of interest. Yet, some nuclear instrumentation calculations inherently need to work with statistical weights equal to 1, since either individual events have to be collected (such as the arrival of a particle at a detector, the measurement of a time of flight, etc), or the coincidence of events or also correlations between individual events have to be taken into account. To address these specific applications with Monte-Carlo simulation codes, users need a full analog simulation mode. The continuous-energy Monte-Carlo code TRIPOLI4{sup R} is mainly dedicated to shielding, reactor physics and criticality safety calculations. Its capabilities have recently been extended to widen its use to nuclear instrumentation with the possibility of γ-spectrometry calculations and the simulation of photonuclear reactions for instance. Other features needed by nuclear instrumentation applications have been available in TRIPOLI-4 for a long time, such as the sampling of the time variable and the possibility of tallying in a time grid for most of the available tallies (fluxes, reaction rates, dose equivalent rates, energy depositions, etc). In TRIPOLI-4, the transport between two consecutive collisions is analog if no variance reduction technique is requested by the user to handle deep-penetration configurations. However, up to the version 9 of the code, the collision itself is sampled in a non-analog way. This paper presents a first implementation of a full analog neutron transport mode in TRIPOLI-4, preliminary verification results and an application of this functionality to the simulation of the Nucifer detector located in Saclay, France. It should be noted that only neutron transport is dealt with in this work and that all nuclear data come from JEFF-3.1.1 or ENDF/B-VII.0 evaluations, including fission data when needed. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2017

Systematic Biases in Weak Lensing Cosmology with the Dark Energy Survey

This thesis sets out a practical guide to applying shear measurements as a cosmological tool. We first present one of two science-ready galaxy shape catalogues from Year 1 of the Dark Energy Survey (DES Y1), which covers 1500 square degrees in four bands $griz$, with a median redshift of $0.59$. We describe the shape measurement process implemented by the DES Y1 imshape catalogue, which contains 21.9 million high-quality $r$-band bulge/disc fits. In Chapter 3 a new suite of image simulations, referred to as Hoopoe, are presented. The Hoopoe dataset is tailored to DES Y1 and includes realistic blending, spatial masks and variation in the point spread function. We derive shear corrections, which we show are robust to changes in calibration method, galaxy binning and variance within the simulated dataset. Sources of systematic uncertainty in the simulation-based shear calibration are discussed, leading to a final estimate of the $1\sigma$ uncertainties in the residual multiplica tive bias after calibration of 0.025. Chapter 4 describes an extension of the analysis on the Hoopoe simulations into a detailed investigation of the impact of galaxy neighbours on shape measurement and shear cosmology. Four mechanisms by which neighbours can have a non-negligible influence on shear measurement are identified. These effects, if ignored, would contribute a net multiplicative bias of $m \sim 0.03 - 0.09$ in DES Y1, though the precise impact will depend on both the measurement code and the selection cuts applied. We use the cosmological inference pipeline of DES Y1 to explore the cosmological implications of neighbour bias and show that omitting blending from the calibration simulation for DES Y1 would bias the inferred clustering amplitude $S_8 \equiv \sigma_8 (\omegam /0.3)^{0.5}$ by $1.5 \sigma$ towards low values. Finally, we use the Hoopoe simulations to test the effect of neighbour-induced spatial correlations in the multiplicative bias. We find the cosmo logical impact to be subdominant to statistical error at the! current level of precision. Another major uncertainity in shear cosmology is the accuracy of our ensemble redshift distributions. Chapter 5 presents a numerical investigation into the combined constraining power of cosmic shear, galaxy clustering and their cross-correlation in DES Y1, and the potential for internal calibration of redshift errors. Introducing a moderate uniform bias into the redshift distributions used to model the weak lensing (WL) galaxies is shown to produce a $> 2\sigma$ bias in $S_8$. We demonstrate that this cosmological bias can be eliminated by marginalising over redshift error nuisance parameters. Strikingly, the cosmological constraint of the combined dataset is largely undiminished by the loss of prior information on the WL distributions. We demonstrate that this implicit self-calibration is the result of complementary degeneracy directions in the combined data. In Chapter 6 we present the preliminary results of an investigation into galaxy intrin sic alignments. Using the DES Y1 data, we show a clear dependence in alignment amplitude on galaxy type, in agreement with previous results. We subject these findings to a series of initial robustness tests. We conclude with a short overview of the work presented, and discuss prospects for the future.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Simulation study of 3–5 keV x-ray conversion efficiency from Ar K-shell vs. Ag L-shell targets on the National Ignition Facility laser

Tailored, high-flux, multi-keV x-ray sources are desirable for studying x-ray interactions with matter for various civilian, space and military applications. For this study, we focus on designing an efficient laser-driven non-local thermodynamic equilibrium 3–5 keV x-ray source from photon-energy-matched Ar K-shell and Ag L-shell targets at sub-critical densities (∼n{sub c}/10) to ensure supersonic, volumetric laser heating with minimal losses to kinetic energy, thermal x rays and laser-plasma instabilities. Using HYDRA, a multi-dimensional, arbitrary Lagrangian-Eulerian, radiation-hydrodynamics code, we performed a parameter study by varying initial target density and laser parameters for each material using conditions readily achievable on the National Ignition Facility (NIF) laser. We employ a model, benchmarked against Kr data collected on the NIF, that uses flux-limited Lee-More thermal conductivity and multi-group implicit Monte-Carlo photonics with non-local thermodynamic equilibrium, detailed super-configuration accounting opacities from CRETIN, an atomic-kinetics code. While the highest power laser configurations produced the largest x-ray yields, we report that the peak simulated laser to 3–5 keV x-ray conversion efficiencies of 17.7% and 36.4% for Ar and Ag, respectively, occurred at lower powers between ∼100–150 TW. For identical initial target densities and laser illumination, the Ag L-shell is observed to have ≳10× higher emissivity per ion per deposited laser energy than the Ar K-shell. Although such low-density Ag targets have not yet been demonstrated, simulations of targets fabricated using atomic layer deposition of Ag on silica aerogels (∼20% by atomic fraction) suggest similar performance to atomically pure metal foams and that either fabrication technique may be worth pursuing for an efficient 3–5 keV x-ray source on NIF.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Ethylene glycol reforming on Pt(111): first-principles microkinetic modeling in vapor and aqueous phases

First-principles, periodic density functional theory (DFT) calculations and mean-field microkinetic modeling have been used to investigate the decomposition of ethylene glycol for hydrogen production on Pt(111) in vapor and aqueous phases. All dehydrogenated species derived from ethylene glycol (C 2 H x O 2 , x = 0–6) and methanol (CH y O, y = 0–4), and all elementary C–C, C–H, and O–H bond breaking steps are included in the microkinetic model. Reaction path analysis in vapor phase indicates that both initial C–H and O–H dehydrogenation steps are kinetically relevant at all temperatures (470–530 K). Initial O–H bond cleavage is reversible at low temperatures but accounts for an increasingly dominant fraction of the total reaction flux at higher temperatures. C–C bond scission is observed only after significant dehydrogenation (x ≤ 3) and is more likely to happen in surface intermediates where one of the cleavage products is CO. Here, the process is highly selective to the production of H2 compared to methanol. For aqueous-phase model development, free energies of solvation were computed for all surface intermediates and transition states using a continuum solvation approach. Our aqueous-phase microkinetic model predicts a 0.4 eV lower apparent activation energy and an order of magnitude larger turnover frequencies. Initial C–H bond cleavage becomes more important but the general trends are similar to the vapor phase, suggesting that the reaction chemistry is similar in both vapor and aqueous phases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Linear and Nonlinear Solvers for Simulating Multiphase Flow within Large-Scale Engineered Subsurface Systems

Simulation of multiphase flow in the subsurface is well-known to be computationally challenging. While there have been many studies that have explored approaches to overcoming these challenges, they often utilize relatively simple case studies. In this paper, we focus on the unique numerical challenges posed by modeling large-scale engineered subsurface systems, characterized by discrete features embedded in a heterogeneous natural subsurface setting. The man-made features such as shafts, tunnels, and barriers often cause multiple challenges in modeling the domain for multiphase porous media flow. This flow scenario can have a wide range of applications such as nuclear waste repositories, enhanced recovery of a petroleum reservoir, geothermal engineering, and carbon sequestration. An example of these severe numerical challenges is the case of performance assessment (PA) for Waste Isolation Pilot Plant (WIPP), the only operating deep geological repository in the US, which simulates extreme material properties of bedded salt rock formation and extreme contrast due to open excavation next to the formation. The models have extremes not only of permeability and porosity but also of the constitutive models needed for multiphase flow; additionally, they have process models like salt creep closure reducing porosity over time, fracturing in clay and anhydrite interbeds of the bedded salt, gas generation from the waste materials, and unintentional human borehole intrusions in some scenarios. Numerical simulations require the solution of coupled systems of nonlinear PDEs; in our work, we use the open-source simulator PFLOTRAN which is based on Finite Volume discretization. The solution of the nonlinear equations requires use of the Newton-Raphson iteration at each time step, which entails the solution of the linearized Jacobian system at each iteration. The effects of all the processes (i.e., large number of unknowns, highly nonlinear constitutive relations, large contrasts in material properties in short distances) lead to an ill-conditioned Jacobian matrix that severely challenges traditional linear solver, i.e., stabilized biconjugate gradient with block Jacobi incomplete LU preconditioner (BCGS-ILU) leading to non-convergence for traditional Newton-Raphson nonlinear solver causing unacceptably long computation time for each model. This paper presents linear solvers such as constrained pressure residual (CPR) two-stage preconditioner with alternate-block-factorization (ABF) and quasi- implicit pressure and explicit saturation (QIMPES) decouplers and flexible generalized residual solver (FGMRES). The new general-purpose nonlinear solver, Newton trust-region dogleg Cauchy (NTRDC), is also introduced to resolve extreme nonlinearities in the models. We demonstrate the effectiveness of each method relative to the default BCGS-Newton solver. The two best cases had nearly 50 times speed-up and achieved completion of a simulation in 14 hours that never completed due to non-convergence with the default solver. We also investigate the strong scalability of each method and discuss some of the deficiencies found for Block Jacobi preconditioner using parallel domain decomposition, and node packing effects of modern processor architecture.

Preconditioner, Nonlinear, Porous media, Multiphas↗
DOE OSTI2013

Optimization of energy window for {sup 90}Y bremsstrahlung SPECT imaging for detection tasks using the ideal observer with model-mismatch

Purpose: In yttrium-90 ({sup 90}Y) microsphere brachytherapy (radioembolization) of unresectable liver cancer, posttherapy {sup 90}Y bremsstrahlung single photon emission computed tomography (SPECT) has been used to document the distribution of microspheres in the patient and to help predict potential side effects. The energy window used during projection acquisition can have a significant effect on image quality. Thus, using an optimal energy window is desirable. However, there has been great variability in the choice of energy window due to the continuous and broad energy distribution of {sup 90}Y bremsstrahlung photons. The area under the receiver operating characteristic curve (AUC) for the ideal observer (IO) is a widely used figure of merit (FOM) for optimizing the imaging system for detection tasks. The IO implicitly assumes a perfect model of the image formation process. However, for {sup 90}Y bremsstrahlung SPECT there can be substantial model-mismatch (i.e., difference between the actual image formation process and the model of it assumed in reconstruction), and the amount of the model-mismatch depends on the energy window. It is thus important to account for the degradation of the observer performance due to model-mismatch in the optimization of the energy window. The purpose of this paper is to optimize the energy window for {sup 90}Y bremsstrahlung SPECT for a detection task while taking into account the effects of the model-mismatch. Methods: An observer, termed the ideal observer with model-mismatch (IO-MM), has been proposed previously to account for the effects of the model-mismatch on IO performance. In this work, the AUC for the IO-MM was used as the FOM for the optimization. To provide a clinically realistic object model and imaging simulation, the authors used a background-known-statistically and signal-known-statistically task. The background was modeled as multiple compartments in the liver with activity parameters independently following a Gaussian distribution; the signal was modeled as a tumor with a Gaussian-distributed activity parameter located randomly with equal probability at one of three positions. The IO test statistics (i.e., likelihood ratios) were estimated using Markov-chain Monte Carlo methods. The authors realistically modeled human anatomy using a digital phantom code, and realistically simulated {sup 90}Y bremsstrahlung SPECT imaging with a clinical SPECT system and typical imaging parameters using a previously validated Monte Carlo bremsstrahlung simulation method. Model-mismatch was included by modeling image formation process in the calculation of IO test statistics using an analytic modeling method previously developed for quantitative {sup 90}Y bremsstrahlung SPECT. To demonstrate the effects of the model-mismatch on the detection task, the authors optimized the energy window both with and without model-mismatch included in the IO. Results: For all the energy windows, the AUC values for the IO-MM were smaller than that for the IO. The optimal windows for the IO-MM and the IO were 80-180 and 60-400 keV, respectively. Conclusions: The authors have demonstrated the degradation of the ideal performance due to model-mismatch and optimized the energy window for {sup 90}Y bremsstrahlung SPECT for detection tasks by accounting for the effects of the model-mismatch. The obtained optimal window was much narrower when taking into account the model-mismatch and similar to that obtained previously for estimation tasks.

61 RADIATION PROTECTION AND DOSIMETRY↗