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Numerically approximating centrality for graph ranking guarantees

Many real-world datasets can be represented as graphs. Using iterative solvers to approximate graph centrality measures allows us to obtain a ranking vector on the nodes of the graph, consisting of a number for each vertex in the graph identifying its relative importance. In this study the centrality measures we use are Katz Centrality and PageRank. Given an approximate solution, we use the residual to accurately estimate how much of the ranking matches the ranking given by the exact solution. Using probabilistic matrix norms, we obtain bounds on the accuracy of the approximation compared to the exact solution with respect to the highly ranked nodes and apply numerical analysis to the computation of centrality with iterative methods. This relates the numerical accuracy of the linear solver to the data analysis accuracy of finding the correct ranking. In particular, we answer the question of which pairwise rankings are reliable given an approximate solution to the linear system. Experiments on many real-world undirected and directed networks up to several million vertices and several hundred million edges validate our theory and show that we are able to accurately estimate large portions of the approximation. We also analyze the difference between global centrality scores and personalized scores (w.r.t. specific seed vertices). By analyzing convergence error, we develop confidence in the ranking schemes of data mining. We show we are able to accurately guarantee ranking of vertices with an approximation to centrality metrics faster than current methods.

97 MATHEMATICS AND COMPUTING↗

WE-G-BRF-04: Robust Real-Time Volumetric Imaging Based On One Single Projection

Purpose: Real-time volumetric imaging is highly desirable to provide instantaneous image guidance for lung radiation therapy. This study proposes a scheme to achieve this goal using one single projection by utilizing sparse learning and a principal component analysis (PCA) based lung motion model. Methods: A patient-specific PCA-based lung motion model is first constructed by analyzing deformable vector fields (DVFs) between a reference image and 4DCT images at each phase. At the training stage, we “learn” the relationship between the DVFs and the projection using sparse learning. Specifically, we first partition the projections into patches, and then apply sparse learning to automatically identify patches that best correlate with the principal components of the DVFs. Once the relationship is established, at the application stage, we first employ a patchbased intensity correction method to overcome the problem of different intensity scale between the calculated projection in the training stage and the measured projection in the application stage. The corrected projection image is then fed to the trained model to derive a DVF, which is applied to the reference image, yielding a volumetric image corresponding to the projection. We have validated our method through a NCAT phantom simulation case and one experiment case. Results: Sparse learning can automatically select those patches containing motion information, such as those around diaphragm. For the simulation case, over 98% of the lung region pass the generalized gamma test (10HU/1mm), indicating combined accuracy in both intensity and spatial domain. For the experimental case, the average tumor localization errors projected to the imager are 0.68 mm and 0.4 mm on the axial and tangential direction, respectively. Conclusion: The proposed method is capable of accurately generating a volumetric image using one single projection. It will potentially offer real-time volumetric image guidance to facilitate lung radiotherapy. This study is supported in part by NIH (1R01CA154747-01), The Core Technology Research in Strategic Emerging Industry, Guangdong, China(2011A081402003)

60 APPLIED LIFE SCIENCES↗

The magnetic field of active region 11158 during the 2011 February 12-17 flares: Differences between photospheric extrapolation and coronal forward-fitting methods

We developed a coronal nonlinear force-free field (COR-NLFFF) forward-fitting code that fits an approximate nonlinear force-free field (NLFFF) solution to the observed geometry of automatically traced coronal loops. In contrast to photospheric NLFFF codes, which calculate a magnetic field solution from the constraints of the transverse photospheric field, this new code uses coronal constraints instead, and this way provides important information on systematic errors of each magnetic field calculation method, as well as on the non-force-freeness in the lower chromosphere. In this study we applied the COR-NLFFF code to NOAA Active Region 11158, during the time interval of 2011 February 12-17, which includes an X2.2 GOES-class flare plus 35 M- and C-class flares. We calculated the free magnetic energy with a 6 minute cadence over 5 days. We find good agreement between the two types of codes for the total nonpotential E{sub N} and potential energy E{sub P} but find up to a factor of 4 discrepancy in the free energy E {sub free} = E{sub N} – E{sub P} and up to a factor of 10 discrepancy in the decrease of the free energy ΔE {sub free} during flares. The coronal NLFFF code exhibits a larger time variability and yields a decrease of free energy during the flare that is sufficient to satisfy the flare energy budget, while the photospheric NLFFF code shows much less time variability and an order of magnitude less free-energy decrease during flares. The discrepancy may partly be due to the preprocessing of photospheric vector data but more likely is due to the non-force-freeness in the lower chromosphere. We conclude that the coronal field cannot be correctly calculated on the basis of photospheric data alone and requires additional information on coronal loop geometries.

79 ASTRONOMY AND ASTROPHYSICS↗

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↗

TU-AB-303-11: Predict Parotids Deformation Applying SIS Epidemiological Model in H&N Adaptive RT

Purpose: The aim is to investigate the use of epidemiological models to predict morphological variations in patients undergoing radiation therapy (RT). The susceptible-infected-susceptible (SIS) deterministic model was applied to simulate warping within a focused region of interest (ROI). Hypothesis is to consider each voxel like a single subject of the whole sample and to treat displacement vector fields like an infection. Methods: Using Raystation hybrid deformation algorithms and automatic re-contouring based on mesh grid, we post-processed 360 MVCT images of 12 H&N patients treated with Tomotherapy. Study focused on parotid glands, identified by literature and previous analysis, as ROI more susceptible to warping in H&N region. Susceptible (S) and infectious (I) cases were identified in voxels with inter-fraction movement respectively under and over a set threshold. IronPython scripting allowed to export positions and displacement data of surface voxels for every fraction. A MATLAB homemade toolbox was developed to model the SIS. Results: SIS model was validated simulating organ motion on QUASAR phantom. Applying model in patients, within a [0–1cm] range, a single voxel movement of 0.4cm was selected as displacement threshold. SIS indexes were evaluated by MATLAB simulations. Dynamic time warping algorithm was used to assess matching between model and parotids behavior days of treatments. The best fit of the model was obtained with contact rate of 7.89±0.94 and recovery rate of 2.36±0.21. Conclusion: SIS model can follow daily structures evolutions, making possible to compare warping conditions and highlighting challenges due to abnormal variation and set-up errors. By epidemiology approach, organ motion could be assessed and predicted not in terms of average of the whole ROI, but in a voxel-by-voxel deterministic trend. Identifying anatomical region subjected to variations, would be possible to focus clinic controls within a cohort of pre-selected patients eligible for adaptive RT. The research is partially co-funded by the Italian Research Grant: Dose warping methods for IGRT and Adaptive RT: dose accumulation based on organ motion and anatomical variations of the patients during radiation therapy treatments,MoH (GR-2010-2318757) and Tecnologie Avanzate S.r.l.(Italy)

60 APPLIED LIFE SCIENCES↗

WE-AB-202-09: Feasibility and Quantitative Analysis of 4DCT-Based High Precision Lung Elastography

Purpose: The purpose of this project is to derive high precision elastography measurements from 4DCT lung scans to facilitate the implementation of elastography in a radiotherapy context. Methods: 4DCT scans of the lungs were acquired, and breathing stages were subsequently registered to each other using an optical flow DIR algorithm. The displacement of each voxel gleaned from the registration was taken to be the ground-truth deformation. These vectors, along with the 4DCT source datasets, were used to generate a GPU-based biomechanical simulation that acted as a forward model to solve the inverse elasticity problem. The lung surface displacements were applied as boundary constraints for the model-guided lung tissue elastography, while the inner voxels were allowed to deform according to the linear elastic forces within the model. A biomechanically-based anisotropic convergence magnification technique was applied to the inner voxels in order to amplify the subtleties of the interior deformation. Solving the inverse elasticity problem was accomplished by modifying the tissue elasticity and iteratively deforming the biomechanical model. Convergence occurred when each voxel was within 0.5 mm of the ground-truth deformation and 1 kPa of the ground-truth elasticity distribution. To analyze the feasibility of the model-guided approach, we present the results for regions of low ventilation, specifically, the apex. Results: The maximum apical boundary expansion was observed to be between 2 and 6 mm. Simulating this expansion within an apical lung model, it was observed that 100% of voxels converged within 0.5 mm of ground-truth deformation, while 91.8% converged within 1 kPa of the ground-truth elasticity distribution. A mean elasticity error of 0.6 kPa illustrates the high precision of our technique. Conclusion: By utilizing 4DCT lung data coupled with a biomechanical model, high precision lung elastography can be accurately performed, even in low ventilation regions of the lungs. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1144087.

60 APPLIED LIFE SCIENCES↗

Application of a new hybrid particle swarm optimization-mixed kernels function-based support vector machine model for reservoir porosity prediction: A case study in Jacksonburg-Stringtown oil field, West Virginia, USA

Porosity is a fundamental property that characterizes the storage capability of fluid and gas-bearing formations in a reservoir. An accurate porosity value can be measured from core samples in the laboratory; however, core analysis is expensive and time consuming. Well-log data can be used to calculate porosity, but the availability of log suites is often limited in mature fields. Therefore, robust porosity prediction requires integration of core-measured porosity with available well-log suites to control for changes in lithology and fluid content. A support vector machine (SVM) model with mixed kernel function (MKF) is used to construct the relationship between limited conventional well-log suites and sparse core data. Porosity is the desired output, and two conventional well-log responses (gamma ray [GR] and bulk density) and three well-log-derived parameters (the slope of GR, the slope of density, and [Formula: see text]) are input parameters. A global stochastic searching algorithm, particle swarm optimization (PSO), is applied to improve the efficiency of locating the appropriate values of five control parameters in MKF-SVM model. The results of SVM with different traditional kernel functions were compared, and the MKF-SVM model provided an improvement over the traditional SVM model. To confirm the advantage of the hybrid PSO-MKF-SVM model, the results from three models: (1) radial basis function (RBF)-based least-squares SVM, (2) multilayer perceptron artificial neural network (ANN), and (3) RBF ANN, are compared with the result of the hybrid PSO-MKF-SVM model. The results indicate that the hybrid PSO-MKF-SVM model improves porosity prediction with the highest correlation coefficient ([Formula: see text] of 0.9560), the highest coefficient of determination ([Formula: see text] of 0.9140), the lowest root-mean-square error (1.6505), average absolute error value (1.4050), and maximum absolute error (2.717).

Geochemistry & Geophysics↗

3D delivered dose assessment using a 4DCT-based motion model

Purpose: The purpose of this work is to develop a clinically feasible method of calculating actual delivered dose distributions for patients who have significant respiratory motion during the course of stereotactic body radiation therapy (SBRT). Methods: A novel approach was proposed to calculate the actual delivered dose distribution for SBRT lung treatment. This approach can be specified in three steps. (1) At the treatment planning stage, a patient-specific motion model is created from planning 4DCT data. This model assumes that the displacement vector field (DVF) of any respiratory motion deformation can be described as a linear combination of some basis DVFs. (2) During the treatment procedure, 2D time-varying projection images (either kV or MV projections) are acquired, from which time-varying “fluoroscopic” 3D images of the patient are reconstructed using the motion model. The DVF of each timepoint in the time-varying reconstruction is an optimized linear combination of basis DVFs such that the 2D projection of the 3D volume at this timepoint matches the projection image. (3) 3D dose distribution is computed for each timepoint in the set of 3D reconstructed fluoroscopic images, from which the total effective 3D delivered dose is calculated by accumulating deformed dose distributions. This approach was first validated using two modified digital extended cardio-torso (XCAT) phantoms with lung tumors and different respiratory motions. The estimated doses were compared to the dose that would be calculated for routine 4DCT-based planning and to the actual delivered dose that was calculated using “ground truth” XCAT phantoms at all timepoints. The approach was also tested using one set of patient data, which demonstrated the application of our method in a clinical scenario. Results: For the first XCAT phantom that has a mostly regular breathing pattern, the errors in 95% volume dose (D95) are 0.11% and 0.83%, respectively for 3D fluoroscopic images reconstructed from kV and MV projections compared to the ground truth, which is clinically comparable to 4DCT (0.093%). For the second XCAT phantom that has an irregular breathing pattern, the errors are 0.81% and 1.75% for kV and MV reconstructions, both of which are better than that of 4DCT (4.01%). In the case of real patient, although it is impossible to obtain the actual delivered dose, the dose estimation is clinically reasonable and demonstrates differences between 4DCT and MV reconstruction-based dose estimates. Conclusions: With the availability of kV or MV projection images, the proposed approach is able to assess delivered doses for all respiratory phases during treatment. Compared to the planning dose based on 4DCT, the dose estimation using reconstructed 3D fluoroscopic images was as good as 4DCT for regular respiratory pattern and was a better dose estimation for the irregular respiratory pattern.

60 APPLIED LIFE SCIENCES↗

Greenhouse Gas Source Attribution: Measurements Modeling and Uncertainty Quantification

In this project we have developed atmospheric measurement capabilities and a suite of atmospheric modeling and analysis tools that are well suited for verifying emissions of green- house gases (GHGs) on an urban-through-regional scale. We have for the first time applied the Community Multiscale Air Quality (CMAQ) model to simulate atmospheric CO 2 . This will allow for the examination of regional-scale transport and distribution of CO 2 along with air pollutants traditionally studied using CMAQ at relatively high spatial and temporal resolution with the goal of leveraging emissions verification efforts for both air quality and climate. We have developed a bias-enhanced Bayesian inference approach that can remedy the well-known problem of transport model errors in atmospheric CO 2 inversions. We have tested the approach using data and model outputs from the TransCom3 global CO 2 inversion comparison project. We have also performed two prototyping studies on inversion approaches in the generalized convection-diffusion context. One of these studies employed Polynomial Chaos Expansion to accelerate the evaluation of a regional transport model and enable efficient Markov Chain Monte Carlo sampling of the posterior for Bayesian inference. The other approach uses de- terministic inversion of a convection-diffusion-reaction system in the presence of uncertainty. These approaches should, in principle, be applicable to realistic atmospheric problems with moderate adaptation. We outline a regional greenhouse gas source inference system that integrates (1) two ap- proaches of atmospheric dispersion simulation and (2) a class of Bayesian inference and un- certainty quantification algorithms. We use two different and complementary approaches to simulate atmospheric dispersion. Specifically, we use a Eulerian chemical transport model CMAQ and a Lagrangian Particle Dispersion Model - FLEXPART-WRF. These two models share the same WRF assimilated meteorology fields, making it possible to perform a hybrid simulation, in which the Eulerian model (CMAQ) can be used to compute the initial condi- tion needed by the Lagrangian model, while the source-receptor relationships for a large state vector can be efficiently computed using the Lagrangian model in its backward mode. In ad- dition, CMAQ has a complete treatment of atmospheric chemistry of a suite of traditional air pollutants, many of which could help attribute GHGs from different sources. The inference of emissions sources using atmospheric observations is cast as a Bayesian model calibration problem, which is solved using a variety of Bayesian techniques, such as the bias-enhanced Bayesian inference algorithm, which accounts for the intrinsic model deficiency, Polynomial Chaos Expansion to accelerate model evaluation and Markov Chain Monte Carlo sampling, and Karhunen-Lo %60 eve (KL) Expansion to reduce the dimensionality of the state space. We have established an atmospheric measurement site in Livermore, CA and are collect- ing continuous measurements of CO 2 , CH 4 and other species that are typically co-emitted with these GHGs. Measurements of co-emitted species can assist in attributing the GHGs to different emissions sectors. Automatic calibrations using traceable standards are performed routinely for the gas-phase measurements. We are also collecting standard meteorological data at the Livermore site as well as planetary boundary height measurements using a ceilometer. The location of the measurement site is well suited to sample air transported between the San Francisco Bay area and the California Central Valley.

54 ENVIRONMENTAL SCIENCES↗

A linear, separable two-parameter model for dual energy CT imaging of proton stopping power computation

Purpose: To evaluate the accuracy and robustness of a simple, linear, separable, two-parameter model (basis vector model, BVM) in mapping proton stopping powers via dual energy computed tomography (DECT) imaging. Methods: The BVM assumes that photon cross sections (attenuation coefficients) of unknown materials are linear combinations of the corresponding radiological quantities of dissimilar basis substances (i.e., polystyrene, CaCl{sub 2} aqueous solution, and water). The authors have extended this approach to the estimation of electron density and mean excitation energy, which are required parameters for computing proton stopping powers via the Bethe–Bloch equation. The authors compared the stopping power estimation accuracy of the BVM with that of a nonlinear, nonseparable photon cross section Torikoshi parametric fit model (VCU tPFM) as implemented by the authors and by Yang et al. [“Theoretical variance analysis of single- and dual-energy computed tomography methods for calculating proton stopping power ratios of biological tissues,” Phys. Med. Biol. 55, 1343–1362 (2010)]. Using an idealized monoenergetic DECT imaging model, proton ranges estimated by the BVM, VCU tPFM, and Yang tPFM were compared to International Commission on Radiation Units and Measurements (ICRU) published reference values. The robustness of the stopping power prediction accuracy of tissue composition variations was assessed for both of the BVM and VCU tPFM. The sensitivity of accuracy to CT image uncertainty was also evaluated. Results: Based on the authors’ idealized, error-free DECT imaging model, the root-mean-square error of BVM proton stopping power estimation for 175 MeV protons relative to ICRU reference values for 34 ICRU standard tissues is 0.20%, compared to 0.23% and 0.68% for the Yang and VCU tPFM models, respectively. The range estimation errors were less than 1 mm for the BVM and Yang tPFM models, respectively. The BVM estimation accuracy is not dependent on tissue type and proton energy range. The BVM is slightly more vulnerable to CT image intensity uncertainties than the tPFM models. Both the BVM and tPFM prediction accuracies were robust to uncertainties of tissue composition and independent of the choice of reference values. This reported accuracy does not include the impacts of I-value uncertainties and imaging artifacts and may not be achievable on current clinical CT scanners. Conclusions: The proton stopping power estimation accuracy of the proposed linear, separable BVM model is comparable to or better than that of the nonseparable tPFM models proposed by other groups. In contrast to the tPFM, the BVM does not require an iterative solving for effective atomic number and electron density at every voxel; this improves the computational efficiency of DECT imaging when iterative, model-based image reconstruction algorithms are used to minimize noise and systematic imaging artifacts of CT images.

61 RADIATION PROTECTION AND DOSIMETRY↗

Metrics for the Diurnal Cycle of Precipitation: Toward Routine Benchmarks for Climate Models

In this paper, metrics are proposed—that is, a few summary statistics that condense large amounts of data from observations or model simulations—encapsulating the diurnal cycle of precipitation. Vector area averaging of Fourier amplitude and phase produces useful information in a reasonably small number of harmonic dial plots, a procedure familiar from atmospheric tide research. The metrics cover most of the globe but down-weight high-latitude wintertime ocean areas where baroclinic waves are most prominent. This enables intercomparison of a large number of climate models with observations and with each other. The diurnal cycle of precipitation has features not encountered in typical climate model intercomparisons, notably the absence of meaningful “average model” results that can be displayed in a single two-dimensional map. Displaying one map per model guides development of the metrics proposed here by making it clear that land and ocean areas must be averaged separately, but interpreting maps from all models becomes problematic as the size of a multimodel ensemble increases. Global diurnal metrics provide quick comparisons with observations and among models, using the most recent version of the Coupled Model Intercomparison Project (CMIP). This includes, for the first time in CMIP, spatial resolutions comparable to global satellite observations. Finally, consistent with earlier studies of resolution versus parameterization of the diurnal cycle, the longstanding tendency of models to produce rainfall too early in the day persists in the high-resolution simulations, as expected if the error is due to subgrid-scale physics.

54 ENVIRONMENTAL SCIENCES↗

TU-FG-BRB-03: Basis Vector Model Based Method for Proton Stopping Power Estimation From Experimental Dual Energy CT Data

Purpose: This work aims at reducing the uncertainty in proton stopping power (SP) estimation by a novel combination of a linear, separable basis vector model (BVM) for stopping power calculation (Med Phys 43:600) and a statistical, model-based dual-energy CT (DECT) image reconstruction algorithm (TMI 35:685). The method was applied to experimental data. Methods: BVM assumes the photon attenuation coefficients, electron densities, and mean excitation energies (I-values) of unknown materials can be approximated by a combination of the corresponding quantities of two reference materials. The DECT projection data for a phantom with 5 different known materials was collected on a Philips Brilliance scanner using two scans at 90 kVp and 140 kVp. The line integral alternating minimization (LIAM) algorithm was used to recover the two BVM coefficient images using the measured source spectra. The proton stopping powers are then estimated from the Bethe-Bloch equation using electron densities and I-values derived from the BVM coefficients. The proton stopping powers and proton ranges for the phantom materials estimated via our BVM based DECT method are compared to ICRU reference values and a post-processing DECT analysis (Yang PMB 55:1343) applied to vendorreconstructed images using the Torikoshi parametric fit model (tPFM). Results: For the phantom materials, the average stopping power estimations for 175 MeV protons derived from our method are within 1% of the ICRU reference values (except for Teflon with a 1.48% error), with an average standard deviation of 0.46% over pixels. The resultant proton ranges agree with the reference values within 2 mm. Conclusion: Our principled DECT iterative reconstruction algorithm, incorporating optimal beam hardening and scatter corrections, in conjunction with a simple linear BVM model, achieves more accurate and robust proton stopping power maps than the post-processing, nonlinear tPFM based DECT analysis applied to conventional reconstructions of low and high energy scans. Funding Support: NIH R01CA 75371; NCI grant R01 CA 149305.

60 APPLIED LIFE SCIENCES↗

MO-AB-BRA-09: Development and Evaluation of a Biomechanical Modeling-Assisted CBCT Reconstruction Technique (Bio-Recon)

Purpose: To develop a Bio-recon technique by incorporating the biomechanical properties of anatomical structures into the deformation-based CBCT reconstruction process. Methods: Bio-recon reconstructs the CBCT by deforming a prior high-quality CT/CBCT using a deformation-vector-field (DVF). The DVF is solved through two alternating steps: 2D–3D deformation and finite-element-analysis based biomechanical modeling. 2D–3D deformation optimizes the DVF through an ‘intensity-driven’ approach, which updates the DVF to minimize intensity mismatches between the acquired projections and the simulated projections from the deformed CBCT. In contrast, biomechanical modeling optimizes the DVF through a ‘biomechanical-feature-driven’ approach, which updates the DVF based on the biophysical properties of anatomical structures. In general, Biorecon extracts the 2D–3D deformation-optimized DVF at high-contrast structure boundaries, and uses it as the boundary condition to drive biomechanical modeling to optimize the overall DVF, especially at low-contrast regions. The optimized DVF is fed back into the 2D–3D deformation for further optimization, which forms an iterative loop. The efficacy of Bio-recon was evaluated on 11 lung patient cases, each with a prior CT and a new CT. Cone-beam projections were generated from the new CTs to reconstruct CBCTs, which were compared with the original new CTs for evaluation. 872 anatomical landmarks were also manually identified by a clinician on both the prior and new CTs to track the lung motion, which was used to evaluate the DVF accuracy. Results: Using 10 projections for reconstruction, the average (± s.d.) relative errors of reconstructed CBCTs by the clinical FDK technique, the 2D–3D deformation-only technique and Bio-recon were 46.5±5.9%, 12.0±2.3% and 10.4±1.3%, respectively. The average residual errors of DVF-tracked landmark motion by the 2D–3D deformation-only technique and Bio-recon were 5.6±4.3mm and 3.1±2.4mm, respectively. Conclusion: Bio-recon improved accuracy for both the reconstructed CBCT and the DVF. The accurate DVF can benefit multiple clinical practices, such as image-guided adaptive radiotherapy. We acknowledge funding support from the American Cancer Society (RSG-13-326-01-CCE), from the US National Institutes of Health (R01 EB020366), and from the Cancer Prevention and Research Institute of Texas (RP130109).

60 APPLIED LIFE SCIENCES↗

An optimal FFT-based anisotropic power spectrum estimator

Measurements of line-of-sight dependent clustering via the galaxy power spectrum's multipole moments constitute a powerful tool for testing theoretical models in large-scale structure. Recent work shows that this measurement, including a moving line-of-sight, can be accelerated using Fast Fourier Transforms (FFTs) by decomposing the Legendre polynomials into products of Cartesian vectors. Here, we present a faster, optimal means of using FFTs for this measurement. We avoid redundancy present in the Cartesian decomposition by using a spherical harmonic decomposition of the Legendre polynomials. With this method, a given multipole of order ℓ requires only 2ℓ+1 FFTs rather than the (ℓ+1)(ℓ+2)/2 FFTs of the Cartesian approach. For the hexadecapole (ℓ = 4), this translates to 40% fewer FFTs, with increased savings for higher ℓ. The reduction in wall-clock time enables the calculation of finely-binned wedges in P ( k ,μ), obtained by computing multipoles up to a large ℓ{sub max} and combining them. This transformation has a number of advantages. We demonstrate that by using non-uniform bins in μ, we can isolate plane-of-sky (angular) systematics to a narrow bin at 0μ ≅ while eliminating the contamination from all other bins. We also show that the covariance matrix of clustering wedges binned uniformly in μ becomes ill-conditioned when combining multipoles up to large values of ℓ{sub max}, but that the problem can be avoided with non-uniform binning. As an example, we present results using ℓ{sub max}=16, for which our procedure requires a factor of 3.4 fewer FFTs than the Cartesian method, while removing the first μ bin leads only to a 7% increase in statistical error on f σ{sub 8}, as compared to a 54% increase with ℓ{sub max}=4.

79 ASTRONOMY AND ASTROPHYSICS↗

Noise suppression for dual-energy CT via penalized weighted least-square optimization with similarity-based regularization

Purpose: Dual-energy CT (DECT) expands applications of CT imaging in its capability to decompose CT images into material images. However, decomposition via direct matrix inversion leads to large noise amplification and limits quantitative use of DECT. Their group has previously developed a noise suppression algorithm via penalized weighted least-square optimization with edge-preservation regularization (PWLS-EPR). In this paper, the authors improve method performance using the same framework of penalized weighted least-square optimization but with similarity-based regularization (PWLS-SBR), which substantially enhances the quality of decomposed images by retaining a more uniform noise power spectrum (NPS). Methods: The design of PWLS-SBR is based on the fact that averaging pixels of similar materials gives a low-noise image. For each pixel, the authors calculate the similarity to other pixels in its neighborhood by comparing CT values. Using an empirical Gaussian model, the authors assign high/low similarity value to one neighboring pixel if its CT value is close/far to the CT value of the pixel of interest. These similarity values are organized in matrix form, such that multiplication of the similarity matrix to the image vector reduces image noise. The similarity matrices are calculated on both high- and low-energy CT images and averaged. In PWLS-SBR, the authors include a regularization term to minimize the L-2 norm of the difference between the images without and with noise suppression via similarity matrix multiplication. By using all pixel information of the initial CT images rather than just those lying on or near edges, PWLS-SBR is superior to the previously developed PWLS-EPR, as supported by comparison studies on phantoms and a head-and-neck patient. Results: On the line-pair slice of the Catphan{sup ©}600 phantom, PWLS-SBR outperforms PWLS-EPR and retains spatial resolution of 8 lp/cm, comparable to the original CT images, even at 90% reduction in noise standard deviation (STD). Similar performance on spatial resolution is observed on an anthropomorphic head phantom. In addition, results of PWLS-SBR show substantially improved image quality due to preservation of image NPS. On the Catphan{sup ©}600 phantom, NPS using PWLS-SBR has a correlation of 93% with that via direct matrix inversion, while the correlation drops to −52% for PWLS-EPR. Electron density measurement studies indicate high accuracy of PWLS-SBR. On seven different materials, the measured electron densities calculated from the decomposed material images using PWLS-SBR have a root-mean-square error (RMSE) of 1.20%, while the results of PWLS-EPR have a RMSE of 2.21%. In the study on a head-and-neck patient, PWLS-SBR is shown to reduce noise STD by a factor of 3 on material images with image qualities comparable to CT images, whereas fine structures are lost in the PWLS-EPR result. Additionally, PWLS-SBR better preserves low contrast on the tissue image. Conclusions: The authors propose improvements to the regularization term of an optimization framework which performs iterative image-domain decomposition for DECT with noise suppression. The regularization term avoids calculation of image gradient and is based on pixel similarity. The proposed method not only achieves a high decomposition accuracy, but also improves over the previous algorithm on NPS as well as spatial resolution.

60 APPLIED LIFE SCIENCES↗

Improving anatomical mapping of complexly deformed anatomy for external beam radiotherapy and brachytherapy dose accumulation in cervical cancer

Purpose: In the treatment of cervical cancer, large anatomical deformations, caused by, e.g., tumor shrinkage, bladder and rectum filling changes, organ sliding, and the presence of the brachytherapy (BT) applicator, prohibit the accumulation of external beam radiotherapy (EBRT) and BT dose distributions. This work proposes a structure-wise registration with vector field integration (SW+VF) to map the largely deformed anatomies between EBRT and BT, paving the way for 3D dose accumulation between EBRT and BT. Methods: T2w-MRIs acquired before EBRT and as a part of the MRI-guided BT procedure for 12 cervical cancer patients, along with the manual delineations of the bladder, cervix-uterus, and rectum-sigmoid, were used for this study. A rigid transformation was used to align the bony anatomy in the MRIs. The proposed SW+VF method starts by automatically segmenting features in the area surrounding the delineated organs. Then, each organ and feature pair is registered independently using a feature-based nonrigid registration algorithm developed in-house. Additionally, a background transformation is calculated to account for areas far from all organs and features. In order to obtain one transformation that can be used for dose accumulation, the organ-based, feature-based, and the background transformations are combined into one vector field using a weighted sum, where the contribution of each transformation can be directly controlled by its extent of influence (scope size). The optimal scope sizes for organ-based and feature-based transformations were found by an exhaustive analysis. The anatomical correctness of the mapping was independently validated by measuring the residual distances after transformation for delineated structures inside the cervix-uterus (inner anatomical correctness), and for anatomical landmarks outside the organs in the surrounding region (outer anatomical correctness). The results of the proposed method were compared with the results of the rigid transformation and nonrigid registration of all structures together (AST). Results: The rigid transformation achieved a good global alignment (mean outer anatomical correctness of 4.3 mm) but failed to align the deformed organs (mean inner anatomical correctness of 22.4 mm). Conversely, the AST registration produced a reasonable alignment for the organs (6.3 mm) but not for the surrounding region (16.9 mm). SW+VF registration achieved the best results for both regions (3.5 and 3.4 mm for the inner and outer anatomical correctness, respectively). All differences were significant (p < 0.02, Wilcoxon rank sum test). Additionally, optimization of the scope sizes determined that the method was robust for a large range of scope size values. Conclusions: The novel SW+VF method improved the mapping of large and complex deformations observed between EBRT and BT for cervical cancer patients. Future studies that quantify the mapping error in terms of dose errors are required to test the clinical applicability of dose accumulation by the SW+VF method.

60 APPLIED LIFE SCIENCES↗

Discovering Blind Geothermal Systems in the Great Basin Region: An Integrated Geologic and Geophysical Approach for Establishing Geothermal Play Fairways: All Phases

Most geothermal resources in the Great Basin region of the western USA are blind, and thus the discovery of new commercial-grade systems requires synthesis of favorable characteristics for geothermal activity. The geothermal play fairway concept involves integration of multiple parameters indicative of geothermal activity to identify promising areas for new development. This project integrated multiple datasets to apply the play fairway concept and assess geothermal potential in a large region of the Great Basin in Nevada. It is therefore referred to as the Nevada play fairway project. This project was a strong collaborative effort between several organizations, led by the Nevada Bureau of Mines and Geology at the University of Nevada, Reno, but with key support from the U.S. Geological Survey, ATLAS Geosciences, Inc,, Hi-Q Geophysical, Inc., Lawrence Berkeley National Laboratory, Utah Geological Survey, and Innovative Geothermal Ltd. In Budget Period 1 of this project, available data for nine geologic, geochemical, and geophysical parameters were initially synthesized to produce a new detailed geothermal potential map of 96,000 km2 from west-central to eastern Nevada. These parameters were grouped into subsets and individually weighted to delineate rankings for local permeability, intermediate permeability, regional permeability, and thermal potential, which collectively defined geothermal play fairways (i.e., most likely locations for significant geothermal fluid flow). This initial work was aimed at reducing the risks in regional exploration and therefore facilitating discovery of new commercial-grade systems in blind settings, as well as in areas with surface expressions of geothermal activity. Budget Period 2 of the project involved detailed analysis of some of the most promising areas identified in Phase 1. Twenty-four highly prospective areas, including both known undeveloped systems and previously undiscovered potential blind systems, were identified for further analysis. After reconnaissance of these areas, five of the most promising sites were selected for detailed studies. Multiple techniques were employed in the detailed studies, including geologic mapping, shallow temperature surveys, gravity surveys, Lidar, geochemical studies, seismic reflection analysis, and 3D modeling. The goal of the detailed studies was to identify specific areas with the highest likelihood for high permeability and thermal fluids, such that drill sites could be targeted. Three main sets of predictive maps were generated for each detailed study area: 1) play fairway maps, 2) play fairway error maps, and 3) direct evidence maps. Local- and intermediate-scale permeability models were revised to reflect results of the detailed geologic, geophysical, and geochemical analyses. Budget Period 3 of the project involved more detailed geophysical analyses and temperature-gradient (TG) drilling in southeastern Gabbs Valley and northern Granite Springs Valley, deemed the two most promising sites, with the goal of providing preliminary validation of the play fairway methodology. In southeastern Gabbs Valley, the collocation of a favorable structural setting (displacement transfer zone and fault intersections), Quaternary faults, intersecting and terminating gravity gradients, magnetic low, shallow (2 m) temperature anomaly, low resistivity anomaly, and promising geothermometry from nearby water wells provided evidence for a blind system. Drilling of six TG holes defines an apparent geothermal system at this locality with temperatures as high as 124°C at 152 m. This system is blind, with no surface hot springs, fumaroles, or paleo-geothermal deposits. For northern Granite Springs Valley, a favorable structural setting (termination of a major Quaternary normal fault), terminating gravity gradient, magnetic gradient, newly discovered sinter deposits, nearby warm water wells, previously drilled TG holes in the vicinity, and promising geothermometry suggest a hidden system. Drilling of six new TG holes yields temperatures of ~96°C at ~250 m, suggesting the presence of a geothermal system. Major lessons learned in the course of this project include: 1) initially identified sites commonly include multiple favorable structural settings at a finer scale; 2) promising sites in Cenozoic basins cannot be recognized without detailed geophysical surveys; and 3) play fairway analysis should be refined as the exploration program vectors into the most promising sites and finer-scale data are acquired. In addition to producing copious amounts of data, this project resulted in 16 published papers, 10 abstracts, more than 40 presentations across the U.S. and abroad (including several keynote addresses), 2 Masters theses, and 7 media reports.

15 GEOTHERMAL ENERGY↗

Nuclear Data and Cross Section Testing Using ENDF/B-VIII.0

With the release of the Evaluated Nuclear Data File (ENDF)/B-VIII.0 library, nuclear criticality safety practitioners and engineers have access to the latest cross section sets available for their analyses. However, these cross sections must be rigorously tested and validated to ensure that the nuclear data are responsive to the needs of the individuals responsible for developing, implementing, and maintaining computational tools for criticality safety applications. Thus, the ENDF/B-VIII.0 library is tested and validated with a large collection of experiments that were vetted by the International Criticality Safety Benchmark Evaluation Project and made available in the International Handbook of Evaluated Criticality Safety Benchmark Experiments. A selection of benchmark experiments for use within the criticality safety community were prepared and reviewed within the Verified, Archived Library of Inputs and Data (VALID), which is maintained by the Nuclear Energy and Fuel Cycle Division at Oak Ridge National Laboratory. The performance of the ENDF/B-VIII.0 library is assessed by using VALID models of benchmark experiments with the beta 12 version of SCALE 6.3 KENO V.a and KENO-VI Monte Carlo codes. The performance is compared with the results obtained from with the ENDF/B-VII.1 library. This report considers multigroup (MG) and continuous energy (CE) formats of the ENDF/B-VIII.0 and -VII.1 libraries. The benchmark experiments within VALID that validate the ENDF/B-VIII.0 library cover 15 broad system categories by using a range of fissile materials, uranium enrichments, plutonium isotopic vectors, and mixed uranium/plutonium systems. These forms are represented as metals, solutions, or various arrays of rods or plates that cover a variety of neutron energy spectra: thermal, fast, mixed, and intermediate. Over 600 cases were considered for use with the KENO V.a and KENO-VI codes with the ENDF/B-VIII.0 library. The results of the Monte Carlo comparison of ENDF/B-VIII.0 to ENDF/B-VII.1 with both KENO V.a and KENO-VI indicate that there is a less than 0.53% Δk difference between the bias of calculated k eff from the expected values. The CE ENDF/B-VIII.0 library results in smaller magnitude biases than the ENDF/B-VII.1 data for HEU-MET-FAST, HEU-SOL-THERM, IEU-MET-FAST, LEU-SOL-THERM, PU-SOL-THERM, and U233-MET-FAST systems, while the MG results yielded smaller magnitude biases for HEU-MET-FAST, HEU-SOL-THERM, IEU-MET-FAST, LEU-COMP-THERM, LEU-SOL THERM, MIX-COMP-FAST, and U233-MET-FAST systems. Most notable are the adjustments to the plutonium and 233 U cross section data, which has resulted in noticeably lower biases in the ENDF/B VIII.0 results for the mixed, plutonium, and 233 U systems. Results of the sensitivity data file comparison generated from TSUNAMI-3D for selected VALID cases for the ENDF/B-VIII.0 library indicate a very high level of agreement with correlation coefficients of the effect of nuclear data uncertainty on k eff (the c k integral parameter) all above 0.99. This indicates that cases with the ENDF/B-VIII.0 library would see very similar responses to any nuclear data errors or change as those with the ENDF/B-VII.1 library.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗