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All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Game-Theoretic strategies for systems of components using product-form utilities

Many critical infrastructures are composed of multiple systems of components which are correlated so that disruptions to one may propagate to others. We consider such infrastructures with correlations characterized in two ways: (i) an aggregate failure correlation function specifies the conditional failure probability of the infrastructure given the failure of an individual system, and (ii) a pairwise correlation function between two systems specifies the failure probability of one system given the failure of the other. We formulate a game for ensuring the resilience of the infrastructure, wherein the utility functions of the provider and attacker are products of an infrastructure survival probability term and a cost term, both expressed in terms of the numbers of system components attacked and reinforced. The survival probabilities of individual systems satisfy first-order differential conditions that lead to simple Nash Equilibrium conditions. We then derive sensitivity functions that highlight the dependence of infrastructure resilience on the cost terms, correlation functions, and individual system survival probabilities. We apply these results to simplified models of distributed cloud computing and energy grid infrastructures.

Rao, Nageswara S↗
DOE OSTI2016

Defense strategies for infrastructures with multiple systems of components

In several critical infrastructures correlations between the constituent systems represent certain vulnerabilities: disruptions to one may propagate to others and possibly to the entire infrastructure. The correlations between the systems are characterized in two ways in this paper: (i) the aggregate failure correlation function specifies the conditional failure probability of the infrastructure given the failure of an individual system, and (ii) the pairwise correlation function between two systems specifies the failure probability of one system given the failure of the other. The survival probabilities of individual systems satisfy firstorder differential conditions that generalize the contest success functions and statistical independence conditions. We formulate a problem of ensuring the resilience of an infrastructure as a game between the provider and attacker; their utility functions are sums of infrastructure survival probability terms and cost terms, both expressed in terms of the numbers of system components attacked and reinforced. We derive Nash Equilibrium conditions and sensitivity functions that highlight the dependence of infrastructure resilience on the cost terms, correlation functions, and individual system survival probabilities. We apply these results to models of distributed cloud computing and energy grid infrastructures.

Rao, Nageswara S↗
DOE OSTI2015

Quantifying Safety Margin Using the Risk-Informed Safety Margin Characterization (RISMC)

The Risk-Informed Safety Margin Characterization (RISMC), developed by Idaho National Laboratory as part of the Light-Water Reactor Sustainability Project, utilizes a probabilistic safety margin comparison between a load and capacity distribution, rather than a deterministic comparison between two values, as is usually done in best-estimate plus uncertainty analyses. The goal is to determine the failure probability, or in other words, the probability of the system load equaling or exceeding the system capacity. While this method has been used in pilot studies, there has been little work conducted investigating the statistical significance of the resulting failure probability. In particular, it is difficult to determine how many simulations are necessary to properly characterize the failure probability. This work uses classical (frequentist) statistics and confidence intervals to examine the impact in statistical accuracy when the number of simulations is varied. Two methods are proposed to establish confidence intervals related to the failure probability established using a RISMC analysis. The confidence interval provides information about the statistical accuracy of the method utilized to explore the uncertainty space, and offers a quantitative method to gauge the increase in statistical accuracy due to performing additional simulations.

Grabaskas, David↗
DOE OSTI2016

HUMAN FAILURE EVENT DEPENDENCE: WHAT ARE THE LIMITS

Abstract Objectives: This paper discusses the differences between classical human reliability analysis (HRA) dependence and the full spectrum of probabilistic dependence. Positive influence suggests an error increases the likelihood of subsequent errors or success increases the likelihood of subsequent success. Currently the typical method for dependence in HRA implements the Technique for Human Error Rate Prediction (THERP) positive dependence equations. This assumes that the dependence between two human failure events varies at discrete levels between zero and complete dependence (as defined by THERP). Dependence in THERP does not consistently span dependence values between 0 and 1. In contrast, probabilistic dependence employs Bayes Law, and addresses a continuous range of dependence. Methods: Using the laws of probability, complete dependence and maximum positive dependence do not always agree. Maximum dependence is when two events overlap to their fullest amount. Maximum negative dependence is the smallest amount that two events can overlap. When the minimum probability of two events overlapping is less than independence, negative dependence occurs. For example, negative dependence is when an operator fails to actuate Pump A, thereby increasing his or her chance of actuating Pump B. The initial error actually increases the chance of subsequent success. Results: Comparing THERP and probability theory yields different results in certain scenarios; with the latter addressing negative dependence. Given that most human failure events are rare, the minimum overlap is typically 0. And when the second event is smaller than the first event the max dependence is less than 1, as defined by Bayes Law. As such alternative dependence equations are provided along with a look-up table defining the maximum and maximum negative dependence given the probability of two events. Conclusions: THERP dependence has been used ubiquitously for decades, and has provided approximations of the dependencies between two events. Since its inception, computational abilities have increased exponentially, and alternative approaches that follow the laws of probability dependence need to be implemented. These new approaches need to consider negative dependence and identify when THERP output is not appropriate.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

Checkpointing using compute node health information

A method is disclosed, as well as an associated apparatus and computer program product, for checkpointing using a plurality of communicatively coupled compute nodes. The method comprises acquiring health information for a first node of the plurality of compute nodes, and determining a first failure probability for the first node using the health information. The first failure probability corresponds to a predetermined time interval. The method further comprises selecting a second node of the plurality of compute nodes as a partner node for the first node. The second node has a second failure probability for the time interval. A composite failure probability of the first node and the second node is less than the first failure probability. The method further comprises copying checkpoint information from the first node to the partner node.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Temperature Uncertainty Modeling with Proxy Structural Data as Geostatistical Constraints for Well Siting: An Example Applied to Granite Springs Valley, NV, USA

Utilizing existing temperature and structural information around Granite Springs Valley, Nevada, we build 3D stochastic temperature models with the aim of evaluating the 3D uncertainty of temperature and choosing between candidate exploration well locations . The data used to support the modeling are measured temperatures and structural proxies from 3D geologic modeling, the latter considered "secondary" data. Two stochastic geostatistical techniques are explored for incorporating the structural proxies: cosimulation and local varying mean. With both the cosimulation and local varying mean methods, many equally likely temperature models (i.e., realizations) are produced, from which temperature probability profiles are calculated at candidate well locations. To aid in choosing between the candidate locations, two quantities summarize the temperature probabilities: Vprior and entropy. Vprior quantifies the likelihood for economic temperatures at each candidate location, whereas entropy identifies where new information has the most potential to reduce uncertainty. In general, the cosimulation realizations have smoother spatial structure, and extrapolate high temperatures at candidate locations that are located along the direction of the longest spatial correlation, which are down dip from existing temperature logs. The smooth realizations result in tight temperature probability profiles that are easier to interpret, but they have unrealistic temperature reversals in some locations because the cosimulation technique does not enforce a conductive geothermal gradient as a baseline (i.e., linearly increasing temperature with depth). The local varying mean results produce realizations with more realistic geothermal gradients, with temperatures increasing downward since a depth-temperature relationship is included. However, because they have much noisier spatial nature compared to cosimulation, it is harder to interpret the temperature probability profiles. The different local varying mean results allow the geologist to determine which proxy (e.g., dilation versus distance to fault termination) should be used given the specific geothermal system. In general, Vprior from local varying mean results identify locations that are close to high values for the structural proxies: areas with highe r probabilities for higher temperatures. The entropy results identify where uncertainty is greatest and therefore new drilling information could be most useful. Though these techniques provide useful information, even when applied to areas of sparse data, our comp arison of these two techniques demonstrates the need for new geothermal geostatistics techniques that combine the advantages of these two methods and that are tailored to the spatial uncertainty issues inherent in geothermal exploration.

3D temperature modeling↗
DOE OSTI2016

Accident-tolerant fuel: quantifying relative risks and timescales in severe accidents

For such severe accident scenarios, a key objective for alternative 'accident tolerant' fuels (or ATFs) is to increase the threshold temperature for possible accelerated hydrogen production and/or fuel damage and core degradation. By reducing hydrogen production, this change to more ATF should also give more time for restoring power and cooling, for mitigating actions like emergency equipment deployment, and consequently effect on- and off-site evacuation decisions. There is always a finite and non-zero probability of core damage due to the likelihood and chance of not restoring power and cooling. Using the Fukushima complete Station Black Out (SBO) and Loss-of-Cooling (LOC) scenario as a starting point, this paper establishes a simple limiting estimate for the potential changes in the timescales available for power and cooling recovery and for emergency evacuation decision-making made possible by using ATFs. The straightforward analysis also provides a basis for estimating the realistic probability of avoiding core damage for a range of assumed ATF failure properties or criteria, and the needed backup cooling requirements. The analysis includes the effects on the recovery probability caused by significant disruption and chaos. The results show that for this accident scenario, there is a relatively small benefit or increase in recovery probability due to only having higher ATF failure limits. The largest relative benefit arises from not only having ATF but also assuring longer cooling by extending the boil off or time before core uncover and damage onset, from somehow adding and/or injecting sufficient make up water, and/or rejecting decay heat, say for five or more days. Obviously, as an added benefit, some ATF concepts avoid or reduce hydrogen production, which improves containment integrity but does not significantly alter the core damage or failure probability.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

WIPP PA Sensitivity Studies in Support of CRA-2014 Completeness Determination and Compliance Decision - 18209

The Waste Isolation Pilot Plant (WIPP) has been developed by the U.S. Department of Energy (DOE) for the geologic (deep underground) disposal of transuranic (TRU) waste. Containment of TRU waste at the WIPP is regulated by the U.S. Environmental Protection Agency (EPA). The DOE demonstrates compliance with the containment requirements by means of performance assessment (PA) calculations. WIPP PA calculations estimate the probability and consequence of potential radionuclide releases from the repository to the accessible environment for a regulatory period of 10,000 years after facility closure. Since TRU waste was first received at the WIPP in 1999, compliance recertification applications (CRAs) have been required by the EPA on five-year cycle. The latest CRA (CRA-2014) was submitted by the DOE to the EPA in 2014. As part of the application, a formal set of PA calculations (CRA-2014 PA) was performed and results were documented in detail. The CRA-2014 PA incorporated several parameter updates based on new data, as well as the implementation of a different model for panel closures, barriers planned for the opening of each waste panel. The results presented as part of the CRA-2014 showed via the required complementary cumulative distribution function (CCDF) release curves that the estimated releases were within compliance limits. As part of their process for reviewing the completeness of the CRA-2014 [1], the EPA formally requested that the DOE perform sensitivity studies based on EPA-requested changes to model parameters. The DOE performed and documented the results of three sensitivity studies described below: CRA14-SEN2 [2], CRA14-SEN3 [3], and CRA14-SEN4 [4]. In each case, the new analysis results were compared to CRA- 2014 PA (CRA14) results to determine the impact of the EPA-requested changes. CRA14-SEN2: the application of EPA-requested modified parameters in the operations and experimental (non-waste) areas of the repository to simulate an accelerated (instantaneous) creep closure, the inclusion of capillary pressure effects on relative permeability, and an increase in initial/residual brine saturation and residual gas saturation. The modifications to the repository model resulted in increased pressures and decreased brine saturations in waste areas and increased pressures and brine saturations in the operations and experimental areas. However, the overall effects on total high-probability mean releases from the repository were entirely insignificant. It was concluded that the modeling assumptions associated with the operations and experimental areas of the repository have an insignificant effect on the prediction of total releases from the repository and/or adequacy of the current (CRA14) model to demonstrate compliance with the regulatory limits. CRA14-SEN3: the application of EPA-requested modified parameters in the panel closure areas and operations and experimental (non-waste) areas of the repository to simulate an accelerated (instantaneous) creep closure, the inclusion of capillary pressure effects on relative permeability, and an increase in initial/residual brine saturation and residual gas saturation. The modifications to the repository model predominantly result in increased pressures and decreased brine saturations in waste areas, increased pressures and brine saturations in the operations and experimental areas, and decreased brine and gas flows across all panel closures. The pressure increases in repository waste regions yielded slightly decreased brine saturations (on average) in those areas. However, the overall effects on total high-probability mean releases from the repository are entirely insignificant. It was concluded that the modeling assumptions made for this sensitivity study which were associated with the panel closures and north end areas of the repository have only a small effect on the prediction of total releases from the repository and/or adequacy of the current (CRA14) model to demonstrate compliance with the regulatory limits. CRA14-SEN4: the application of several changes to the current WIPP PA model (CRA14), including: parameter changes, use of an updated code, and a revised computational grid for the BRAGFLO code. The modifications to the repository model resulted in increased releases in all primary release mechanisms. The impacts of each EPA-requested change to CRA14 were analyzed with respect to each release mechanism in the CRA14-SEN4 study. Overall, total high-probability predicted mean releases from the repository were increased by about 15%. Total low-probability predicted mean releases were increased by about 107%. It was concluded that the EPA-requested changes to the CRA14 result in increases to the predicted total releases from the repository. However, releases calculated in the CRA14-SEN4 analysis remained below regulatory limits, demonstrating continued compliance of the WIPP. In January 2017, the EPA determined that CRA-2014 was complete and then began a technical evaluation of CRA-2014 to determine whether the WIPP continued to comply with the radiation protection standards for disposal. During their evaluation, the EPA utilized the sensitivity study results to inform their ultimate determination in July 2017 that the WIPP continues to comply with regulatory standards. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

GIS-Based Modeling of Contaminated Soil Volumes at Multiple Sites in the Formerly Utilized Sites Remedial Action Program - 20149

The remediation of hazardous, toxic, and radioactive waste (HTRW) sites produces cost-related risks associated with the estimation of contaminated soil or debris volumes. Historical risk-management techniques include cost contingencies to cover volume uncertainties that affect project budgeting and decision-making. The Buffalo District teamed with project partners to lessen volume uncertainty and reduce project risks at multiple HTRW sites managed under the Formerly Utilized Sites Remedial Action Program (FUSRAP). Historical remedial investigations under FUSRAP commonly identified the presence of radiological material in site media, the associated human health risk, and then areas of remediation. To manage remedial execution and reduce risk, pre-design or remediation-phase sampling essentially 'chased' contamination, which was not conducive to efficient predictive budgeting derived from Feasibility Study (FS) cost analyses. The Buffalo District first optimized their approach to better understand volume uncertainty by utilizing the Argonne National Laboratory's Bayesian Approaches for Adaptive Spatial Sampling (BAASS) software [1]. BAASS processed soft data (e.g., gamma walk-over data) and spatial sampling data to estimate the lateral extent of contaminated soil irrespective of depth (i.e., gross contamination extent) and define areas of contaminant uncertainty. The software performed a binary transformation of contaminant concentrations at all sampling points based upon remedial action goals or a sum of ratios approach (i.e., clean, impacted, or range of impacts in soil). The model produced two-dimensional (horizontal) contaminant probability contours and statistical uncertainty in the sampling coverage and resulting contaminant extents. This method was translated vertically by partitioning the sampling data into depth brackets that produced a stacked representation of contaminant extents and uncertainty in the subsurface (i.e., similar to construction lifts). The results commonly led to a better understanding of project uncertainty and the need for sampling strategies that produce high-confidence soil volumes, which control costs. The BAASS-based delineations were eventually replaced by Empirical Bayesian Kriging (EBK) methods available in ArcGIS Spatial or 3D Analysts [2]. The EBK method calculates contaminant probability zones derived from user-controlled semivariograms of the spatial datasets. The resulting probability zones (e.g., 50% or 80% of contaminant probability) represent the two-dimensional surface delineation of the overall horizontal remedial area, similarly to BAASS. However, unlike BAASS, the vertical sampling data within these probability zones became vertical control points to contour a subterranean surface that connects subsurface points to the land-surface delineations of contamination. The resulting representation of horizontal and vertical impacts within an enclosed envelop (volume) of soil included uncertainty distributions that are used to plan uncertainty-reduction sampling. These data-driven and math-based models of three-dimensional sampling results produced well-bounded remedial volumes for project planning and better uncertainty predictions during project budgeting. The EBK method was applied to several FUSRAP sites managed by the Buffalo District and compared to less rigorously modeled sites previously remediated by the District. The comparison of modeled to actual remediated volumes provide a basis for validating the volume-estimation method. This comparison is important to ensure modeled volumes match physical boundaries of site remediation. FUSRAP sites with denser investigative sampling and lesser volume uncertainty proved useful in remedial planning and contracting. The Buffalo District noted that historical sites with sparser sampling arrays had greater disparity between estimated volumes and final remedial volumes. The benefit achieved over the cost of detailed soil sampling appears positive for FUSRAP projects, especially where impacts vary widely and appear unbounded by investigation-phase sampling. The subsequent Empirical Bayesian Kriging of contamination coupled with vertical contouring for soil estimations reduces uncertainty in soil volumes or indicates where sampling is required to reduce uncertainty, which together optimize remedial planning and budgeting. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2017

Application of a bayesian belief network model to reliability assessment of nuclear safety-related software - 207

As the instrumentation and control (I and C) systems in nuclear power plants (NPPs) have been replaced with digital-based systems, the need to incorporate software failures into NPP probabilistic risk assessments has arisen. In order to assess the probability of software failure on demand, a Bayesian belief network (BBN) model was developed which estimates the number of defects and the resulting probability of software failure on demand in nuclear safety-related software. To assess the feasibility of the BBN framework, the BBN model was applied to the prototype Integrated Digital Protection System-Reactor Protection System (IDiPS-RPS) to estimate the number of remaining faults and the software failure probability of a target software. The developmental- and V and V-activities carried out during the IDiPS-RPS development process were evaluated based on the well-defined checklist derived by the V and V team and were estimated based on expert elicitation. In addition, the attribute evaluations and the number of FPs of the target software is provided as the inputs for the BBN model. The application results showed the feasibility of using BBNs for quantifying software failure probabilities and several insights were gained from the applications of the BBN model. The proposed BBN framework can be applied to estimate the software failure probability for other safety-related NPP software and provide an insight on modeling the software development process that involves iterations between different development phases. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2017

Speed and Memory Improvements to MCNP6 Delayed-Gamma Line Treatment

The delayed-gamma (DG) line-emission (line) sampling was first introduced into MCNPX in 2005. At the time, storage demands for problems with large numbers of DG lines was a major concern. In order to accommodate large amounts of line data while keeping the memory footprint of such a problem from exceeding memory limits, complicated logic was included to sift through various storage options. In mid-2015 concerns arose over the adequacy of the MCNP6 DG source option (inherited from MCNPX) with line sampling for modeling high-fidelity problems. One indication that there was a problem came when studying the MCNP6 produced DG spectra of U-238 and its progeny using high-fidelity spectroscopic tallies when compared to DG line amplitudes directly from ENDF/B-VII.1 emission data. Despite producing a correct integral number of gammas, the comparison to ENDF data showed a broadening in the energy lines and a reduction in the amplitude of more prominent lines. It was later found that the cause of this broadening was one of the memory-saving techniques used to store DG line data when problems required many DG lines. Specifically, the DG lines were integrated into fine energy bins for sampling. When a DG line was to be sampled, a random number would be used to choose which energy bin to sample based on emission probability. Once chosen, a second random number was used to perform nearest-line sampling in that bin. The integration of lines led to an oversampling of low-probability lines, especially when in close proximity to high-probability lines. This treatment also caused a similar issue with the time-dependent behavior of DG line emission which occurred when low-probability lines were sampled near high probability lines with the former decay constant being used. The effect on time-dependent gamma production was demonstrated in analytic benchmarks performed by Weldon et al.. To address these issues a new gamma line storage and sampling treatment was introduced in 2015. This new treatment, stores gamma emission data in a line-by-line CDF which is sampled directly, thereby resolving both the line-broadening issue, and the time-dependence issue as was demonstrated by Tutt el al.. In addition, the new DG sampling treatment was written to use dynamically dimensioned storage arrays as opposed to large fixed-dimensioned arrays, as in the former treatment, and also makes more efficient use of line data that is stored by reducing or eliminating repeated data. As a result, storage arrays are generated only for DG data relevant to the problem being executed. The result should be a reduction in both memory requirements and runtime. However, these reductions could not be realized until the logic for the old treatment could be removed. This paper provides an update on recent work which has focused on the removal of the old DG sampling logic and attempts to quantify the memory reduction and speed up of selected problems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Entanglement-Enhanced Neyman-Pearson Target Detection

Quantum illumination (QI) provides entanglement-enabled target-detection enhancement, despite operating in an entanglement-breaking environment. Existing experimental studies of QI have utilized a Bayesian approach, assuming that the target is equally likely to be present or absent before detection, to demonstrate an advantage over classical target detection. However, such a premise breaks down in practical operational scenarios in which the prior probability is unknown, thereby hindering QI's applicability to real-world target-detection scenarios. In this work, we adopt the Neyman-Pearson criterion in lieu of the error probability for equally likely target absence or presence as our figure of merit for QI. We demonstrate an unconditional quantum advantage over the optimal classical-illumination protocol as benchmarked by the receiver operating characteristic, which examines detection probability versus false-alarm probability without resorting to known prior probabilities. Our work represents a critical advancement in adapting quantum-enhanced sensing to practical operational settings.

Ward, William↗
DOE OSTI2014

A family of random walks with generalized Dirichlet steps

We analyze a class of continuous time random walks in R{sup d},d≥2, with uniformly distributed directions. The steps performed by these processes are distributed according to a generalized Dirichlet law. Given the number of changes of orientation, we provide the analytic form of the probability density function of the position (X{sub {sub d}}(t),t>0) reached, at time t > 0, by the random motion. In particular, we analyze the case of random walks with two steps. In general, it is a hard task to obtain the explicit probability distributions for the process (X{sub {sub d}}(t),t>0). Nevertheless, for suitable values for the basic parameters of the generalized Dirichlet probability distribution, we are able to derive the explicit conditional density functions of (X{sub {sub d}}(t),t>0). Furthermore, in some cases, by exploiting the fractional Poisson process, the unconditional probability distributions of the random walk are obtained. This paper extends in a more general setting, the random walks with Dirichlet displacements introduced in some previous papers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

The Tightness of the Kesten–Stigum Reconstruction Bound of Symmetric Model with Multiple Mutations

It is well known that reconstruction problems, as the interdisciplinary subject, have been studied in numerous contexts including statistical physics, information theory and computational biology, to name a few. We consider a 2q-state symmetric model, with two categories of q states in each category, and 3 transition probabilities: the probability to remain in the same state, the probability to change states but remain in the same category, and the probability to change categories. We construct a nonlinear second-order dynamical system based on this model and show that the Kesten–Stigum reconstruction bound is not tight when q≥4.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Predictive drug dosage control through a Fokker–Planck observer

During the years, various techniques have been presented for optimal control of tumor growth for which its stochastic behavior has rarely been considered. This article uses the well-known Gompertz stochastic model, for describing tumor growth, and by receding horizon model predictive control (RH-MPC) scheme computes the drug dosage for minimizing the tumor-cell population. To do this, a predictive control problem is defined based on the difference between the probability density function of tumor-cell population and the desired probability density function. In the model, both the drug dosage limitation and the Fokker–Planck equation have been considered as constraints. By solving this problem, the drug dosage which is considered as an external input to tumor model, is computed. In this article, the Fokker–Planck equation is used (1) as a nonlinear observer of probability density function of tumor-cell population and (2) a mapping vehicle from stochastic to deterministic domain. The Fokker–Planck equation is written for the Gompertz stochastic model of tumor growth. The equation is then solved through the path integral method. In this way, the probability density function of tumor-cell population, which contains the entire stochastic characteristics of the tumor growth, is obtained for any instance of time. The simulation results have also been presented for the evaluation of the suggested approach. The results show that the tumor-cell population can be controlled within a number of time windows (15 time windows in our case study) if an appropriate desired PDF is selected.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

A probabilistic perspective on thermodynamic parameter uncertainties: Understanding aqueous speciation of mercury

Speciation plays an important role in determining the fate and transport of metals in terrestrial surface and subsurface systems. Equilibrium speciation modeling in aqueous systems relies on thermodynamic constants (log K values) of complexes, which are subject to uncertainties. In this study, using Monte Carlo (MC) simulations with Latin hypercube sampling (LHS) we systematically analyze the propagation of thermodynamic constant uncertainty through speciation modeling of an inorganic mercury-sulfide-chloride-water system. We find that seemingly small variances of the input log K normal distributions can lead to output species concentrations spanning multiple orders of magnitude, with highly skewed probability distributions. When equilibrium with mineral metacinnabar (β-HgS(s)) is neglected, the relative uncertainty of each output species is strongly positively correlated with the skewness of its concentration probability distribution, i.e., the lowest uncertainty occurs when the species concentration probability distribution is the most negatively skewed as its concentration approaches the total element concentration limit. The highest uncertainty in the identity of dominant species is located around species equivalence points. For cases where the mineral equilibrium is included, we derive analytical probability density functions for the log concentrations of all major species in the system. The mineral log K uncertainty is found to be an important contributor to all output concentration uncertainties. The analysis of combined effects of both pH and total sulfide concentration on output concentration uncertainties shows that high concentration uncertainties occur under highly sulfidic alkaline conditions and low uncertainties at low pH and sulfide concentrations. Finally, an analysis as presented here can distinguish between conditions that require a full uncertainty analysis and those for which the classical deterministic speciation modeling suffices.

58 GEOSCIENCES↗
DOE OSTI2012

Propensity Score-based Comparison of Long-term Outcomes With 3-Dimensional Conformal Radiotherapy vs Intensity-Modulated Radiotherapy for Esophageal Cancer

Purpose: Although 3-dimensional conformal radiotherapy (3D-CRT) is the worldwide standard for the treatment of esophageal cancer, intensity modulated radiotherapy (IMRT) improves dose conformality and reduces the radiation exposure to normal tissues. We hypothesized that the dosimetric advantages of IMRT should translate to substantive benefits in clinical outcomes compared with 3D-CRT. Methods and Materials: An analysis was performed of 676 nonrandomized patients (3D-CRT, n=413; IMRT, n=263) with stage Ib-IVa (American Joint Committee on Cancer 2002) esophageal cancers treated with chemoradiotherapy at a single institution from 1998-2008. An inverse probability of treatment weighting and inclusion of propensity score (treatment probability) as a covariate were used to compare overall survival time, interval to local failure, and interval to distant metastasis, while accounting for the effects of other clinically relevant covariates. The propensity scores were estimated using logistic regression analysis. Results: A fitted multivariate inverse probability weighted-adjusted Cox model showed that the overall survival time was significantly associated with several well-known prognostic factors, along with the treatment modality (IMRT vs 3D-CRT, hazard ratio 0.72, P<.001). Compared with IMRT, 3D-CRT patients had a significantly greater risk of dying (72.6% vs 52.9%, inverse probability of treatment weighting, log-rank test, P<.0001) and of locoregional recurrence (P=.0038). No difference was seen in cancer-specific mortality (Gray's test, P=.86) or distant metastasis (P=.99) between the 2 groups. An increased cumulative incidence of cardiac death was seen in the 3D-CRT group (P=.049), but most deaths were undocumented (5-year estimate, 11.7% in 3D-CRT vs 5.4% in IMRT group, Gray's test, P=.0029). Conclusions: Overall survival, locoregional control, and noncancer-related death were significantly better after IMRT than after 3D-CRT. Although these results need confirmation, IMRT should be considered for the treatment of esophageal cancer.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2014

Functional Data Analysis in NTCP Modeling: A New Method to Explore the Radiation Dose-Volume Effects

Purpose/Objective(s): To describe a novel method to explore radiation dose-volume effects. Functional data analysis is used to investigate the information contained in differential dose-volume histograms. The method is applied to the normal tissue complication probability modeling of rectal bleeding (RB) for patients irradiated in the prostatic bed by 3-dimensional conformal radiation therapy. Methods and Materials: Kernel density estimation was used to estimate the individual probability density functions from each of the 141 rectum differential dose-volume histograms. Functional principal component analysis was performed on the estimated probability density functions to explore the variation modes in the dose distribution. The functional principal components were then tested for association with RB using logistic regression adapted to functional covariates (FLR). For comparison, 3 other normal tissue complication probability models were considered: the Lyman-Kutcher-Burman model, logistic model based on standard dosimetric parameters (LM), and logistic model based on multivariate principal component analysis (PCA). Results: The incidence rate of grade ≥2 RB was 14%. V{sub 65Gy} was the most predictive factor for the LM (P=.058). The best fit for the Lyman-Kutcher-Burman model was obtained with n=0.12, m = 0.17, and TD50 = 72.6 Gy. In PCA and FLR, the components that describe the interdependence between the relative volumes exposed at intermediate and high doses were the most correlated to the complication. The FLR parameter function leads to a better understanding of the volume effect by including the treatment specificity in the delivered mechanistic information. For RB grade ≥2, patients with advanced age are significantly at risk (odds ratio, 1.123; 95% confidence interval, 1.03-1.22), and the fits of the LM, PCA, and functional principal component analysis models are significantly improved by including this clinical factor. Conclusion: Functional data analysis provides an attractive method for flexibly estimating the dose-volume effect for normal tissues in external radiation therapy.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

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