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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Hydropower Optimization Using Artificial Neural Network Surrogate Models of a High-Fidelity Hydrodynamics and Water Quality Model

Hydropower operations optimization subject to environmental constraints is limited by challenges associated with dimensionality and spatial and temporal resolution. The need for high-fidelity hydrodynamic and water quality models within optimization schemes is driven by improved computational capabilities, increased requirements to meet specific points of compliance with greater resolution, and the need to optimize operations of not just single reservoirs but systems of reservoirs. This study describes an important advancement for computing hourly power generation schemes for a hydropower reservoir using high-fidelity models, surrogate modeling techniques, and optimization methods. The predictive power of the high-fidelity hydrodynamic and water quality model CE-QUAL-W2 is successfully emulated by an artificial neural network, then integrated into a genetic algorithm optimization approach to maximize hydropower generation subject to constraints on dam operations and water quality. This methodology is applied to a multipurpose reservoir near Nashville, Tennessee, USA. The model successfully reproduced high-fidelity reservoir information while enabling 6.8% and 6.6% increases in hydropower production value relative to actual operations for dissolved oxygen (DO) limits of 5 and 6 mg/L, respectively, while witnessing an expected decrease in power generation at more restrictive DO constraints. Exploration of simultaneous temperature and DO constraints revealed capability to address multiple water quality constraints at specified locations. Here, the reduced computational requirements of the new modeling approach demonstrated an ability to provide decision support for reservoir operations scheduling while maintaining high-fidelity hydrodynamic and water quality information as part of the optimization decision support routines.

13 HYDRO ENERGY↗
DOE OSTI2023

Macrocyclic β‐Sheets Stabilized by Hydrogen Bond Surrogates

Abstract Mimics of protein secondary and tertiary structure offer rationally‐designed inhibitors of biomolecular interactions. β‐Sheet mimics have a storied history in bioorganic chemistry and are typically designed with synthetic or natural turn segments. We hypothesized that replacement of terminal inter‐β‐strand hydrogen bonds with hydrogen bond surrogates (HBS) may lead to conformationally‐defined macrocyclic β‐sheets without the requirement for natural or synthetic β‐turns, thereby providing a minimal mimic of a protein β‐sheet. To access turn‐less antiparallel β‐sheet mimics, we developed a facile solid phase synthesis protocol. We surveyed a dataset of protein β‐sheets for naturally observed interstrand side chain interactions. This bioinformatics survey highlighted an over‐abundance of aromatic–aromatic, cation‐π and ionic interactions in β‐sheets. In correspondence with natural β‐sheets, we find that minimal HBS mimics show robust β‐sheet formation when specific amino acid residue pairings are incorporated. In isolated β‐sheets, aromatic interactions endow superior conformational stability over ionic or cation‐π interactions. Circular dichroism and NMR spectroscopies, along with high‐resolution X‐ray crystallography, support our design principles.

Chemistry↗
DOE OSTI2023

Mallat Scattering Transformation based surrogate for Magnetohydrodynamics

Abstract A Machine and Deep Learning (MLDL) methodology is developed and applied to give a high fidelity, fast surrogate for 2D resistive MagnetoHydroDynamic (MHD) simulations of Magnetic Liner Inertial Fusion (MagLIF) implosions. The resistive MHD code is used to generate an ensemble of implosions with different liner aspect ratios, initial gas preheat temperatures (that is, different adiabats), and different liner perturbations. The liner density and magnetic field as functions of x , y , and z were generated. The Mallat Scattering Transformation (MST) is taken of the logarithm of both fields and a Principal Components Analysis (PCA) is done on the logarithm of the MST of both fields. The fields are projected onto the PCA vectors and a small number of these PCA vector components are kept. Singular Value Decompositions of the cross correlation of the input parameters to the output logarithm of the MST of the fields, and of the cross correlation of the SVD vector components to the PCA vector components are done. This allows the identification of the PCA vectors vis-a-vis the input parameters. Finally, a Multi Layer Perceptron (MLP) neural network with ReLU activation and a simple three layer encoder/decoder architecture is trained on this dataset to predict the PCA vector components of the fields as a function of time. Details of the implosion, stagnation, and the disassembly are well captured. Examination of the PCA vectors and a permutation importance analysis of the MLP show definitive evidence of an inverse turbulent cascade into a dipole emergent behavior. The orientation of the dipole is set by the initial liner perturbation. The analysis is repeated with a version of the MST which includes phase, called Wavelet Phase Harmonics (WPH). While WPH do not give the physical insight of the MST, they can and are inverted to give field configurations as a function of time, including field-to-field correlations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Theory of Surrogate Nuclear and Atomic Reactions with Three Charged Particles in the Final State Proceeding Through a Resonance in the Intermediate Subsystem

Within a few-body formalism, we develop a general theory of surrogate nuclear and atomic reactions with excitation of a resonance in the intermediate binary subsystem leading to three charged particles in the final state. Additionally, the Coulomb interactions between the spectator and the resonance in the intermediate state and between the three particles in the final state are taken into account. Final-state three-body Coulomb multiple-scattering effects are accounted for using the formalism of the three-body Coulomb asymptotic states based on the work published by one of the authors (A.M.M.) under the guidance of L. D. Faddeev. The formalism of the three-body Coulomb asymptotic states (CAS) was used to calculate the reaction amplitudes with three charged particles in the final state. An expression is derived for the triply differential cross section. It can be used for investigation of the Coulomb effects on the resonance line shape as well as the energy dependence of the cross section. In conclusion, we find that simultaneous inclusion of the Coulomb effects in the intermediate and final state decreases the effect of the final-state Coulomb interactions on the triply differential cross section.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Modeling design and control problems involving neural network surrogates

Here, we consider nonlinear optimization problems that involve surrogate models represented by neural networks. We demonstrate first how to directly embed neural network evaluation into optimization models, highlight a difficulty with this approach that can prevent convergence, and then characterize stationarity of such models. We then present two alternative formulations of these problems in the specific case of feedforward neural networks with ReLU activation: as a mixed-integer optimization problem and as a mathematical program with complementarity constraints. For the latter formulation we prove that stationarity at a point for this problem corresponds to stationarity of the embedded formulation. Each of these formulations may be solved with state-of-the-art optimization methods, and we show how to obtain good initial feasible solutions for these methods. We compare our formulations on three practical applications arising in the design and control of combustion engines, in the generation of adversarial attacks on classifier networks, and in the determination of optimal flows in an oil well network.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Predicting concrete compressive strength using hybrid ensembling of surrogate machine learning models

This study aims to implement a hybrid ensemble surrogate machine learning technique in predicting the compressive strength (CS) of concrete, an important parameter used for durability design and service life prediction of concrete structures in civil engineering projects. For this purpose, an experimental database consisting of 1030 records has been compiled from the machine learning repository of the University of California, Irvine. The database was used to train and validate four conventional machine learning (CML) models, namely Artificial Neural Network (ANN), Linear and Non-Linear Multivariate Adaptive Regression Splines (MARS-L and MARS-C), Gaussian Process Regression (GPR), and Minimax Probability Machine Regression (MPMR). Subsequently, the predicted outputs of CML models were combined and trained using ANN to construct the Hybrid Ensemble Model (HENSM). It is observed that the proposed HENSM produces higher predictive accuracy compared to the CML models used in the present study. The predictive performance of all models for CS prediction was compared using the testing dataset and it is found that the HENSM model attained the highest predictive accuracy in both phases. Based on the experimental results, the newly constructed HENSM model is very potential to be a new alternative in handling the overfitting issues of CML models and hence, can be used to predict the concrete CS, including the design of less polluting and more sustainable concrete constructions.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Machine learning materials physics: Surrogate optimization and multi-fidelity algorithms predict precipitate morphology in an alternative to phase field dynamics

Machine learning has been effective at detecting patterns and predicting the response of systems that behave free of natural laws. Examples include learning crowd dynamics, recommender systems and autonomous mobility. There also have been applications to the search for new materials that draw upon big-data classification problems. Though, when it comes to physical systems governed by conservation laws, the role of machine learning has been more limited. Here, we present our recent work in exploring the role of machine learning methods in discovering, or aiding, the search for physics. Specifically, we focus on using machine learning algorithms to represent high-dimensional free energy surfaces with the goal of identifying precipitate morphologies in alloy systems. Traditionally, this problem has been approached by combining phase field models, which impose first-order dynamics, with elasticity, to traverse a free energy landscape in search of minima. Equilibrium precipitate morphologies occur at these minima. Here, we exploit the machine learning methods to represent high-dimensional data, combined with surrogate optimization, sensitivity analysis and multifidelity modeling as an alternate framework to explore phenomena controlled by energy extremization. This combination of data-driven methods offers an alternative to the imposition of first-order dynamics via phase field methods, and represents one aspect of applying machine learning to materials physics.

42 ENGINEERING↗
DOE OSTI2020

Effects of fuel composition and octane sensitivity on polycyclic aromatic hydrocarbon and soot emissions of gasoline–ethanol blend surrogates

The sooting propensity of a fuel is closely coupled with the fuel composition and chemistry. A detailed understanding of their effects is, therefore, needed to develop next-generation fuels which can minimize particulate emissions. With this overarching goal, the present work numerically investigates the effects of fuel composition and octane sensitivity (S) on polycyclic aromatic hydrocarbons (PAH) and soot emissions, for four-component gasoline-ethanol blend surrogates comprising isooctane, n-heptane, toluene, and ethanol. A partially-premixed counterflow flame is chosen as the canonical configuration for this study and simulations are performed using CHEMKIN-Pro-employing a kinetic mechanism developed by Park et al. (2017). In addition, a, detailed soot model based on the sectional method is used to capture the spatial characteristics of soot emissions. The kinetic mechanism and soot model are validated using available experimental data for various targets. A total of 86 TPRF-E mixtures, spanning a wide range of concentration of each component, and a wide range of S are analyzed. The effect of each non-paraffinic fuel component on the resultant PAH and soot emissions is investigated. PAH and soot emissions are found to vary significantly depending upon the blend composition. Additionally, based on the parametric sweeps, a regression analysis is carried out to identify global parameters that govern the formation of PAHs and soot. The analysis shows that both toluene content and S have a prominent effect on the formation of PAHs and soot, with toluene content having a stronger impact. Moreover, larger PAHs have higher dependency on toluene content and S. Furthermore, a detailed analysis is carried out to understand the physical and chemical phenomena associated with the observed trends of PAH and soot emissions.

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

Effect of nitric oxide and exhaust gases on gasoline surrogate autoignition: iso-octane experiments and modeling

Exhaust gas recirculation (EGR) is widely used in advanced internal combustion engines to reduce engine emissions as well as control combustion phasing. Among various species present in EGR gases, CO 2 and H 2 O are two major components that can thermally and chemically affect fuel autoignition. It is of fundamental interest to isolate the thermal and chemical effects of CO 2 and H 2 O on fuel autoignition, especially as such an effort has not been reported in the literature. Moreover, nitric oxide (NO) is known to exhibit strong chemical effects on fuel autoignition, which in turn affects engine combustion phasing. The effects of ultra-low NO addition (< 100 ppm) on fuel autoignition at low temperatures are also not well understood. Recognizing these problems, autoignition experiments of iso-octane (a major gasoline surrogate component) in air are performed in this study using a rapid compression machine at varying compressed pressures, equivalence ratios, dilution levels with an EGR gas analogue (consisting of CO 2 , H 2 O, O 2 , and N 2 ) and N 2 only, and varying amounts of NO addition. Furthermore, the thermal and chemical effects of the EGR gas analogue are isolated and evaluated by comparing the ignition delay time datasets of EGR and N2-only diluted cases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Fuel-rich oxidation of gasoline surrogate components in an atmospheric flow reactor

Fuel-rich oxidation of three typical gasoline surrogate components, toluene, isooctane, and n-heptane, was investigated in an atmospheric-pressure flow reactor at mean gas temperatures from 1050 to 1350 K, equivalence ratio of 9.0, and residence times of 0.45 and 1.2 s. Not only polycyclic aromatic hydrocarbons (PAHs) up to 3 ring structure but also small intermediate products from C 1 to C 5 were quantified by a gas chromatograph mass spectrometry coupled with photon ionization and gas chromatograph with flame ionization detector, respectively. The kinetic model recently developed by Lawrence Livermore National Laboratory was revised to reflect the results of many recent investigations. Basically, the updated model could satisfactorily reproduce the experimental mole fractions of many species. The experimental and simulated results showed that PAH mole fractions produced were in the order of toluene, isooctane, and n-heptane. The kinetic analysis using the model was carried out to explore PAH formation pathways, especially focusing on naphthalene, acenaphthylene, and phenanthrene. Through rate of production analysis, it was found that the main formation pathways of many PAHs were affected by the fuels. Although resonantly stabilized radicals, such as benzyl and fulvenallenyl radicals, played a crucial role in the formation pathways of many PAHs in every fuel, they were produced through hydrogen elimination of toluene in toluene fuel, while they were formed from small intermediate products in isooctane and n-heptane fuels. Sensitivity analysis revealed the difference and similarity of the reactions with large positive coefficients according to the fuels studied here. In conclusion, the molecular growth reactions of aromatic species were influential in PAH production in every fuel, whereas the ring formation reactions from small species and the reactions involving toluene had large positive sensitivity coefficients in isooctane/n-heptane and toluene fuels, respectively.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2021

Water vapor oxidation of SiC layer in surrogate TRISO fuel particles

Under accidental conditions for high temperature gas-cooled reactors (HTGR), the SiC layer in tri-structural-isotropic (TRISO) fuel particles can be exposed to water vapor. In this study, oxidation behaviors of surrogate TRISO fuel particles were investigated in a He-20 vol% water vapor mixed atmosphere at temperatures up to 1600 °C. The growth of the crystalline oxide passivation layer with cracks and pores followed a parabolic law with time, where the maximum was 2.3 μm at 1600 °C. The oxide layer and the SiC surface under the oxide became flattened with increasing temperature, as a function of the silica viscosity and the diffusion path of water vapor. Volatilization of the oxide layer was analyzed using a mechanistic model that an inert gas in oxidizing atmospheres could influence the magnitude of volatilization. The fracture load and strength of the oxidized and thinned SiC layer were numerically estimated to decrease from 2.27 to 1.69 N and from 317 to 299 MPa, respectively, with the SiC thickness decrease from 35 to 32 μm. This prediction indicates that the oxidized SiC layer should retain fission products. Additionally, the mechanical integrity of each layer in the TRISO fuel particle after oxidation was evaluated. The results in this work provide important data for the safety analysis of accidental scenarios in HTGRs.

36 MATERIALS SCIENCE↗
DOE OSTI2025

GPR_calculator: An on-the-fly surrogate model to accelerate massive nudged elastic band calculations

We present GPR_calculator, a package based on Python and C++ programming languages to build an on-the-fly surrogate model using Gaussian Process Regression (GPR) to approximate computationally expensive electronic structure calculations. The key idea is to dynamically train a GPR model during the simulation that can accurately predict energies and forces with uncertainty quantification. When the uncertainty is high, the costly electronic structure calculation is performed to obtain the ground truth data, which is then used to update the GPR model. To illustrate the effectiveness of GPR_calculator, we demonstrate its application in Nudged Elastic Band (NEB) simulations of surface diffusion and reactions, achieving 3-10 times acceleration compared to pure ab initio calculations. The source code is available at https://github.com/MaterSim/GPR_calculator.

Gaussian process regression↗
DOE OSTI2026

A hybrid CNN-LSTM surrogate model for hyper-resolution spatiotemporal flood forecasting in Norfolk, Virginia

Study region: Norfolk, Virginia, United States Study focus: Accurate and timely flood forecasting is essential for enhancing resilience in coastal urban areas in the context of increasing frequency and intensity of rainfall, sea level rise and urbanization. This study presents a hybrid deep learning-based surrogate model that integrates Convolutional Neural Networks (CNN) and Long Short-Term Memory (LSTM) networks to enable real-time spatiotemporal flood forecasting. The model leverages CNN to capture spatial features from inputs such as elevation and Topographic Wetness Index (TWI), while LSTM processes time-series inputs of rainfall and tide data to capture temporal features. New hydrologic insights for the region: The hybrid CNN-LSTM model was trained using the physics-based hydrodynamic model simulations obtained from the Two-dimensional Unsteady FLOW (TUFLOW) model for Norfolk, Virginia, and achieved high predictive accuracy across diverse flood-prone areas. The reduced computational time from four to six hours using TUFLOW to 3.2 min per event using CNN-LSTM enables rapid flood inundation mapping and early warning applications. The model effectively captured both spatial flood extents and their temporal evolution across different flooding scenarios, providing forecasts at a 2.5-m spatial resolution and 15-min temporal resolution and a one-hour-ahead prediction horizon. While challenges remain in terms of transferability to new regions and real-time data assimilation, this approach demonstrates strong potential for supporting operational flood risk management in coastal urban environments.

Coastal urban flooding↗
DOE OSTI2024

Optimal control of the electron temperature profile in DIII-D using machine learning surrogate models

The viability of the tokamak as a potential fusion reactor depends on the ability to keep the plasma in a stable regime while achieving temperatures, densities, and confinement times that are as high as possible. Tokamak scenario development attempts to find plasma regimes that achieve all of these conditions and are accessible with a given set of hardware constraints. This requires the ability to control plasma properties such as the normalized beta, the internal inductance, safety factor, rotation, etc. One property that has received less attention than some of the others, but is no less critical to achieving high performance, is the electron temperature (T e ) profile. In this work, Linear Quadratic Integral (LQI) control is used to develop a controller for the electron temperature profile in DIII-D. The controller is based on a linearized model derived from the transport equation that describes the evolution of the electron temperature, and includes contributions from the neural network surrogate models NubeamNet and MMMnet. Furthermore, the controller is tested in simulation using COTSIM, and is proven capable of tracking a target T e profile.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Observations of multi-ion physics and kinetic effects in a surrogate to the solar CNO reactions

The ‘CNO process’ occurs in heavier stars with finite metallicity in which hydrogen burning is catalyzed in the presence of 12 C. These reactions are more strongly dependent on temperature than the pp cycle reactions, and thus the CNO cycle dominates only in massive stars. For these types of reactions to be studied at ICF facilities such as OMEGA, an implosion platform using heavier nuclei in the fuel and capable of creating ion temperatures on the order of at least 20 keV is required. A potential route to reach these conditions is to take advantage of kinetic effects in low-convergence shock-driven ‘exploding pusher’ implosions. In this experiment, shots were conducted at the OMEGA laser facility using the surrogate reaction 13 C + D. Its cross section is substantially higher than the actual astrophysical CNO reactions. The yield of this reaction in these implosions was much lower than expected. Finally, physical explanations are discussed, with significant species stratification the likely explanation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Robust PCA-Deep Belief Network Surrogate Model for Distribution System Topology Identification with DERs

With the expansion of distribution networks and increased penetration of distributed energy resources (DERs), it is becoming increasingly important to obtain accurate distribution network topology in real-time. In this paper, a robust principal component analysis coupled deep belief network (PCA-DBN) surrogate model is proposed for distribution system topology identification. It integrates the benefits of robust feature extraction from PCA to deal with data quality issues and filter out noise, and the strength of DBN in capturing the nonlinear relationship between voltage amplitudes and the binary states of switchable connections. This also significantly reduces the DBN training complexity without loss of accuracy. It is shown that the widely used standard deviation of voltage drop and the voltage covariance matrix features yield less accuracy as compared to that of the voltage amplitudes in presence of high penetration of DERs and ZIP loads. Comparison results with other alternatives, such as the random forest (RF), multi-output regression (MOR) and the traditional DBN methods demonstrate that the proposed method can achieve a much higher topology identification accuracy while maintaining robustness to missing data and measurement noise under various penetration levels of DERs.

deep belief network↗
DOE OSTI2014

Four-Dimensional Magnetic Resonance Imaging Using Axial Body Area as Respiratory Surrogate: Initial Patient Results

Purpose: To evaluate the feasibility of a retrospective binning technique for 4-dimensional magnetic resonance imaging (4D-MRI) using body area (BA) as a respiratory surrogate. Methods and Materials: Seven patients with hepatocellular carcinoma (4 of 7) or liver metastases (3 of 7) were enrolled in an institutional review board-approved prospective study. All patients were simulated with both computed tomography (CT) and MRI to acquire 3-dimensinal and 4D images for treatment planning. Multiple-slice multiple-phase cine-MR images were acquired in the axial plane for 4D-MRI reconstruction. Image acquisition time per slice was set to 10-15 seconds. Single-slice 2-dimensinal cine-MR images were also acquired across the center of the tumor in orthogonal planes. Tumor motion trajectories from 4D-MRI, cine-MRI, and 4D-CT were analyzed in the superior–inferior (SI), anterior–posterior (AP), and medial–lateral (ML) directions, respectively. Their correlation coefficients (CC) and differences in tumor motion amplitude were determined. Tumor-to-liver contrast-to-noise ratio (CNR) was measured and compared between 4D-CT, 4D-MRI, and conventional T2-weighted fast spin echo MRI. Results: The means (±standard deviations) of CC comparing 4D-MRI with cine-MRI were 0.97 ± 0.03, 0.97 ± 0.02, and 0.99 ± 0.04 in SI, AP, and ML directions, respectively. The mean differences were 0.61 ± 0.17 mm, 0.32 ± 0.17 mm, and 0.14 ± 0.06 mm in SI, AP, and ML directions, respectively. The means of CC comparing 4D-MRI and 4D-CT were 0.95 ± 0.02, 0.94 ± 0.02, and 0.96 ± 0.02 in SI, AP, and ML directions, respectively. The mean differences were 0.74 ± 0.02 mm, 0.33 ± 0.13 mm, and 0.18 ± 0.07 mm in SI, AP, and ML directions, respectively. The mean tumor-to-tissue CNRs were 2.94 ± 1.51, 19.44 ± 14.63, and 39.47 ± 20.81 in 4D-CT, 4D-MRI, and T2-weighted MRI, respectively. Conclusions: The preliminary evaluation of our 4D-MRI technique results in oncologic patients demonstrates its potential usefulness to accurately measure tumor respiratory motion with improved tumor CNR compared with 4D-CT.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2014

Is Diaphragm Motion a Good Surrogate for Liver Tumor Motion?

Purpose: To evaluate the relationship between liver tumor motion and diaphragm motion. Methods and Materials: Fourteen patients with hepatocellular carcinoma (10 of 14) or liver metastases (4 of 14) undergoing radiation therapy were included in this study. All patients underwent single-slice cine–magnetic resonance imaging simulations across the center of the tumor in 3 orthogonal planes. Tumor and diaphragm motion trajectories in the superior–inferior (SI), anterior–posterior (AP), and medial–lateral (ML) directions were obtained using an in-house-developed normalized cross-correlation–based tracking technique. Agreement between the tumor and diaphragm motion was assessed by calculating phase difference percentage, intraclass correlation coefficient, and Bland-Altman analysis (Diff). The distance between the tumor and tracked diaphragm area was analyzed to understand its impact on the correlation between the 2 motions. Results: Of all patients, the mean (±standard deviation) phase difference percentage values were 7.1% ± 1.1%, 4.5% ± 0.5%, and 17.5% ± 4.5% in the SI, AP, and ML directions, respectively. The mean intraclass correlation coefficient values were 0.98 ± 0.02, 0.97 ± 0.02, and 0.08 ± 0.06 in the SI, AP, and ML directions, respectively. The mean Diff values were 2.8 ± 1.4 mm, 2.4 ± 1.1 mm, and 2.2 ± 0.5 mm in the SI, AP, and ML directions, respectively. Tumor and diaphragm motions had high concordance when the distance between the tumor and tracked diaphragm area was small. Conclusions: This study showed that liver tumor motion had good correlation with diaphragm motion in the SI and AP directions, indicating diaphragm motion in the SI and AP directions could potentially be used as a reliable surrogate for liver tumor motion.

62 RADIOLOGY AND NUCLEAR MEDICINE↗