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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Development and Integration of a Stochastic Clad Damage Propagation Model into PRONGHORN-SC Subchannel Analysis Code

The failure of fuel pins in nuclear reactors is intrinsically stochastic. Typically, a combination of variation in manufacturing that affects the material characteristics and the fuel assembly dimensions, variation in operating conditions, such as local power, coolant flow rate, and irradiation induced changes in material properties lead to a large uncertainty in failure margin of the fuel pins. Failure, therefore, may occur in exceptional pins with adverse combinations of these variations. Upon a metal fuel pin (U-Pu-Zr/HT9) failure, depressurization of the fuel pin takes place by release of fission gas, liquid sodium bond, and potentially solid fuel particles or molten/eutectic fuel droplets through the hole in cladding. The effect of a fission gas jet on neighbor fuel pins and possible propagation of a clad damage during normal operation was studied experimentally in 1970s and it was found that the post-failure fission gas jet insulates the jet impingement area of the target fuel pin surface and could increase the target pin’s surface temperature by as much as 100 – 200 K during the failed pin depressurization. It was concluded that the effect should not lead to fuel pin failure propagation during normal operation. In accident scenarios of sodium and lead fast reactors such as Unprotected Loss-Of-Flow (ULOF) or Unprotected Transient Over Power (UTOP), the fuel pins can be subjected to higher clad temperatures and fuel pin pressures or fuel clad mechanical/chemical interaction where thermal creep margin becomes significantly lower compared to the normal operation conditions. Therefore, possible stochastic failure and the post-failure fission gas/fuel jet impingement could be critical in order to predict fuel pin failure propagation. Pin depressurization due to fission gas release may degrade the heat transfer by formation of a gas blanket on a neighboring pin surface, which is a local phenomenon, and by causing coolant flow deceleration and starvation, which could affect a surrounding region as well. Furthermore, the potential presence of solid fuel particles or molten fuel at the time of clad failure could boost post-failure jet induced degradation even further. The present study models the U-Pu-Zr/HT9 metal fuel pin failure and stochastic clad damage propagation by biased sampling based on a Cumulative Damage Fraction (CDF) type clad failure criterion and the normal distribution of fuel failure probability density as a function of logarithm of Cumulative Damage Fraction. In addition, the effect of post-failure fission gas jet on heat transfer degradation is modeled for the target pins. This model is called stochastic Clad Damage Propagation (CDAP). The CDAP model is now fully integrated into developmental version of PRONGHORN-SC subchannel analysis code, allowing for modeling local failures and its propagation potential. Section 2 describes the components of the CDAP models. Section 3 describes the model implementation to PRONGHORN-SC and input specifications. Section 4 describes the CDAP model validation coupled to PRONGHORN-SC.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2011

Wave functions of the proton ground state in the presence of a uniform background magnetic field in lattice QCD

We calculate the probability distributions of quarks in the ground state of the proton, and how they are affected in the presence of a constant background magnetic field. We focus on wave functions in the Landau and Coulomb gauges. We observe the formation of a scalar u-d diquark clustering. The overall distortion of the quark probability distribution under a very large magnetic field, as demanded by the quantization conditions on the field, is quite small. The effect is to elongate the distributions along the external field axis while localizing the remainder of the distribution.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2012

Respiratory motion sampling in 4DCT reconstruction for radiotherapy

Purpose: Phase-based and amplitude-based sorting techniques are commonly used in four-dimensional CT (4DCT) reconstruction. However, effect of these sorting techniques on 4D dose calculation has not been explored. In this study, the authors investigated a candidate 4DCT sorting technique by comparing its 4D dose calculation accuracy with that for phase-based and amplitude-based sorting techniques.Method: An optimization model was formed using organ motion probability density function (PDF) in the 4D dose convolution. The objective function for optimization was defined as the maximum difference between the expected 4D dose in organ of interest and the 4D dose calculated using a 4DCT sorted by a candidate sampling method. Sorting samples, as optimization variables, were selected on the respiratory motion PDF assessed during the CT scanning. Breathing curves obtained from patients' 4DCT scanning, as well as 3D dose distribution from treatment planning, were used in the study. Given the objective function, a residual error analysis was performed, and k-means clustering was found to be an effective sampling scheme to improve the 4D dose calculation accuracy and independent with the patient-specific dose distribution. Results: Patient data analysis demonstrated that the k-means sampling was superior to the conventional phase-based and amplitude-based sorting and comparable to the optimal sampling results. For phase-based sorting, the residual error in 4D dose calculations may not be further reduced to an acceptable accuracy after a certain number of phases, while for amplitude-based sorting, k-means sampling, and the optimal sampling, the residual error in 4D dose calculations decreased rapidly as the number of 4DCT phases increased to 6.Conclusion: An innovative phase sorting method (k-means method) is presented in this study. The method is dependent only on tumor motion PDF. It could provide a way to refine the phase sorting in 4DCT reconstruction and is effective for 4D dose accumulation. Optimized sorting techniques could achieve acceptable residuals (less than 0.5% of the prescription dose) using 6 sorting samples, which is much better than amplitude-based or phase-based sorting. Further increase in sorting phase number exceeding 6 or more may not be necessary when using the k-means sampling or optimal sampling points.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2020

Reliability-Informed Life-Cycle Warranty Cost Analysis: A Case Study on a Transmission in Agricultural Equipment

In agricultural and industrial equipment, both new and remanufactured systems are often available for warranty coverage. In such cases, it may be challenging for equipment manufacturers to properly trade-off between the system reliability and the cost associated with a replacement option (e.g., replace with a new or remanufactured system). To address this problem, we present a reliability-informed life-cycle warranty cost (LCWC) analysis framework that enables equipment manufacturers to evaluate different warranty policies. These warranty policies differ in whether a new or remanufactured system is used for replacement in the case of product failure. The novelty of this LCWC analysis framework lies in its ability to incorporate real-world field reliability data into warranty policy assessment using probabilistic warranty cost models that consider multiple life cycles. First, the reliability functions for the new and remanufactured systems are built as the time-to-failure distributions that provide the best-fit to the field reliability data. Then, these reliability functions and their corresponding warranty policies are used to build the LCWC models according to the specific warranty terms. Finally, Monte Carlo simulation is used to propagate the time-to-failure uncertainty of each system, modeled by its reliability function, through each LCWC model to produce a probability distribution of the LCWC. The effectiveness of the proposed reliability-informed LCWC analysis framework is demonstrated with a real-world case study on a transmission used in some agricultural equipment.

agricultural equipment↗
DOE OSTI2011

A Bayesian approach to real-time 3D tumor localization via monoscopic x-ray imaging during treatment delivery

Purpose: Monoscopic x-ray imaging with on-board kV devices is an attractive approach for real-time image guidance in modern radiation therapy such as VMAT or IMRT, but it falls short in providing reliable information along the direction of imaging x-ray. By effectively taking consideration of projection data at prior times and/or angles through a Bayesian formalism, the authors develop an algorithm for real-time and full 3D tumor localization with a single x-ray imager during treatment delivery. Methods: First, a prior probability density function is constructed using the 2D tumor locations on the projection images acquired during patient setup. Whenever an x-ray image is acquired during the treatment delivery, the corresponding 2D tumor location on the imager is used to update the likelihood function. The unresolved third dimension is obtained by maximizing the posterior probability distribution. The algorithm can also be used in a retrospective fashion when all the projection images during the treatment delivery are used for 3D localization purposes. The algorithm does not involve complex optimization of any model parameter and therefore can be used in a ''plug-and-play'' fashion. The authors validated the algorithm using (1) simulated 3D linear and elliptic motion and (2) 3D tumor motion trajectories of a lung and a pancreas patient reproduced by a physical phantom. Continuous kV images were acquired over a full gantry rotation with the Varian TrueBeam on-board imaging system. Three scenarios were considered: fluoroscopic setup, cone beam CT setup, and retrospective analysis. Results: For the simulation study, the RMS 3D localization error is 1.2 and 2.4 mm for the linear and elliptic motions, respectively. For the phantom experiments, the 3D localization error is < 1 mm on average and < 1.5 mm at 95th percentile in the lung and pancreas cases for all three scenarios. The difference in 3D localization error for different scenarios is small and is not statistically significant. Conclusions: The proposed algorithm eliminates the need for any population based model parameters in monoscopic image guided radiotherapy and allows accurate and real-time 3D tumor localization on current standard LINACs with a single x-ray imager.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2015

PROBABILISTIC MODEL OF BEAM–PLASMA INTERACTION IN RANDOMLY INHOMOGENEOUS PLASMA

We propose a new model that describes beam–plasma interaction in the presence of random density fluctuations with a known probability distribution. We use the property that, for the given frequency, the probability distribution of the density fluctuations uniquely determines the probability distribution of the phase velocity of waves. We present the system as discrete and consisting of small, equal spatial intervals with a linear density profile. This approach allows one to estimate variations in wave energy density and particle velocity, depending on the density gradient on any small spatial interval. Because the characteristic time for the evolution of the electron distribution function and the wave energy is much longer than the time required for a single wave–particle resonant interaction over a small interval, we determine the description for the relaxation process in terms of averaged quantities. We derive a system of equations, similar to the quasi-linear approximation, with the conventional velocity diffusion coefficient D and the wave growth rate γ replaced by the average in phase space, by making use of the probability distribution for phase velocities and by assuming that the interaction in each interval is independent of previous interactions. Functions D and γ are completely determined by the distribution function for the amplitudes of the fluctuations. For the Gaussian distribution of the density fluctuations, we show that the relaxation process is determined by the ratio of beam velocity to plasma thermal velocity, the dispersion of the fluctuations, and the width of the beam in the velocity space.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2012

Structure of Hydrated Poly(d,l-lactic acid) Studied with X-ray Diffraction and Molecular Simulation Methods

The effect of hydration on the molecular structure of amorphous poly(D,L-lactic acid) (PDLLA) with 50:50 L-to-D ratio has been studied by combining experiments with molecular simulations. X-ray diffraction measurements revealed significant changes upon hydration in the structure functions of the copolymer. Large changes in the structure functions at 10 days of incubation coincided with the large increase in the water uptake from {approx} 1 to {approx} 40% and the formation of voids in the film. Computer modeling based on the recently developed TIGER2/TIGER3 mixed sampling scheme was used to interpret these changes by efficiently equilibrating both dry and hydrated models of PDLLA. Realistic models of bulk amorphous PDLLA structure were generated as demonstrated by close agreement between the calculated and the experimental structure functions. These molecular simulations were used to identify the interactions between water and the polymer at the atomic level including the change of positional order between atoms in the polymer due to hydration. Changes in the partial O-O structure functions, about 95% of which were due to water-polymer interactions, were apparent in the radial distribution functions. These changes, and somewhat smaller changes in the C-C and C-O partial structure functions, clearly demonstrated the ability of the model to capture the hydrogen-bonding interactions between water and the polymer, with the probability of water forming hydrogen bonds with the carbonyl oxygen of the ester group being about 4 times higher than with its ether oxygen.

08 HYDROGEN↗
DOE OSTI2010

THE LACK OF INTENSE Ly{alpha} IN ULTRADEEP SPECTRA OF z = 7 CANDIDATES IN GOODS-S: IMPRINT OF REIONIZATION?

We present ultradeep optical spectroscopy obtained with FORS2 on the Very Large Telescope (VLT) of seven Lyman-break galaxy (LBG) candidates at z>6.5 selected in the GOODS-S field from Hawk-I/VLT and WFC3/HST imaging. For one galaxy we detect a low significance emission line (S/N {<=} 7), located at {lambda} = 9691.5 {+-} 0.5 A and with flux 3.4 x 10{sup -18} erg cm{sup -2} s{sup -1}. If identified as Ly{alpha}, it places the LBG at redshift z = 6.972 {+-} 0.002, with a rest-frame equivalent width EW{sub rf} = 13 A. Using Monte Carlo simulations and conservative EW distribution functions at 2 < z < 6, we estimate that the probability of observing no galaxies in our data with S/N>10 is {approx_equal}2%, and that of observing only one galaxy out of seven with S/N = 5 is {approx_equal}4%, but these can be as small as {approx}10{sup -3}, depending on the details of the EW distribution. We conclude that either a significant fraction of the candidates is not at high redshift or that some physical mechanism quenches the Ly{alpha} emission emerging from the galaxies at z>6.5, abruptly reversing the trend of the increasing fraction of strong emitters with increasing redshift observed up to z {approx} 6.5. We discuss the possibility that an increasingly neutral intergalactic medium is responsible for such quenching.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Frequency domain analysis of errors in cross-correlations of ambient seismic noise

We analyse random errors (variances) in cross-correlations of ambient seismic noise in the frequency domain, which differ from previous time domain methods. Extending previous theoretical results on ensemble averaged cross-spectrum, we estimate confidence interval of stacked cross-spectrum of finite amount of data at each frequency using non-overlapping windows with fixed length. The extended theory also connects amplitude and phase variances with the variance of each complex spectrum value. Analysis of synthetic stationary ambient noise is used to estimate the confidence interval of stacked cross-spectrum obtained with different length of noise data corresponding to different number of evenly spaced windows of the same duration. This method allows estimating Signal/Noise Ratio (SNR) of noise cross-correlation in the frequency domain, without specifying filter bandwidth or signal/noise windows that are needed for time domain SNR estimations. Based on synthetic ambient noise data, we also compare the probability distributions, causal part amplitude and SNR of stacked cross-spectrum function using one-bit normalization or pre-whitening with those obtained without these pre-processing steps. Natural continuous noise records contain both ambient noise and small earthquakes that are inseparable from the noise with the existing pre-processing steps. Using probability distributions of random cross-spectrum values based on the theoretical results provides an effective way to exclude such small earthquakes, and additional data segments (outliers) contaminated by signals of different statistics (e.g. rain, cultural noise), from continuous noise waveforms. This technique is applied to constrain values and uncertainties of amplitude and phase velocity of stacked noise cross-spectrum at different frequencies, using data from southern California at both regional scale (~35 km) and dense linear array (~20 m) across the plate-boundary faults. A block bootstrap resampling method is used to account for temporal correlation of noise cross-spectrum at low frequencies (0.05–0.2 Hz) near the ocean microseismic peaks.

58 GEOSCIENCES↗
DOE OSTI2017

Analytical Assessment for Transient Stability Under Stochastic Continuous Disturbances

Here, with the growing integration of renewable power generation, plug-in electric vehicles, and other sources of uncertainty, increasing stochastic continuous disturbances are brought to power systems. The impact of stochastic continuous disturbances on power system transient stability attracts significant attention. To address this problem, this paper proposes an analytical assessment method for transient stability of multi-machine power systems under stochastic continuous disturbances. In the proposed method, a probability measure of transient stability is presented and analytically solved by stochastic averaging. Compared with the conventional method (Monte Carlo simulation), the proposed method is many orders of magnitude faster, which makes it very attractive in practice when many plans for transient stability must be compared or when transient stability must be analyzed quickly. Also, it is found that the evolution of system energy over time is almost a simple diffusion process by the proposed method, which explains the impact mechanism of stochastic continuous disturbances on transient stability in theory.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2016

SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

A new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability. The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistical moments of the input random variables to develop the polynomial chaos expansion. This approach provides the possibility to propagate continuous or discrete probability density functions and also histograms (data sets) as long as their moments exist, are finite and the determinant of the moment matrix is strictly positive. For cases with limited data availability, this approach avoids bias and fitting errors caused by wrong assumptions. In this work, an alternative way to calculate the aPC is suggested, which provides the optimal polynomials, Gaussian quadrature collocation points and weights from the moments using only a handful of matrix operations on the Hankel matrix of moments. It can therefore be implemented without requiring prior knowledge about statistical data analysis or a detailed understanding of the mathematics of polynomial chaos expansions. The extension to more input variables suggested in this work, is an anisotropic and adaptive version of Smolyak's algorithm that is solely based on the moments of the input probability distributions. It is referred to as SAMBA (PC), which is short for Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos. It is illustrated that for moderately high-dimensional problems (up to 20 different input variables or histograms) SAMBA can significantly simplify the calculation of sparse Gaussian quadrature rules. SAMBA's efficiency for multivariate functions with regard to data availability is further demonstrated by analysing higher order convergence and accuracy for a set of nonlinear test functions with 2, 5 and 10 different input distributions or histograms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Beyond the universal Dyson singularity for 1-D chains with hopping disorder

We study a simple non-interacting nearest neighbor tight-binding model in one dimension with disorder, where the hopping terms are chosen randomly. This model exhibits a well-known singularity at the band center both in the density of states and localization length. If the probability distribution of the hopping terms is well-behaved, then the singularities exhibit universal behavior, the functional form of which was first discovered by Freeman Dyson in the context of a chain of classical harmonic oscillators. We show here that this universal form can be violated in a tunable manner if the hopping elements are chosen from a divergent probability distribution. We also demonstrate a connection between a breakdown of universality in this quantum problem and an analogous scenario in the classical domain — that of random walks and diffusion with anomalous exponents.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Evolution of the electron energy distribution function during genesis of breakdown plasma

During the process of plasma initiation by an electromagnetic wave, it is found that the electron energy distribution function (EEDF) that is initially Maxwellian with the most probable energy at room temperature, evolves with time and tends toward a Bi-Maxwellian – indicating attainment of thermodynamic equilibrium in the individual electron populations prior to breakdown, with a significant increase in hot electron density. In the intermediate states during the evolution, however, non-equilibrium processes are prevalent under fast pulse excitation and the EEDF initially exhibits substantial deviation from a Maxwellian. An analysis of the deviation has been carried out by optimizing the residual sum of squares of the probabilities obtained from the simulation and a fitted Maxwellian curve. The equilibrium regain time defined as the time required to attain thermodynamic equilibrium again, is investigated as a function of neutral pressure, wave electric, and external magnetostatic fields.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Evaluation of long-term surface-retrieved cloud droplet number concentration with in situ aircraft observations

A new cloud-droplet number concentration (NDROP) value added product (VAP) has been produced at the Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) site for the 13 years from January 1998 to January 2011. The retrieval is based on surface radiometer measurements of cloud optical depth from the multi-filter rotating shadow-band radiometer (MFRSR) and liquid water path from the microwave radiometer (MWR). It is only applicable for single-layered warm clouds. Validation with in situ aircraft measurements during the extended-term aircraft field campaign, Routine ARM Aerial Facility (AAF) CLOWD Optical Radiative Observations (RACORO), shows that the NDROP VAP robustly reproduces the primary mode of the in situ measured probability density function (PDF), but produces a too wide distribution, primarily caused by frequent high cloud-droplet number concentration. Our analysis shows that the error in the MWR retrievals at low liquid water paths is one possible reason for this deficiency. Modification through the diagnosed liquid water path from the coordinate solution improves not only the PDF of the NDROP VAP but also the relationship between the cloud-droplet number concentration and cloud-droplet effective radius. Consideration of entrainment effects rather than assuming an adiabatic cloud improves the values of the NDROP retrieval by reducing the magnitude of cloud-droplet number concentration. Aircraft measurements and retrieval comparisons suggest that retrieving the vertical distribution of cloud-droplet number concentration and effective radius is feasible with an improvement of the parameter representing the mixing effects between environment and clouds and with a better understanding of the effect of mixing degree on cloud properties.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Stochastic Inflation at NNLO

Stochastic Inflation is an important framework for understanding the physics of de Sitter space and the phenomenology of inflation. In the leading approximation, this approach results in a Fokker-Planck equation that calculates the probability distribution for a light scalar field as a function of time. Despite its successes, the quantum field theoretic origins and the range of validity for this equation have remained elusive, and establishing a formalism to systematically incorporate higher order effects has been an area of active study. In this paper, we calculate the next-to-next-to-leading order (NNLO) corrections to Stochastic Inflation using Soft de Sitter Effective Theory (SdSET). In this effective description, Stochastic Inflation manifests as the renormalization group evolution of composite operators. The leading impact of non-Gaussian quantum fluctuations appears at NNLO, which is presented here for the first time; we derive the coefficient of this term from a two-loop anomalous dimension calculation within SdSET. We solve the resulting equation to determine the NNLO equilibrium distribution and the low-lying relaxation eigenvalues. In the process, we must match the UV theory onto SdSET at one-loop order, which provides a non-trivial confirmation that the separation into Wilson-coefficient corrections and contributions to initial conditions persists beyond tree level. Furthermore, these results illustrate how the naive factorization of time and momentum integrals in SdSET no longer holds in the presence of logarithmic divergences. It is these effects that ultimately give rise to the renormalization group flow that yields Stochastic Inflation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Statistical characterization of twin transmission across grain boundaries in magnesium

Here, a detailed statistical analysis of twin transmission (TT) across grain boundaries is performed in rolled, commercial purity magnesium compressed along the rolling direction. EBSD images are acquired from two different cuts: a section containing the rolling (RD) and normal (ND) directions; and a section at 35° to the ND which contains transverse direction (TD). An automated twinning analysis software, METIS, is used to obtain the statistical correlations between deformation twins and other microstructural features by analyzing EBSD microstructures comprising thousands of grains and twins. This detailed statistical analysis reveals that the TT propensity is sensitive to the grain boundary (GB) misorientation angle but not to the GB misorientation axis. Specifically, TT propensity decreases with increasing GB misorientation angle; however, the decreasing trend is not monotonic. Further, the detailed analysis of TT events combining macroscopic Schmid factor and the geometric measures (m’: accounts for the alignment of both twin plane normal and shear directions; m”: accounts for the alignment of only twin shear directions; and m”’: accounts for the alignment of only twin plane normal) helps in understanding and identifying the process of twin-pair formation, i.e., co-nucleation versus transmission, also to identify the role of local stresses at GBs induced by inter-grain interaction versus twinning shear transformation processes. In addition, Bayesian inference is used to draw statistically meaningful conclusions as to the likelihood of transmission given misorientation angles. Lastly, twin chain frequency as a function of chain length is predicted using the probability distribution obtained from the Bayesian inference and compared with the actual data from the EBSD microstructures.

36 MATERIALS SCIENCE↗
DOE OSTI2010

A STUDY OF HIGH-ORDER NON-GAUSSIANITY WITH APPLICATIONS TO MASSIVE CLUSTERS AND LARGE VOIDS

The statistical meaning of the local non-Gaussianity parameters f{sub NL} and g{sub NL} is examined in detail. Their relations to the skewness and the kurtosis of the initial distribution are shown to obey simple fitting formulae, accurate on galaxy-cluster scales. We argue that the knowledge of f{sub NL} and g{sub NL} is insufficient for reconstructing a well-defined distribution of primordial fluctuations. Requiring the reconstructed probability density function (pdf) to be positive enforces a theoretical lower bound g{sub NL} {approx}> -1.2 x 10{sup 5}, competitive with the observational bounds in the current literature. By weakening the statistical significance of f{sub NL} and g{sub NL}, it is possible to reconstruct a well-defined pdf by using a truncated Edgeworth series. We give some general guidelines on the use of such a series, noting in particular that (1) the Edgeworth series cannot represent models with nonzero f{sub NL}, unless g{sub NL} is nonzero, and also (2) the series cannot represent models with g{sub NL} < 0, unless some higher-order non-Gaussianities are known. Finally, we apply the Edgeworth series to calculate the effects of g{sub NL} on the abundances of massive clusters and large voids. We show that the abundance of voids may generally be more sensitive to high-order non-Gaussianities than the cluster abundance.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

Organ sample generator for expected treatment dose construction and adaptive inverse planning optimization

Purpose: To create an organ sample generator (OSG) for expected treatment dose construction and adaptive inverse planning optimization. The OSG generates random samples of organs of interest from a distribution obeying the patient specific organ variation probability density function (PDF) during the course of adaptive radiotherapy. Methods: Principle component analysis (PCA) and a time-varying least-squares regression (LSR) method were used on patient specific geometric variations of organs of interest manifested on multiple daily volumetric images obtained during the treatment course. The construction of the OSG includes the determination of eigenvectors of the organ variation using PCA, and the determination of the corresponding coefficients using time-varying LSR. The coefficients can be either random variables or random functions of the elapsed treatment days depending on the characteristics of organ variation as a stationary or a nonstationary random process. The LSR method with time-varying weighting parameters was applied to the precollected daily volumetric images to determine the function form of the coefficients. Eleven h and n cancer patients with 30 daily cone beam CT images each were included in the evaluation of the OSG. The evaluation was performed using a total of 18 organs of interest, including 15 organs at risk and 3 targets. Results: Geometric variations of organs of interest during h and n cancer radiotherapy can be represented using the first 3 {approx} 4 eigenvectors. These eigenvectors were variable during treatment, and need to be updated using new daily images obtained during the treatment course. The OSG generates random samples of organs of interest from the estimated organ variation PDF of the individual. The accuracy of the estimated PDF can be improved recursively using extra daily image feedback during the treatment course. The average deviations in the estimation of the mean and standard deviation of the organ variation PDF for h and n cancer radiotherapy were less than 2 and 1 mm, respectively, for most organs after the second week of treatment. After the first three weeks of treatment, the mean discrepancy of the dose estimation accuracy was within 1% for most of organs, the corresponding standard deviation was within 2.5% for parotids, the brain stem and the cochleae, and within 1% for other organs. Conclusions: A patient specific OSG is feasible and can be used to generate random samples of organs of interest for the expected treatment dose construction and adaptive inverse planning. The accuracy of the OSG can be improved continuously and recursively during the adaptive treatment course using daily volumetric image feedback.

60 APPLIED LIFE SCIENCES↗