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Numerical analysis of flows of rarefied gases in long channels with octagonal cross section shapes

Isothermal, pressure driven rarefied gas flows through long channels with octagonal cross section shapes are analyzed computationally. The capillary is between inlet and outlet reservoirs. The cross section is constant along the axial direction. The boundary condition at the solid-gas interface is assumed to be diffuse reflection. Since the channel is long, the gaseous velocity is small compared to the average molecular speed. Consequently, a linearized description can be used. The flow is described by the linearized Bhatnagar-Gross-Krook kinetic model. The solution of the problem is divided into two stages. First, the local flow field is determined by assuming the local pressure gradient. Secondly, the global flow behavior is deduced by the consideration of the conservation of the mass along the axis of the capillary. The kinetic equation is solved by the discrete velocity method on the cross section. Both spatial and velocity spaces are discretized. A body fitted rectangular grid is used for the spatial space. Near the boundary, first-order, while in the interior part of the flow domain, second-order finite-differences are applied to approximate the spatial derivatives. This combination results into an efficient and straightforward numerical treatment. The velocity space is represented by a Gauss-Legendre quadrature. The kinetic equation is solved in an iterative manner. The local dimensionless flow rate is calculated and tabulated for a wide range of the gaseous rarefaction for octagonal cross sections with various geometrical parameters. It exhibits the Knudsen minimum phenomenon. The flow rates in the octagonal channel are compared to those through capillaries with circular and square cross sections. Typical velocity profiles are also shown. The mass flow rate and the distribution of the pressure are determined and presented for global pressure driven flows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A multilevel method for coupling the neutron kinetics and heat transfer equations

We present a computational method for adequate and efficient coupling the neutron transport equation with the precursor and heat transfer equations. It is based on the multilevel nonlinear quasidiffusion (QD) method for solving the multigroup transport equation. The system of equations includes the time-dependent high-order transport equation and time-dependent multigroup and effective one-group low-order QD equations. We also formulate a method applying the {alpha}-approximation for the time-dependent high-order transport equation. This approach enables one to avoid storing the angular flux from the previous time step. Numerical results for a model transient problem are presented. (authors)

97 MATHEMATICS AND COMPUTING↗

A DATA-DRIVEN MODEL FOR SPECTRA: FINDING DOUBLE REDSHIFTS IN THE SLOAN DIGITAL SKY SURVEY

We present a data-driven method-heteroscedastic matrix factorization, a kind of probabilistic factor analysis-for modeling or performing dimensionality reduction on observed spectra or other high-dimensional data with known but non-uniform observational uncertainties. The method uses an iterative inverse-variance-weighted least-squares minimization procedure to generate a best set of basis functions. The method is similar to principal components analysis (PCA), but with the substantial advantage that it uses measurement uncertainties in a responsible way and accounts naturally for poorly measured and missing data; it models the variance in the noise-deconvolved data space. A regularization can be applied, in the form of a smoothness prior (inspired by Gaussian processes) or a non-negative constraint, without making the method prohibitively slow. Because the method optimizes a justified scalar (related to the likelihood), the basis provides a better fit to the data in a probabilistic sense than any PCA basis. We test the method on Sloan Digital Sky Survey (SDSS) spectra, concentrating on spectra known to contain two redshift components: these are spectra of gravitational lens candidates and massive black hole binaries. We apply a hypothesis test to compare one-redshift and two-redshift models for these spectra, utilizing the data-driven model trained on a random subset of all SDSS spectra. This test confirms 129 of the 131 lens candidates in our sample and all of the known binary candidates, and turns up very few false positives.

79 ASTRONOMY AND ASTROPHYSICS↗

Comparison of analytic models of instability of rarefied gas flow in a channel

Numerical and analytical results are compared concerning the limit properties of the trajectories, attractors and bifurcations of rarefied gas flows in channels. The cascade of bifurcations obtained in our previous analytical and numerical investigations is simulated numerically for different scattering functions V generalizing the ray-diffuse reflection of gas particles from the surface. The main purpose of numerical simulation by Monte Carlo method is the investigation of the properties of different analytic nonlinear dynamic systems corresponding to rarefied gas flow in a channel. The results are compared as well for the models suggested originally by R. N. Miroshin, as for the approximations considered for the first time or for studied in our subsequent papers. Analytical solutions we obtained earlier for the ray reflection which means only one determined velocity of scattered from the walls gas atoms, generally different from the specular reflection. The nonlinear iterative equation describing a rarefied gas flow in a long channel becomes unstable in some regions of corresponding parameters of V (it means the sensitivity to boundary conditions). The values of the parameters are found from analytical approximations in these regions. Numerical results show that the chaotic behavior of the nonlinear dynamic system corresponds to strange attractors and distinguishes clearly from Maxwellian distribution and from the equilibrium on the whole. In the regions of instability (as the dimension of the attractor increases) the search for a corresponding state requires a lot more computation time and a lot of data (the amount of data required increases exponentially with embedding dimension). Therefore the main complication in the computation is reducing as well the computing time as the amount of data to find a suitably close solution. To reduce the computing time our analytical results are applied. Flow conditions satisfying the requirements to the experiment are indicated where the instability of considered type can be detected. The advantages and the drawbacks of considered approximations are detected and the features of obtained solutions are indicated. The recommendations are given for applying the results in practical applications and in numerical calculations of rarefied gas flows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A digitally reconstructed radiograph algorithm calculated from first principles

Purpose: To develop an algorithm for computing realistic digitally reconstructed radiographs (DRRs) that match real cone-beam CT (CBCT) projections with no artificial adjustments. Methods: The authors used measured attenuation data from cone-beam CT projection radiographs of different materials to obtain a function to convert CT number to linear attenuation coefficient (LAC). The effects of scatter, beam hardening, and veiling glare were first removed from the attenuation data. Using this conversion function the authors calculated the line integral of LAC through a CT along rays connecting the radiation source and detector pixels with a ray-tracing algorithm, producing raw DRRs. The effects of scatter, beam hardening, and veiling glare were then included in the DRRs through postprocessing. Results: The authors compared actual CBCT projections to DRRs produced with all corrections (scatter, beam hardening, and veiling glare) and to uncorrected DRRs. Algorithm accuracy was assessed through visual comparison of projections and DRRs, pixel intensity comparisons, intensity histogram comparisons, and correlation plots of DRR-to-projection pixel intensities. In general, the fully corrected algorithm provided a small but nontrivial improvement in accuracy over the uncorrected algorithm. The authors also investigated both measurement- and computation-based methods for determining the beam hardening correction, and found the computation-based method to be superior, as it accounted for nonuniform bowtie filter thickness. The authors benchmarked the algorithm for speed and found that it produced DRRs in about 0.35 s for full detector and CT resolution at a ray step-size of 0.5 mm. Conclusions: The authors have demonstrated a DRR algorithm calculated from first principles that accounts for scatter, beam hardening, and veiling glare in order to produce accurate DRRs. The algorithm is computationally efficient, making it a good candidate for iterative CT reconstruction techniques that require a data fidelity term based on the matching of DRRs and projections.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

SU-F-T-195: Systematic Constraining of Contralateral Parotid Gland Led to Improved Dosimetric Outcomes for Multi-Field Optimization with Scanning Beam Proton Therapy: Promising Results From a Pilot Study in Patients with Base of Tongue Carcinoma

Purpose: Treatment planning for Intensity Modulated Proton Therapy (IMPT) for head and neck cancer is time-consuming due to the large number of organs-at-risk (OAR) to be considered. As there are many competing objectives and also wide range of acceptable OAR constraints, the final approved plan may not be most optimal for the given structures. We evaluated the dose reduction to the contralateral parotid by implementing standardized constraints during optimization for scanning beam proton therapy planning. Methods: Twenty-four (24) consecutive patients previously treated for base of tongue carcinoma were retrospectively selected. The doses were 70Gy, 63Gy and 57Gy (SIB in 33 fractions) for high-, intermediate-, and standard-risk clinical target volumes (CTV), respectively; the treatment included bilateral neck. Scanning beams using MFO with standardized bilateral anterior oblique and PA fields were applied. New plans where then developed and optimized by employing additional contralateral parotid constraints at multiple defined dose levels. Using a step-wise iterative process, the volume-based constraints at each level were then further reduced until known target coverages were compromised. The newly developed plans were then compared to the original clinically approved plans using paired student t-testing. Results: All 24 newly optimized treatment plans maintained initial plan quality as compared to the approved plans, and the 98% prescription dose coverage to the CTV’s were not compromised. Representative DVH comparison is shown in FIGURE 1. The contralateral parotid doses were reduced at all levels of interest when systematic constraints were applied to V10, V20, V30 and V40Gy (All P<0.0001; TABLE 1). Overall, the mean contralateral parotid doses were reduced by 2.26 Gy on average, a ∼13% relative improvement. Conclusion: Applying systematic and volume-based contralateral parotid constraints for IMPT planning significantly reduced the dose at all dosimetric levels for patients with base of tongue cancer.

60 APPLIED LIFE SCIENCES↗

Assessment of volumetric noise and resolution performance for linear and nonlinear CT reconstruction methods

Purpose: For nonlinear iterative image reconstructions (IR), the computed tomography (CT) noise and resolution properties can depend on the specific imaging conditions, such as lesion contrast and image noise level. Therefore, it is imperative to develop a reliable method to measure the noise and resolution properties under clinically relevant conditions. This study aimed to develop a robust methodology to measure the three-dimensional CT noise and resolution properties under such conditions and to provide guidelines to achieve desirable levels of accuracy and precision. Methods: The methodology was developed based on a previously reported CT image quality phantom. In this methodology, CT noise properties are measured in the uniform region of the phantom in terms of a task-based 3D noise-power spectrum (NPS{sub task}). The in-plane resolution properties are measured in terms of the task transfer function (TTF) by applying a radial edge technique to the rod inserts in the phantom. The z-direction resolution properties are measured from a supplemental phantom, also in terms of the TTF. To account for the possible nonlinearity of IR, the NPS{sub task} is measured with respect to the noise magnitude, and the TTF with respect to noise magnitude and edge contrast. To determine the accuracy and precision of the methodology, images of known noise and resolution properties were simulated. The NPS{sub task} and TTF were measured on the simulated images and compared to the truth, with criteria established to achieve NPS{sub task} and TTF measurements with <10% error. To demonstrate the utility of this methodology, measurements were performed on a commercial CT system using five dose levels, two slice thicknesses, and three reconstruction algorithms (filtered backprojection, FBP; iterative reconstruction in imaging space, IRIS; and sinogram affirmed iterative reconstruction with strengths of 5, SAFIRE5). Results: To achieve NPS{sub task} measurements with <10% error, the number of regions of interest needed to be greater than 65. To achieve TTF measurements with <10% error, the contrast-to-noise ratio of the edge needed to be ≥15, achievable by averaging multiple slices across the same edge. The NPS{sub task} measured on a commercial CT system showed IR's reduced noise (IRIS, 30% and SAFIRE5, 55%) and “waxier” texture (peak frequencies: FBP, 0.25 mm{sup −1}; IRIS, 0.23 mm{sup −1}; and SAFIRE5, 0.16 mm{sup −1}). The TTF measured within the axial plane showed improved in-plane resolution with SAFIRE5 at the TTF 50% frequency, f{sub 50} (FBP, 0.36–0.41 mm{sup −1}; SAFIRE5, 0.37–0.46 mm{sup −1}). The TTF measured along the axial direction showed improved z-direction resolution with thinner slice thickness (f{sub 50}: 0.6 mm, 0.35–0.79 mm{sup −1}; 1.5 mm, 0.22–0.3 mm{sup −1}) and with SAFIRE5 (f{sub 50}: FBP, 0.35–0.52 mm{sup −1}; SAFIRE5, 0.42–0.79 mm{sup −1}). Both in-plane and z-direction resolution of SAFIRE5 showed strong dependency on contrast, reflecting SAFIRE5's nonlinearity. Conclusions: A methodology was developed to measure three-dimensional CT noise and resolution properties for iterative reconstruction, especially at challenging measurement conditions with low contrast and high image noise. The methodology also demonstrated its utility for evaluating commercial CT systems.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Being WISE II: reducing the influence of star formation history on the mass-to-light ratio of quiescent galaxies

Stellar population synthesis models can now reproduce the photometry of old stellar systems (age > 2 Gyr) in the near-infrared (NIR) bands at 3.4 and 4.6 μm (WISE W1 and W2 or IRAC 1 and 2). In this paper, we derive stellar mass-to-light ratios for these and optical bands, and confirm that the NIR M/L shows dramatically reduced sensitivity to both age and metallicity compared to optical bands, and further, that this behavior leads to significantly more robust stellar masses for quiescent galaxies with [Fe/H] ≳ −0.5 regardless of star-formation history (SFH). We then use realistic early-type galaxy SFHs and metallicity distributions from the EAGLE simulations of galaxy formation to investigate two methods to determine the appropriate M/L for a galaxy. (1) We show that the uncertainties introduced by an unknown SFH can be largely removed using a spectroscopically inferred luminosity-weighted age and metallicity for the population to select the appropriate single stellar population (SSP) equivalent M/L. Using this method, the maximum systematic error due to SFH on the M/L of an early-type galaxy is <4% at 3.4 μm and typical uncertainties due to errors in the age and metallicity create a scatter of ≲13%. The equivalent values for optical bands are more than two to three times greater, even before considering uncertainties associated with internal dust extinction. (2) We demonstrate that if the EAGLE SFHs and metallicities accurately reproduce the true properties of early-type galaxies, the use of an iterative approach to select a mass dependent M/L can provide even more accurate stellar masses for early-type galaxies, with typical uncertainties of <9%.

79 ASTRONOMY AND ASTROPHYSICS↗

Automatic projection image registration for nanoscale X-ray tomographic reconstruction

Novel developments in X-ray sources, optics and detectors have significantly advanced the capability of X-ray microscopy at the nanoscale. Depending on the imaging modality and the photon energy, state-of-the-art X-ray microscopes are routinely operated at a spatial resolution of tens of nanometres for hard X-rays or ~ 10 nm for soft X-rays. The improvement in spatial resolution, however, has led to challenges in the tomographic reconstruction due to the fact that the imperfections of the mechanical system become clearly detectable in the projection images.Without proper registration of the projection images, a severe point spread function will be introduced into the tomographic reconstructions, causing the reduction of the three-dimensional (3D) spatial resolution as well as the enhancement of image artifacts. In this work, the development of a method that iteratively performs registration of the experimentally measured projection images to those that are numerically calculated by reprojecting the 3D matrix in the corresponding viewing angles is shown. Multiple algorithms are implemented to conduct the registration, which corrects the translational and/ or the rotational errors. A sequence that offers a superior performance is presented and discussed. Going beyond the visual assessment of the reconstruction results, the morphological quantification of a battery electrode particle that has gone through substantial cycling is investigated. The results show that the presented method has led to a better quality tomographic reconstruction, which, subsequently, promotes the fidelity in the quantification of the sample morphology.

42 ENGINEERING↗

SU-E-T-500: Initial Implementation of GPU-Based Particle Swarm Optimization for 4D IMRT Planning in Lung SBRT

Purpose 4D-IMRT planning, combined with dynamic MLC tracking delivery, utilizes the temporal dimension as an additional degree of freedom to achieve improved OAR-sparing. The computational complexity for such optimization increases exponentially with increase in dimensionality. In order to accomplish this task in a clinically-feasible time frame, we present an initial implementation of GPU-based 4D-IMRT planning based on particle swarm optimization (PSO). Methods The target and normal structures were manually contoured on ten phases of a 4DCT scan of a NSCLC patient with a 54cm3 right-lower-lobe tumor (1.5cm motion). Corresponding ten 3D-IMRT plans were created in the Eclipse treatment planning system (Ver-13.6). A vendor-provided scripting interface was used to export 3D-dose matrices corresponding to each control point (10 phases × 9 beams × 166 control points = 14,940), which served as input to PSO. The optimization task was to iteratively adjust the weights of each control point and scale the corresponding dose matrices. In order to handle the large amount of data in GPU memory, dose matrices were sparsified and placed in contiguous memory blocks with the 14,940 weight-variables. PSO was implemented on CPU (dual-Xeon, 3.1GHz) and GPU (dual-K20 Tesla, 2496 cores, 3.52Tflops, each) platforms. NiftyReg, an open-source deformable image registration package, was used to calculate the summed dose. Results The 4D-PSO plan yielded PTV coverage comparable to the clinical ITV-based plan and significantly higher OAR-sparing, as follows: lung Dmean=33%; lung V20=27%; spinal cord Dmax=26%; esophagus Dmax=42%; heart Dmax=0%; heart Dmean=47%. The GPU-PSO processing time for 14940 variables and 7 PSO-particles was 41% that of CPU-PSO (199 vs. 488 minutes). Conclusion Truly 4D-IMRT planning can yield significant OAR dose-sparing while preserving PTV coverage. The corresponding optimization problem is large-scale, non-convex and computationally rigorous. Our initial results indicate that GPU-based PSO with further software optimization can make such planning clinically feasible. This work was supported through funding from the National Institutes of Health and Varian Medical Systems.

60 APPLIED LIFE SCIENCES↗

Leveraging operator learning to accelerate convergence of the preconditioned conjugate gradient method

We propose a new deflation strategy to accelerate the convergence of the preconditioned conjugate gradient (PCG) method for solving parametric large-scale linear systems of equations. Unlike traditional deflation techniques that rely on eigenvector approximations or recycled Krylov subspaces, we generate the deflation subspaces using operator learning, specifically the Deep Operator Network (DeepONet). To this aim, we introduce two complementary approaches for assembling the deflation operators. The first approach approximates near-null space vectors of the discrete PDE operator using the basis functions learned by the DeepONet. The second approach directly leverages solutions predicted by the DeepONet. To further enhance convergence, we also propose several strategies for prescribing the sparsity pattern of the deflation operator. Here, a comprehensive set of numerical experiments encompassing steady-state, time-dependent, scalar, and vector-valued problems posed on both structured and unstructured geometries is presented and demonstrates the effectiveness of the proposed DeepONet-based deflated PCG method, as well as its generalization across a wide range of model parameters and problem resolutions.

Deflation↗

What a difference a delay makes! CT urogram: a pictorial essay

Purpose: The aim of this pictorial essay is to demonstrate several cases where the diagnosis would have been difficult or impossible without the excretory phase image of CT urography. Methods: A brief discussion of CT urography technique and dose reduction is followed by several cases illustrating the utility of CT urography. Results: CT urography has become the primary imaging modality for evaluation of hematuria, as well as in the staging and surveillance of urinary tract malignancies. CT urography includes a non-contrast phase and contrast-enhanced nephrographic and excretory (delayed) phases. While the three phases add to the diagnostic ability of CT urography, it also adds potential patient radiation dose. Several techniques including automatic exposure control, iterative reconstruction algorithms, higher noise tolerance, and split-bolus have been successfully used to mitigate dose. The excretory phase is timed such that the excreted contrast opacifies the urinary collecting system and allows for greater detection of filling defects or other abnormalities. Sixteen cases illustrating the utility of excretory phase imaging are reviewed. Conclusions: Excretory phase imaging of CT urography can be an essential tool for detecting and appropriately characterizing urinary tract malignancies, renal papillary and medullary abnormalities, CT radiolucent stones, congenital abnormalities, certain chronic inflammatory conditions, and perinephric collections.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Passive seismic tomography application for cave monitoring in DOZ underground mine PT. Freeport Indonesia

It is already known that tomography has a great impact for analyzing and mapping unknown objects based on inversion, travel time as well as waveform inversion. Therefore, tomography has used in wide area, not only in medical but also in petroleum as well as mining. Recently, tomography method is being applied in several mining industries. A case study of tomography imaging has been carried out in DOZ ( Deep Ore Zone ) block caving mine, Tembagapura, Papua. Many researchers are undergoing to investigate the properties of DOZ cave not only outside but also inside which is unknown. Tomography takes a part for determining this objective.The sources are natural from the seismic events that caused by mining induced seismicity and rocks deformation activity, therefore it is called as passive seismic. These microseismic travel time data are processed by Simultaneous Iterative Reconstruction Technique (SIRT). The result of the inversion can be used for DOZ cave monitoring. These information must be used for identifying weak zone inside the cave. In addition, these results of tomography can be used to determine DOZ and cave information to support mine activity in PT. Freeport Indonesia.

58 GEOSCIENCES↗

A new, coupled transport-diffusion method for radiative transfer calculations

We derive and present a new frequency- and angle-integrated low-order system of equations designed to enhance the accuracy of a coupled, high-order (transport) solution of the thermal radiative transfer equations. In particular, our new low-order system is designed to use intensity-weighted opacities and anisotropic diffusion coefficients generated by a solution of the Implicit Monte Carlo (IMC) equations in order to predict the spatial dependence of the material temperature and radiation energies in the ensuing time cycle. The predicted temperature solution can then be exploited to generate appropriately time-centered opacities, specific heats, and Planck emission spectra for the upcoming IMC solution. Additionally, the relatively inexpensive solution of the low-order system can be iteratively solved to recommend an adaptive time step size before the IMC solution is computed. A test implementation has been implemented using existing software available from the Jayenne and Capsaicin projects at Los Alamos National Laboratory. We present initial results from a new driver code that has integrated these stochastic and deterministic software packages. (authors)

97 MATHEMATICS AND COMPUTING↗

TU-F-BRF-04: Registration of 3D Transesophageal Echocardiography and X-Ray Fluoroscopy Using An Inverse Geometry X-Ray System

Purpose: To develop a method for the fusion of 3D echocardiography and Scanning-Beam Digital X-ray (SBDX) fluoroscopy to assist with catheter device and soft tissue visualization during interventional procedures. Methods: SBDX is a technology for low-dose inverse geometry x-ray fluoroscopy that performs digital tomosynthesis at multiple planes in real time. In this study, transesophageal echocardiography (TEE) images were fused with SBDX images by estimating the 3D position and orientation (the “pose”) of the TEE probe within the x-ray coordinate system and then spatially transforming the TEE image data to match this pose. An initial pose estimate was obtained through tomosynthesis-based 3D localization of points along the probe perimeter. Position and angle estimates were then iteratively refined by comparing simulated projections of a 3D probe model against SBDX x-ray images. Algorithm performance was quantified by imaging a TEE probe in different known orientations and locations within the x-ray field (0-30 degree tilt angle, up to 50 mm translation). Fused 3D TEE/SBDX imaging was demonstrated by imaging a tissue-mimicking polyvinyl alcohol cylindrical cavity as a catheter was navigated along the cavity axis. Results: Detected changes in probe tilt angle agreed with the known changes to within 1.2 degrees. For a 50 mm translation along the source-detector axis, the detected translation was 50.3 mm. Errors for in-plane translations ranged from 0.1 to 0.9 mm. In a fused 3D TEE/SBDX display, the catheter device was well visualized and coincident with the device shadow in the TEE images. The TEE images portrayed phantom boundaries that were not evident under x-ray. Conclusion: Registration of soft tissue anatomy derived from TEE imaging and device imaging from SBDX x-ray fluoroscopy is feasible. The simultaneous 3D visualization of these two modalities may be useful in interventional procedures involving the navigation of devices to soft tissue anatomy.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

SU-E-J-56: Static Gantry Digital Tomosynthesis From the Beam’s-Eye-View

Purpose We have designed a novel TumoTrak™ x-ray system that delivers 19 distinct kV views with the linac gantry stationary. It images MV treatment beam above and below the patient with a kV tomosysthesis slice image from the therapy beam’s-eye-view. Results will be high quality images without MLC shadowing for notable improvements relative to conventional fluoroscopic MV imaging and fluoroscopic kV imaging. Methods A complete design has a kV electron beam multisource X-ray tube that fits around the MV treatment beam path, with little interference with normal radiotherapy and unblocked by the multi-leaf-collimator. To simulate digital tomosynthesis, we used cone-beam CT projection data from a lung SBRT patient. These data were acquired at 125 kVp and 11 fps (0.4 mAs per projection). We chose 19 projections evenly spaced over 27° around one of the treatment angles (240°). Digital tomosynthesis reconstruction of a slice through the tumor was performed using iterative reconstruction. The visibility of the lesion was assessed for the reconstructed digital tomosynthesis (DTS), using fluoroscopy MV images acquired during radiation therapy, and a kV single projection image acquired at the same angle as the treatment field (240°). Results The fluoroscopic DTS images provide the best tumor contrast, surpassing the conventional radiographic and the in-treatment MV portal images. The electron beam multisource X-ray tube design has been completed and the tube is being fabricated. The estimated time to cycle through all 19 projections is 700 ms, enabling high frame-rate imaging. While the initial proposed use case is for image guided and gated treatment delivery, the enhanced imaging will also deliver superior radiographic images for patient setup. Conclusion The proposed device will deliver high quality planar images from the beam’s-eye-view without MLC obstruction. The prototype has been designed and is being assembled with first imaging scheduled for May 2015. L. Partain, J. Kwon, D. Boyd: NIH/SBIR R43CA192489-01. J. Rottmann, G. Zentai, R. Berbeco: NIH/NCI 1R01CA188446-01. R. Berbeco: E. Research Grant, Varian Medical Systems.

60 APPLIED LIFE SCIENCES↗

SU-E-T-498: Energy Minimization and Dose-Volume Inverse Optimization in Prostate Cancer

Purpose: To compare dose-volume (DVH) and energy minimization-based (EM) optimization for prostate cancer cases. Methods: A dozen of prostate plans were retrospectively studied. For each case two IMRT plans were generated, one with DVH and the other with EM objective cost function. Those different objective functions were used only for the organs at risk (OARs), while target objectives were achieved through DVH cost functions. The plans used the same beam angles, maximum number of segments per plan, minimum segment area and MUs per segment. Both plans were normalized such that 95% of the PTV was covered by the same prescription dose. After prescription was achieved, doses to the OARs were iteratively lowered until the standard deviation of the dose across the PTV was ~3.5%. Plan quality was evaluated by several dose indices (DIs). A DI represents the dose delivered to certain volume of a structure. Tallied DIs were for rectum and bladder 10%, 40%, 60% volumes, and 1% volumes of the femoral heads as surrogate for maximum doses. Statistical significance in the differences among DIs was quantified with two-tailed paired t-tests. Results: On average EM plans performed better than DVH plans. Statistically significant dose reduction in rectum DI10, DI40, and DI60, were 2.6%, 25.7%, and 35.9%, respectively. For bladder DI10, DI40, and DI60 the differences were 1.1%, 20.8%, and 29.7%. Left and right femoral head DI1s were better by 33.8% and 27.8% in EM plans. The quoted dose reduction is with respect to EM absolute doses for the DIs. Conclusion: The performance of EM optimization with respect to DVH optimization is patient and DI dependent. While in some cases specific DIs were better with DVH optimization, on average the energy minimization allows better (ranging from 1% to ~40%) OAR sparing than DVH optimization. NIH-NCI.

60 APPLIED LIFE SCIENCES↗

Permanent-magnet energy spectrometer for electron beams from radiotherapy accelerators

Purpose: The purpose of this work was to adapt a lightweight, permanent magnet electron energy spectrometer for the measurement of energy spectra of therapeutic electron beams. Methods: An irradiation geometry and measurement technique were developed for an approximately 0.54-T, permanent dipole magnet spectrometer to produce suitable latent images on computed radiography (CR) phosphor strips. Dual-pinhole electron collimators created a 0.318-cm diameter, approximately parallel beam incident on the spectrometer and an appropriate dose rate at the image plane (CR strip location). X-ray background in the latent image, reduced by a 7.62-cm thick lead block between the pinhole collimators, was removed using a fitting technique. Theoretical energy-dependent detector response functions (DRFs) were used in an iterative technique to transform CR strip net mean dose profiles into energy spectra on central axis at the entrance to the spectrometer. These spectra were transformed to spectra at 95-cm source to collimator distance (SCD) by correcting for the energy dependence of electron scatter. The spectrometer was calibrated by comparing peak mean positions in the net mean dose profiles, initially to peak mean energies determined from the practical range of central-axis percent depth-dose (%DD) curves, and then to peak mean energies that accounted for how the collimation modified the energy spectra (recalibration). The utility of the spectrometer was demonstrated by measuring the energy spectra for the seven electron beams (7–20 MeV) of an Elekta Infinity radiotherapy accelerator. Results: Plots of DRF illustrated their dependence on energy and position in the imaging plane. Approximately 15 iterations solved for the energy spectra at the spectrometer entrance from the measured net mean dose profiles. Transforming those spectra into ones at 95-cm SCD increased the low energy tail of the spectra, while correspondingly decreasing the peaks and shifting them to slightly lower energies. Energy calibration plots of peak mean energy versus peak mean position of the net mean dose profiles for each of the seven electron beams followed the shape predicted by the Lorentz force law for a uniform z-component of the magnetic field, validating its being modeled as uniform (0.542 ± 0.027 T). Measured Elekta energy spectra and their peak mean energies correlated with the 0.5-cm (7–13 MeV) and the 1.0-cm (13–20 MeV) R{sub 90} spacings of the %DD curves. The full-width-half-maximum of the energy spectra decreased with decreasing peak mean energy with the exception of the 9-MeV beam, which was anomalously wide. Similarly, R{sub 80–20} decreased linearly with peak mean energy with the exception of the 9 MeV beam. Both were attributed to suboptimal tuning of the high power phase shifter for the recycled radiofrequency power reentering the traveling wave accelerator. Conclusions: The apparatus and analysis techniques of the authors demonstrated that an inexpensive, lightweight, permanent magnet electron energy spectrometer can be used for measuring the electron energy distributions of therapeutic electron beams (6–20 MeV). The primary goal of future work is to develop a real-time spectrometer by incorporating a real-time imager, which has potential applications such as beam matching, ongoing beam tune maintenance, and measuring spectra for input into Monte Carlo beam calculations.

60 APPLIED LIFE SCIENCES↗