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At least 379 records · Page 21

TH-A-19A-10: Fast Four Dimensional Monte Carlo Dose Computations for Proton Therapy of Lung Cancer

Purpose: To develop and validate a fast and accurate four dimensional (4D) Monte Carlo (MC) dose computation system for proton therapy of lung cancer and other thoracic and abdominal malignancies in which the delivered dose distributions can be affected by respiratory motion of the patient. Methods: A 4D computer tomography (CT) scan for a lung cancer patient treated with protons in our clinic was used to create a time dependent patient model using our in-house, MCNPX-based Monte Carlo system (“MC{sup 2}”). The beam line configurations for two passively scattered proton beams used in the actual treatment were extracted from the clinical treatment plan and a set of input files was created automatically using MC{sup 2}. A full MC simulation of the beam line was computed using MCNPX and a set of phase space files for each beam was collected at the distal surface of the range compensator. The particles from these phase space files were transported through the 10 voxelized patient models corresponding to the 10 phases of the breathing cycle in the 4DCT, using MCNPX and an accelerated (fast) MC code called “FDC”, developed by us and which is based on the track repeating algorithm. The accuracy of the fast algorithm was assessed by comparing the two time dependent dose distributions. Results: The error of less than 1% in 100% of the voxels in all phases of the breathing cycle was achieved using this method with a speedup of more than 1000 times. Conclusion: The proposed method, which uses full MC to simulate the beam line and the accelerated MC code FDC for the time consuming particle transport inside the complex, time dependent, geometry of the patient shows excellent accuracy together with an extraordinary speed.

60 APPLIED LIFE SCIENCES↗

SU-E-T-584: Optical Tracking Guided Patient-Specific VMAT QA with ArcCHECK

Purpose: To investigate the novel use of an in-house optical tracking system (OTS) to improve the efficacy of VMAT QA with a cylindrical dosimeter (ArcCHECK™). Methods: The translational and rotational setup errors of ArcCHECK are convoluted which makes it challenging to position the device efficiently and accurately. We first aligned the ArcCHECK to the machine cross-hair at three cardinal angles (0°, 90°, and 270°) to establish a reference position. Four infrared reflective markers were attached to the back of the device. An OTS with 0.2mm/0.2° accuracy was used to control its setup uncertainty. Translational uncertainties of 1 mm and 2 mm in three directions (in, right, and up) were applied on the device. Four open beams of various field sizes and six clinical VMAT arcs were delivered and measured for all simulated setup errors. The measurements were compared with Pinnacle™ calculations using Gamma analysis to evaluate the impact of setup uncertainty. This study also evaluated the improvement in setup reproducibility and efficiency with the aid of the OTS. Results: For open beams, with 3%/3mm, the mean passing rates dropped by less than 5% for all shifts; with 2%/2mm, two significant drops(>5%) were observed: 15.38±6.75% for 2 mm lateral shift and 9.35±4.88% for 2 mm longitudinal shift. For VMAT arcs, the mean passing rates using 2%/2mm dropped by 10.47±7.46% and 22.02±11.39% for 1 and 2 mm shift, respectively. With 3%/3mm, significant drop only occurred with 2 mm longitudinal shift (13.73±8.30%). Setup time could be reduced by >15 min with the aid of the OTS. Conclusion: OTS is an effective tool for separating translational and rotational uncertainties. The current VMAT QA solution was not strongly sensitive to translation errors of 2mm with widely accepted criterion (3%/3mm). This finding raises concerns regarding the efficacy of such QA system in detecting errors in the dynamic VMAT delivery.

61 RADIATION PROTECTION AND DOSIMETRY↗

DSCOVR/EPIC-derived global hourly and daily downward shortwave and photosynthetically active radiation data at 0.1° × 0.1° resolution

Downward shortwave radiation (SW) and photosynthetically active radiation (PAR) play crucial roles in Earth system dynamics. Spaceborne remote sensing techniques provide a unique means for mapping accurate spatiotemporally continuous SW–PAR, globally. However, any individual polar-orbiting or geostationary satellite cannot satisfy the desired high temporal resolution (sub-daily) and global coverage simultaneously, while integrating and fusing multisource data from complementary satellites/sensors is challenging because of co-registration, intercalibration, near real-time data delivery and the effects of discrepancies in orbital geometry. The Earth Polychromatic Imaging Camera (EPIC) on board the Deep Space Climate Observatory (DSCOVR), launched in February 2015, offers an unprecedented possibility to bridge the gap between high temporal resolution and global coverage and characterize the diurnal cycles of SW–PAR globally. In this study, we adopted a suite of well-validated data-driven machine-learning models to generate the first global land products of SW–PAR, from June 2015 to June 2019, based on DSCOVR/EPIC data. The derived products have high temporal resolution (hourly) and medium spatial resolution (0.1°×0.1°), and they include estimates of the direct and diffuse components of SW–PAR. We used independently widely distributed ground station data from the Baseline Surface Radiation Network (BSRN), the Surface Radiation Budget Network (SURFRAD), NOAA's Global Monitoring Division and the U.S. Department of Energy's Atmospheric System Research (ASR) program to evaluate the performance of our products, and we further analyzed and compared the spatiotemporal characteristics of the derived products with the benchmarking Clouds and the Earth's Radiant Energy System Synoptic (CERES) data. We found both the hourly and daily products to be consistent with ground-based observations (e.g., hourly and daily total SWs have low biases of -3.96 and -0.71 W m -2 and root-mean-square errors (RMSEs) of 103.50 and 35.40 W m -2 , respectively). The developed products capture the complex spatiotemporal patterns well and accurately track substantial diurnal, monthly, and seasonal variations in SW–PAR when compared to CERES data. They provide a reliable and valuable alternative for solar photovoltaic applications worldwide and can be used to improve our understanding of the diurnal and seasonal variabilities of the terrestrial water, carbon and energy fluxes at various spatial scales.

54 ENVIRONMENTAL SCIENCES↗

TH-AB-202-01: Daily Lung Tumor Motion Characterization On EPIDs Using a Markerless Tiling Model

Purpose: Tracking lung tumor motion in real time allows for target dose escalation while simultaneously reducing dose to sensitive structures, thus increasing local control without increasing toxicity. We present a novel intra-fractional markerless lung tumor tracking algorithm using MV treatment beam images acquired during treatment delivery. Strong signals superimposed on the tumor significantly reduced the soft tissue resolution; while different imaging modalities involved introduce global imaging discrepancies. This reduced the comparison accuracies. A simple yet elegant Tiling algorithm is reported to overcome the aforementioned issues. Methods: MV treatment beam images were acquired continuously in beam’s eye view (BEV) by an electronic portal imaging device (EPID) during treatment and analyzed to obtain tumor positions on every frame. Every frame of the MV image was simulated by a composite of two components with separate digitally reconstructed radiographs (DRRs): all non-moving structures and the tumor. This Titling algorithm divides the global composite DRR and the corresponding MV projection into sub-images called tiles. Rigid registration is performed independently on tile-pairs in order to improve local soft tissue resolution. This enables the composite DRR to be transformed accurately to match the MV projection and attain a high correlation value through a pixel-based linear transformation. The highest cumulative correlation for all tile-pairs achieved over a user-defined search range indicates the 2-D coordinates of the tumor location on the MV projection. Results: This algorithm was successfully applied to cine-mode BEV images acquired during two SBRT plans delivered five times with different motion patterns to each of two phantoms. Approximately 15000 beam’s eye view images were analyzed and tumor locations were successfully identified on every projection with a maximum/average error of 1.8 mm / 1.0 mm. Conclusion: Despite the presence of strong anatomical signal overlapping with tumor images, this markerless detection algorithm accurately tracks intrafractional lung tumor motions. This project is partially supported by an Elekta research grant.

60 APPLIED LIFE SCIENCES↗

Unmanned Aerial Vehicle Path Generation for Image Collection to Assist Heliostat Field Optical Characterization

This paper focuses on applications of unmanned aerial vehicles (UAVs) for measuring optical error of heliostats in concentrating solar power (CSP) plants. In CSP, there is a need to measure solar-field optical errors, which is critical for future production improvement as well as for operations and maintenance of a heliostat field. This latter need is particularly challenging because of the large number of heliostats (over 10,000 for a utility-scale power plant) that individually track the sun in the field. To address this issue, a camera-equipped UAV, with an optimized drone flight path developed and uploaded to it, collects images of a precise reflection of the tower on each heliostat to evaluate optical error sources without interrupting plant operation. Generation of the drone path for capturing the reflected images is affected by a number technical and realistic constraints, which include the camera angle used to capture the image, the blocking of the camera view due to surrounding heliostats, the location of the camera in reference to the target heliostat, and the target heliostat position with reference to the tower. The effect of these constraints on calculating the camera position will be discussed in detail in this article. An effective drone-path algorithm is generated to fulfil the need of image collection under various constraints.

concentrated solar power↗

Speeding up particle track reconstruction using a parallel Kalman filter algorithm

One of the most computationally difficult problems expected for the High-Luminosity Large Hadron Collider (HL-LHC) is determining the trajectory of charged particles during event reconstruction. Algorithms used at the LHC today rely on Kalman filtering, which builds physical trajectories incrementally while incorporating material effects and error estimation. Recognizing the need for faster computational throughput, we have adapted Kalman-filter-based methods for highly parallel, many-core SIMD architectures that are now prevalent in high-performance hardware. In this paper, we discuss the design and performance of the improved tracking algorithm, referred to as mkFit. A key piece of the algorithm is the Matriplex library, containing dedicated code to optimally vectorize operations on small matrices. The physics performance of the mkFit algorithm is comparable to the nominal CMS tracking algorithm when reconstructing tracks from simulated proton-proton collisions within the CMS detector. We study the scaling of the algorithm as a function of the parallel resources utilized and find large speedups both from vectorization and multi-threading. mkFit achieves a speedup of a factor of 6 compared to the nominal algorithm when run in a single-threaded application within the CMS software framework.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Solving phase appearance/disappearance two-phase flow problems with high resolution staggered grid and fully implicit schemes by the Jacobian-free Newton–Krylov Method

The phase appearance/disappearance issue presents serious numerical challenges in two-phase flow simulations. Many existing reactor safety analysis codes use different kinds of treatments for the phase appearance/disappearance problem. However, to our best knowledge, there are no fully satisfactory solutions. Additionally, the majority of the existing reactor system analysis codes were developed using low-order numerical schemes in both space and time. In many situations, it is desirable to use high-resolution spatial discretization and fully implicit time integration schemes to reduce numerical errors. In this work, we adapted a high-resolution spatial discretization scheme on staggered grid mesh and fully implicit time integration methods (such as BDF1 and BDF2) to solve the two-phase flow problems. The discretized nonlinear system was solved by the Jacobian-free Newton Krylov (JFNK) method, which does not require the derivation and implementation of analytical Jacobian matrix. These methods were tested with a few two-phase flow problems with phase appearance/disappearance phenomena considered, such as a linear advection problem, an oscillating manometer problem, and a sedimentation problem. The JFNK method demonstrated extremely robust and stable behaviors in solving the two-phase flow problems with phase appearance/disappearance. No special treatments such as water level tracking or void fraction limiting were used. High-resolution spatial discretization and second- order fully implicit method also demonstrated their capabilities in significantly reducing numerical errors.

97 MATHEMATICS AND COMPUTING↗

Magellan adaptive optics first-light observations of the exoplanet β PIC b. II. 3–5 μm direct imaging with MagAO+Clio, and the empirical bolometric luminosity of a self-luminous giant planet

Young giant exoplanets are a unique laboratory for understanding cool, low-gravity atmospheres. A quintessential example is the massive extrasolar planet β Pic b, which is 9 AU from and embedded in the debris disk of the young nearby A6V star β Pictoris. We observed the system with first light of the Magellan Adaptive Optics (MagAO) system. In Paper I we presented the first CCD detection of this planet with MagAO+VisAO. Here we present four MagAO+Clio images of β Pic b at 3.1 μm, 3.3 μm, L′, and M{sup ′}, including the first observation in the fundamental CH{sub 4} band. To remove systematic errors from the spectral energy distribution (SED), we re-calibrate the literature photometry and combine it with our own data, for a total of 22 independent measurements at 16 passbands from 0.99 to 4.8 μm. Atmosphere models demonstrate the planet is cloudy but are degenerate in effective temperature and radius. The measured SED now covers >80% of the planet’s energy, so we approach the bolometric luminosity empirically. We calculate the luminosity by extending the measured SED with a blackbody and integrating to find log(L{sub bol}/L{sub ⊙}) = −3.78±0.03. From our bolometric luminosity and an age of 23 ± 3 Myr, hot-start evolutionary tracks give a mass of 12.7 ± 0.3 M{sub Jup}, radius of 1.45 ± 0.02 R{sub Jup}, and T{sub eff} of 1708 ± 23 K (model-dependent errors not included). Our empirically determined luminosity is in agreement with values from atmospheric models (typically −3.8 dex), but brighter than values from the field-dwarf bolometric correction (typically −3.9 dex), illustrating the limitations in comparing young exoplanets to old brown dwarfs.

79 ASTRONOMY AND ASTROPHYSICS↗

Interactive initialization of 2D/3D rigid registration

Purpose: Registration is one of the key technical components in an image-guided navigation system. A large number of 2D/3D registration algorithms have been previously proposed, but have not been able to transition into clinical practice. The authors identify the primary reason for the lack of adoption with the prerequisite for a sufficiently accurate initial transformation, mean target registration error of about 10 mm or less. In this paper, the authors present two interactive initialization approaches that provide the desired accuracy for x-ray/MR and x-ray/CT registration in the operating room setting. Methods: The authors have developed two interactive registration methods based on visual alignment of a preoperative image, MR, or CT to intraoperative x-rays. In the first approach, the operator uses a gesture based interface to align a volume rendering of the preoperative image to multiple x-rays. The second approach uses a tracked tool available as part of a navigation system. Preoperatively, a virtual replica of the tool is positioned next to the anatomical structures visible in the volumetric data. Intraoperatively, the physical tool is positioned in a similar manner and subsequently used to align a volume rendering to the x-ray images using an augmented reality (AR) approach. Both methods were assessed using three publicly available reference data sets for 2D/3D registration evaluation. Results: In the authors' experiments, the authors show that for x-ray/MR registration, the gesture based method resulted in a mean target registration error (mTRE) of 9.3 ± 5.0 mm with an average interaction time of 146.3 ± 73.0 s, and the AR-based method had mTREs of 7.2 ± 3.2 mm with interaction times of 44 ± 32 s. For x-ray/CT registration, the gesture based method resulted in a mTRE of 7.4 ± 5.0 mm with an average interaction time of 132.1 ± 66.4 s, and the AR-based method had mTREs of 8.3 ± 5.0 mm with interaction times of 58 ± 52 s. Conclusions: Based on the authors' evaluation, the authors conclude that the registration approaches are sufficiently accurate for initializing 2D/3D registration in the OR setting, both when a tracking system is not in use (gesture based approach), and when a tracking system is already in use (AR based approach)

62 RADIOLOGY AND NUCLEAR MEDICINE↗

ANALYSIS OF CHARACTERISTIC PARAMETERS OF LARGE-SCALE CORONAL WAVES OBSERVED BY THE SOLAR-TERRESTRIAL RELATIONS OBSERVATORY/EXTREME ULTRAVIOLET IMAGER

The kinematical evolution of four extreme ultraviolet waves, well observed by the Extreme Ultraviolet Imager on board the Solar-Terrestrial Relations Observatory (STEREO), is studied by visually tracking wave fronts as well as by a semi-automatized perturbation profile method, which leads to results matching each other within the error limits. The derived mean velocities of the events under study lie in the range of 220-350 km s{sup -1}. The fastest of the events (2007 May 19) reveals a significant deceleration of {approx} - 190 m s{sup -2}, while the others are consistent with a constant velocity during wave propagation. The evolution of maximum-intensity values reveals initial intensification of 20%-70% and decays to original levels within 40-60 minutes, while the widths at half-maximum and full-maximum of the perturbation profiles broaden by a factor of two to four. The integral below the perturbation profile remains basically constant in two cases, while it shows a decrease by a factor of three to four in the other two cases. From the peak perturbation amplitudes, we estimate the corresponding magnetosonic Mach numbers M{sub ms}, which range from 1.08-1.21. The perturbation profiles reveal three distinct features behind the propagating wave fronts: coronal dimmings, stationary brightenings, and rarefaction regions. All features appear after the wave passage and only slowly fade away. Our findings indicate that the events under study are weak-shock fast-mode magnetohydrodynamic waves initiated by the CME lateral expansion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Field quality of the 4.5 m-long MQXFA pre-series magnets for the HL-LHC Upgrade as observed during magnet assembly

We report that the U.S. High-Luminosity LHC Accelerator Upgrade Project (HL-LHC AUP) is developing MQXFA magnets, a series of 4.5 m long 150 mm aperture high-field Nb 3 Sn quadrupole magnets for the HL-LHC upgrade at CERN. Five pre-series magnets, MQXFA03 through MQXFA07, have been developed. During the magnet assembly stage, we perform magnetic measurements on the coil-pack sub-assembly and magnets after loading to track the field quality for two purposes. First, it serves as a quality assurance tool to check if the magnetic field quality is on track to meet the acceptance criteria. Magnetic measurements are used to understand if magnetic shims are needed to compensate low-order field errors and to meet the field quality targets. Second, the measurements during the assembly stage can also help understand the field quality, especially the geometric field errors, for Nb 3 Sn accelerator magnets. Here we summarize the measurement results of the pre-series MQXFA magnets, including the magnetic axis and twist angle. The results will provide useful feedback for the series production of Nb 3 Sn magnets and on the optimization of field quality of accelerator magnets based on the wind-and-react Nb 3 Sn technology.

43 PARTICLE ACCELERATORS↗

Theoretical Control-Centric Modeling for Precision Model-Based Sliding Mode Control of a Hydraulic Artificial Muscle Actuator

Artificial muscles (AMs) typically rely on pneumatic sources of fluid power. The use of hydraulics can increase the power and force to weight and volume ratios of AM actuators. This paper develops a control-centric third-order single-input single-output (SISO) lumped-parameter dynamic model and sliding mode position controller based on Filippov's principle of equivalent dynamics for a braided hydraulic artificial muscle (HAM) actuator. The model predicts the nonlinear behavior of the HAM free contraction and captures the fluid and actuator nonlinear dynamic interactions in addition to the braid deformation. Model simulations are compared to experimental results for quasi-static pressurization, isometric pressurization, and open-loop square wave commands at 0.25, 0.5, and 1 Hz. Experiments of sine wave tracking at 0.25, 0.5, and 1 Hz and continuous square wave tracking at 0.067 Hz are conducted using a sliding mode controller (SMC) derived from the model. The SMC achieves a steady-state error of 6 μm at multiple setpoints within the actuator's 17 mm stroke. Compared to a proportional-integral-derivative (PID) controller, the SMC root-mean-square (RMS) error, mean error, and absolute maximum error are reduced on average by 53%, 61%, and 44%, respectively, demonstrating the benefit of model-based approaches for controlling HAMs.

42 ENGINEERING↗

VMAT QA: Measurement-guided 4D dose reconstruction on a patient

Purpose: To develop and validate a volume-modulated arc therapy (VMAT) quality assurance (QA) tool that takes as input a time-resolved, low-density ({approx}10 mm) cylindrical surface dose map from a commercial helical diode array, and outputs a high density, volumetric, time-resolved dose matrix on an arbitrary patient dataset. This first validation study is limited to a homogeneous 'patient.'Methods: A VMAT treatment is delivered to a diode array phantom (ARCCHECK, Sun Nuclear Corp., Melbourne, FL). 3DVH software (Sun Nuclear) derives the high-density volumetric dose using measurement-guided dose reconstruction (MGDR). MGDR cylindrical phantom results are then used to perturb the three-dimensional (3D) treatment planning dose on the patient dataset, producing a semiempirical volumetric dose grid. Four-dimensional (4D) dose reconstruction on the patient is also possible by morphing individual sub-beam doses instead of the composite. For conventional (3D) dose comparison two methods were developed, using the four plans (Multi-Target, C-shape, Mock Prostate, and Head and Neck), including their structures and objectives, from the AAPM TG-119 report. First, 3DVH and treatment planning system (TPS) cumulative point doses were compared to ion chamber in a cube water-equivalent phantom ('patient'). The shape of the phantom is different from the ARCCHECK and furthermore the targets were placed asymmetrically. Second, coronal and sagittal absolute film dose distributions in the cube were compared with 3DVH and TPS. For time-resolved (4D) comparisons, three tests were performed. First, volumetric dose differences were calculated between the 3D MGDR and cumulative time-resolved patient (4D MGDR) dose at the end of delivery, where they ideally should be identical. Second, time-resolved (10 Hz sampling rate) ion chamber doses were compared to cumulative point dose vs time curves from 4D MGDR. Finally, accelerator output was varied to assess the linearity of the 4D MGDR with global fluence change. Results: Across four TG-119 plans, the average PTV point dose difference in the cube between 3DVH and ion chamber is 0.1 {+-} 1.0%. Average film vs TPS {gamma}-analysis passing rates are 83.0%, 91.1%, and 98.4% for 1%/2 mm, 2%/2 mm, and 3%/3 mm threshold combinations, respectively, while average film vs 3DVH {gamma}-analysis passing rates are 88.6%, 96.1%, and 99.5% for the same respective criteria. 4D MGDR was also sufficiently accurate. First, for 99.5% voxels in each case, the doses from 3D and 4D MGDR at the end of delivery agree within 0.5%local dose-error/1 mm distance. Moreover, all failing voxels are confined to the edge of the cylindrical reconstruction volume. Second, dose vs time curves track between the ion chamber and 4D MGDR within 1%. Finally, 4D MGDR dose changes linearly with the accelerator output: the difference between cumulative ion chamber and MGDR dose changed by no more than 1% (randomly) with the output variation range of 10%. Conclusions: Even for a well-commissioned TPS, comparison metrics show better agreement on average to MGDR than to TPS on the arbitrary-shaped measurable 'patient.' The method requires no more accelerator time than standard QA, while producing more clinically relevant information. Validation in a heterogeneous thoracic phantom is under way, as is the ultimate application of 4D MGDR to virtual motion studies.

60 APPLIED LIFE SCIENCES↗

System and method for implementing periodic early discard in on-chip buffer memories of network elements

An advance is made over the prior art in accordance with the principles of the present invention that is directed to a new approach for a system and method for a buffer management scheme called Periodic Early Discard (PED). The invention builds on the observation that, in presence of TCP traffic, the length of a queue can be stabilized by selection of an appropriate frequency for packet dropping. For any combination of number of TCP connections and distribution of the respective RTT values, there exists an ideal packet drop frequency that prevents the queue from over-flowing or under-flowing. While the value of the ideal packet drop frequency may quickly change over time and is sensitive to the series of TCP connections affected by past packet losses, and most of all is impossible to compute inline, it is possible to approximate it with a margin of error that allows keeping the queue occupancy within a pre-defined range for extended periods of time. The PED scheme aims at tracking the (unknown) ideal packet drop frequency, adjusting the approximated value based on the evolution of the queue occupancy, with corrections of the approximated packet drop frequency that occur at a timescale that is comparable to the aggregate time constant of the set of TCP connections that traverse the queue.

97 MATHEMATICS AND COMPUTING↗

A Time Projection Chamber for High Accuracy and Precision Fission Cross-Section Measurements

The fission Time Projection Chamber (fissionTPC) is a compact (15 cm diameter) two-chamber MICROMEGAS TPC designed to make precision cross-section measurements of neutron-induced fission. The actinide targets are placed on the central cathode and irradiated with a neutron beam that passes axially through the TPC inducing fission in the target. The 4p acceptance for fission fragments and complete charged particle track reconstruction are powerful features of the fissionTPC which will be used to measure fission cross-sections and examine the associated systematic errors. This paper provides a detailed description of the design requirements, the design solutions, and the initial performance of the fissionTPC.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Prostate Bed Motion During Intensity-Modulated Radiotherapy Treatment

Purpose: Conformal radiation therapy in the postprostatectomy setting requires accurate setup and localization of the prostatic fossa. In this series, we report prostate bed localization and motion characteristics, using data collected from implanted radiofrequency transponders. Methods and Materials: The Calypso four-dimensional localization system uses three implanted radiofrequency transponders for daily target localization and real-time tracking throughout a course of radiation therapy. We reviewed the localization and tracking reports for 20 patients who received ultrasonography-guided placement of Calypso transponders within the prostate bed prior to a course of intensity-modulated radiation therapy at Fox Chase Cancer Center. Results: At localization, prostate bed displacement relative to bony anatomy exceeded 5 mm in 9% of fractions in the anterior-posterior (A-P) direction and 21% of fractions in the superior-inferior (S-I) direction. The three-dimensional vector length from skin marks to Calypso alignment exceeded 1 cm in 24% of all 652 fractions with available setup data. During treatment, the target exceeded the 5-mm tracking limit for at least 30 sec in 11% of all fractions, generally in the A-P or S-I direction. In the A-P direction, target motion was twice as likely to move posteriorly, toward the rectum, than anteriorly. Fifteen percent of all treatments were interrupted for repositioning, and 70% of patients were repositioned at least once during their treatment course. Conclusion: Set-up errors and motion of the prostatic fossa during radiotherapy are nontrivial, leading to potential undertreatment of target and excess normal tissue toxicity if not taken into account during treatment planning. Localization and real-time tracking of the prostate bed via implanted Calypso transponders can be used to improve the accuracy of plan delivery.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

A Polynomial-Time Classical Algorithm for Noisy Quantum Circuits

We provide a polynomial-time classical algorithm for noisy quantum circuits. The algorithm computes the expectation value of any observable for any circuit, with a small average error over input states drawn from an ensemble (e.g., the computational basis). Our approach is based upon the intuition that noise exponentially damps nonlocal correlations relative to local correlations. This enables one to classically simulate a noisy quantum circuit by keeping track of only the dynamics of local quantum information. Our algorithm also enables sampling from the output distribution of a circuit in quasipolynomial time, so long as the distribution anticoncentrates. A number of implications are discussed, including a fundamental limit on the efficacy of noise mitigation strategies: For constant noise rates, any quantum circuit for which error mitigation succeeds in polynomial-time on most input states can also be classically simulated in polynomial-time on most input states. Our algorithms scale exponentially in the inverse noise rate, which is fundamental and makes them impractical for current quantum devices.

decoherence↗