A posteriori error estimates for mixed finite element and finite volume methods
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© 2002-2011 IEEE. In the framework of the high-luminosity upgrade of the large hadron collider, the U.S. LARP collaboration and CERN are jointly developing a 150-mm aperture Nb3Sn quadrupole for the Large Hadron Collider (LHC) interaction regions. Due to the large beam size and orbit displacement in the final focusing triplet, MQXF has challenging targets for field quality at nominal operation conditions. Three short model magnets have been tested and around 30 coils have been built, allowing a first analysis of the reproducibility of the coil size and turns positioning. The impact of the coil shimming on field quality is evaluated, with special emphasis on the warm magnetic measurements and the correlation to field measurements at cold and nominal field. The variability of the field harmonics along the magnet axis is studied by means of a Monte-Carlo analysis and the effects of the corrective actions implemented to suppress the low-order unallowed multipoles are discussed.
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Purpose: The gamma comparison is widely used to evaluate the agreement between measurements and treatment planning system calculations in patient-specific intensity modulated radiation therapy (IMRT) quality assurance (QA). However, recent publications have raised concerns about the lack of sensitivity when employing commonly used gamma criteria. Understanding the actual sensitivity of a wide range of different gamma criteria may allow the definition of more meaningful gamma criteria and tolerance limits in IMRT QA. We present a method that allows the quantitative determination of gamma criteria sensitivity to induced errors which can be applied to any unique combination of device, delivery technique, and software utilized in a specific clinic. Methods: A total of 21 DMLC IMRT QA measurements (ArcCHECK®, Sun Nuclear) were compared to QA plan calculations with induced errors. Three scenarios were studied: MU errors, multi-leaf collimator (MLC) errors, and the sensitivity of the gamma comparison to changes in penumbra width. Gamma comparisons were performed between measurements and error-induced calculations using a wide range of gamma criteria, resulting in a total of over 20 000 gamma comparisons. Gamma passing rates for each error class and case were graphed against error magnitude to create error curves in order to represent the range of missed errors in routine IMRT QA using 36 different gamma criteria. Results: This study demonstrates that systematic errors and case-specific errors can be detected by the error curve analysis. Depending on the location of the error curve peak (e.g., not centered about zero), 3%/3 mm threshold = 10% at 90% pixels passing may miss errors as large as 15% MU errors and ±1 cm random MLC errors for some cases. As the dose threshold parameter was increased for a given %Diff/distance-to-agreement (DTA) setting, error sensitivity was increased by up to a factor of two for select cases. This increased sensitivity with increasing dose threshold was consistent across all studied combinations of %Diff/DTA. Criteria such as 2%/3 mm and 3%/2 mm with a 50% threshold at 90% pixels passing are shown to be more appropriately sensitive without being overly strict. However, a broadening of the penumbra by as much as 5 mm in the beam configuration was difficult to detect with commonly used criteria, as well as with the previously mentioned criteria utilizing a threshold of 50%. Conclusions: We have introduced the error curve method, an analysis technique which allows the quantitative determination of gamma criteria sensitivity to induced errors. The application of the error curve method using DMLC IMRT plans measured on the ArcCHECK® device demonstrated that large errors can potentially be missed in IMRT QA with commonly used gamma criteria (e.g., 3%/3 mm, threshold = 10%, 90% pixels passing). Additionally, increasing the dose threshold value can offer dramatic increases in error sensitivity. This approach may allow the selection of more meaningful gamma criteria for IMRT QA and is straightforward to apply to other combinations of devices and treatment techniques.
Purpose: This study investigates the calibration error of detector sensitivity for MapCheck due to inaccurate positioning of the device, which is not taken into account by the current commercial iterative calibration algorithm. We hypothesize the calibration is more vulnerable to the positioning error for the flatten filter free (FFF) beams than the conventional flatten filter flattened beams. Methods: MapCheck2 was calibrated with 10MV conventional and FFF beams, with careful alignment and with 1cm positioning error during calibration, respectively. Open fields of 37cmx37cm were delivered to gauge the impact of resultant calibration errors. The local calibration error was modeled as a detector independent multiplication factor, with which propagation error was estimated with positioning error from 1mm to 1cm. The calibrated sensitivities, without positioning error, were compared between the conventional and FFF beams to evaluate the dependence on the beam type. Results: The 1cm positioning error leads to 0.39% and 5.24% local calibration error in the conventional and FFF beams respectively. After propagating to the edges of MapCheck, the calibration errors become 6.5% and 57.7%, respectively. The propagation error increases almost linearly with respect to the positioning error. The difference of sensitivities between the conventional and FFF beams was small (0.11 ± 0.49%). Conclusion: The results demonstrate that the positioning error is not handled by the current commercial calibration algorithm of MapCheck. Particularly, the calibration errors for the FFF beams are ~9 times greater than those for the conventional beams with identical positioning error, and a small 1mm positioning error might lead to up to 8% calibration error. Since the sensitivities are only slightly dependent of the beam type and the conventional beam is less affected by the positioning error, it is advisable to cross-check the sensitivities between the conventional and FFF beams to detect potential calibration errors due to inaccurate positioning. This work was partially supported by a DOD Grant No.; DOD W81XWH1010862.
Purpose: This study presents an adaptive error detection algorithm (AEDA) for real-timein vivo point dosimetry during high dose rate (HDR) or pulsed dose rate (PDR) brachytherapy (BT) where the error identification, in contrast to existing approaches, does not depend on an a priori reconstruction of the dosimeter position. Instead, the treatment is judged based on dose rate comparisons between measurements and calculations of the most viable dosimeter position provided by the AEDA in a data driven approach. As a result, the AEDA compensates for false error cases related to systematic effects of the dosimeter position reconstruction. Given its nearly exclusive dependence on stable dosimeter positioning, the AEDA allows for a substantially simplified and time efficient real-time in vivo BT dosimetry implementation. Methods: In the event of a measured potential treatment error, the AEDA proposes the most viable dosimeter position out of alternatives to the original reconstruction by means of a data driven matching procedure between dose rate distributions. If measured dose rates do not differ significantly from the most viable alternative, the initial error indication may be attributed to a mispositioned or misreconstructed dosimeter (false error). However, if the error declaration persists, no viable dosimeter position can be found to explain the error, hence the discrepancy is more likely to originate from a misplaced or misreconstructed source applicator or from erroneously connected source guide tubes (true error). Results: The AEDA applied on twoin vivo dosimetry implementations for pulsed dose rate BT demonstrated that the AEDA correctly described effects responsible for initial error indications. The AEDA was able to correctly identify the major part of all permutations of simulated guide tube swap errors and simulated shifts of individual needles from the original reconstruction. Unidentified errors corresponded to scenarios where the dosimeter position was sufficiently symmetric with respect to error and no-error source position constellations. The AEDA was able to correctly identify all false errors represented by mispositioned dosimeters contrary to an error detection algorithm relying on the original reconstruction. Conclusions: The study demonstrates that the AEDA error identification during HDR/PDR BT relies on a stable dosimeter position rather than on an accurate dosimeter reconstruction, and the AEDA’s capacity to distinguish between true and false error scenarios. The study further shows that the AEDA can offer guidance in decision making in the event of potential errors detected with real-timein vivo point dosimetry.
Purpose: To develop a strategy for defining meaningful tolerance limits and studying the sensitivity of IMRT QA gamma criteria by inducing known errors in QA plans. Methods: IMRT QA measurements (ArcCHECK, Sun Nuclear) were compared to QA plan calculations with induced errors. Many (>24) gamma comparisons between data and calculations were performed for each of several kinds of cases and classes of induced error types with varying magnitudes (e.g. MU errors ranging from -10% to +10%), resulting in over 3,000 comparisons. Gamma passing rates for each error class and case were graphed against error magnitude to create error curves in order to represent the range of missed errors in routine IMRT QA using various gamma criteria. Results: This study demonstrates that random, case-specific, and systematic errors can be detected by the error curve analysis. Depending on location of the peak of the error curve (e.g., not centered about zero), 3%/3mm threshold=10% criteria may miss MU errors of up to 10% and random MLC errors of up to 5 mm. Additionally, using larger dose thresholds for specific devices may increase error sensitivity (for the same X%/Ymm criteria) by up to a factor of two. This analysis will allow clinics to select more meaningful gamma criteria based on QA device, treatment techniques, and acceptable error tolerances. Conclusion: We propose a strategy for selecting gamma parameters based on the sensitivity of gamma criteria and individual QA devices to induced calculation errors in QA plans. Our data suggest large errors may be missed using conventional gamma criteria and that using stricter criteria with an increased dose threshold may reduce the range of missed errors. This approach allows quantification of gamma criteria sensitivity and is straightforward to apply to other combinations of devices and treatment techniques.
Purpose: To use receiver operating characteristic (ROC) analysis to quantify the Varian Portal Dosimetry (VPD) application's ability to detect delivery errors in IMRT fields. Methods: EPID and VPD were calibrated/commissioned using vendor-recommended procedures. Five clinical plans comprising 56 modulated fields were analyzed using VPD. Treatment sites were: pelvis, prostate, brain, orbit, and base of tongue. Delivery was on a Varian Trilogy linear accelerator at 6MV using a Millenium120 multi-leaf collimator. Image pairs (VPD-predicted and measured) were exported in dicom format. Each detection test imported an image pair into Matlab, optionally inserted a simulated error (rectangular region with intensity raised or lowered) into the measured image, performed 3%/3mm gamma analysis, and saved the gamma distribution. For a given error, 56 negative tests (without error) were performed, one per 56 image pairs. Also, 560 positive tests (with error) with randomly selected image pairs and randomly selected in-field error location. Images were classified as errored (or error-free) if percent pixels with γ<κ was < (or ≥) τ. (Conventionally, κ=1 and τ=90%.) A ROC curve was generated from the 616 tests by varying τ. For a range of κ and τ, true/false positive/negative rates were calculated. This procedure was repeated for inserted errors of different sizes. VPD was considered to reliably detect an error if images were correctly classified as errored or error-free at least 95% of the time, for some κ+τ combination. Results: 20mm{sup 2} errors with intensity altered by ≥20% could be reliably detected, as could 10mm{sup 2} errors with intensity was altered by ≥50%. Errors with smaller size or intensity change could not be reliably detected. Conclusion: Varian Portal Dosimetry using 3%/3mm gamma analysis is capable of reliably detecting only those fluence errors that exceed the stated sizes. Images containing smaller errors can pass mathematical analysis, though may be detected by visual inspection. This work was not funded by Varian Oncology Systems. Some authors have other work partly funded by Varian Oncology Systems.
Purpose: Dosimetric errors in radiotherapy dose delivery lead to suboptimal treatments and outcomes. This work reviews the frequency and severity of dosimetric and programmatic errors identified by on-site audits performed by the IROC Houston QA center. Methods: IROC Houston on-site audits evaluate absolute beam calibration, relative dosimetry data compared to the treatment planning system data, and processes such as machine QA. Audits conducted from 2000-present were abstracted for recommendations, including type of recommendation and magnitude of error when applicable. Dosimetric recommendations corresponded to absolute dose errors >3% and relative dosimetry errors >2%. On-site audits of 1020 accelerators at 409 institutions were reviewed. Results: A total of 1280 recommendations were made (average 3.1/institution). The most common recommendation was for inadequate QA procedures per TG-40 and/or TG-142 (82% of institutions) with the most commonly noted deficiency being x-ray and electron off-axis constancy versus gantry angle. Dosimetrically, the most common errors in relative dosimetry were in small-field output factors (59% of institutions), wedge factors (33% of institutions), off-axis factors (21% of institutions), and photon PDD (18% of institutions). Errors in calibration were also problematic: 20% of institutions had an error in electron beam calibration, 8% had an error in photon beam calibration, and 7% had an error in brachytherapy source calibration. Almost all types of data reviewed included errors up to 7% although 20 institutions had errors in excess of 10%, and 5 had errors in excess of 20%. The frequency of electron calibration errors decreased significantly with time, but all other errors show non-significant changes. Conclusion: There are many common and often serious errors made during the establishment and maintenance of a radiotherapy program that can be identified through independent peer review. Physicists should be cautious, particularly in areas highlighted herein that show a tendency for errors.