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Russo S, Saez J, Esposito M, Bruschi A, Ghirelli A, Pini S, Scoccianti S, Hernandez V. Incorporating plan complexity into the statistical process control of volumetric modulated arc therapy pre-treatment verifications. Med Phys 2024; 51:3961-3971. [PMID: 38630979 DOI: 10.1002/mp.17081] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2023] [Revised: 03/14/2024] [Accepted: 03/30/2024] [Indexed: 04/19/2024] Open
Abstract
BACKGROUND Statistical process control (SPC) is a powerful statistical tool for process monitoring that has been highly recommended in healthcare applications, including radiation therapy quality assurance (QA). The AAPM TG-218 report described the clinical implementation of SPC for Volumetric Modulated Arc Therapy (VMAT) pre-treatment verifications, pointing out the need to adjust tolerance limits based on plan complexity. However, the quantification of plan complexity and its integration into SPC remains an unresolved challenge. PURPOSE The primary aim of this study is to investigate the incorporation of plan complexity into the SPC framework for VMAT pre-treatment verifications. The study explores and evaluates various strategies for this incorporation, discussing their merits and limitations, and provides recommendations for clinical application. METHODS A retrospective analysis was conducted on 309 VMAT plans from diverse anatomical sites using the PTW OCTAVIUS 4D device for QA measurements. Gamma Passing Rates (GPR) were obtained, and lower control limits were computed using both the conventional Shewhart method and three heuristic methods (scaled weighted variance, weighted standard deviations, and skewness correction) to accommodate non-normal data distributions. The 'Identify-Eliminate-Recalculate' method was employed for robust analysis. Eight complexity metrics were analyzed and two distinct strategies for incorporating plan complexity into SPC were assessed. The first strategy focused on establishing control limits for different treatment sites, while the second was based on the determination of control limits as a function of individual plan complexity. The study extensively examines the correlation between control limits and plan complexity and assesses the impact of complexity metrics on the control process. RESULTS The control limits established using SPC were strongly influenced by the complexity of treatment plans. In the first strategy, a clear correlation was found between control limits and average plan complexity for each site. The second approach derived control limits based on individual plan complexity metrics, enabling tailored tolerance limits. In both strategies, tolerance limits inversely correlated with plan complexity, resulting in all highly complex plans being classified as in control. In contrast, when plans were collectively analyzed without considering complexity, all the out-of-control plans were highly complex. CONCLUSIONS Incorporating plan complexity into SPC for VMAT verifications requires meticulous and comprehensive analysis. To ensure overall process control, we advocate for stringent control and minimization of plan complexity during treatment planning, especially when control limits are adjusted based on plan complexity.
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Affiliation(s)
- Serenella Russo
- Medical Physics Unit, Azienda USL Toscana Centro, Florence, Italy
| | - Jordi Saez
- Department of Radiation Oncology, Hospital Clínic de Barcelona, Barcelona, Spain
| | - Marco Esposito
- Medical Physics Unit, Azienda USL Toscana Centro, Florence, Italy
- Medical Physics Program, The Abdus Salam International Centre for Theoretical Physics Trieste-Italy, Trieste, Italy
| | - Andrea Bruschi
- Medical Physics Unit, Azienda USL Toscana Centro, Florence, Italy
| | | | - Silvia Pini
- Medical Physics Unit, Azienda USL Toscana Centro, Florence, Italy
| | | | - Victor Hernandez
- Department of Medical Physics, Hospital Sant Joan de Reus, IISPV, Reus, Spain
- Universitat Rovira i Virgili (URV), Tarragona, Spain
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2
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Xiao Q, Li G. Application and Challenges of Statistical Process Control in Radiation Therapy Quality Assurance. Int J Radiat Oncol Biol Phys 2024; 118:295-305. [PMID: 37604239 DOI: 10.1016/j.ijrobp.2023.08.020] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2023] [Revised: 07/21/2023] [Accepted: 08/08/2023] [Indexed: 08/23/2023]
Abstract
Quality assurance (QA) is important for ensuring precision in radiation therapy. The complexity and resource-intensive nature of QA has increased with the continual evolution of equipment and techniques. An effective approach is to improve the process control technology and resource optimization. Statistical process control is an economical and efficient tool that has been widely used to monitor, control, and improve quality management processes and is now being increasingly used for radiation therapy QA. This article reviews the development and methodology of statistical process control technology, evaluates its suitability in radiation therapy QA practices, and assesses its importance and challenges in optimizing radiation therapy QA processes.
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Affiliation(s)
- Qing Xiao
- Department of Radiation Oncology, Cancer Center, West China Hospital, Sichuan University, Chengdu, Sichuan, China; Department of Radiotherapy Physics & Technology, West China Hospital, Sichuan University, Chengdu, Sichuan, China
| | - Guangjun Li
- Department of Radiation Oncology, Cancer Center, West China Hospital, Sichuan University, Chengdu, Sichuan, China; Department of Radiotherapy Physics & Technology, West China Hospital, Sichuan University, Chengdu, Sichuan, China.
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Raveendran V, R GR, P T A, Bhasi S, C P R, Kinhikar RA. Moving towards process-based radiotherapy quality assurance using statistical process control. Phys Med 2023; 112:102651. [PMID: 37562233 DOI: 10.1016/j.ejmp.2023.102651] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 10/29/2022] [Revised: 07/16/2023] [Accepted: 08/01/2023] [Indexed: 08/12/2023] Open
Abstract
Monitoring Radiotherapy Quality Assurance (QA) using Statistical Process Control (SPC) methods has gained wide acceptance. The significance of understanding the SPC methodologies has increased among the medical physics community with the release of Task Group (TG) reports from the American Association of Physicists in Medicine (AAPM) on patient-specific QA (PSQA) (TG-218) and Proton therapy QA (TG-224). Even though these reports recommend using SPC for QA analysis, physicists have ambiguities and doubts in choosing proper SPC tools and methodologies. This review article summarises the utilisation of SPC methods for different Radiotherapy QAs published in the literature, such as PSQA, routine Linac QA and patient positional verification. QA analysis using SPC could assist the user in distinguishing between 'special' and 'routine' sources of variations in the QA, which can aid in reducing actions on false positive QA results. For improved PSQA monitoring, machine-specific, site-specific, and technique-specific Tolerance Limits and Action Limits derived from a two-stage SPC-based approach can be used. Adopting a combination of Shewhart's control charts and time-weighted control charts for routine Linac QA monitoring could add more insights to the QA process. Incorporating SPC tools into existing image review modules or introducing new SPC software packages specifically designed for clinical use can significantly enhance the image review process. Proper selection and having adequate knowledge of SPC tools are essential for efficient QA monitoring, which is a function of the type of QA data available, and the magnitude of process drift to be monitored.
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Affiliation(s)
- Vysakh Raveendran
- Department of Radiation Oncology, Advanced Centre for Treatment Research and Education in Cancer, Tata Memorial Centre, Homi Bhabha National Institute, Navi Mumbai, Maharashtra, India.; Department of Physics, Noorul Islam Centre for Higher Education, Kumaracoil, Kanyakumari District, Tamil Nadu, India..
| | - Ganapathi Raman R
- Department of Physics, Saveetha Engineering College (Autonomous), Chennai, Tamil Nadu, India
| | - Anjana P T
- Department of Radiation Oncology, Advanced Centre for Treatment Research and Education in Cancer, Tata Memorial Centre, Homi Bhabha National Institute, Navi Mumbai, Maharashtra, India
| | - Saju Bhasi
- Division of Radiation Physics, Regional Cancer Centre, Trivandrum, India
| | - Ranjith C P
- Department of Radiation Oncology, Advanced Centre for Treatment Research and Education in Cancer, Tata Memorial Centre, Homi Bhabha National Institute, Navi Mumbai, Maharashtra, India
| | - Rajesh Ashok Kinhikar
- Department of Medical Physics, Tata Memorial Centre, Homi Bhabha National Institute Parel, Mumbai, India
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4
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Li G, Xiao Q, Dai G, Wang Q, Bai L, Zhang X, Zhang X, Duan L, Zhong R, Bai S. Guaranteed performance of individual control chart used in gamma passing rate-based patient-specific quality assurance. Phys Med 2023; 109:102581. [PMID: 37084678 DOI: 10.1016/j.ejmp.2023.102581] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 11/09/2022] [Revised: 03/20/2023] [Accepted: 04/06/2023] [Indexed: 04/23/2023] Open
Abstract
PURPOSE To assess the effect of sampling variability on the performance of individual charts (I-charts) for PSQA and provide a robust and reliable method for unknown PSQA processes. MATERIALS AND METHODS A total of 1327 pretreatment PSQAs were analyzed. Different datasets with samples in the range of 20-1000 were used to estimate the lower control limit (LCL). Based on the iterative "Identify-Eliminate-Recalculate" and direct calculation without any outlier filtering procedures, five I-charts methods, namely the Shewhart, quantile, scaled weighted variance (SWV), weighted standard deviation (WSD), and skewness correction (SC) method, were used to compute the LCL. The average run length (ARL0) and false alarm rate (FAR0) were calculated to evaluate the performance of LCL. RESULTS The ground truth of the values of LCL, FAR0, and ARL0 obtained via in-control PSQAs were 92.31%, 0.135%, and 740.7, respectively. Further, for in-control PSQAs, the width of the 95% confidence interval of LCL values for all methods tended to decrease with the increase in sample size. In all sample ranges of in-control PSQAs, only the median LCL and ARL0 values obtained via WSD and SWV methods were close to the ground truth. For the actual unknown PSQAs, based on the "Identify-Eliminate-Recalculate" procedure, only the median LCL values obtained by the WSD method were closest to the ground truth. CONCLUSIONS Sampling variability seriously affected the I-chart performance in PSQA processes, particularly for small samples. For unknown PSQAs, the WSD method based on the implementation of the iterative "Identify-Eliminate-Recalculate" procedure exhibited sufficient robustness and reliability.
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Affiliation(s)
- Guangjun Li
- Radiotherapy Physics & Technology Center, Cancer Center, West China Hospital, Sichuan University, Chengdu, Sichuan 610041, China
| | - Qing Xiao
- Radiotherapy Physics & Technology Center, Cancer Center, West China Hospital, Sichuan University, Chengdu, Sichuan 610041, China
| | - Guyu Dai
- Radiotherapy Physics & Technology Center, Cancer Center, West China Hospital, Sichuan University, Chengdu, Sichuan 610041, China
| | - Qiang Wang
- Radiotherapy Physics & Technology Center, Cancer Center, West China Hospital, Sichuan University, Chengdu, Sichuan 610041, China
| | - Long Bai
- Radiotherapy Physics & Technology Center, Cancer Center, West China Hospital, Sichuan University, Chengdu, Sichuan 610041, China
| | - Xiangbin Zhang
- Radiotherapy Physics & Technology Center, Cancer Center, West China Hospital, Sichuan University, Chengdu, Sichuan 610041, China
| | - Xiangyu Zhang
- Radiotherapy Physics & Technology Center, Cancer Center, West China Hospital, Sichuan University, Chengdu, Sichuan 610041, China
| | - Lian Duan
- Department of Radiation Oncology, Perelman School of Medicine, University of Pennsylvania, Philadelphia 19104, United States
| | - Renming Zhong
- Radiotherapy Physics & Technology Center, Cancer Center, West China Hospital, Sichuan University, Chengdu, Sichuan 610041, China
| | - Sen Bai
- Radiotherapy Physics & Technology Center, Cancer Center, West China Hospital, Sichuan University, Chengdu, Sichuan 610041, China; Department of Radiation Oncology, Cancer Center, West China Hospital, Sichuan University, Chengdu, Sichuan 610041, China.
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Guo Y, Hu J, Li Y, Ran J, Cai H. Correlation between patient-specific quality assurance in volumetric modulated arc therapy and 2D dose image features. Sci Rep 2023; 13:4051. [PMID: 36899027 PMCID: PMC10006091 DOI: 10.1038/s41598-023-30719-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2022] [Accepted: 02/28/2023] [Indexed: 03/12/2023] Open
Abstract
In radiotherapy, air-filled ion chamber detectors are ubiquitously used in routine dose measurements for treatment planning. However, its use has been restricted by intrinsic low spatial resolution barriers. We developed one procedure for patient-specific quality assurance (QA) in arc radiotherapy by coalescing two adjacent measurement images into a single image to improve spatial resolution and sampling frequency, and investigated how different spatial resolutions affect the QA results. PTW 729 and 1500 ion chamber detectors were used for dosimetric verification via coalescing two measurements with 5 mm-couch shift and the isocenter, and only isocenter measurement, which we call coalescence and standard acquisition (SA). Statistical process control (SPC), process capability analysis (PCA), and receiver operating characteristic (ROC) curve were used to compare the performance of the two procedures in determining tolerance levels and identifying clinically relevant errors. By analyzing 1256 γ values calculated on interpolated data points, our results indicated that detector 1500 showed higher averages in coalescence cohorts at different tolerance criteria and the dispersion degrees were spread out smaller. Detector 729 yielded a slightly lower process capability of 0.79, 0.76, 1.10, and 1.34, but detector 1500 exhibited somewhat different results of 0.94, 1.42, 1.19, and 1.60 in magnitude. The results of SPC individual control chart showed that cases in coalescence cohorts with γ values lowering its lower control limit (LCL) were greater than those in SA cohorts for detector 1500. A combination of the width of multi-leaf collimator (MLC) leaf, the cross-sectional area of the single detector, and the spacing between adjacent detectors might lead to discrepancies in percent γ values across diverse spatial resolution scenarios. The accuracy of reconstructed volume dose is mainly determined by the interpolation algorithm used in dosimetric systems. The magnitude of filling factor in the ion chamber detectors determined its ability to detect dose deviations. SPC and PCA results indicated that coalescence procedure could detect more potential failure QA results than SA while enhancing action thresholds.
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Affiliation(s)
- Yixiao Guo
- Department of Radiation Oncology, Gansu Provincial Hospital, Lanzhou, 730000, People's Republic of China
| | - Jinyan Hu
- Department of Oncology, Longhua District People's Hospital, Shenzhen, 518109, People's Republic of China
| | - Yang Li
- Department of Radiation Oncology, Weifang People's Hospital, Weifang, 261000, People's Republic of China
| | - Juntao Ran
- Department of Radiation Oncology, The First Hospital of Lanzhou University, Lanzhou, 730000, People's Republic of China
| | - Hongyi Cai
- Department of Radiation Oncology, Gansu Provincial Hospital, Lanzhou, 730000, People's Republic of China.
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Liu M, Cygler JE, Dennis K, Vandervoort E. A dose perturbation tool for robotic radiosurgery: Experimental validation and application to liver lesions. J Appl Clin Med Phys 2022; 23:e13766. [PMID: 36094024 PMCID: PMC9680574 DOI: 10.1002/acm2.13766] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2022] [Revised: 07/09/2022] [Accepted: 08/04/2022] [Indexed: 11/07/2022] Open
Abstract
BACKGROUND An analytical tool is empirically validated and used to assess the delivered dose to liver lesions accounting for different types of errors in robotic radiosurgery treatment. MATERIAL AND METHODS A tool is proposed to estimate the target doses taking into account the translation, rotation, and deformation of a target. Translational errors are modeled as a spatial convolution of the planned dose with a probability distribution function derived from treatment data. Rotations are modeled by rotating the target volume about the imaging isocenter. Target deformation is simulated as an isotropic target expansion or contraction based on changes in inter-fiducial spacing. The estimated dose is validated using radiochromic film measurements in nine experimental conditions, including in-phase and out-of-phase internal-and-external breathing motion patterns, with and without uncorrectable rotations, and for homogenous and heterogeneous phantoms. The measured dose is compared to the perturbed and planned doses using gamma analyses. This proposed tool is applied to assess the dose coverage for liver treatments using D99/Rx where D99 and Rx are the minimum target and prescription doses, respectively. These metrics are used to evaluate plan robustness to different magnitudes of rotational errors. Case studies are presented to illustrate how to improve plan robustness against delivery errors. RESULTS In the experimental validations, measured dose agrees with the estimated dose at the 2%/2 mm level. When accounting for translational and rotational tracking residual errors using this tool, approximately one-fifth of targets are considered underdosed (D99/Rx < 1.0). If target expansion or contraction is modeled, approximately one-third of targets are underdosed. The dose coverage can be improved if treatments are planned following proposed guidelines. CONCLUSION The dose perturbation model can be used to assess dose delivery accuracy and investigate plan robustness to different types of errors.
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Affiliation(s)
- Ming Liu
- Department of Medical PhysicsThe Ottawa Hospital Cancer CenterOttawaCanada
- Department of PhysicsCarleton UniversityOttawaCanada
| | - Joanna E. Cygler
- Department of Medical PhysicsThe Ottawa Hospital Cancer CenterOttawaCanada
- Department of PhysicsCarleton UniversityOttawaCanada
- Division of Medical Physics, Department of RadiologyThe University of OttawaOttawaCanada
| | - Kristopher Dennis
- Division of Radiation OncologyThe Ottawa Hospital and the University of OttawaOttawaCanada
| | - Eric Vandervoort
- Department of Medical PhysicsThe Ottawa Hospital Cancer CenterOttawaCanada
- Department of PhysicsCarleton UniversityOttawaCanada
- Division of Medical Physics, Department of RadiologyThe University of OttawaOttawaCanada
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van der Heyden B, Heymans SV, Carlier B, Collado-Lara G, Sterpin E, D’hooge J. Deep learning for dose assessment in radiotherapy by the super-localization of vaporized nanodroplets in high frame rate ultrasound imaging. Phys Med Biol 2022; 67. [DOI: 10.1088/1361-6560/ac6cc3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2022] [Accepted: 05/04/2022] [Indexed: 11/12/2022]
Abstract
Abstract
Objective. External beam radiotherapy is aimed to precisely deliver a high radiation dose to malignancies, while optimally sparing surrounding healthy tissues. With the advent of increasingly complex treatment plans, the delivery should preferably be verified by quality assurance methods. Recently, online ultrasound imaging of vaporized radiosensitive nanodroplets was proposed as a promising tool for in vivo dosimetry in radiotherapy. Previously, the detection of sparse vaporization events was achieved by applying differential ultrasound (US) imaging followed by intensity thresholding using subjective parameter tuning, which is sensitive to image artifacts. Approach. A generalized deep learning solution (i.e. BubbleNet) is proposed to localize vaporized nanodroplets on differential US frames, while overcoming the aforementioned limitation. A 5-fold cross-validation was performed on a diversely composed 5747-frame training/validation dataset by manual segmentation. BubbleNet was then applied on a test dataset of 1536 differential US frames to evaluate dosimetric features. The intra-observer variability was determined by scoring the Dice similarity coefficient (DSC) on 150 frames segmented twice. Additionally, the BubbleNet generalization capability was tested on an external test dataset of 432 frames acquired by a phased array transducer at a much lower ultrasound frequency and reconstructed with unconventional pixel dimensions with respect to the training dataset. Main results. The median DSC in the 5-fold cross validation was equal to ∼0.88, which was in line with the intra-observer variability (=0.86). Next, BubbleNet was employed to detect vaporizations in differential US frames obtained during the irradiation of phantoms with a 154 MeV proton beam or a 6 MV photon beam. BubbleNet improved the bubble-count statistics by ∼30% compared to the earlier established intensity-weighted thresholding. The proton range was verified with a −0.8 mm accuracy. Significance. BubbleNet is a flexible tool to localize individual vaporized nanodroplets on experimentally acquired US images, which improves the sensitivity compared to former thresholding-weighted methods.
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Zhang H, Lu W, Cui H, Li Y, Yi X. Assessment of Statistical Process Control Based DVH Action Levels for Systematic Multi-Leaf Collimator Errors in Cervical Cancer RapidArc Plans. Front Oncol 2022; 12:862635. [PMID: 35664736 PMCID: PMC9157499 DOI: 10.3389/fonc.2022.862635] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2022] [Accepted: 04/19/2022] [Indexed: 11/18/2022] Open
Abstract
Background In the patient-specific quality assurance (QA), DVH is a critical clinically relevant parameter that is finally used to determine the safety and effectiveness of radiotherapy. However, a consensus on DVH-based action levels has not been reached yet. The aim of this study is to explore reasonable DVH-based action levels and optimal DVH metrics in detecting systematic MLC errors for cervical cancer RapidArc plans. Methods In this study, a total of 148 cervical cancer RapidArc plans were selected and measured with COMPASS 3D dosimetry system. Firstly, the patient-specific QA results of 110 RapidArc plans were retrospectively reviewed. Then, DVH-based action limits (AL) and tolerance limits (TL) were obtained by statistical process control. Secondly, systematic MLC errors were introduced in 20 RapidArc plans, generating 380 modified plans. Then, the dose difference (%DE) in DVH metrics between modified plans and original plans was extracted from measurement results. After that, the linear regression model was used to investigate the detection limits of DVH-based action levels between %DE and systematic MLC errors. Finally, a total of 180 test plans (including 162 error-introduced plans and 18 original plans) were prepared for validation. The error detection rate of DVH-based action levels was compared in different DVH metrics of 180 test plans. Results A linear correlation was found between systematic MLC errors and %DE in all DVH metrics. Based on linear regression model, the systematic MLC errors between -0.94 mm and 0.88 mm could be caught by the TL of PTV95 ([-1.54%, 1.51%]), and the systematic MLC errors between -1.00 mm and 0.80 mm could also be caught by the TL of PTVmean ([-2.06%, 0.38%]). In the validation, for original plans, PTV95 showed the minimum error detection rate of 5.56%. For error-introduced plans with systematic MLC errors more than 1mm, PTVmean showed the maximum error detection rate of 88.89%, and then was followed by PTV95 (86.67%). All the TL of DVH metrics showed a poor error detection rate in identifying error-induced plans with systematic MLC errors less than 1mm. Conclusion In 3D quality assurance of cervical cancer RapidArc plans, process-based tolerance limits showed greater advantages in distinguishing plans introduced with systematic MLC errors more than 1mm, and reasonable DVH-based action levels can be acquired through statistical process control. During DVH-based verification, main focus should be on the DVH metrics of target volume. OARs in low-dose regions were found to have a relatively higher dose sensitivity to smaller systematic MLC errors, but may be accompanied with higher false error detection rate.
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Affiliation(s)
- Hanyin Zhang
- Department of Oncology, The First Affiliated Hospital of Chongqing Medical University, Chongqing, China
| | - Wenli Lu
- Department of Oncology, The First Affiliated Hospital of Chongqing Medical University, Chongqing, China
| | - Haixia Cui
- Department of Oncology, The First Affiliated Hospital of Chongqing Medical University, Chongqing, China
| | - Ying Li
- Department of Oncology, The First Affiliated Hospital of Chongqing Medical University, Chongqing, China
| | - Xin Yi
- Department of Oncology, The First Affiliated Hospital of Chongqing Medical University, Chongqing, China
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Xiao Q, Bai L, Li G, Zhang X, Li Z, Duan L, Peng R, Zhong R, Wang Q, Wang X, Bai S. A robust approach to establish tolerance limits for the gamma passing rate-based patient-specific quality assurance using the heuristic control charts. Med Phys 2021; 49:1312-1330. [PMID: 34778963 DOI: 10.1002/mp.15346] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2021] [Revised: 10/29/2021] [Accepted: 11/01/2021] [Indexed: 02/05/2023] Open
Abstract
PURPOSE Establishing the tolerance limits of patient-specific quality assurance (PSQA) processes based on the gamma passing rate (GPR) by using normal statistical process control (SPC) methods involves certain problems. The aim of this study was threefold: (a) to show that the heuristic SPC method can replace the quantile method for establishing tolerance limits in PSQA processes and is more robust, (b) to introduce an iterative procedure of "Identify-Eliminate-Recalculate" for establishing the tolerance limits in PSQA processes with unknown states based on retrospective GPRs, and (c) to recommend a workflow to define tolerance limits based on actual clinical retrospective GPRs. MATERIALS AND METHODS A total of 1671 volumetric-modulated arc therapy (VMAT) pretreatment plans were measured on four linear accelerators (linacs) and analyzed by treatment sites using the GPRs under the 2%/2 mm, 3%/2 mm, and 3%/3 mm criteria. Normality testing was performed using the Anderson-Darling (AD) statistic and the optimal distributions of GPRs were determined using the Fitter Python package. The iterative "Identify-Eliminate-Recalculate" procedure was used to identify the PSQA outliers. The tolerance limits of the initial PSQAs, remaining PSQAs after elimination, and in-control PSQAs after correction were calculated using the conventional Shewhart method, two transformation methods, three heuristic methods, and two quantile methods. The tolerance limits of PSQA processes with different states for the respective methods, linacs, and treatment sites were comprehensively compared and analyzed. RESULTS It was found that 75% of the initial PSQA processes and 63% of the in-control processes were non-normal (AD test, p < 0.05). The optimal distributions of GPRs for the initial and in-control PSQAs varied with different linacs and treatment sites. In the implementation of the "Identify-Eliminate-Recalculate" procedure, the quantile methods could not identify the out-of-control PSQAs effectively due to the influence of outliers. The tolerance limits of the in-control PSQAs, calculated using the quantile of optimal fitting distributions, represented the ground truth. The tolerance limits of the in-control PSQAs and remaining PSQAs after elimination calculated using the heuristic methods were considerably close to the ground truth (the maximum average absolute deviations were 0.50 and 1.03%, respectively). Some transformation failures occurred under both transformation methods. For the in-control PSQAs at 3%/2 mm gamma criteria, the maximum differences in the tolerance limits for four linacs and different treatment sites were 3.10 and 5.02%, respectively. CONCLUSIONS The GPR distributions of PSQA processes vary with different linacs and treatment sites but most are skewed. In applying SPC methodologies to PSQA processes, heuristic methods are robust. For in-control PSQA processes, the tolerance limits calculated by heuristic methods are in good agreement with the ground truth. For unknown PSQA processes, the tolerance limits calculated by the heuristic methods after the iterative "Identify-Eliminate-Recalculate" procedure are closest to the ground truth. Setting linac- and treatment site-specific tolerance limits for PSQA processes is necessary for clinical applications.
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Affiliation(s)
- Qing Xiao
- Department of Radiation Oncology, Cancer Center and State Key Laboratory of Biotherapy, West China Hospital, Sichuan University, Chengdu, Sichuan, P. R. China
| | - Long Bai
- Department of Radiation Oncology, Cancer Center and State Key Laboratory of Biotherapy, West China Hospital, Sichuan University, Chengdu, Sichuan, P. R. China
| | - Guangjun Li
- Department of Radiation Oncology, Cancer Center and State Key Laboratory of Biotherapy, West China Hospital, Sichuan University, Chengdu, Sichuan, P. R. China
| | - Xiangbin Zhang
- Department of Radiation Oncology, Cancer Center and State Key Laboratory of Biotherapy, West China Hospital, Sichuan University, Chengdu, Sichuan, P. R. China
| | - Zhibin Li
- Department of Radiation Oncology, Cancer Center and State Key Laboratory of Biotherapy, West China Hospital, Sichuan University, Chengdu, Sichuan, P. R. China
| | - Lian Duan
- Department of Radiation Oncology, Cancer Center and State Key Laboratory of Biotherapy, West China Hospital, Sichuan University, Chengdu, Sichuan, P. R. China
| | - Ruilin Peng
- Department of Radiation Oncology, Cancer Center and State Key Laboratory of Biotherapy, West China Hospital, Sichuan University, Chengdu, Sichuan, P. R. China
| | - Renming Zhong
- Department of Radiation Oncology, Cancer Center and State Key Laboratory of Biotherapy, West China Hospital, Sichuan University, Chengdu, Sichuan, P. R. China
| | - Qiang Wang
- Department of Radiation Oncology, Cancer Center and State Key Laboratory of Biotherapy, West China Hospital, Sichuan University, Chengdu, Sichuan, P. R. China
| | - Xuetao Wang
- Department of Radiation Oncology, Cancer Center and State Key Laboratory of Biotherapy, West China Hospital, Sichuan University, Chengdu, Sichuan, P. R. China
| | - Sen Bai
- Department of Radiation Oncology, Cancer Center and State Key Laboratory of Biotherapy, West China Hospital, Sichuan University, Chengdu, Sichuan, P. R. China
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Performance assessment of surface-guided radiation therapy and patient setup in head-and-neck and breast cancer patients based on statistical process control. Phys Med 2021; 89:243-249. [PMID: 34428608 DOI: 10.1016/j.ejmp.2021.08.007] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 05/05/2021] [Revised: 07/17/2021] [Accepted: 08/10/2021] [Indexed: 02/05/2023] Open
Abstract
PURPOSE To assess the effectiveness of SGRT in clinical applications through statistical process control (SPC). METHODS Taking the patients' positioning through optical surface imaging (OSI) as a process, the average level of process execution was defined as the process mean. Setup errors detected by cone-beam computed tomography (CBCT) and OSI were extracted for head-and-neck cancer (HNC) and breast cancer patients. These data were used to construct individual and exponentially weighted moving average (EWMA) control charts to analyze outlier fractions and small process shifts from the process mean. Using the control charts and process capability indices derived from this process, the patient positioning-related OSI performance and setup error were analyzed for each patient. RESULTS Outlier fractions and small shifts from the process mean that are indicative of setup errors were found to be widely prevalent, with the outliers randomly distributed between fractions. A systematic error of up to 1.6 mm between the OSI and CBCT results was observed in all directions, indicating a significantly degraded OSI performance. Adjusting this systematic error for each patient using setup errors of the first five fractions could effectively mitigate these effects. Process capability analysis following adjustment for systematic error indicated that OSI performance was acceptable (process capability index Cpk = 1.0) for HNC patients but unacceptable (Cpk < 0.75) for breast cancer patients. CONCLUSION SPC is a powerful tool for detecting the outlier fractions and process changes. Our application of SPC to patient-specific evaluations validated the suitability of OSI in clinical applications involving patient positioning.
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Schlesinger DJ, Sanders JC, Muller DA, Nordström H, Sheehan JP. 8+ Year Performance of the Gamma Knife Perfexion/Icon Patient Positioning System and Possibilities for Preemptive Fault Detection Using Statistical Process Control. Med Phys 2021; 48:3425-3437. [PMID: 33959977 DOI: 10.1002/mp.14924] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2021] [Revised: 04/23/2021] [Accepted: 04/24/2021] [Indexed: 01/03/2023] Open
Abstract
BACKGROUND The large fractional doses, steep dose gradients, and small targets found in intracranial radiosurgery require extremely low beam delivery uncertainty. In the case of Gamma Knife radiosurgery (GKRS), this includes minimizing patient positioning system (PPS) positioning uncertainty. Existing QA techniques are recipe based, and feature point in time pass/fail tolerances. However, modern treatment machines, including the Gamma Knife Perfexion/Icon systems, record extensive internal data in treatment logs. These data can be analyzed through statistical process control (SPC) methods which are designed to detect changes in process behavior. The purpose of this study was to characterize the long-term (8+ year) performance of a Perfexion/Icon unit and use SPC methods to determine if performance changes could be detected at levels lower than existing QA and internal manufacturer performance tolerances. METHODS In-house software was developed to parse Perfexion/Icon log-files and store relevant information on shot delivery in a relational database. A last-in, first-out (LIFO) queuing algorithm was created to heuristically match messages associated with a given delivered shot. Filtering criteria were developed to filter QA and uncompleted shots. The resulting matched shots were extracted. Achieved versus planned PPS position was determined for each PPS motor as well as for the vector magnitude difference in PPS position. Exponentially weighted moving average (EWMA) control charts were plotted to determine when process behavior changed over time. RESULTS 53833 shots were delivered over an 8+ year span in the study. The mean vector magnitude PPS difference was 32.7 µm, with 97.5% of all shots within 70.1 µm. Several changes in PPS positioning behavior were observed over time, corresponding with control system faults on several occasions requiring PPS recalibration. EWMA control charts clearly demonstrate that these faults could be identified and possibly predicted as many as 3 years before there were faults beyond control system tolerance. CONCLUSION The PPS of Gamma Knife Perfexion/Icon systems has extremely low positioning uncertainties. EWMA control chart method can be utilized to track PPS performance over time and can potentially detect changes in performance that may indicate a component requiring maintenance. This would allow planned service visits to mitigate problems and prevent unplanned downtime.
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Affiliation(s)
- David J Schlesinger
- Departments of Radiation Oncology, University of Virginia, Charlottesville, VA, USA.,Department of Neurological Surgery, University of Virginia, Charlottesville, VA, USA
| | - Jason C Sanders
- Departments of Radiation Oncology, University of Virginia, Charlottesville, VA, USA
| | - Donald A Muller
- Departments of Radiation Oncology, University of Virginia, Charlottesville, VA, USA
| | | | - Jason P Sheehan
- Departments of Radiation Oncology, University of Virginia, Charlottesville, VA, USA.,Department of Neurological Surgery, University of Virginia, Charlottesville, VA, USA.,Department of Biomedical Engineering, University of Virginia, Charlottesville, VA, USA
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Milder MTW, Alber M, Söhn M, Hoogeman MS. Commissioning and clinical implementation of the first commercial independent Monte Carlo 3D dose calculation to replace CyberKnife M6™ patient-specific QA measurements. J Appl Clin Med Phys 2020; 21:304-311. [PMID: 33103343 PMCID: PMC7700940 DOI: 10.1002/acm2.13046] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2020] [Revised: 03/21/2020] [Accepted: 07/31/2020] [Indexed: 11/10/2022] Open
Abstract
PURPOSE To report on the commissioning and clinical validation of the first commercially available independent Monte Carlo (MC) three-dimensional (3D) dose calculation for CyberKnife robotic radiosurgery system® (Accuray, Sunnyvale, CA). METHODS The independent dose calculation (IDC) by SciMoCa® (Scientific RT, Munich, Germany) was validated based on water measurements of output factors and dose profiles (unshielded diode, field-size dependent corrections). A set of 84 patient-specific quality assurance (QA) measurements for multi-leaf collimator (MLC) plans, using an Octavius two-dimensional SRS1000 array (PTW, Freiburg, Germany), was compared to results of respective calculations. Statistical process control (SPC) was used to detect plans outside action levels. RESULTS Of all output factors for the three collimator systems of the CyberKnife, 99% agreed within 2% and 81% within 1%, with a maximum deviation of 3.2% for a 5-mm fixed cone. The profiles were compared using a one-dimensional gamma evaluation with 2% dose difference and 0.5 mm distance-to-agreement (Γ(2,0.5)). The off-centre ratios showed an average pass rate >99% (92-100%). The agreement of the depth dose profiles depended on field size, with lowest pass rates for the smallest MLC field sizes. The average depth dose pass rate was 88% (35-99%). The IDCs showed a Γ(2,1) pass rate of 98%. Statistical process control detected six plans outside tolerance levels in the measurements, all of which could be attributed the measurement setup. Independent dose calculations showed problems in five plans, all due to differences in the algorithm between TPS and IDC. Based on these results changes were made in the class solution for treatment plans. CONCLUSION The first commercially available MC 3D dose IDC was successfully commissioned and validated for the CyberKnife and replaced all routine patient-specific QA measurements in our clinic.
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Affiliation(s)
- Maaike T W Milder
- Department of Radiotherapy, Erasmus MC, University Medical Center Rotterdam, Rotterdam, Netherlands
| | - Markus Alber
- Section for Medical Physics, Department of Radiation Oncology, University Clinic Heidelberg, Heidelberg, Germany.,Scientific RT GmbH, Munich, Germany
| | | | - Mischa S Hoogeman
- Department of Radiotherapy, Erasmus MC, University Medical Center Rotterdam, Rotterdam, Netherlands
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Tiplica T, Dufreneix S, Legrand C. A Bayesian control chart based on the beta distribution for monitoring the two-dimensional gamma index pass rate in the context of patient-specific quality assurance. Med Phys 2020; 47:5408-5418. [PMID: 32970863 DOI: 10.1002/mp.14472] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2020] [Revised: 09/01/2020] [Accepted: 09/03/2020] [Indexed: 11/06/2022] Open
Abstract
PURPOSE In the context of quality assurance in intensity modulated radiation therapy (IMRT), the aim of this work was two-fold: (a) to show that the beta distribution characterizes the two-dimensional gamma index pass rate (GIPR), and that the quantiles of the distribution should be used in order to compute the control limit (CL) for the detection of abnormally low GIPR, and (b) to introduce a Bayesian control chart that allows calculation of CLs from the first measurement. METHODS In order to enable monitoring of the GIPR from the first measurement, we developed a Bayesian control chart based on the beta distribution, elaborated according to the following two steps: (a) an iterative bayesian inference approach without any prior information on the GIPR distribution was used at the start of monitoring and the CL was progressively updated; and (b) when sufficient in-control arcs had been recorded and the estimators of the parameters of the beta distribution were sufficiently accurate, the CL of the chart was fixed to a constant value corresponding to the quantile of the beta distribution. The clinical utility of this approach is illustrated through a real data case study: monitoring the GIPR of patients treated with a moving gantry IMRT technique RapidArcTM on a Novalis TrueBeam STx (Varian Medical Systems) linear accelerator equipped with an aS1200 electronic portal imager device. RESULTS We showed that some commonly used distributions for monitoring GIPR in the literature, such as normal or logarithm transformation, are not appropriate. We compared the CLs of those solutions with the CL of our chart based on the BD (CL = 95.14%). The comparison revealed that the CL for the normal law (CL = 97.62%) generated too many false positives, and that the CL of the Logarithm transformation (CL = 83.74%) could fail to efficiently detect (i.e., sufficiently early on or faster) changes in the process. CONCLUSIONS Successful GIPR monitoring requires careful and rigorous application of well-established statistical concepts in the field of statistical process control. In this paper, we stress the importance of carefully analyzing the distribution of the monitored characteristic that is plotted on the control chart. We propose a Bayesian control chart that can be viewed as a practical solution for early implementation of GIPR monitoring, starting from the first arc. We demonstrate that beta distribution is a better method for characterizing the GIPR, and thus, the use of this approach is expected to improve patient-specific quality assurance plans in radiotherapy.
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Affiliation(s)
- Teodor Tiplica
- LARIS Systems Engineering Research Laboratory, University of Angers, Angers, France
| | - Stéphane Dufreneix
- Department of Medical Physics, Institut de Cancérologie de l'Ouest, Angers, France
| | - Christophe Legrand
- Department of Medical Physics, Institut de Cancérologie de l'Ouest, Angers, France
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Xiao Q, Bai S, Li G, Yang K, Bai L, Li Z, Chen L, Xian L, Hu Z, Zhong R. Statistical process control and process capability analysis for non‐normal volumetric modulated arc therapy patient‐specific quality assurance processes. Med Phys 2020; 47:4694-4702. [PMID: 32677053 DOI: 10.1002/mp.14399] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2020] [Revised: 07/03/2020] [Accepted: 07/08/2020] [Indexed: 11/11/2022] Open
Affiliation(s)
- Qing Xiao
- Department of Radiation Oncology Cancer Center and State Key Laboratory of Biotherapy West China HospitalSichuan University Chengdu Sichuan610041 China
| | - Sen Bai
- Department of Radiation Oncology Cancer Center and State Key Laboratory of Biotherapy West China HospitalSichuan University Chengdu Sichuan610041 China
| | - Guangjun Li
- Department of Radiation Oncology Cancer Center and State Key Laboratory of Biotherapy West China HospitalSichuan University Chengdu Sichuan610041 China
| | - Kaixuan Yang
- Department of Radiation Oncology Cancer Center and State Key Laboratory of Biotherapy West China HospitalSichuan University Chengdu Sichuan610041 China
| | - Long Bai
- Department of Radiation Oncology Cancer Center and State Key Laboratory of Biotherapy West China HospitalSichuan University Chengdu Sichuan610041 China
| | - Zhibin Li
- Department of Radiation Oncology Cancer Center and State Key Laboratory of Biotherapy West China HospitalSichuan University Chengdu Sichuan610041 China
| | - Li Chen
- Department of Radiation Oncology Cancer Center and State Key Laboratory of Biotherapy West China HospitalSichuan University Chengdu Sichuan610041 China
| | - Lixun Xian
- Department of Radiation Oncology Cancer Center and State Key Laboratory of Biotherapy West China HospitalSichuan University Chengdu Sichuan610041 China
| | - Zhenyao Hu
- Department of Radiation Oncology Cancer Center and State Key Laboratory of Biotherapy West China HospitalSichuan University Chengdu Sichuan610041 China
| | - Renming Zhong
- Department of Radiation Oncology Cancer Center and State Key Laboratory of Biotherapy West China HospitalSichuan University Chengdu Sichuan610041 China
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Schmitt D, Blanck O, Gauer T, Fix MK, Brunner TB, Fleckenstein J, Loutfi-Krauss B, Manser P, Werner R, Wilhelm ML, Baus WW, Moustakis C. Technological quality requirements for stereotactic radiotherapy : Expert review group consensus from the DGMP Working Group for Physics and Technology in Stereotactic Radiotherapy. Strahlenther Onkol 2020; 196:421-443. [PMID: 32211939 PMCID: PMC7182540 DOI: 10.1007/s00066-020-01583-2] [Citation(s) in RCA: 66] [Impact Index Per Article: 16.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2020] [Accepted: 01/13/2020] [Indexed: 12/25/2022]
Abstract
This review details and discusses the technological quality requirements to ensure the desired quality for stereotactic radiotherapy using photon external beam radiotherapy as defined by the DEGRO Working Group Radiosurgery and Stereotactic Radiotherapy and the DGMP Working Group for Physics and Technology in Stereotactic Radiotherapy. The covered aspects of this review are 1) imaging for target volume definition, 2) patient positioning and target volume localization, 3) motion management, 4) collimation of the irradiation and beam directions, 5) dose calculation, 6) treatment unit accuracy, and 7) dedicated quality assurance measures. For each part, an expert review for current state-of-the-art techniques and their particular technological quality requirement to reach the necessary accuracy for stereotactic radiotherapy divided into intracranial stereotactic radiosurgery in one single fraction (SRS), intracranial fractionated stereotactic radiotherapy (FSRT), and extracranial stereotactic body radiotherapy (SBRT) is presented. All recommendations and suggestions for all mentioned aspects of stereotactic radiotherapy are formulated and related uncertainties and potential sources of error discussed. Additionally, further research and development needs in terms of insufficient data and unsolved problems for stereotactic radiotherapy are identified, which will serve as a basis for the future assignments of the DGMP Working Group for Physics and Technology in Stereotactic Radiotherapy. The review was group peer-reviewed, and consensus was obtained through multiple working group meetings.
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Affiliation(s)
- Daniela Schmitt
- Klinik für Radioonkologie und Strahlentherapie, National Center for Radiation Research in Oncology (NCRO), Heidelberger Institut für Radioonkologie (HIRO), Universitätsklinikum Heidelberg, Heidelberg, Germany.
| | - Oliver Blanck
- Klinik für Strahlentherapie, Universitätsklinikum Schleswig-Holstein, Kiel, Germany
| | - Tobias Gauer
- Klinik für Strahlentherapie und Radioonkologie, Universitätsklinikum Hamburg-Eppendorf, Hamburg, Germany
| | - Michael K Fix
- Abteilung für Medizinische Strahlenphysik und Universitätsklinik für Radio-Onkologie, Inselspital-Universitätsspital Bern, Universität Bern, Bern, Switzerland
| | - Thomas B Brunner
- Universitätsklinik für Strahlentherapie, Universitätsklinikum Magdeburg, Magdeburg, Germany
| | - Jens Fleckenstein
- Klinik für Strahlentherapie und Radioonkologie, Universitätsmedizin Mannheim, Universität Heidelberg, Mannheim, Germany
| | - Britta Loutfi-Krauss
- Klinik für Strahlentherapie und Onkologie, Universitätsklinikum Frankfurt, Frankfurt am Main, Germany
| | - Peter Manser
- Abteilung für Medizinische Strahlenphysik und Universitätsklinik für Radio-Onkologie, Inselspital-Universitätsspital Bern, Universität Bern, Bern, Switzerland
| | - Rene Werner
- Institut für Computational Neuroscience, Universitätsklinikum Hamburg-Eppendorf, Hamburg, Germany
| | - Maria-Lisa Wilhelm
- Klinik für Strahlentherapie, Universitätsmedizin Rostock, Rostock, Germany
| | - Wolfgang W Baus
- Klinik für Radioonkologie, CyberKnife- und Strahlentherapie, Universitätsklinikum Köln, Cologne, Germany
| | - Christos Moustakis
- Klinik für Strahlentherapie-Radioonkologie, Universitätsklinikum Münster, Münster, Germany
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Becker S, Sabouri P, Niu Y, Prado K, Chen S, Nichols E, Yi B. Commissioning and acceptance guide for the GammaPod. ACTA ACUST UNITED AC 2019; 64:205021. [DOI: 10.1088/1361-6560/ab41bd] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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CyberKnife MLC-based treatment planning for abdominal and pelvic SBRT: Analysis of multiple dosimetric parameters, overall scoring index and clinical scoring. Phys Med 2018; 56:25-33. [DOI: 10.1016/j.ejmp.2018.11.012] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 06/13/2018] [Revised: 11/13/2018] [Accepted: 11/17/2018] [Indexed: 12/31/2022] Open
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Mackeprang PH, Vuong D, Volken W, Henzen D, Schmidhalter D, Malthaner M, Mueller S, Frei D, Stampanoni MFM, Dal Pra A, Aebersold DM, Fix MK, Manser P. Independent Monte-Carlo dose calculation for MLC based CyberKnife radiotherapy. ACTA ACUST UNITED AC 2017; 63:015015. [DOI: 10.1088/1361-6560/aa97f8] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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