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Tonneau M, Roos M, Cayez R, Wagner A, Leguillette C, Le Deley MC, Lals S, Martinage G, Pasquier D, Mirabel X, Lacornerie T, Liem X. Multicriteria optimization of radiation therapy: Towards empowerment and standardization of reverse planning for head and neck squamous cell carcinoma. Cancer Radiother 2024; 28:317-322. [PMID: 38937203 DOI: 10.1016/j.canrad.2024.01.003] [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: 10/16/2023] [Revised: 12/15/2023] [Accepted: 01/09/2024] [Indexed: 06/29/2024]
Abstract
PURPOSE The purpose of this study was to assess if multicriteria optimization could limit interoperator variability in radiation therapy planning and assess if this method could contribute to target volume coverage and sparing of organ at risk for intensity-modulated curative radiation therapy of head and neck cancers. MATERIAL AND METHODS We performed a retrospective analysis on 20 patients treated for an oropharyngeal or oral cavity squamous cell carcinoma. We carried out a comparative dosimetric study of manual plans produced with Precision® software, compared with the plans proposed using the multicriteria optimization method (RayStation®). We assessed interoperator reproducibility on the first six patients, and dosimetric contribution in sparing organs at risk using the multicriteria optimization method. RESULTS Median age was 69 years, most lesions were oropharyngeal carcinoma (65%), and 35% lesions were stage T3. First, we obtained a high degree of similarity between the four operator measurements for each patient at the level of each organ. Intraclass correlation coefficients were greater than 0.85. Second, we observed a significant dosimetric benefit for contralateral parotid gland, homolateral and contralateral masseter muscles, homolateral and contralateral pterygoid muscles and for the larynx (P<0.05). For the contralateral parotid gland, the mean dose difference between the multicriteria optimization and manual plans was -2.0Gy (P=0.01). Regarding the larynx, the mean dose difference between the two plans was -4.6Gy (P<0.001). CONCLUSION Multicriteria optimization is a reproducible technique and faster than manual optimization. It allows dosimetric advantages on organs at risk, especially for those not usually taken into consideration in manual dosimetry. This may lead to improved quality of life.
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Affiliation(s)
- M Tonneau
- Département de radiothérapie curiethérapie, centre Oscar-Lambret, Lille, France
| | - M Roos
- Département de physique médicale, centre Oscar-Lambret, Lille, France
| | - R Cayez
- Département de physique médicale, centre Oscar-Lambret, Lille, France
| | - A Wagner
- Département de physique médicale, centre Oscar-Lambret, Lille, France
| | - C Leguillette
- Département de biostatistique, centre Oscar-Lambret, Lille, France
| | - M-C Le Deley
- Département de biostatistique, centre Oscar-Lambret, Lille, France
| | - S Lals
- Département de radiothérapie curiethérapie, centre Oscar-Lambret, Lille, France
| | - G Martinage
- Département de radiothérapie curiethérapie, centre Oscar-Lambret, Lille, France
| | - D Pasquier
- Département de radiothérapie curiethérapie, centre Oscar-Lambret, Lille, France; CRISTAL UMR 9189, université de Lille, Lille, France
| | - X Mirabel
- Département de radiothérapie curiethérapie, centre Oscar-Lambret, Lille, France
| | - T Lacornerie
- Département de physique médicale, centre Oscar-Lambret, Lille, France
| | - X Liem
- Département de radiothérapie curiethérapie, centre Oscar-Lambret, Lille, France.
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Bai X, Shan G, Chen M, Wang B. Approach and assessment of automated stereotactic radiotherapy planning for early stage non-small-cell lung cancer. Biomed Eng Online 2019; 18:101. [PMID: 31619263 PMCID: PMC6796412 DOI: 10.1186/s12938-019-0721-7] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2019] [Accepted: 10/09/2019] [Indexed: 12/25/2022] Open
Abstract
BACKGROUND Intensity-modulated radiotherapy (IMRT) and volumetric-modulated arc therapy (VMAT) are standard physical technologies of stereotactic body radiotherapy (SBRT) that are used for patients with non-small-cell lung cancer (NSCLC). The treatment plan quality depends on the experience of the planner and is limited by planning time. An automated planning process can save time and ensure a high-quality plan. This study aimed to introduce and demonstrate an automated planning procedure for SBRT for patients with NSCLC based on machine-learning algorithms. The automated planning was conducted in two steps: (1) determining patient-specific optimized beam orientations; (2) calculating the organs at risk (OAR) dose achievable for a given patient and setting these dosimetric parameters as optimization objectives. A model was developed using data of historical expertise plans based on support vector regression. The study cohort comprised patients with NSCLC who were treated using SBRT. A training cohort (N = 125) was used to calculate the beam orientations and dosimetric parameters for the lung as functions of the geometrical feature of each case. These plan-geometry relationships were used in a validation cohort (N = 30) to automatically establish the SBRT plan. The automatically generated plans were compared with clinical plans established by an experienced planner. RESULTS All 30 automated plans (100%) fulfilled the dose criteria for OARs and planning target volume (PTV) coverage, and were deemed acceptable according to evaluation by experienced radiation oncologists. An automated plan increased the mean maximum dose for ribs (31.6 ± 19.9 Gy vs. 36.6 ± 18.1 Gy, P < 0.05). The minimum, maximum, and mean dose; homogeneity index; conformation index to PTV; doses to other organs; and the total monitor units showed no significant differences between manual plans established by experts and automated plans (P > 0.05). The hands-on planning time was reduced from 40-60 min to 10-15 min. CONCLUSION An automated planning method using machine learning was proposed for NSCLC SBRT. Validation results showed that the proposed method decreased planning time without compromising plan quality. Plans generated by this method were acceptable for clinical use.
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Affiliation(s)
- Xue Bai
- Department of Radiation Physics, Zhejiang Key Laboratory of Radiation Oncology, Zhejiang Cancer Hospital, Hangzhou, 310022, Zhejiang, People's Republic of China
| | - Guoping Shan
- Department of Radiation Physics, Zhejiang Key Laboratory of Radiation Oncology, Zhejiang Cancer Hospital, Hangzhou, 310022, Zhejiang, People's Republic of China
| | - Ming Chen
- Department of Radiation Physics, Zhejiang Key Laboratory of Radiation Oncology, Zhejiang Cancer Hospital, Hangzhou, 310022, Zhejiang, People's Republic of China
| | - Binbing Wang
- Department of Radiation Physics, Zhejiang Key Laboratory of Radiation Oncology, Zhejiang Cancer Hospital, Hangzhou, 310022, Zhejiang, People's Republic of China.
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3
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Hussein M, Heijmen BJM, Verellen D, Nisbet A. Automation in intensity modulated radiotherapy treatment planning-a review of recent innovations. Br J Radiol 2018; 91:20180270. [PMID: 30074813 DOI: 10.1259/bjr.20180270] [Citation(s) in RCA: 148] [Impact Index Per Article: 24.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
Radiotherapy treatment planning of complex radiotherapy techniques, such as intensity modulated radiotherapy and volumetric modulated arc therapy, is a resource-intensive process requiring a high level of treatment planner intervention to ensure high plan quality. This can lead to variability in the quality of treatment plans and the efficiency in which plans are produced, depending on the skills and experience of the operator and available planning time. Within the last few years, there has been significant progress in the research and development of intensity modulated radiotherapy treatment planning approaches with automation support, with most commercial manufacturers now offering some form of solution. There is a rapidly growing number of research articles published in the scientific literature on the topic. This paper critically reviews the body of publications up to April 2018. The review describes the different types of automation algorithms, including the advantages and current limitations. Also included is a discussion on the potential issues with routine clinical implementation of such software, and highlights areas for future research.
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Affiliation(s)
- Mohammad Hussein
- 1 Metrology for Medical Physics Centre, National Physical Laboratory , Teddington , UK
| | - Ben J M Heijmen
- 2 Division of Medical Physics, Erasmus MC Cancer Institute , Rotterdam , The Netherlands
| | - Dirk Verellen
- 3 Faculty of Medicine and Pharmacy, Vrije Universiteit Brussel (VUB) , Brussels , Belgium.,4 Radiotherapy Department, Iridium Kankernetwerk , Antwerp , Belgium
| | - Andrew Nisbet
- 5 Department of Medical Physics, Royal Surrey County Hospital NHS Foundation Trust , Guildford , UK.,6 Department of Physics, University of Surrey , Guildford , UK
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Wang J, Chen Z, Li W, Qian W, Wang X, Hu W. A new strategy for volumetric-modulated arc therapy planning using AutoPlanning based multicriteria optimization for nasopharyngeal carcinoma. Radiat Oncol 2018; 13:94. [PMID: 29769101 PMCID: PMC5956620 DOI: 10.1186/s13014-018-1042-x] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2018] [Accepted: 05/01/2018] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND A new strategy for making the appropriate choice of the representative optimization parameters in planning processes and accurate selection criteria during Pareto surface navigation for general multicriteria optimization (MCO) was recommended in the study. The purpose was to combine both benefits of AutoPlanning optimization and MCO (APMCO) for achieving an individual volumetric-modulated arc therapy (VMAT) plan according to the clinically achieved patient-specific tradeoff among conflicting priorities. The preclinical investigation of this optimization approach for nasopharyngeal carcinoma (NPC) radiotherapy was performed and compared to general MCO VMAT. METHODS A total of 60 NPC patients with various stages were enrolled in this study. General MCO and APMCO plans were generated for each patient on the treatment planning system. The differences between two planning schemes were evaluated and compared. RESULTS All plans were capable of achieving the prescription requirement. The planning target volume coverage and conformation number were remarkably similar between general MCO and APMCO plans. There were no significant differences in most of organs at risk (OARs) sparing. However, in APMCO plans, relatively remarkable decreases were observed in the mean dose (Dmean) to the glottic larynx and pharyngeal constrictor muscles. The reductions of average Dmean to the two OARs were 10.5% (p < 0.0001) and 8.4% (p < 0.0001), respectively. APMCO technique was found to increase the planning time for an average of approximately 5 h and did not lead to a significant increase of monitor units compared to general MCO. CONCLUSIONS The potential of the APMCO strategy is best realized with a clinical implementation that exploits individual generation of Pareto surface representations without manual interaction. It also assists physicians to ensure navigation in a more efficient and straightforward manner.
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Affiliation(s)
- Juanqi Wang
- Department of Radiation Oncology, Fudan University Shanghai Cancer Center, Shanghai, China.,Department of Oncology, Shanghai Medical College, Fudan University, Shanghai, China
| | - Zhi Chen
- Department of Radiation Oncology, Fudan University Shanghai Cancer Center, Shanghai, China.,Department of Oncology, Shanghai Medical College, Fudan University, Shanghai, China
| | - Weiwei Li
- Department of Radiation Oncology, Fudan University Shanghai Cancer Center, Shanghai, China.,Department of Oncology, Shanghai Medical College, Fudan University, Shanghai, China
| | - Wei Qian
- Department of Radiation Oncology, Fudan University Shanghai Cancer Center, Shanghai, China.,Department of Oncology, Shanghai Medical College, Fudan University, Shanghai, China
| | - Xiaosheng Wang
- Department of Radiation Oncology, Fudan University Shanghai Cancer Center, Shanghai, China.,Department of Oncology, Shanghai Medical College, Fudan University, Shanghai, China
| | - Weigang Hu
- Department of Radiation Oncology, Fudan University Shanghai Cancer Center, Shanghai, China. .,Department of Oncology, Shanghai Medical College, Fudan University, Shanghai, China.
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5
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A clinical distance measure for evaluating treatment plan quality difference with Pareto fronts in radiotherapy. Phys Imaging Radiat Oncol 2017. [DOI: 10.1016/j.phro.2017.09.003] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
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Craft D, Papp D, Unkelbach J. Plan averaging for multicriteria navigation of sliding window IMRT and VMAT. Med Phys 2014; 41:021709. [PMID: 24506600 DOI: 10.1118/1.4859295] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022] Open
Abstract
PURPOSE To describe a method for combining sliding window plans [intensity modulated radiation therapy (IMRT) or volumetric modulated arc therapy (VMAT)] for use in treatment plan averaging, which is needed for Pareto surface navigation based multicriteria treatment planning. METHODS The authors show that by taking an appropriately defined average of leaf trajectories of sliding window plans, the authors obtain a sliding window plan whose fluence map is the exact average of the fluence maps corresponding to the initial plans. In the case of static-beam IMRT, this also implies that the dose distribution of the averaged plan is the exact dosimetric average of the initial plans. In VMAT delivery, the dose distribution of the averaged plan is a close approximation of the dosimetric average of the initial plans. RESULTS The authors demonstrate the method on three Pareto optimal VMAT plans created for a demanding paraspinal case, where the tumor surrounds the spinal cord. The results show that the leaf averaged plans yield dose distributions that approximate the dosimetric averages of the precomputed Pareto optimal plans well. CONCLUSIONS The proposed method enables the navigation of deliverable Pareto optimal plans directly, i.e., interactive multicriteria exploration of deliverable sliding window IMRT and VMAT plans, eliminating the need for a sequencing step after navigation and hence the dose degradation that is caused by such a sequencing step.
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Affiliation(s)
- David Craft
- Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, Massachusetts 02114
| | - Dávid Papp
- Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, Massachusetts 02114
| | - Jan Unkelbach
- Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, Massachusetts 02114
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Predicting patient survival after liver transplantation using evolutionary multi-objective artificial neural networks. Artif Intell Med 2013; 58:37-49. [DOI: 10.1016/j.artmed.2013.02.004] [Citation(s) in RCA: 41] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2011] [Revised: 02/04/2013] [Accepted: 02/05/2013] [Indexed: 12/27/2022]
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Wala J, Craft D, Paly J, Zietman A, Efstathiou J. Maximizing dosimetric benefits of IMRT in the treatment of localized prostate cancer through multicriteria optimization planning. Med Dosim 2013; 38:298-303. [PMID: 23540492 DOI: 10.1016/j.meddos.2013.02.012] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2012] [Revised: 01/23/2013] [Accepted: 02/21/2013] [Indexed: 12/25/2022]
Abstract
We examine the quality of plans created using multicriteria optimization (MCO) treatment planning in intensity-modulated radiation therapy (IMRT) in treatment of localized prostate cancer. Nine random cases of patients receiving IMRT to the prostate were selected. Each case was associated with a clinically approved plan created using Corvus. The cases were replanned using MCO-based planning in RayStation. Dose-volume histogram data from both planning systems were presented to 2 radiation oncologists in a blinded evaluation, and were compared at a number of dose-volume points. Both physicians rated all 9 MCO plans as superior to the clinically approved plans (p<10(-5)). Target coverage was equivalent (p = 0.81). Maximum doses to the prostate and bladder and the V50 and V70 to the anterior rectum were reduced in all MCO plans (p<0.05). Treatment planning time with MCO took approximately 60 minutes per case. MCO-based planning for prostate IMRT is efficient and produces high-quality plans with good target homogeneity and sparing of the anterior rectum, bladder, and femoral heads, without sacrificing target coverage.
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Bokrantz R. Multicriteria optimization for volumetric-modulated arc therapy by decomposition into a fluence-based relaxation and a segment weight-based restriction. Med Phys 2013; 39:6712-25. [PMID: 23127065 DOI: 10.1118/1.4754652] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022] Open
Abstract
PURPOSE To develop a method for inverse volumetric-modulated arc therapy (VMAT) planning that combines multicriteria optimization (MCO) with direct machine parameter optimization. The ultimate goal is to provide an efficient and intuitive method for generating high quality VMAT plans. METHODS Multicriteria radiation therapy treatment planning amounts to approximating the relevant treatment options by a discrete set of plans, and selecting the combination thereof that strikes the best possible balance between conflicting objectives. This approach is applied to two decompositions of the inverse VMAT planning problem: a fluence-based relaxation considered at a coarsened gantry angle spacing and under a regularizing penalty on fluence modulation, and a segment weight-based restriction in a neighborhood of the solution to the relaxed problem. The two considered variable domains are interconnected by direct machine parameter optimization toward reproducing the dose-volume histogram of the fluence-based solution. RESULTS The dose distribution quality of plans generated by the proposed MCO method was assessed by direct comparison with benchmark plans generated by a conventional VMAT planning method. The results for four patient cases (prostate, pancreas, lung, and head and neck) are highly comparable between the MCO plans and the benchmark plans: Discrepancies between studied dose-volume statistics for organs at risk were-with the exception of the kidneys of the pancreas case-within 1 Gy or 1 percentage point. Target coverage of the MCO plans was comparable with that of the benchmark plans, but with a small tendency toward a shift from conformity to homogeneity. CONCLUSIONS MCO allows tradeoffs between conflicting objectives encountered in VMAT planning to be explored in an interactive manner through search over a continuous representation of the relevant treatment options. Treatment plans selected from such a representation are of comparable dose distribution quality to conventionally optimized VMAT plans.
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Affiliation(s)
- Rasmus Bokrantz
- Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden.
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10
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Xhaferllari I, Wong E, Bzdusek K, Lock M, Chen J. Automated IMRT planning with regional optimization using planning scripts. J Appl Clin Med Phys 2013; 14:4052. [PMID: 23318393 PMCID: PMC5714048 DOI: 10.1120/jacmp.v14i1.4052] [Citation(s) in RCA: 72] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2012] [Revised: 08/10/2012] [Accepted: 09/04/2012] [Indexed: 12/01/2022] Open
Abstract
Intensity‐modulated radiation therapy (IMRT) has become a standard technique in radiation therapy for treating different types of cancers. Various class solutions have been developed for simple cases (e.g., localized prostate, whole breast) to generate IMRT plans efficiently. However, for more complex cases (e.g., head and neck, pelvic nodes), it can be time‐consuming for a planner to generate optimized IMRT plans. To generate optimal plans in these more complex cases which generally have multiple target volumes and organs at risk, it is often required to have additional IMRT optimization structures such as dose limiting ring structures, adjust beam geometry, select inverse planning objectives and associated weights, and additional IMRT objectives to reduce cold and hot spots in the dose distribution. These parameters are generally manually adjusted with a repeated trial and error approach during the optimization process. To improve IMRT planning efficiency in these more complex cases, an iterative method that incorporates some of these adjustment processes automatically in a planning script is designed, implemented, and validated. In particular, regional optimization has been implemented in an iterative way to reduce various hot or cold spots during the optimization process that begins with defining and automatic segmentation of hot and cold spots, introducing new objectives and their relative weights into inverse planning, and turn this into an iterative process with termination criteria. The method has been applied to three clinical sites: prostate with pelvic nodes, head and neck, and anal canal cancers, and has shown to reduce IMRT planning time significantly for clinical applications with improved plan quality. The IMRT planning scripts have been used for more than 500 clinical cases. PACS numbers: 87.55.D, 87.55.de
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Affiliation(s)
- Ilma Xhaferllari
- Department of Medical Biophysics, University of Western Ontario, London, Ontario, Canada.
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Thor M, Benedek H, Knöös T, Engström P, Behrens CF, Hauer AK, Sjöström D, Ceberg C. Introducing multiple treatment plan-based comparison to investigate the performance of gantry angle optimisation (GAO) in IMRT for head and neck cancer. Acta Oncol 2012; 51:743-51. [PMID: 22530922 DOI: 10.3109/0284186x.2012.673733] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
Abstract
BACKGROUND AND PURPOSE The purpose of this study was to evaluate the performance of gantry angle optimisation (GAO) compared to equidistant beam geometry for two inverse treatment planning systems (TPSs) by utilising the information obtained from a range of treatment plans. MATERIAL AND METHODS The comparison was based on treatment plans generated for four different head and neck (H&N) cancer cases using two inverse treatment planning systems (TPSs); Varian Eclipse™ representing dynamic MLC intensity modulated radiotherapy (IMRT) and Oncentra® Masterplan representing segmented MLC-based IMRT. The patient cases were selected on the criterion of representing different degrees of overlap between the planning target volume (PTV) and the investigated organ at risk, the ipsilateral parotid gland. For each case, a number of 'Pareto optimal' plans were generated in order to investigate the trade-off between the under-dosage to the PTV (V(PTV,D < 95%)) or the decrease in dose homogeneity (D(5)-D(95)) to the PTV as a function of the mean absorbed dose to the ipsilateral parotid gland (<D>(parotid gland)). RESULTS For the Eclipse system, GAO had a clear advantage for the cases with smallest overlap (Cases 1 and 2). The set of data points, representing the underlying trade-offs, generated with and without using GAO were, however, not as clearly separated for the cases with larger overlap (Cases 3 and 4). With the OMP system, the difference was less pronounced for all cases. The Eclipse GAO displays the most favourable trade-off for all H&N cases. CONCLUSIONS We have found differences in the effectiveness of GAO as compared to equidistant beam geometry, in terms of handling conflicting trade-offs for two commercial inverse TPSs. A comparison, based on a range of treatment plans, as developed in this study, is likely to improve the understanding of conflicting trade-offs and might apply to other thorough comparison techniques.
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Affiliation(s)
- Maria Thor
- Departments of Oncology and Medical Physics, Aarhus University Hospital, Denmark.
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Fenwick JD, Pardo-Montero J. Numbers of beam angles required for near-optimal IMRT: theoretical limits and numerical studies. Med Phys 2011; 38:4518-30. [PMID: 21928622 DOI: 10.1118/1.3606457] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022] Open
Abstract
PURPOSE To derive limits on the numbers of beams needed to deliver near-optimal IMRT, and to assess the accuracy of the limits. METHODS The authors four different limits have been derived. One, K(A), has been obtained by coupling Fourier techniques with a proof used to obtain Bortfeld's limit, K, that if all the cross-profiles of a many-field plan can be represented as polynomials of order (K-1) over the range [-R, + R], then within the radius R circle an identical dose-distribution can be created using just K fields. Two further limits, K(H) and K(N), have been obtained using sampling theory, the K(N) limit describing fields spaced at the Nyquist frequency. K(N) can be generalized to K(N,Fbeamlet), a limit that accounts for the finite size of the beamlets from which modulated fields are constructed. Using Bortfeld's theoretical framework, the accuracy of the limits has been explored by testing how well the cross-profiles of an 8 MV double-Gaussian pencil beam and of 1 and 4 cm wide fields can be approximated by polynomials of orders equal to the different limits minus one. The dependence of optimized cost function values of IMRT plans, generated for a simple geometry and for a head-and-neck (oropharynx) case, on the numbers of beams used to construct the plans has also been studied. RESULTS The limits are all multiples of R/W (W being the 20%-80% penumbra-width of a broad field) and work out at K = 27, K(A) = 43, K(H) = 34, and K(N) = 68 fields for R = 10 cm and W = 5.3 mm. All and none of the cross-profiles are approximated well by polynomials of order K(N)-1 and K-1, respectively, suggesting some inaccuracy in the assumptions used to derive the limit K. Order K(A)-1 polynomials cannot accurately describe the pencil beam profile, but do approximate the 1- and 4-cm profiles reasonably well because higher spatial frequencies are attenuated in these wider fields. All the profiles are represented well by polynomials of order K(N,Fbeamlet(-1)), which decreases from K(N) as beamlet width increases. Cost functions generated in the IMRT planning study fall as greater numbers of fields are used, before plateauing out around K(N,Fbeamlet) fields. CONCLUSIONS Numerical calculations suggest that the minimum number of fields required for near-optimal IMRT lies around the generalized Nyquist limit K(N,Fbeamlet). For a clinically realistic 20%-80% penumbra-width of 5.3 mm and a radius of interest of 10 cm, K(N,Fbeamlet) falls from 68 to 47 fields as the beamlet width rises from 0 to 1 cm.
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Affiliation(s)
- John D Fenwick
- School of Cancer Studies, University of Liverpool, Liverpool L69 3GA, United Kingdom.
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