From analytic inversion to contemporary IMRT optimization: Radiation therapy planning revisited from a mathematical perspective |
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| Authors: | Yair Censor Jan Unkelbach |
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| Institution: | 1. Department of Mathematics, University of Haifa, Mt. Carmel, Haifa 31905, Israel;2. Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, MA 02114, USA;1. Research Center of Digital Radiation Imaging, Beijing University of Aeronautics and Astronautics, 100191 Beiijng, China;2. Department of Physics (E17) and Institute of Medical Engineering (IMETUM), Technische Universität München, 85748 Garching, Germany;3. Lund University, 22185 Lund, Sweden;4. Lyncean Technologies Inc., Palo Alto, 94306 CA, USA;5. SLAC National Accelerator Laboratory, Menlo Park, 94025 CA, USA;1. Department of Biomedical Engineering, Hotchkiss Brain Institute, University of Calgary, Calgary, Alberta, Canada;2. Seaman Family Magnetic Resonance Research Centre, Foothills Medical Centre, Calgary;3. Department of Radiology and Clinical Neuroscience, Hotchkiss Brain Institute, Calgary;4. Seaman Family Magnetic Resonance Research Centre Foothills Medical Centre;1. FAMAF (Facultad de Matemática Astronomía, Física and Computación), Universidad Nacional de Córdoba, Medina Allende and Haya de la Torre, (5000) Ciudad Universitaria, Córdoba, Argentina;2. IFEG-CONICET (Instituto de Física “Enrique Gaviola”) Universidad Nacional de Córdoba, Medina Allende and Haya de la Torre, (5000) Ciudad Universitaria, Córdoba, Argentina;1. Radiotherapy Centre, National Institute of Oncology, Budapest, Hungary;2. Department of Oncology, Semmelweis University, Budapest, Hungary;3. Budapest University of Technology and Economics, Budapest, Hungary |
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| Abstract: | In this paper we look at the development of radiation therapy treatment planning from a mathematical point of view. Historically, planning for Intensity-Modulated Radiation Therapy (IMRT) has been considered as an inverse problem. We discuss first the two fundamental approaches that have been investigated to solve this inverse problem: Continuous analytic inversion techniques on one hand, and fully-discretized algebraic methods on the other hand. In the second part of the paper, we review another fundamental question which has been subject to debate from the beginning of IMRT until the present day: The rotation therapy approach versus fixed angle IMRT. This builds a bridge from historic work on IMRT planning to contemporary research in the context of Intensity-Modulated Arc Therapy (IMAT). |
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