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https://hdl.handle.net/1959.11/26803
Title: | The complexity of minimizing the number of shape matrices subject to minimal beam-on time in multileaf collimator field decomposition with bounded fluence | Contributor(s): | Kalinowski, Thomas (author) | Publication Date: | 2009-05-06 | Early Online Version: | 2008-08-20 | Open Access: | Yes | DOI: | 10.1016/j.dam.2008.06.027 | Handle Link: | https://hdl.handle.net/1959.11/26803 | Abstract: | The use of multileaf collimators (MLCs) is a modern way to realize intensity modulated fields in radiotherapy. An important step in the treatment planning is the shape matrix decomposition: the desired fluence distribution, given by an integer matrix, has to be decomposed into a small number shape matrices, i.e. (0,1)-matrices corresponding to the field shapes that can be delivered by the MLC used. The two main objectives are to minimize the total irradiation time, and the number of shape matrices. Assuming that the entries of the fluence matrix are bounded by a constant, we prove that a shape matrix decomposition with minimal number of shape matrices under the condition that the total irradiation time is minimal, can be determined in time polynomial in the matrix dimensions. The results of our algorithm are compared with Engel’s [K. Engel, A new algorithm for optimal multileaf collimator field segmentation, Discrete Appl. Math. 152 (1–3) (2005) 35–51.] heuristic for the reduction of the number of shape matrices. | Publication Type: | Journal Article | Source of Publication: | Discrete Applied Mathematics, 157(9), p. 2089-2104 | Publisher: | Elsevier BV, North-Holland | Place of Publication: | Netherlands | ISSN: | 1872-6771 0166-218X |
Fields of Research (FoR) 2008: | 010303 Optimisation 010206 Operations Research |
Socio-Economic Objective (SEO) 2008: | 970101 Expanding Knowledge in the Mathematical Sciences | Peer Reviewed: | Yes | HERDC Category Description: | C1 Refereed Article in a Scholarly Journal | CC License of All Rights Reserved: | https://www.elsevier.com/about/policies/open-access-licenses/elsevier-user-license |
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Appears in Collections: | Journal Article School of Science and Technology |
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