Decomposition of matrices and static multileaf collimators: a survey

Matthias Ehrgott (), Horst W. Hamacher () and Marc Nußbaum
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Matthias Ehrgott: The University of Auckland
Horst W. Hamacher: Technische Universität Kaiserslautern
Marc Nußbaum: Technische Universität Kaiserslautern

A chapter in Optimization in Medicine, 2008, pp 25-46 from Springer

Abstract: Summary Multileaf Collimators (MLC) consist of (currently 20-100) pairs of movable metal leaves which are used to block radiation in Intensity Modulated Radiation Therapy (IMRT). The leaves modulate a uniform source of radiation to achieve given intensity profiles. The modulation process is modeled by the decomposition of a given non-negative integer matrix into a non-negative linear combination of matrices with the (strict) consecutive ones property. In this paper we review some results and algorithms which can be used to minimize the time a patient is exposed to radiation (corresponding to the sum of coefficients in the linear combination), the set-up time (corresponding to the number of matrices used in the linear combination), and other objectives which contribute to an improved radiation therapy.

Keywords: Intensity modulated radiation therapy; multileaf collimator; intensity map segmentation; complexity; multi objective optimization (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/978-0-387-73299-2_2

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