Decomposition of matrices and static multileaf collimators: a survey

Ehrgott, Matthias and Hamacher, Horst W. and Nußbaum, Marc (2008) Decomposition of matrices and static multileaf collimators: a survey. In: Optimization in medicine. Springer Optimization and Its Applications . Springer, New York, pp. 22-46. ISBN 978-0-387-73298-5

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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.

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10 May 2013 12:59
Last Modified:
21 Nov 2022 15:13