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

## Abstract

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.