Decomposition of matrices and static multileaf collimators: a survey

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 setup time (corresponding to the number of matrices used in the linear combination), and other objectives which contribute to an improved radiation therapy.