**Thomas Kalinowski**

**An algorithm for optimal multileaf collimator field segmentation with interleaf collision constraint**

**Preprint series:**
Preprints aus dem Fachbereich Mathematik, Universität Rostock

**MSC:**- 90Cxx Mathematical programming

**Abstract:** Intensity maps are nonnegative matrices describing the intensity modulation of beams in radiotherapy. An important step in the planning process is to determine a segmentation, that is a representation of an intensity map as a positive combination of special matrices corresponding to fixed positions of the multileaf collimator, called segments. We consider the problem of constructing segmentations with small total numbers of monitor units and segments. Generalizing the approach of \cite{Eng02} so that it applies to the segmentation problem with interleaf collision constraint, we show that the minimal number of monitor units in this case can be interpreted as the length of a longest path in a layered digraph. In addition we derive an efficient

algorithm that constructs a segmentation with this minimal number of monitor units.

**Keywords:** *leaf sequencing, radiation therapy, optimization, intensity modulation, multileaf collimator, IMRT*