Multileaf collimator shape matrix decomposition

An important method in cancer treatment is the use of high energetic radiation. In order to kill tumor cells the patient is exposed to radiation that is delivered by a linear accelerator whose beam head can be rotated about the treatment couch. Inevitably the healthy tissue surrounding the tumor is also exposed to some radiation. So the problem arises to arrange the treatment in a way such that the tumor receives a sufficiently high uniform dose while the damage to the normal tissue is as small as possible. The standard approach to this problem is as follows. First the patient body is discretized into so called voxels. The set of voxels is then partitioned into three sets: the clinical target volume, the critical structures and the remaining tissue. There are certain dose constraints for each of these parts. Basically the dose in the target volume has to be sufficient to kill the cancerous cells and the dose in the critical structures must not destroy the functionality of the corresponding organs. The determination of a combination of radiation fields is usually done by inverse methods based on certain physical models of how the radiation passes through a body. In the early 1990’s the method of intensity modulated radiation therapy (IMRT) was developed in order to obtain additional flexibility. Using a multileaf collimator (MLC) it is possible to form homogeneous fields of different shapes. By superimposing of some homogeneous fields an intensity modulated field is delivered. An MLC consists of two banks of metal leaves which block the radiation and can be shifted to form irregularly shaped beams (Fig. 1). The most common approach in treatment planning is to divide the optimization into two phases. At first, a set of beam angles and corresponding fluence matrices are determined. In a second step a sequence of leaf positions for the MLC for each of the angles is determined that yields the desired fluence distribution. Very recently there have been attempts to combine both steps into one optimization routine [22, 9].