A network approach for segmentation in intensity modulated arc therapy

Abstract

We consider the approximation of a given m×n non-negative real matrix A by a weighted non-negative sum of binary matrices. Such approximation problems arise in intensity modulated arc therapy (IMAT), an advanced form of radiotherapy for cancer. In that context, the binary matrices S i represent the ‘open’ positions for the radiation beamlets in a so-called aperture, and the corresponding weights denote the radiation intensity associated with the aperture. The weighted sum of apertures thus represents an approximation (typically based on a small number of apertures) to the ideal radiation distribution at a given angle given by the matrix A. The determination of an optimal approximation of this type for a limited number of S i ’s is termed a segmentation problem. The approximation problem considered here (IMAT) is a set of coupled segmentation problems with delivery constraints. The delivery constraints are mechanical and limit both the types of apertures that may be employed as well as the changes that may be made to apertures between successive angles as the radiation delivery equipment moves in sweeps along an arc around the patient. We present an effective heuristic algorithm using network optimization models to solve this IMAT optimization problem.