A Minimum Cost Flow Formulation for Approximated MLC Segmentation

Shape matrix decomposition is a sub-problem in radiation therapy planning. A given fluence matrix 𝐴 has to be written as a sum of shape matrices corresponding to homogeneous fields that can be shaped by a multileaf collimator. We solve the problem of finding an approximation 𝐵 of 𝐴 satisfying prescribed upper and lower bounds for each entry. The approximation 𝐵 is determined such that the corresponding fluence can be realized with a prescribed delivery time using a multileaf collimator with an interleaf collision constraint, and under this condition the distance between 𝐴 and 𝐵 is minimized.