A function approximation approach to the segmentation step in IMRT planning

In the segmentation step of intensity modulated radiation therapy planning, given intensity profiles have to be decomposed into a number of leaf positions of a multileaf collimator (MLC) such that the superposition of the corresponding field shapes is close to the desired profile. Until now, these decomposition problems have been formulated as discrete optimization problems where the profiles are nonnegative integer matrices. The segments are modeled as 0‐1‐matrices, 1 indicating that radiation is transmitted through this part of the field and 0 for the areas that are covered by the leaves of the MLC. But in physical reality, radiation has a penumbra at the boundary of the segment causing a decline of the intensity, that is not modeled in these formulations. This paper embeds the segmentation task into the wider context of function approximation and models both profiles and segments as real‐valued functions of two variables. This leads to convex optimization problems whose objective is to minimize the approximation error between the profile and the superposition of the real weighted segments. Thus, a more realistic model of radiation is used and may enable an improvement in treatment quality.