Field Splitting Problems in Intensity-Modulated Radiation Therapy
Intensity-modulated radiation therapy (IMRT) is a modern cancer treatment technique that delivers prescribed radiation dose distributions, called intensity maps (IMs), to target tumors via the help of a device called the multileaf collimator (MLC). Due to the maximum leaf spread constraint of the MLCs, IMs whose widths exceed a given threshold cannot be delivered as a whole, and thus must be split into multiple subfields. Field splitting problems in IMRTnormally aim to minimize the total beam-on time (i.e., the total time when a patient is exposed to actual radiation during the delivery) of the resulting subfields. In this paper, we present efficient polynomial time algorithms for two general field splitting problems with guaranteed output optimality. Our algorithms are based on interesting observations and analysis, as well as new techniques and modelings. We formulate the first field splitting problem as a special integer linear programming (ILP) problem that can be solved optimally by linear programming due to its geometry; from an optimal integer solution for the ILP, we compute an optimal field splitting by solving a set of shortest path problems on graphs. We tackle the second field splitting problem by using a novel path-sweeping technique on IMs.
KeywordsDirect Acyclic Graph Integer Linear Programming Short Path Problem Multileaf Collimator Short Path
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