title: An Almost Linear Time Algorithm for Field Splitting in Radiation Therapy.
abstract: In this paper, we study an interesting geometric partition problem, calledoptimal field splitting, which arises inIntensity-Modulated Radiation Therapy(IMRT). In current clinical practice, a multi-leaf collimator (MLC) with amaximum leaf spreadconstraint is used to deliver the prescribed intensity maps (IMs). However, the maximum leaf spread of an MLC may require to split a large intensity map into several overlapping sub-IMs with each being delivered separately. We develop a close-to-linear time algorithm for solving the field splitting problem while minimizing the total complexity of the resulting sub-IMs, thus improving the treatment delivery efficiency. Meanwhile, our algorithm strives to minimize the maximum beam-on time of those sub-IMs. Our basic idea is to formulate the field splitting problem as computing a shortest path in a directed acyclic graph, which expresses a special "layered" structure. The edge weights of the graph satisfy the Monge property, which enables us to solve this shortest path problem by examining only a small portion of the graph, yielding a close-to-linear time algorithm. To minimize the maximum beam-on time of the resulting sub-IMs, we consider an interesting min-max slope path problem in a monotone polygon which is solvable in linear time. The min-max slope path problem may be of interest in its own right. Experimental results based on real medical data and computer generated IMs showed that our new algorithm runs fast and produces high quality field splitting results.
authors.affiliation: Department of Electrical & Computer Engineering, University of Iowa, Iowa City, IA 52242, USA ; Department of Radiation Oncology, University of Iowa, Iowa City, IA 52242, USA.
authors.forename: Xiaodong
authors.initials: X
authors.lastname: Wu
authors.affiliation: EDDA Technology Inc, 5 Independence Way, Princeton, NJ 08540, USA.
authors.forename: Xin
authors.initials: X
authors.lastname: Dou
authors.affiliation: Department of Radiation Oncology, University of Iowa, Iowa City, IA 52242, USA.
authors.forename: John E
authors.initials: JE
authors.lastname: Bayouth
authors.affiliation: Department of Radiation Oncology, University of Iowa, Iowa City, IA 52242, USA.
authors.forename: John M
authors.initials: JM
authors.lastname: Buatti
keywords: IMRT field splitting; Monge property; algorithms; min-max slope paths; shortest paths