An almost linear time algorithm for field splitting in radiation therapy

In this paper, we study an interesting geometric partition problem, called optimal field splitting, which arises in Intensity-Modulated Radiation Therapy (IMRT). In current clinical practice, a multi-leaf collimator (MLC) with a maximum leaf spread constraint is used to deliver the prescribed intens...

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Vydáno v:Computational geometry : theory and applications Ročník 46; číslo 6; s. 673 - 687
Hlavní autoři: Wu, Xiaodong, Dou, Xin, Bayouth, John E., Buatti, John M.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Netherlands Elsevier B.V 01.08.2013
Témata:
Algorithms
Computational efficiency
Graphs
IMRT field splitting
Min–max slope paths
Monge property
Radiation therapy
Shortest paths
Shortest-path problems
Splitting
Spreads
Monge property
Algorithms
Min–max slope paths
IMRT field splitting
Shortest paths
algorithms
min-max slope paths
shortest paths
ISSN:0925-7721, 1879-081X
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Shrnutí:In this paper, we study an interesting geometric partition problem, called optimal field splitting, which arises in Intensity-Modulated Radiation Therapy (IMRT). In current clinical practice, a multi-leaf collimator (MLC) with a maximum leaf spread constraint is used to deliver the prescribed intensity maps (IMs). However, the maximum leaf spread of a 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.
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This work was done when X. Dou was with the Department of Electrical and Computer Engineering, The University of Iowa, Iowa City, IA, 52242.
ISSN:0925-7721
1879-081X
DOI:10.1016/j.comgeo.2012.11.001