Mountain reduction, block matching, and applications in intensity-modulated radiation therapy
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Efficient algorithms for intensity map splitting problems in radiation therapy
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Shape rectangularization problems in intensity-modulated radiation therapy
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
An almost linear time algorithm for field splitting in radiation therapy
Computational Geometry: Theory and Applications
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In this paper, we study an interesting geometric partition problem, called optimal field splitting with feathering(OFSF), which arises in Intensity-Modulated Radiation Therapy(IMRT). In current clinical practice, a multi-leaf collimator (MLC) with a maximum field sizeis used to deliver the prescribed intensity maps (IMs). However, the maximum field size of an MLC may require to split a large intensity map into several overlapping sub-IMs each being delivered separately, which may result in sacrificed treatment quality. Few IM splitting techniques reported in the literature have addressed the issue of treatment delivery accuracy for large IMs. We develop a new algorithm for solving the OFSF problem while minimizing the total delivery error. Our basic idea is to formulate the OFSF problem as computing a d-link 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 d-link shortest path problem by examining only a small portion of the graph, yielding an optimal linear time algorithm for the OFSF problem.