Abstract
The 3-D static leaf sequencing (SLS) problem arises in radiation therapy for cancer treatments, aiming to deliver a prescribed radiation dose to a target tumor accurately and efficiently. The treatment time and machine delivery error are two crucial factors of a solution (i.e., a treatment plan) for the SLS problem. In this paper, we prove that the 3-D SLS problem is NP-hard, and present the first ever algorithm for the 3-D SLS problem that can determine a tradeoff between the treatment time and machine delivery error (also called the “tongue-and-groove” error in medical literature). Our new 3-D SLS algorithm with error control gives the users (e.g., physicians) the option of specifying a machine delivery error bound, and subject to the given error bound, the algorithm computes a treatment plan with the minimum treatment time. We formulate the SLS problem with error control as computing a k-weight shortest path in a directed graph and build the graph by computing g-matchings and minimum cost flows. Further, we extend our 3-D SLS algorithm to the popular radiotherapy machine models with different constraints. In our extensions, we model the SLS problems for some of the radiotherapy systems as computing a minimum g-path cover of a directed acyclic graph. We implemented our new 3-D SLS algorithm suite and conducted an extensive comparison study with commercial planning systems and well-known algorithms in medical literature. Some of our experimental results based on real medical data are presented.
Due to mistakes during data conversion, this paper was originally published in LNCS 3341 (ISAAC 2004) with several special characters missing in text and figures.
This research was supported in part by the National Science Foundation under Grant CCR-9988468.
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Chen, D.Z., Hu, X.S., Luan, S., Naqvi, S.A., Wang, C., Yu, C.X. (2005). Generalized Geometric Approaches for Leaf Sequencing Problems in Radiation Therapy,. In: Deng, X., Du, DZ. (eds) Algorithms and Computation. ISAAC 2005. Lecture Notes in Computer Science, vol 3827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11602613_116
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DOI: https://doi.org/10.1007/11602613_116
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