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Approximation and Segment Count Reduction in Intensity Modulated Radiation Therapy

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2 Author(s)
Gunawardena, A.D. ; Dept. of Math. & Comput. Sci., Wisconsin Univ., Whitewater, WI ; Meyer, R.R.

For a given mtimesn nonnegative real matrix A, a binary segmentation with 1-norm relative error e is a set of pairs (alpha,S)={(alpha1, S1), (alpha2, S2), ..., (alphak, Sk)}, where each alphai is a positive number and Si is an mtimesn binary matrix, and e=|A-Sigmai k=alphaiSi |1/|A|1 where |A|1 is the 1-norm of a vector which consists of exactly all the entries of the matrix A. Given A and positive scalars gamma, delta, we consider the optimization problem of finding a binary segmentation alphaS that minimizes z=Sigmai k=alphai+gammak+deltae subject to certain constraints on Si. This problem provides a major challenge in preparing a clinically acceptable treatment plan for intensity modulated radiation therapy (IMRT) and is known to be NP-hard. In this paper, we present an effective heuristic algorithm for the above problem with an additional constraint klesK, where K is a given positive integer. Reducing k subject to achieving an acceptable value of e is very desirable in both IMRT and intensity modulated arc therapy (IMAT). Our algorithm can be used as a valuable tool to find a clinically deliverable solution with a tradeoff between these two competing metrics

Published in:

Industrial and Information Systems, First International Conference on

Date of Conference:

8-11 Aug. 2006