Randomized algorithms for mixed matching and covering in hypergraphs in 3D seed reconstruction in brachytherapy

Helena Fohlin (), Lasse Kliemann () and Anand Srivastav ()
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Helena Fohlin: Linköping University Hospital
Lasse Kliemann: Christian-Albrechts-Universität zu Kiel
Anand Srivastav: Christian-Albrechts-Universität zu Kiel

A chapter in Optimization in Medicine, 2008, pp 71-102 from Springer

Abstract: Summary Brachytherapy is a radiotherapy method for cancer. In its low dose radiation (LDR) variant a number of radioactive implants, so-called seeds, are inserted into the affected organ through an operation. After the implantation, it is essential to determine the locations of the seeds in the organ. A common method is to take three X-ray photographs from different angles; the seeds show up on the X-ray photos as small white lines. In order to reconstruct the three-dimensional configuration from these X-ray photos, one has to determine which of these white lines belong to the same seed. We model the problem as a mixed packing and covering hypergraph optimization problem and present a randomized approximation algorithm based on linear programming. We analyse the worst-case performance of the algorithm by discrete probabilistic methods and present results for data of patients with prostate cancer from the university clinic of Schleswig-Holstein, Campus Kiel. These examples show an almost optimal performance of the algorithm which presently cannot be matched by the theoretical analysis.

Keywords: Prostate cancer; seed reconstruction; neuro-dynamic programming; combinatorial optimization; randomized algorithms; probabilistic methods; concentration inequalities (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/978-0-387-73299-2_4

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