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.
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© 2008 Springer Science+Business Media, LLC
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Fohlin, H., Kliemann, L., Srivastav, A. (2008). Randomized algorithms for mixed matching and covering in hypergraphs in 3D seed reconstruction in brachytherapy. In: Alves, C.J.S., Pardalos, P.M., Vicente, L.N. (eds) Optimization in Medicine. Springer Optimization and Its Applications, vol 12. Springer, New York, NY. https://doi.org/10.1007/978-0-387-73299-2_4
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DOI: https://doi.org/10.1007/978-0-387-73299-2_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-73298-5
Online ISBN: 978-0-387-73299-2
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