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

In: Optimization in Medicine

Author

Listed:
  • Helena Fohlin

    (Linköping University Hospital)

  • Lasse Kliemann

    (Christian-Albrechts-Universität zu Kiel)

  • Anand Srivastav

    (Christian-Albrechts-Universität zu Kiel)

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.

Suggested Citation

  • Helena Fohlin & Lasse Kliemann & Anand Srivastav, 2008. "Randomized algorithms for mixed matching and covering in hypergraphs in 3D seed reconstruction in brachytherapy," Springer Optimization and Its Applications, in: Carlos J. S. Alves & Panos M. Pardalos & Luis Nunes Vicente (ed.), Optimization in Medicine, pages 71-102, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-73299-2_4
    DOI: 10.1007/978-0-387-73299-2_4
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