Tarek Halabi et al 2006 Phys. Med. Biol. 51 3809 doi:10.1088/0031-9155/51/15/014
Tarek Halabi, David Craft and Thomas Bortfeld
Show affiliationsUnlike conventional optimization with dose–volume (DV) constraints, multi-criteria optimization (MCO) with DV objectives provides tradeoff information which we believe is necessary for choosing better treatment plans. We show that the MCO formulation with DV objectives is better suited to convex approximation than conventional formulations with DV constraints. We provide a relaxation of the integer programming formulation which reduces the computation time for a single plan from over 5 h to about 2 min, without significantly compromising the results. We also derive a heuristic to improve on the relaxed solutions, adding only a few additional minutes of computation time. We apply these techniques to a skull based tumour case and a paraspinal tumour case. Based on a careful examination of the driving terms in the relaxed formulation and the heuristic, we argue that our techniques should apply more generally for DV objectives in multi-objective IMRT treatment planning.
Issue 15 (7 August 2006)
Received 25 February 2006, in final form 25 May 2006
Published 20 July 2006
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Birol Ozturk et al 2007 Nanotechnology 18 365302
David Craft et al 2005 Phys. Med. Biol. 50 5857
Alex D Charpentier et al 2009 Environ. Res. Lett. 4 014005
Ilaria Cacciari et al 2007 J. Phys. A: Math. Theor. 40 12439
C. Abia 2008 The Astronomical Journal 136 250
D R Grigore 2000 J. Phys. A: Math. Gen. 33 8443
S I Kuchanov and M A Aliev 1997 J. Phys. A: Math. Gen. 30 8479
Jochen M Schneider et al 2005 J. Phys.: Condens. Matter 17 6047