zbMATH — the first resource for mathematics

An optimization framework for conformal radiation treatment planning. (English) Zbl 1241.90199
Summary: An optimization framework for three-dimensional conformal radiation therapy is presented. In conformal therapy, beams of radiation are applied to a patient from different directions, where the aperture through which the beam is delivered from each direction is chosen to match the shape of the tumor, as viewed from that direction. Wedge filters may be used to produce a gradient in beam intensity across the aperture. Given a set of equispaced beam angles, a mixed-integer linear program can be solved to determine the most effective angles to be used in a treatment plan, the weight (exposure time) to be used for each beam, and the type and orientation of wedges to be used. Practical solution techniques for this problem are described; they include strengthening of the formulation and solution of smaller approximate problems obtained by a reduced parametrization of the treatment region. In addition, techniques for controlling the dose-volume histogram implicitly for various parts of the treatment region using hot- and cold-spot control parameters are presented. Computational results are given that show the effectiveness of the proposed approach on practical data sets.

90C90 Applications of mathematical programming
92C50 Medical applications (general)
Full Text: DOI