- Title
- Minimizing beam-on time in cancer radiation treatment using multileaf collimators
- Creator
- Boland, Natashia; Hamacher, Horst W.; Lenzen, Frank
- Relation
- Networks Vol. 43, Issue 4, p. 226-240
- Publisher Link
- http://dx.doi.org/10.1002/net.20007
- Publisher
- Wiley Blackwell Publishing
- Resource Type
- journal article
- Date
- 2004
- Description
- In this article the modulation of intensity matrices arising in cancer radiation therapy using multileaf collimators (MLC) is investigated. It is shown that the problem is equivalent to decomposing a given integer matrix into a positive linear combination of (0, 1) matrices. These matrices, called shape matrices, must have the strict consecutive-1-property, together with another property derived from the technological restrictions of the MLC equipment. Various decompositions can be evaluated by their beam-on time (time during which radiation is applied to the patient) or the treatment time (beam-on time plus time for setups). We focus on the former, and develop a nonlinear mixed-integer programming formulation of the problem. This formulation can be decomposed to yield a column generation formulation: a linear program with a large number of variables that can be priced by solving a subproblem. We then develop a network model in which paths in the network correspond to feasible shape matrices. As a consequence, we deduce that the column generation subproblem can be solved as a shortest path problem. Furthermore, we are able to develop two alternative models of the problem as side-constrained network flow formulations, and so obtain our main theoretical result that the problem is solvable in polynomial time. Finally, a numerical comparison of our exact solutions with those of well-known heuristic methods shows that the beam-on time can be reduced by a considerable margin.
- Subject
- cancer radiation treatment; intensity modulation radiation treatment; IMRT; multileaf collimator; integer programming; network flow with side constraints
- Identifier
- http://hdl.handle.net/1959.13/939405
- Identifier
- uon:12798
- Identifier
- ISSN:0028-3045
- Language
- eng
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