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Mathematical optimization in intensity modulated radiation therapy

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Abstract

The design of an intensity modulated radiotherapy treatment includes the selection of beam angles (geometry problem), the computation of an intensity map for each selected beam angle (intensity problem), and finding a sequence of configurations of a multileaf collimator to deliver the treatment (realization problem). Until the end of the last century research on radiotherapy treatment design has been published almost exclusively in the medical physics literature. However, since then, the attention of researchers in mathematical optimization has been drawn to the area and important progress has been made. In this paper we survey the use of optimization models, methods, and theories in intensity modulated radiotherapy treatment design.

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Authors and Affiliations

  1. Department of Engineering Science, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand

    Matthias Ehrgott & Lizhen Shao

  2. Department of Mathematics, Technical University of Kaiserslautern, Postfach 3049, 67653, Kaiserslautern, Germany

    Çiğdem Güler & Horst W. Hamacher

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  1. Matthias Ehrgott
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  2. Çiğdem Güler
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  3. Horst W. Hamacher
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  4. Lizhen Shao
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Correspondence to Matthias Ehrgott.

Additional information

This is an updated version of the paper that appeared in 4OR, 6(3), 199–262 (2008).

Support for H.W. Hamacher: The research has been partially supported by the Deutsche Forschungsgemeinschaft (DFG), Grant HA 1737/7 “Algorithmik großer und komplexer Netzwerke”, the Julius-von-Haast Award of New Zealand’s MORST, and by the Rhineland-Palatinate cluster of excellence “Dependable adaptive systems and mathematical modeling”.

Support for L. Shao: The research has been supported by The University of Auckland, Grant 3606875/9275.

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Ehrgott, M., Güler, Ç., Hamacher, H.W. et al. Mathematical optimization in intensity modulated radiation therapy. Ann Oper Res 175, 309–365 (2010). https://doi.org/10.1007/s10479-009-0659-4

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