Special Issue Paper

OR Spectrum

, Volume 25, Issue 2, pp 223-249

First online:

Intensity-modulated radiotherapy – a large scale multi-criteria programming problem

  • Karl-Heinz KüferAffiliated withDepartment of Optimization, Fraunhofer Institut for Industrial Mathematics, Gottlieb-Daimler-Straße 49, 67663 Kaiserslautern, Germany (e-mail: {kuefer,scherrer,monz,alonso,trinkaus}@itwm.fhg.de)
  • , Alexander ScherrerAffiliated withDepartment of Optimization, Fraunhofer Institut for Industrial Mathematics, Gottlieb-Daimler-Straße 49, 67663 Kaiserslautern, Germany (e-mail: {kuefer,scherrer,monz,alonso,trinkaus}@itwm.fhg.de)
  • , Michael MonzAffiliated withDepartment of Optimization, Fraunhofer Institut for Industrial Mathematics, Gottlieb-Daimler-Straße 49, 67663 Kaiserslautern, Germany (e-mail: {kuefer,scherrer,monz,alonso,trinkaus}@itwm.fhg.de)
  • , Fernando AlonsoAffiliated withDepartment of Optimization, Fraunhofer Institut for Industrial Mathematics, Gottlieb-Daimler-Straße 49, 67663 Kaiserslautern, Germany (e-mail: {kuefer,scherrer,monz,alonso,trinkaus}@itwm.fhg.de)
  • , Hans TrinkausAffiliated withDepartment of Optimization, Fraunhofer Institut for Industrial Mathematics, Gottlieb-Daimler-Straße 49, 67663 Kaiserslautern, Germany (e-mail: {kuefer,scherrer,monz,alonso,trinkaus}@itwm.fhg.de)
  • , Thomas BortfeldAffiliated withDepartment of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, 30 Fruit Street, Boston, MA 02114, USA (e-mail: tbortfeld@partners.org)
  • , Christian ThiekeAffiliated withDepartment of Medical Physics, German Cancer Research Center, Im Neuenheimer Feld 280, 69120 Heidelberg, Germany (e-mail: c.thieke@dkfz.de)

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Abstract. Radiation therapy planning is often a tight rope walk between dangerous insufficient dose in the target volume and life threatening overdosing of organs at risk. Finding ideal balances between these inherently contradictory goals challenges dosimetrists and physicians in their daily practice. Todays inverse planning systems calculate treatment plans based on a single evaluation function that measures the quality of a radiation treatment plan. Unfortunately, such a one dimensional approach cannot satisfactorily map the different backgrounds of physicians and the patient dependent necessities. So, too often a time consuming iterative optimization process between evaluation of the dose distribution and redefinition of the evaluation function is needed. In this paper we propose a generic multi-criteria approach based on Pareto's solution concept. For each entity of interest – target volume or organ at risk – a structure dependent evaluation function is defined measuring deviations from ideal doses that are calculated from statistical functions. A reasonable bunch of clinically meaningful Pareto optimal solutions are stored in a data base, which can be interactively searched by physicians. The system guarantees dynamic planning as well as the discussion of tradeoffs between different entities. Mathematically, we model the inverse problem as a multi-criteria linear programming problem. Because of the large scale nature of the problem it is not possible to solve the problem in a 3D-setting without adaptive reduction by appropriate approximation schemes. Our approach is twofold: First, the discretization of the continuous problem results from an adaptive hierarchical clustering process which is used for a local refinement of constraints during the optimization procedure. Second, the set of Pareto optimal solutions is approximated by an adaptive grid of representatives that are found by a hybrid process of calculating extreme compromises and interpolation methods.

Key words:Multi-criteria optimization – Representative Pareto solutions – Adaptive triangulation – Clustering techniques – Radiotherapy