From analytic inversion to contemporary IMRT optimization: Radiation therapy planning revisited from a mathematical perspective

Yair Censor, Jan Unkelbach

Research output: Contribution to journalReview articlepeer-review


In this paper we look at the development of radiation therapy treatment planning from a mathematical point of view. Historically, planning for Intensity-Modulated Radiation Therapy (IMRT) has been considered as an inverse problem. We discuss first the two fundamental approaches that have been investigated to solve this inverse problem: Continuous analytic inversion techniques on one hand, and fully-discretized algebraic methods on the other hand. In the second part of the paper, we review another fundamental question which has been subject to debate from the beginning of IMRT until the present day: The rotation therapy approach versus fixed angle IMRT. This builds a bridge from historic work on IMRT planning to contemporary research in the context of Intensity-Modulated Arc Therapy (IMAT).

Original languageEnglish
Pages (from-to)109-118
Number of pages10
JournalPhysica Medica
Issue number2
StatePublished - Apr 2012

Bibliographical note

Funding Information:
We thank our colleagues Martin Altschuler, Thomas Bortfeld, Tommy Elfving, James Galvin, Gabor Herman, Uwe Oelfke, William Powlis, Reinhard Schulte, Ying Xiao, Lei Xing and members of their research groups with whom we worked over the years and from whom we learned so much about radiation therapy treatment planning and other inverse problems. We are grateful to the anonymous referees whose insightful comments on earlier versions helped us to improve this paper and to the Editor Fridtjof Nüsslin for his unusual encouragement throughout the evaluation and revisions of the paper. The work of Y.C. on this paper was partially supported by a United States-Israel Binational Science Foundation (BSF) Grant number 200912 and by Award Number R01HL070472 from the National Heart, Lung, And Blood Institute.


  • Algebraic inverse planning
  • IMRT
  • Inverse problem
  • Radiation therapy treatment planning

ASJC Scopus subject areas

  • Biophysics
  • Radiology Nuclear Medicine and imaging
  • Physics and Astronomy (all)


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