An iterative approach to plan combination in radiotherapy

Yair Censor, Shoulamit C. Shwartz

Research output: Contribution to journalArticlepeer-review


Radiation therapy concerns the delivery of a proper dose of radiation to a tumor volume without causing irreparable damage to surrounding healthy tissue and critical organs. The problem of plan combination in radiation therapy treatment planning (RTTP) proposed, formulated and studied here, addresses a situation when for a specific clinical case, a set of several treatment plans is proposed, but each one of them violates the prescribed dose in at least one significant region of the volume that has to be treated. We represent treatment plans as vectors in the Euclidean space, and define their equivalence, acceptability and realizability. A simple linear algebraic model for combining them is then used in order to derive, from the given set of approximate plans, a combined treatment plan, which will be both acceptable, and technically realizable. In the event that such a combined plan does not exist, the alternatives for relaxing the treatment requirements can be systematically considered.

Original languageEnglish
Pages (from-to)191-205
Number of pages15
JournalInternational Journal of Bio-Medical Computing
Issue number3
StatePublished - Sep 1989

Bibliographical note

Funding Information:
We are grateful to our colleagues Martin Altschuler, William Powlis and Morton Kligerman from the Department of Radiation Therapy, Hospital of the University of Pennsylvania, Philadelphia, PA, with whom some of the basic ideas on which this work is based were formulated and discussed in Censor et al. [14]. We greatly appreciate their continued collaboration and advice. Research supported in part by the National Institutes of Health Grant HL-28438 while visiting the Medical Image Processing Group (MIPG), Department of Radiology, and by the Department of Radiation Therapy, Hospital of the University of Pennsylvania, Philadelphia, PA.


  • Acceptability
  • Iterative algorithm
  • Linear programming
  • Plan combination
  • Radiation therapy
  • Realizability
  • Treatment planning

ASJC Scopus subject areas

  • Medicine (miscellaneous)


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