An iterative approach to plan combination in radiotherapy

Yair Censor; Shoulamit C. Shwartz

doi:10.1016/0020-7101(89)90030-5

An iterative approach to plan combination in radiotherapy

Yair Censor, Shoulamit C. Shwartz

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	191-205
Number of pages	15
Journal	International Journal of Bio-Medical Computing
Volume	24
Issue number	3
DOIs	https://doi.org/10.1016/0020-7101(89)90030-5
State	Published - 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.

Keywords

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

ASJC Scopus subject areas

Medicine (miscellaneous)

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10.1016/0020-7101(89)90030-5

Cite this

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title = "An iterative approach to plan combination in radiotherapy",

abstract = "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.",

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author = "Yair Censor and Shwartz, {Shoulamit C.}",

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N2 - 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.

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An iterative approach to plan combination in radiotherapy

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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