Mathematical Aspects of Radiation Therapy Treatment Planning: Continuous Inversion Versus Full Discretization and Optimization Versus Feasibility

Yair Censor

doi:10.1007/978-1-4612-1550-9_6

Mathematical Aspects of Radiation Therapy Treatment Planning: Continuous Inversion Versus Full Discretization and Optimization Versus Feasibility

Yair Censor

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

A mathematical formulation of the radiation therapy problem consists of a pair of forward and inverse problems. The inverse problem is to determine external radiation beams, along with their locations, profiles, and intensities, that will provide a given dose distribution within the irradiated object. We discuss the inverse problem in its fully discretized formulation.

Original language	English
Title of host publication	Computational Radiology and Imaging
Subtitle of host publication	Therapy and Diagnostics
Editors	Christoph Börgers, Frank Natterer
Place of Publication	New York, NY
Publisher	Springer New York LLC
Pages	101-112
Number of pages	12
ISBN (Electronic)	978-1-4612-1550-9
ISBN (Print)	978-1-4612-7189-5
DOIs	https://doi.org/10.1007/978-1-4612-1550-9_6
State	Published - 1999

Publication series

Name	The IMA Volumes in Mathematics and its Applications
Publisher	Springer New York LLC
Volume	110
ISSN (Print)	0940-6573
ISSN (Electronic)	2198-3224

Access to Document

10.1007/978-1-4612-1550-9_6

Cite this

Censor, Y. (1999). Mathematical Aspects of Radiation Therapy Treatment Planning: Continuous Inversion Versus Full Discretization and Optimization Versus Feasibility. In C. Börgers, & F. Natterer (Eds.), Computational Radiology and Imaging: Therapy and Diagnostics (pp. 101-112). (The IMA Volumes in Mathematics and its Applications; Vol. 110). Springer New York LLC. https://doi.org/10.1007/978-1-4612-1550-9_6

Censor, Yair. / Mathematical Aspects of Radiation Therapy Treatment Planning : Continuous Inversion Versus Full Discretization and Optimization Versus Feasibility. Computational Radiology and Imaging: Therapy and Diagnostics. editor / Christoph Börgers ; Frank Natterer. New York, NY : Springer New York LLC, 1999. pp. 101-112 (The IMA Volumes in Mathematics and its Applications).

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title = "Mathematical Aspects of Radiation Therapy Treatment Planning: Continuous Inversion Versus Full Discretization and Optimization Versus Feasibility",

abstract = "A mathematical formulation of the radiation therapy problem consists of a pair of forward and inverse problems. The inverse problem is to determine external radiation beams, along with their locations, profiles, and intensities, that will provide a given dose distribution within the irradiated object. We discuss the inverse problem in its fully discretized formulation.",

author = "Yair Censor",

year = "1999",

doi = "10.1007/978-1-4612-1550-9_6",

language = "English",

isbn = "978-1-4612-7189-5",

series = "The IMA Volumes in Mathematics and its Applications",

publisher = "Springer New York LLC",

pages = "101--112",

editor = "Christoph B{\"o}rgers and Frank Natterer",

booktitle = "Computational Radiology and Imaging",

}

Censor, Y 1999, Mathematical Aspects of Radiation Therapy Treatment Planning: Continuous Inversion Versus Full Discretization and Optimization Versus Feasibility. in C Börgers & F Natterer (eds), Computational Radiology and Imaging: Therapy and Diagnostics. The IMA Volumes in Mathematics and its Applications, vol. 110, Springer New York LLC, New York, NY, pp. 101-112. https://doi.org/10.1007/978-1-4612-1550-9_6

Mathematical Aspects of Radiation Therapy Treatment Planning: Continuous Inversion Versus Full Discretization and Optimization Versus Feasibility. / Censor, Yair.
Computational Radiology and Imaging: Therapy and Diagnostics. ed. / Christoph Börgers; Frank Natterer. New York, NY: Springer New York LLC, 1999. p. 101-112 (The IMA Volumes in Mathematics and its Applications; Vol. 110).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

TY - CHAP

T1 - Mathematical Aspects of Radiation Therapy Treatment Planning

T2 - Continuous Inversion Versus Full Discretization and Optimization Versus Feasibility

AU - Censor, Yair

PY - 1999

Y1 - 1999

N2 - A mathematical formulation of the radiation therapy problem consists of a pair of forward and inverse problems. The inverse problem is to determine external radiation beams, along with their locations, profiles, and intensities, that will provide a given dose distribution within the irradiated object. We discuss the inverse problem in its fully discretized formulation.

AB - A mathematical formulation of the radiation therapy problem consists of a pair of forward and inverse problems. The inverse problem is to determine external radiation beams, along with their locations, profiles, and intensities, that will provide a given dose distribution within the irradiated object. We discuss the inverse problem in its fully discretized formulation.

U2 - 10.1007/978-1-4612-1550-9_6

DO - 10.1007/978-1-4612-1550-9_6

M3 - Chapter

SN - 978-1-4612-7189-5

T3 - The IMA Volumes in Mathematics and its Applications

SP - 101

EP - 112

BT - Computational Radiology and Imaging

A2 - Börgers, Christoph

A2 - Natterer, Frank

PB - Springer New York LLC

CY - New York, NY

ER -

Censor Y. Mathematical Aspects of Radiation Therapy Treatment Planning: Continuous Inversion Versus Full Discretization and Optimization Versus Feasibility. In Börgers C, Natterer F, editors, Computational Radiology and Imaging: Therapy and Diagnostics. New York, NY: Springer New York LLC. 1999. p. 101-112. (The IMA Volumes in Mathematics and its Applications). doi: 10.1007/978-1-4612-1550-9_6

Mathematical Aspects of Radiation Therapy Treatment Planning: Continuous Inversion Versus Full Discretization and Optimization Versus Feasibility

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