Decomposition of matrices and static multileaf collimators: a survey

Management Science

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter

Published

Standard

Decomposition of matrices and static multileaf collimators: a survey. / Ehrgott, Matthias; Hamacher, Horst W.; Nußbaum, Marc.
Optimization in medicine. ed. / Carlos J. S. Alves; Panos M. Pardalos; Luis Nunes Vicente. New York: Springer, 2008. p. 22-46 (Springer Optimization and Its Applications; Vol. 12).

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter

Harvard

Ehrgott, M, Hamacher, HW & Nußbaum, M 2008, Decomposition of matrices and static multileaf collimators: a survey. in CJS Alves, PM Pardalos & LN Vicente (eds), Optimization in medicine. Springer Optimization and Its Applications, vol. 12, Springer, New York, pp. 22-46.

APA

Ehrgott, M., Hamacher, H. W., & Nußbaum, M. (2008). Decomposition of matrices and static multileaf collimators: a survey. In C. J. S. Alves, P. M. Pardalos, & L. N. Vicente (Eds.), Optimization in medicine (pp. 22-46). (Springer Optimization and Its Applications; Vol. 12). Springer.

Vancouver

Ehrgott M, Hamacher HW, Nußbaum M. Decomposition of matrices and static multileaf collimators: a survey. In Alves CJS, Pardalos PM, Vicente LN, editors, Optimization in medicine. New York: Springer. 2008. p. 22-46. (Springer Optimization and Its Applications).

Author

Ehrgott, Matthias ; Hamacher, Horst W. ; Nußbaum, Marc. / Decomposition of matrices and static multileaf collimators: a survey. Optimization in medicine. editor / Carlos J. S. Alves ; Panos M. Pardalos ; Luis Nunes Vicente. New York : Springer, 2008. pp. 22-46 (Springer Optimization and Its Applications).

Bibtex

@inbook{cb1333d6aa8345b38a18d87c3c3ac7fe,

title = "Decomposition of matrices and static multileaf collimators: a survey",

abstract = "Multileaf Collimators (MLC) consist of (currently 20-100) pairs of movable metal leaves which are used to block radiation in Intensity Modulated Radiation Therapy (IMRT). The leaves modulate a uniform source of radiation to achieve given intensity profiles. The modulation process is modeled by the decomposition of a given non-negative integer matrix into a non-negative linear combination of matrices with the (strict) consecutive ones property.In this paper we review some results and algorithms which can be used to minimize the time a patient is exposed to radiation (corresponding to the sum of coefficients in the linear combination), the set-up time (corresponding to the number of matrices used in the linear combination), and other objectives which contribute to an improved radiation therapy.",

author = "Matthias Ehrgott and Hamacher, {Horst W.} and Marc Nu{\ss}baum",

year = "2008",

language = "English",

isbn = "978-0-387-73298-5",

series = "Springer Optimization and Its Applications",

publisher = "Springer",

pages = "22--46",

editor = "Alves, {Carlos J. S.} and Pardalos, {Panos M.} and Vicente, {Luis Nunes}",

booktitle = "Optimization in medicine",

}

RIS

TY - CHAP

T1 - Decomposition of matrices and static multileaf collimators: a survey

AU - Ehrgott, Matthias

AU - Hamacher, Horst W.

AU - Nußbaum, Marc

PY - 2008

Y1 - 2008

N2 - Multileaf Collimators (MLC) consist of (currently 20-100) pairs of movable metal leaves which are used to block radiation in Intensity Modulated Radiation Therapy (IMRT). The leaves modulate a uniform source of radiation to achieve given intensity profiles. The modulation process is modeled by the decomposition of a given non-negative integer matrix into a non-negative linear combination of matrices with the (strict) consecutive ones property.In this paper we review some results and algorithms which can be used to minimize the time a patient is exposed to radiation (corresponding to the sum of coefficients in the linear combination), the set-up time (corresponding to the number of matrices used in the linear combination), and other objectives which contribute to an improved radiation therapy.

AB - Multileaf Collimators (MLC) consist of (currently 20-100) pairs of movable metal leaves which are used to block radiation in Intensity Modulated Radiation Therapy (IMRT). The leaves modulate a uniform source of radiation to achieve given intensity profiles. The modulation process is modeled by the decomposition of a given non-negative integer matrix into a non-negative linear combination of matrices with the (strict) consecutive ones property.In this paper we review some results and algorithms which can be used to minimize the time a patient is exposed to radiation (corresponding to the sum of coefficients in the linear combination), the set-up time (corresponding to the number of matrices used in the linear combination), and other objectives which contribute to an improved radiation therapy.

M3 - Chapter

SN - 978-0-387-73298-5

T3 - Springer Optimization and Its Applications

SP - 22

EP - 46

BT - Optimization in medicine

A2 - Alves, Carlos J. S.

A2 - Pardalos, Panos M.

A2 - Vicente, Luis Nunes

PB - Springer

CY - New York

ER -

Research