X-ray field compensation with multileaf collimators

Bortfeld, Thomas; Kahler, Darren; Waldron, Timothy J.; Boyer, Arthur L.

doi:10.1016/0360-3016(94)90200-3

Cited by 451 publications

(321 citation statements)

References 19 publications

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“…The most prominent reference in which the insight of Lemma 2.1 is used is Bortfeld et al (1994) which introduces the sweep algorithm. They consider each row independently and then check from left to right, if a position of a left or right leaf needs to be changed in order to realize given intensities a mn .…”

Section: Unconstrained Dt Problemmentioning

confidence: 99%

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Decomposition of matrices and static multileaf collimators: a survey

Ehrgott

Hamacher

Nußbaum

Optimization in Medicine

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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.

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Section: Unconstrained Dt Problemmentioning

confidence: 99%

“…It is important to notice that the identification of the flow augmenting path and the determination of the flow value which is sent along this path can be interpreted as the two phases of the step-and-shoot process in the sweep algorithm of Bortfeld et al (1994) thus establishing its optimality.…”

Section: Unconstrained Dt Problemmentioning

confidence: 99%

Decomposition of matrices and static multileaf collimators: a survey

Ehrgott

Hamacher

Nußbaum

Optimization in Medicine

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“…After discretizing the irradiated area into bixels, an intensity function can be considered as an m × n matrix A with nonnegative integer entries, where entry a i,j indicates the desired intensity at bixel (i, j). From works of Galvin et al and Bortfeld et al (7,8), several algorithms have been developed. The BortfeldBoyer algorithm provided the smallest possible total number of monitor unit (TNMU) but a large number of segment (NS).…”

Section: Introductionmentioning

confidence: 99%

A Leaf Sequencing Algorithm for Multileaf Collimator in Intensity Modulated Radiotherapy

Jia

Lin

Chow

2016

Rep Radiother Oncol

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“…Intensity modulated radiation therapy (IMRT) represents a rather sophisticated approach in which each radiation treatment (out of a total of perhaps 10-45 such treatments for a patient) involves the application of intensitymodulated beams of radiation from 5-9 different angles (relative to the patient) [4,6,8,35,44,45,46,51]. The 10X10 centimeter beam cross-section consists of a grid of 100 or more small beamlets of radiation.…”

Section: Imrtmentioning

confidence: 99%

Radiation Treatment Planning: Mixed Integer Programming Formulations and Approaches

Ferris

Meyer

D’Souza

International Series in Operations Research &Amp; Management Science

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Radiation therapy is extensively used to treat a wide range of cancers. Due to the increasing complexities of delivery mechanisms, and the improved imaging devices that allow more accurate determination of cancer location, determination of high quality treatment plans via trial-and-error methods is impractical and computer optimization approaches to planning are becoming more critical and more difficult.We outline three examples of the types of treatment planning problem that can arise in practice and strive to understand the commonalities and differences in these problems. We highlight optimization approaches to the problems, and particularly consider approaches based on mixed integer programming. Details of the mathematical formulations and algorithmic approaches are developed and pointers are given to supporting literature that shows the efficacy of the approaches in practical situations.

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X-ray field compensation with multileaf collimators

Cited by 451 publications

References 19 publications

Decomposition of matrices and static multileaf collimators: a survey

Decomposition of matrices and static multileaf collimators: a survey

A Leaf Sequencing Algorithm for Multileaf Collimator in Intensity Modulated Radiotherapy

Radiation Treatment Planning: Mixed Integer Programming Formulations and Approaches

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