A unified mixed-integer programming model for simultaneous fluence weight and aperture optimization in VMAT, Tomotherapy, and Cyberknife

Kerem Akartunali, Vicky Mak-Hau, Thu Tran

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

In this paper, we propose and study a unified mixed-integer programming model that simultaneously optimizes fluence weights and multi-leaf collimator (MLC) apertures in the treatment planning optimization of VMAT, Tomotherapy, and CyberKnife. The contribution of our model is threefold: i. Our model optimizes the fluence and MLC apertures simultaneously for a given set of control points. ii. Our model can incorporate all volume limits or dose upper bounds for organs at risk (OAR) and dose lower bound limits for planning target volumes (PTV) as hard constraints, but it can also relax either of these constraint sets in a Lagrangian fashion and keep the other set as hard constraints. iii. For faster solutions, we propose several heuristic methods based on the MIP model, as well as a meta-heuristic approach. The meta-heuristic is very efficient in practice, being able to generate dose- and machinery-feasible solutions for problem instances of clinical scale, e.g., obtaining feasible treatment plans to cases with 180 control points, 6,750 sample voxels and 18,000 beamlets in 470 seconds, or cases with 72 control points, 8,000 sample voxels and 28,800 beamlets in 352 seconds. With discretization and down-sampling of voxels, our method is capable of tackling a treatment field of 8000cm3∼64000cm3, depending on the ratio of critical structure versus unspecified tissues.
LanguageEnglish
Pages134-150
Number of pages17
JournalComputers & Operations Research
Volume56
Early online date22 Nov 2014
DOIs
Publication statusPublished - Apr 2015

Fingerprint

Mixed Integer Programming
Integer programming
Programming Model
Control Points
Voxel
Dose
Optimization
Metaheuristics
Leaves
Optimise
Planning
Heuristic Method
Threefolds
Model
Heuristic methods
Discretization
Machinery
Lower bound
Upper bound
Target

Keywords

  • multi-leaf collimator (MLC) apertures
  • mixed-integer programming
  • Tomotherapy
  • CyberKnife
  • heuristics
  • metaheuristics
  • OR in medicine

Cite this

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title = "A unified mixed-integer programming model for simultaneous fluence weight and aperture optimization in VMAT, Tomotherapy, and Cyberknife",
abstract = "In this paper, we propose and study a unified mixed-integer programming model that simultaneously optimizes fluence weights and multi-leaf collimator (MLC) apertures in the treatment planning optimization of VMAT, Tomotherapy, and CyberKnife. The contribution of our model is threefold: i. Our model optimizes the fluence and MLC apertures simultaneously for a given set of control points. ii. Our model can incorporate all volume limits or dose upper bounds for organs at risk (OAR) and dose lower bound limits for planning target volumes (PTV) as hard constraints, but it can also relax either of these constraint sets in a Lagrangian fashion and keep the other set as hard constraints. iii. For faster solutions, we propose several heuristic methods based on the MIP model, as well as a meta-heuristic approach. The meta-heuristic is very efficient in practice, being able to generate dose- and machinery-feasible solutions for problem instances of clinical scale, e.g., obtaining feasible treatment plans to cases with 180 control points, 6,750 sample voxels and 18,000 beamlets in 470 seconds, or cases with 72 control points, 8,000 sample voxels and 28,800 beamlets in 352 seconds. With discretization and down-sampling of voxels, our method is capable of tackling a treatment field of 8000cm3∼64000cm3, depending on the ratio of critical structure versus unspecified tissues.",
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AU - Akartunali, Kerem

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AU - Tran, Thu

N1 - NOTICE: this is the author’s version of a work that was accepted for publication in Computers & Operations Research. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computers & Operations Research, [VOL#, ISSUE#, (22/11/2014)] DOI:10.1016/j.cor.2014.11.009

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N2 - In this paper, we propose and study a unified mixed-integer programming model that simultaneously optimizes fluence weights and multi-leaf collimator (MLC) apertures in the treatment planning optimization of VMAT, Tomotherapy, and CyberKnife. The contribution of our model is threefold: i. Our model optimizes the fluence and MLC apertures simultaneously for a given set of control points. ii. Our model can incorporate all volume limits or dose upper bounds for organs at risk (OAR) and dose lower bound limits for planning target volumes (PTV) as hard constraints, but it can also relax either of these constraint sets in a Lagrangian fashion and keep the other set as hard constraints. iii. For faster solutions, we propose several heuristic methods based on the MIP model, as well as a meta-heuristic approach. The meta-heuristic is very efficient in practice, being able to generate dose- and machinery-feasible solutions for problem instances of clinical scale, e.g., obtaining feasible treatment plans to cases with 180 control points, 6,750 sample voxels and 18,000 beamlets in 470 seconds, or cases with 72 control points, 8,000 sample voxels and 28,800 beamlets in 352 seconds. With discretization and down-sampling of voxels, our method is capable of tackling a treatment field of 8000cm3∼64000cm3, depending on the ratio of critical structure versus unspecified tissues.

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