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Minimax optimization for handling range and setup uncertainties in proton therapy
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.ORCID iD: 0000-0002-6252-7815
2011 (English)In: Medical physics (Lancaster), ISSN 0094-2405, Vol. 38, no 3, 1672-1684 p.Article in journal (Refereed) Published
Abstract [en]

Purpose: Intensity modulated proton therapy (IMPT) is sensitive to errors, mainly due to high stopping power dependency and steep beam dose gradients. Conventional margins are often insufficient to ensure robustness of treatment plans. In this article, a method is developed that takes the uncertainties into account during the plan optimization. Methods: Dose contributions for a number of range and setup errors are calculated and a minimax optimization is performed. The minimax optimization aims at minimizing the penalty of the worst case scenario. Any optimization function from conventional treatment planning can be utilized by the method. By considering only scenarios that are physically realizable, the unnecessary conservativeness of other robust optimization methods is avoided. Minimax optimization is related to stochastic programming by the more general minimax stochastic programming formulation, which enables accounting for uncertainties in the probability distributions of the errors. Results: The minimax optimization method is applied to a lung case, a paraspinal case with titanium implants, and a prostate case. It is compared to conventional methods that use margins, single field uniform dose (SFUD), and material override (MO) to handle the uncertainties. For the lung case, the minimax method and the SFUD with MO method yield robust target coverage. The minimax method yields better sparing of the lung than the other methods. For the paraspinal case, the minimax method yields more robust target coverage and better sparing of the spinal cord than the other methods. For the prostate case, the minimax method and the SFUD method yield robust target coverage and the minimax method yields better sparing of the rectum than the other methods. Conclusions: Minimax optimization provides robust target coverage without sacrificing the sparing of healthy tissues, even in the presence of low density lung tissue and high density titanium implants. Conventional methods using margins, SFUD, and MO do not utilize the full potential of IMPT and deliver unnecessarily high doses to healthy tissues.

Place, publisher, year, edition, pages
2011. Vol. 38, no 3, 1672-1684 p.
Keyword [en]
IMPT optimization, minimax optimization, robust planning, uncertainty
National Category
Radiology, Nuclear Medicine and Medical Imaging Computational Mathematics
URN: urn:nbn:se:kth:diva-31612DOI: 10.1118/1.3556559ISI: 000287879400057ScopusID: 2-s2.0-79952141736OAI: diva2:406106
Swedish Research Council
QC 20110324Available from: 2011-03-24 Created: 2011-03-21 Last updated: 2013-05-16Bibliographically approved
In thesis
1. Robust optimization of radiation therapy accounting for geometric uncertainty
Open this publication in new window or tab >>Robust optimization of radiation therapy accounting for geometric uncertainty
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Geometric errors may compromise the quality of radiation therapy treatments. Optimization methods that account for errors can reduce their effects.

The first paper of this thesis introduces minimax optimization to account for systematic range and setup errors in intensity-modulated proton therapy. The minimax method optimizes the worst case outcome of the errors within a given set. It is applied to three patient cases and shown to yield improved target coverage robustness and healthy structure sparing compared to conventional methods using margins, uniform beam doses, and density override. Information about the uncertainties enables the optimization to counterbalance the effects of errors.

In the second paper, random setup errors of uncertain distribution---in addition to the systematic range and setup errors---are considered in a framework that enables scaling between expected value and minimax optimization. Experiments on a phantom show that the best and mean case tradeoffs between target coverage and critical structure sparing are similar between the methods of the framework, but that the worst case tradeoff improves with conservativeness.

Minimax optimization only considers the worst case errors. When the planning criteria cannot be fulfilled for all errors, this may have an adverse effect on the plan quality. The third paper introduces a method for such cases that modifies the set of considered errors to maximize the probability of satisfying the planning criteria. For two cases treated with intensity-modulated photon and proton therapy, the method increased the number of satisfied criteria substantially. Grasping for a little less sometimes yields better plans.

In the fourth paper, the theory for multicriteria optimization is extended to incorporate minimax optimization. Minimax optimization is shown to better exploit spatial information than objective-wise worst case optimization, which has previously been used for robust multicriteria optimization.

The fifth and sixth papers introduce methods for improving treatment plans: one for deliverable Pareto surface navigation, which improves upon the Pareto set representations of previous methods; and one that minimizes healthy structure doses while constraining the doses of all structures not to deteriorate compared to a reference plan, thereby improving upon plans that have been reached with too weak planning goals.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. xvii, 39 p.
Trita-MAT. OS, ISSN 1401-2294 ; 13:06
Optimization, intensity-modulated proton therapy, uncertainty, robust planning, setup error, range error, intensity-modulated radiation therapy, multicriteria optimization
National Category
urn:nbn:se:kth:diva-122262 (URN)978-91-7501-771-6 (ISBN)
Public defence
2013-06-05, F3, Lindstedtsvägen 26, KTH, Stockholm, 10:00 (English)
Swedish Research Council, VR 2007-4794

QC 20130516

Available from: 2013-05-16 Created: 2013-05-15 Last updated: 2013-05-16Bibliographically approved

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