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A linear programming model for optimizing HDR brachytherapy dose distributions with respect to mean dose in the DVH-tail
Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.
Linköping University, Department of Medical and Health Sciences, Division of Radiological Sciences. Linköping University, Faculty of Health Sciences. Östergötlands Läns Landsting, Center for Surgery, Orthopaedics and Cancer Treatment, Department of Radiation Physics.
2013 (English)In: Medical physics (Lancaster), ISSN 0094-2405, Vol. 40, no 8Article in journal (Refereed) Published
Abstract [en]

Purpose: Recent research has shown that the optimization model hitherto used in high-dose-rate (HDR) brachytherapy corresponds weakly to the dosimetric indices used to evaluate the quality of a dose distribution. Although alternative models that explicitly include such dosimetric indices have been presented, the inclusion of the dosimetric indices explicitly yields intractable models. The purpose of this paper is to develop a model for optimizing dosimetric indices that is easier to solve than those proposed earlier. less thanbrgreater than less thanbrgreater thanMethods: In this paper, the authors present an alternative approach for optimizing dose distributions for HDR brachytherapy where dosimetric indices are taken into account through surrogates based on the conditional value-at-risk concept. This yields a linear optimization model that is easy to solve, and has the advantage that the constraints are easy to interpret and modify to obtain satisfactory dose distributions. less thanbrgreater than less thanbrgreater thanResults: The authors show by experimental comparisons, carried out retrospectively for a set of prostate cancer patients, that their proposed model corresponds well with constraining dosimetric indices. All modifications of the parameters in the authors model yield the expected result. The dose distributions generated are also comparable to those generated by the standard model with respect to the dosimetric indices that are used for evaluating quality. less thanbrgreater than less thanbrgreater thanConclusions: The authors new model is a viable surrogate to optimizing dosimetric indices and quickly and easily yields high quality dose distributions.

Place, publisher, year, edition, pages
American Association of Physicists in Medicine , 2013. Vol. 40, no 8
Keyword [en]
brachytherapy, optimization, treatment planning, dosimetric indices, conditional value-at-risk
National Category
Medical and Health Sciences
URN: urn:nbn:se:liu:diva-97239DOI: 10.1118/1.4812677ISI: 000322735900010OAI: diva2:645811

Funding Agencies|Swedish Cancer Society (Cancerfonden)|100512|

Available from: 2013-09-05 Created: 2013-09-05 Last updated: 2013-11-05
In thesis
1. Mathematical Optimization of HDR Brachytherapy
Open this publication in new window or tab >>Mathematical Optimization of HDR Brachytherapy
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

One out of eight deaths throughout the world is due to cancer. Developing new treatments and improving existing treatments is hence of major importance. In this thesis we have studied how mathematical optimization can be used to improve an existing treatment method: high-dose-rate (HDR) brachytherapy.

HDR brachytherapy is a radiation modality used to treat tumours of for example the cervix, prostate, breasts, and skin. In HDR brachytherapy catheters are implanted into or close to the tumour volume. A radioactive source is moved through the catheters, and by adjusting where the catheters are placed, called catheter positioning, and how the source is moved through the catheters, called the dwelling time pattern, the dose distribution can be controlled.

By constructing an individualized catheter positioning and dwelling time pattern, called dose plan, based on each patient's anatomy, it is possible to improve the treatment result. Mathematical optimization has during the last decade been used to aid in creating individualized dose plans. The dominating optimization model for this purpose is a linear penalty model. This model only considers the dwelling time pattern within already implanted catheters, and minimizes a weighted deviation from dose intervals prescribed by a physician.

In this thesis we show that the distribution of the basic variables in the linear penalty model implies that only dwelling time patterns that have certain characteristics can be optimal. These characteristics cause troublesome inhomogeneities in the plans, and although various measures for mitigating these are already available, it is of fundamental interest to understand their cause.

We have also shown that the relationship between the objective function of the linear penalty model and the measures commonly used for evaluating the quality of the dose distribution is weak. This implies that even if the model is solved to optimality there is no guarantee that the generated plan is optimal with respect to clinically relevant objectives, or even near-optimal. We have therefore constructed a new model for optimizing the dwelling time pattern. This model approximates the quality measures by the concept conditional value-at-risk, and we show that the relationship between our new model and the quality measures is strong. Furthermore, the new model generates dwelling time patterns that yield high-quality dose distributions.

Combining optimization of the dwelling time pattern with optimization of the catheter positioning yields a problem for which it is rarely possible to find a proven optimal solution within a reasonable time frame. We have therefore developed a variable neighbourhood search heuristic that outperforms a state-of-the-art optimization software (CPLEX). We have also developed a tailored branch-and-bound algorithm that is better at improving the dual bound than a general branch-and-bound algorithm. This is a step towards the development of a method that can find proven optimal solutions to the combined problem within a reasonable time frame.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2013. 63 p.
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1550
National Category
Natural Sciences
urn:nbn:se:liu:diva-99795 (URN)10.3384/diss.diva-99795 (DOI)978-91-7519-496-7 (print) (ISBN)
Public defence
2013-11-28, Nobel (BL32), B-huset, ingång 23, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Available from: 2013-11-05 Created: 2013-10-21 Last updated: 2013-11-05Bibliographically approved

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Holm, ÅsaLarsson, TorbjörnCarlsson Tedgren, Åsa
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