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A Tailored Branch-and-Bound Method for Optimizing the Dwelling Time Pattern and Catheter Positioning in HDR Brachytherapy
Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.ORCID iD: 0000-0003-2220-6125
2013 (English)Report (Other academic)
Abstract [en]

High dose-rate (HDR) brachytherapy is one type of treatment for prostate cancer, in which a radioactive source is moved through catheters implanted into the prostate. For each patient, a unique treatment plan is constructed. This plan determines for example the catheter positioning and the dwelling time pattern, that is, where and for how long the source should stop.

Mathematical optimization methods are frequently used to find high-quality dwelling time patterns. However, choosing the catheter positioning is usually done without any aid of mathematical optimization methods. Researchers have recently suggested some optimization models for catheter positioning, and also heuristics for solving them. However, there are no available methods for finding the optimal solution of these models within a clinically acceptable time frame.

In this paper we present the foundation for a branch-and-bound method that has been tailored to the catheter positioning problem. Tests show that this tailored branch-and-bound method has some promising features, for example that the dual bound is improved faster than when using a standard branch-and-bound method. But the tests also show that further research is required to develop it into a method that can find the optimal solution fast enough.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2013. , 10 p.
LiTH-MAT-R, ISSN 0348-2960 ; 2013:12
Keyword [en]
Branch-and-Bound, Branching rules, Brachytherapy, Dose planning, Catheter positioning
National Category
Other Mathematics
URN: urn:nbn:se:liu:diva-99784ISRN: LiTH-MAT-R– 2013/12–SEOAI: diva2:658187
Available from: 2013-10-21 Created: 2013-10-21 Last updated: 2013-11-06Bibliographically approved
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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