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Heuristics for Integrated Optimization of Catheter Positioning and Dwell Time Distribution in Prostate HDR Brachytherapy
Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0003-2220-6125
Linköping University, Department of Medical and Health Sciences, Division of Radiological Sciences. Linköping University, Faculty of Medicine and Health Sciences. Region Östergötland, Center for Surgery, Orthopaedics and Cancer Treatment, Department of Radiation Physics.
Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.ORCID iD: 0000-0003-2094-7376
2016 (English)In: Annals of Operations Research, ISSN 0254-5330, E-ISSN 1572-9338, Vol. 236, no 2, 319-339 p.Article in journal (Refereed) Published
Abstract [en]

High dose-rate (HDR) brachytherapy is a kind of radiotherapy used to treat, among others, prostate cancer. When applied to prostate cancer a radioactive source is moved through catheters implanted into the prostate. For each patient a treatment plan is constructed that decide for example catheter placement and dwell time distribution, that is where to stop the radioactive source and for how long.

Mathematical optimization methods has been used to find quality plans with respect to dwell time distribution, however few optimization approaches regarding catheter placement have been studied. In this article we present an integrated optimization model that optimize catheter placement and dwell time distribution simultaneously. Our results show that integrating the two decisions yields greatly improved plans, from 15% to 94% improvement.

Since the presented model is computationally demanding to solve we also present three heuristics: tabu search, variable neighbourhood search and genetic algorithm. Of these variable neighbourhood search is clearly the best, outperforming a state-of-the-art optimization software (CPLEX) and the two other heuristics.

Place, publisher, year, edition, pages
Springer, 2016. Vol. 236, no 2, 319-339 p.
Keyword [en]
Brachytherapy, Dose planning, Catheter positioning, Mixed integer programming, Metaheuristics
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-67788DOI: 10.1007/s10479-013-1448-7ISI: 000368946400003OAI: oai:DiVA.org:liu-67788DiVA: diva2:412838
Available from: 2011-04-26 Created: 2011-04-26 Last updated: 2017-12-11Bibliographically approved
In thesis
1. Dose Plan Optimization in HDR Brachytherapy using Penalties: Properties and Extensions
Open this publication in new window or tab >>Dose Plan Optimization in HDR Brachytherapy using Penalties: Properties and Extensions
2011 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

High dose-rate (HDR) brachytherapy is a specific type of radiotherapy used to treat tumours of for example the cervix, prostate, and breasts. In HDR brachytherapy applicators are implanted into or close to the tumour volume. A radioactive source is moved through these applicators and stops at certain positions, known as dwell points. For each patient an anatomy-based dose plan is created that decides for example where to place the applicators, which dwell points to use, and for how long. The aim when creating a dose plan is to deliver an as high dose as possible to the tumour while simultaneously keeping the dose to the surrounding healthy organs as low as possible.

In order to improve the quality of dose plans mathematical optimization methods are today used in clinical practice. Usually one solves a linear penalty model that minimizes a weighted deviation from dose intervals provided by a physician. In this thesis we study certain properties and alterations of this model.

One interesting property of the model that we study is the distribution of the basic variables. We show that due to the distribution of these variables only a limited number of dwell positions can be used. Since relatively few dwell positions are used some of the corresponding dwell times have to be long in order for the desired overall dose level to be reached. These long dwell times have been observed in clinical practice and are considered to be a problem.

Another property that we study is the correlation between the objective value of the linear penalty model and dose-volume parameters used for evaluation of dose plans. We show that the correlation is weak, which implies that optimizing the linear penalty model does not give a solution to the correct problem.

Some alternative models are also considered. One that includes into the optimization the decision of where to place the applicators, when HDR brachytherapy is applied for prostate cancer, and one that reduces the long dwell times by using piecewise linear penalties. The solutions to both models show significant improvements.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2011. 46 p.
Series
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1486
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-67790 (URN)9789173931625 (ISBN)
Presentation
2011-05-26, C3, C-huset, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2011-04-26 Created: 2011-04-26 Last updated: 2017-12-12Bibliographically approved
2. 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.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1550
National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-99795 (URN)10.3384/diss.diva-99795 (DOI)978-91-7519-496-7 (ISBN)
Public defence
2013-11-28, Nobel (BL32), B-huset, ingång 23, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2013-11-05 Created: 2013-10-21 Last updated: 2013-11-05Bibliographically approved

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Holm, ÅsaCarlsson Tedgren, ÅsaLarsson, Torbjörn

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