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Impact of Using Linear Optimization Models in Dose Planning for HDR Brachytherapy
Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0003-2220-6125
Linköping University, Department of Mathematics, Optimization . Linköping University, The Institute of Technology.ORCID iD: 0000-0003-2094-7376
Linköping University, Department of Medical and Health Sciences, Radiation Physics. Linköping University, Faculty of Health Sciences.
2012 (English)In: Medical physics (Lancaster), ISSN 0094-2405, Vol. 39, no 2, 1021-1028 p.Article in journal (Refereed) Published
Abstract [en]

Purpose: Dose plans generated with optimization models hitherto used in HDR brachytherapy have shown a tendency to yield longer dwell times than manually optimized plans. Concern has been raised for the corresponding undesired hot spots and various methods to mitigate these have been developed. The hypotheses of this work are a) that one cause for the long dwell times is the use of objective functions comprising simple linear penalties and b) that alternative penalties, being piecewise linear, would lead to reduced length of individual dwell times.

Methods: The characteristics of the linear penalties and the piecewise linear penalties are analysed mathematically. Experimental comparisons between the two types of penalties are carried out retrospectively for a set of prostate cancer patients.

Results: While most dose-volume parameters do not differ significantly between the two types of penalties significant changes can be seen in the dwell times. On the average, total dwell times were reduced by 4.2%, with a reduction of maximum dwell times by 30%, using the alternative penalties.

Conclusion: The use of linear penalties in optimization models for HDR brachytherapy is one cause for undesired longer dwell times appearing in mathematically optimized plans. By introducing alternative penalties significant reduction in dwell times can be achieved for HDR brachytherapy dose plans. Although various constraints as to reduce the long dwell times have been developed our finding is of fundamental interest in showing the shape of the objective function to be one reason for their appearance.

Place, publisher, year, edition, pages
American Association of Physicists in Medicine , 2012. Vol. 39, no 2, 1021-1028 p.
Keyword [en]
Brachytherapy, Optimization, Treatment planning, Linear programming, Piecewise linear functions
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-67786DOI: 10.1118/1.3676179ISI: 000300215800048OAI: oai:DiVA.org:liu-67786DiVA: diva2:412836
Available from: 2011-04-26 Created: 2011-04-26 Last updated: 2013-11-05Bibliographically 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)78-91-7393-162-5 (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: 2013-08-30Bibliographically 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 (print) (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, ÅsaLarsson, TorbjörnCarlsson Tedgren, Åsa
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