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Study of the Relationship Between Dosimetric Indices and Linear Penalties in Dose Distribution Optimization for HDR Prostate Brachytherapy
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)Manuscript (preprint) (Other academic)
Abstract [en]

Purpose: Most clinical software for optimizing dwelling time patterns is based on a linear penalty model. The quality of a dose distribution generated by the dwelling time pattern is, however, evaluated through a number of dosimetric indices. The purpose of this article is to investigate the relationship between the linear penalty model and the dosimetric indices.

Method and Materials: Data sets from three patients, previously treated for prostate cancer with HDR brachytherapy as a boost to external beam therapy, were used for this study, and for each of them 300 random dwelling time patterns were generated. The relationship between the linear penalty model and the dosimetric indices were studied both by the Pearson’s product moment correlation coefficient between the objective function value of the linear penalty model and the values of the dosimetric indices, and by scatter-grams.

Results: For one of the three patients we found a clear connection between the linear penalty model and the values of the dosimetric indices, but not for the other two. For the two patients without a clear connection there where some dosimetric indices that actually improved with deteriorating objective function value.

Conclusion: The dwelling time pattern found by using the linear penalty model does not correspond to the optimal dose distribution with respect to dosimetric indices.

Place, publisher, year, edition, pages
Keyword [en]
Optimization, Linear penalty models, Correlation, HDR Brachytherapy
National Category
Medical and Health Sciences
URN: urn:nbn:se:liu:diva-100388OAI: diva2:661804
Available from: 2013-11-05 Created: 2013-11-05 Last updated: 2013-11-05Bibliographically 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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