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Dose Plan Optimization in HDR Brachytherapy using Penalties: Properties and Extensions
Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0003-2220-6125
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.

##### Series
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1486
Mathematics
##### Identifiers
ISBN: 9789173931625 (print)OAI: oai:DiVA.org:liu-67790DiVA, id: diva2:412846
##### Supervisors
Available from: 2011-04-26 Created: 2011-04-26 Last updated: 2017-12-12Bibliographically approved
##### List of papers
1. Impact of Using Linear Optimization Models in Dose Planning for HDR Brachytherapy
Open this publication in new window or tab >>Impact of Using Linear Optimization Models in Dose Planning for HDR Brachytherapy
2012 (English)In: Medical physics (Lancaster), ISSN 0094-2405, Vol. 39, no 2, p. 1021-1028Article 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
##### Keywords
Brachytherapy, Optimization, Treatment planning, Linear programming, Piecewise linear functions
Mathematics
##### Identifiers
urn:nbn:se:liu:diva-67786 (URN)10.1118/1.3676179 (DOI)000300215800048 ()
Available from: 2011-04-26 Created: 2011-04-26 Last updated: 2017-12-11Bibliographically approved
2. Heuristics for Integrated Optimization of Catheter Positioning and Dwell Time Distribution in Prostate HDR Brachytherapy
Open this publication in new window or tab >>Heuristics for Integrated Optimization of Catheter Positioning and Dwell Time Distribution in Prostate HDR Brachytherapy
2016 (English)In: Annals of Operations Research, ISSN 0254-5330, E-ISSN 1572-9338, Vol. 236, no 2, p. 319-339Article 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.

Springer, 2016
##### Keywords
Brachytherapy, Dose planning, Catheter positioning, Mixed integer programming, Metaheuristics
Mathematics
##### Identifiers
urn:nbn:se:liu:diva-67788 (URN)10.1007/s10479-013-1448-7 (DOI)000368946400003 ()
Available from: 2011-04-26 Created: 2011-04-26 Last updated: 2017-12-11Bibliographically approved
3. On the Correlation Between DVH Parameters and Linear Penalties in Optimization of HDR Prostate Brachytherapy Dose Plans
Open this publication in new window or tab >>On the Correlation Between DVH Parameters and Linear Penalties in Optimization of HDR Prostate Brachytherapy Dose Plans
##### Abstract [en]

When optimizing dwell times for HDR brachytherapy it is common to use a model comprising an objective of linear penalties. However whether a planis considered good or not depends on other measures such as DVH-based parameters. We show through experiments that the correlation between the value of the objective function and the values of DVH-based parameters, such as D90, is weak in some cases. It seems that the objective function can only classify solutions into better or worse, however it can not distinguish the best with respect to DVH-based parameters.

Mathematics
##### Identifiers
urn:nbn:se:liu:diva-67789 (URN)
Available from: 2011-04-26 Created: 2011-04-26 Last updated: 2013-08-30Bibliographically approved

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