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Mathematical Modelling of Dose Planning in High Dose-Rate Brachytherapy
Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
2019 (English)Licentiate thesis, comprehensive summary (Other academic)
##### Abstract [en]

Cancer is a widespread type of diseases that each year affects millions of people. It is mainly treated by chemotherapy, surgery or radiation therapy, or a combination of them. One modality of radiation therapy is high dose-rate brachytherapy, used in treatment of for example prostate cancer and gynecologic cancer. Brachytherapy is an invasive treatment in which catheters (hollow needles) or applicators are used to place the highly active radiation source close to or within a tumour.

The treatment planning problem, which can be modelled as a mathematical optimization problem, is the topic of this thesis. The treatment planning includes decisions on how many catheters to use and where to place them as well as the dwell times for the radiation source. There are multiple aims with the treatment and these are primarily to give the tumour a radiation dose that is sufficiently high and to give the surrounding healthy tissue and organs (organs at risk) a dose that is sufficiently low. Because these aims are in conflict, modelling the treatment planning gives optimization problems which essentially are multiobjective.

To evaluate treatment plans, a concept called dosimetric indices is commonly used and they constitute an essential part of the clinical treatment guidelines. For the tumour, the portion of the volume that receives at least a specified dose is of interest while for an organ at risk it is rather the portion of the volume that receives at most a specified dose. The dosimetric indices are derived from the dose-volume histogram, which for each dose level shows the corresponding dosimetric index. Dose-volume histograms are commonly used to visualise the three-dimensional dose distribution.

The research focus of this thesis is mathematical modelling of the treatment planning and properties of optimization models explicitly including dosimetric indices, which the clinical treatment guidelines are based on. Modelling dosimetric indices explicitly yields mixedinteger programs which are computationally demanding to solve. The computing time of the treatment planning is of clinical relevance as the planning is typically conducted while the patient is under anaesthesia. Research topics in this thesis include both studying properties of models, extending and improving models, and developing new optimization models to be able to take more aspects into account in the treatment planning.

There are several advantages of using mathematical optimization for treatment planning in comparison to manual planning. First, the treatment planning phase can be shortened compared to the time consuming manual planning. Secondly, also the quality of treatment plans can be improved by using optimization models and algorithms, for example by considering more of the clinically relevant aspects. Finally, with the use of optimization algorithms the requirements of experience and skill level for the planners are lower.

This thesis summary contains a literature review over optimization models for treatment planning, including the catheter placement problem. How optimization models consider the multiobjective nature of the treatment planning problem is also discussed.

##### Series
Linköping Studies in Science and Technology. Licentiate Thesis, ISSN 0280-7971 ; 1831
##### National Category
Radiology, Nuclear Medicine and Medical Imaging Computational Mathematics
##### Identifiers
ISBN: 9789176851319 (print)OAI: oai:DiVA.org:liu-154966DiVA, id: diva2:1294457
##### Presentation
2019-03-22, Nobel BL32, B-huset, Campus Valla, Linköping, 10:15 (English)
##### Supervisors
Available from: 2019-03-07 Created: 2019-03-07 Last updated: 2019-04-24Bibliographically approved
##### List of papers
1. Mathematical optimization of high dose-rate brachytherapy-derivation of a linear penalty model from a dose-volume model
Open this publication in new window or tab >>Mathematical optimization of high dose-rate brachytherapy-derivation of a linear penalty model from a dose-volume model
2018 (English)In: Physics in Medicine and Biology, ISSN 0031-9155, E-ISSN 1361-6560, Vol. 63, no 6, article id 065011Article in journal (Refereed) Published
##### Abstract [en]

High dose-rate brachytherapy is a method for cancer treatment where the radiation source is placed within the body, inside or close to a tumour. For dose planning, mathematical optimization techniques are being used in practice and the most common approach is to use a linear model which penalizes deviations from specified dose limits for the tumour and for nearby organs. This linear penalty model is easy to solve, but its weakness lies in the poor correlation of its objective value and the dose-volume objectives that are used clinically to evaluate dose distributions. Furthermore, the model contains parameters that have no clear clinical interpretation. Another approach for dose planning is to solve mixed-integer optimization models with explicit dose-volume constraints which include parameters that directly correspond to dose-volume objectives, and which are therefore tangible. The two mentioned models take the overall goals for dose planning into account in fundamentally different ways. We show that there is, however, a mathematical relationship between them by deriving a linear penalty model from a dose-volume model. This relationship has not been established before and improves the understanding of the linear penalty model. In particular, the parameters of the linear penalty model can be interpreted as dual variables in the dose-volume model.

##### Place, publisher, year, edition, pages
IOP PUBLISHING LTD, 2018
##### Keywords
high dose-rate brachytherapy; mathematical optimization; linear penalty model; dose-volume histogram; dwell time optimization; linear programming; dosimetric index
##### National Category
Radiology, Nuclear Medicine and Medical Imaging
##### Identifiers
urn:nbn:se:liu:diva-147128 (URN)10.1088/1361-6560/aaab83 (DOI)000427702800002 ()29380746 (PubMedID)
##### Note

Funding Agencies|Swedish Research Council [VR-NT 2015-04543]; Swedish Cancer Foundation [CAN 2015/618]

Available from: 2018-04-20 Created: 2018-04-20 Last updated: 2019-05-01
2. Preventing Hot Spots in High Dose-Rate Brachytherapy
Open this publication in new window or tab >>Preventing Hot Spots in High Dose-Rate Brachytherapy
2018 (English)In: Operations Research Proceedings 2017 / [ed] Kliewer, Natalia; Ehmke, Jan Fabian; Borndörfer, Ralf, Springer International Publishing , 2018, p. 369-375Conference paper, Published paper (Refereed)
##### Abstract [en]

High dose-rate brachytherapy is a method of radiation cancer treatment, where the radiation source is placed inside the body. The recommended way to evaluate dose plans is based on dosimetric indices which are aggregate measures of the received dose. Insufficient spatial distribution of the dose may however result in hot spots, which are contiguous volumes in the tumour that receive a dose that is much too high. We use mathematical optimization to adjust a dose plan that is acceptable with respect to dosimetric indices to also take spatial distribution of the dose into account. This results in large-scale nonlinear mixed-binary models that are solved using nonlinear approximations. We show that there are substantial degrees of freedom in the dose planning even though the levels of dosimetric indices are maintained, and that it is possible to improve a dose plan with respect to its spatial properties.

##### Place, publisher, year, edition, pages
Springer International Publishing, 2018
##### Series
Operations Research Proceedings, ISSN 0721-5924 ; 2017
##### National Category
Radiology, Nuclear Medicine and Medical Imaging
##### Identifiers
urn:nbn:se:liu:diva-154967 (URN)10.1007/978-3-319-89920-6_50 (DOI)978-3-319-89919-0 (ISBN)978-3-319-89920-6 (ISBN)
##### Conference
Annual International Conference of the German Operations Research Society (GOR), Freie Universiät Berlin, Germany, September 6-8, 2017
Available from: 2019-03-07 Created: 2019-03-07 Last updated: 2019-03-07

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Morén, Björn

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