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  • 1.
    Morén, Björn
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Mathematical Modelling of Dose Planning in High Dose-Rate Brachytherapy2019Licentiate 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.

    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
  • 2.
    Morén, Björn
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Larsson, Torbjörn
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Carlsson Tedgren, Åsa
    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. Karolinska Univ Hosp, Sweden; Karolinska Inst, Sweden.
    A mathematical optimization model for spatial adjustments of dose distributions in high dose-rate brachytherapy2019In: Physics in Medicine and Biology, ISSN 0031-9155, E-ISSN 1361-6560, Vol. 64, no 22, article id 225012Article in journal (Refereed)
    Abstract [en]

    High dose-rate brachytherapy is a modality of radiation therapy used for cancer treatment, in which the radiation source is placed within the body. The treatment goal is to give a high enough dose to the tumour while sparing nearby healthy tissue and organs (organs-at-risk). The most common criteria for evaluating dose distributions are dosimetric indices. For the tumour, such an index is the portion of the volume that receives at least a specified dose level (e.g. the prescription dose), while for organs-at-risk it is instead the portion of the volume that receives at most a specified dose level. Dosimetric indices are aggregate criteria and do not consider spatial properties of the dose distribution. Further, there are neither any established evaluation criteria for characterizing spatial properties, nor have such properties been studied in the context of mathematical optimization of brachytherapy. Spatial properties are however of clinical relevance and therefore dose plans are sometimes adjusted manually to improve them. We propose an optimization model for reducing the prevalence of contiguous volumes with a too high dose (hot spots) or a too low dose (cold spots) in a tentative dose plan. This model is independent of the process of constructing the tentative plan. We conduct computational experiments with tentative plans obtained both from optimization models and from clinical practice. The objective function considers pairs of dose points and each pair is given a distance-based penalty if the dose is either too high or too low at both dose points. Constraints are included to retain dosimetric indices at acceptable levels. Our model is designed to automate the manual adjustment step in the planning process. In the automatic adjustment step large-scale optimization models are solved. We show reductions of the volumes of the largest hot and cold spots, and the computing times are feasible in clinical practice.

  • 3.
    Morén, Björn
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Larsson, Torbjörn
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Carlsson Tedgren, Åsa
    Linköping University, Department of Medical and Health Sciences, Division of Radiological Sciences. Linköping University, Faculty of Medicine and Health Sciences. Karolinska University Hospital, Stockholm, Sweden.
    An extended dose-volume model in high dose-rate brachytherapy: Using mean-tail-dose to reduce tumor underdosage2019In: Medical physics (Lancaster), ISSN 0094-2405, Vol. 46, no 6, p. 2556-2566Article in journal (Refereed)
    Abstract [en]

    Purpose High dose-rate brachytherapy is a method of radiotherapy for cancer treatment in which the radiation source is placed within the body. In addition to give a high enough dose to a tumor, it is also important to spare nearby healthy organs [organs at risk (OAR)]. Dose plans are commonly evaluated using the so-called dosimetric indices; for the tumor, the portion of the structure that receives a sufficiently high dose is calculated, while for OAR it is instead the portion of the structure that receives a sufficiently low dose that is of interest. Models that include dosimetric indices are referred to as dose-volume models (DVMs) and have received much interest recently. Such models do not take the dose to the coldest (least irradiated) volume of the tumor into account, which is a distinct weakness since research indicates that the treatment effect can be largely impaired by tumor underdosage even to small volumes. Therefore, our aim is to extend a DVM to also consider the dose to the coldest volume. Methods An improved DVM for dose planning is proposed. In addition to optimizing with respect to dosimetric indices, this model also takes mean dose to the coldest volume of the tumor into account. Results Our extended model has been evaluated against a standard DVM in ten prostate geometries. Our results show that the dose to the coldest volume could be increased, while also computing times for the dose planning were improved. Conclusion While the proposed model yields dose plans similar to other models in most aspects, it fulfils its purpose of increasing the dose to cold tumor volumes. An additional benefit is shorter solution times, and especially for clinically relevant times (of minutes) we show major improvements in tumour dosimetric indices.

  • 4.
    Morén, Björn
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Larsson, Torbjörn
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Carlsson Tedgren, Åsa
    Linköping University, Department of Medical and Health Sciences, Division of Radiological Sciences. Linköping University, Faculty of Medicine and Health Sciences. Karolinska Univ Hosp, Sweden; Karolinska Inst, Sweden.
    Mathematical optimization of high dose-rate brachytherapy-derivation of a linear penalty model from a dose-volume model2018In: Physics in Medicine and Biology, ISSN 0031-9155, E-ISSN 1361-6560, Vol. 63, no 6, article id 065011Article in journal (Refereed)
    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.

  • 5.
    Morén, Björn
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering. Linköping University, Department of Medical and Health Sciences.
    Larsson, Torbjörn
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Carlsson Tedgren, Åsa
    Medical Radiation Physics and Nuclear Medicine, Department of Oncology Pathology, Karolinska University Hospital, Solna Sweden.
    Preventing Hot Spots in High Dose-Rate Brachytherapy2018In: Operations Research Proceedings 2017 / [ed] Kliewer, Natalia; Ehmke, Jan Fabian; Borndörfer, Ralf, Springer International Publishing , 2018, p. 369-375Conference 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.

1 - 5 of 5
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