Mixed integer programming improves comprehensibility and plan quality in inverse optimization of prostate HDR brachytherapy

Gorissen, Bram L.; Hertog, Dick den; Hoffmann, Aswin L.

doi:10.1088/0031-9155/58/4/1041

Cited by 51 publications

(113 citation statements)

References 21 publications

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“…This model is based on the linear penalty model and includes catheter placement by introducing a set of feasible catheter positions and assigning to each position a binary variable that describes if it is used or not. This model is very similar to those by Karabis et al 28 and Gorissen et al 21 . Most models for dwell time distribution optimization can be extended to include catheter positioning by adding binary variables in the way described in Section 3.3.4.…”

Section: Methods For Optimization Of the Catheter Positioningsupporting

confidence: 90%

“…Also their results show that improved dose distributions are obtained when the catheter positioning is optimized. Gorissen et al 21 also include catheter positioning in their model in the same way as Karabis et al 28 . To enable for a standard optimization software to solve their model, they specify the constraints (3.4) as indicator constraints.…”

Section: Optimization Of Catheter Positioningmentioning

confidence: 99%

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Mathematical Optimization of HDR Brachytherapy

Holm¹

2013

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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 ...

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Section: Methods For Optimization Of the Catheter Positioningsupporting

confidence: 90%

Section: Optimization Of Catheter Positioningmentioning

confidence: 99%

Mathematical Optimization of HDR Brachytherapy

Holm¹

2013

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“…This study did not compare all existing methods. Recently developed methods like Inverse Planning by Integer Program (IPIP) (24), the method presented by Holm et al (22) and that of Gorissen et al (23), were not included. This choice was based on availability of and experience with the current restricted set of methods.…”

Section: Discussionmentioning

confidence: 99%

“…The downside of such a method is that optimization becomes a trial-and-error process to find the optimal combination of weights and dose objectives because the effect of changing one parameter in the objective function on all other objectives is unknown. The correlation between DVH parameters that are used to evaluate a plan and the objective function is not always evident (22,23).…”

Section: Introductionmentioning

confidence: 99%

A comparison of inverse optimization algorithms for HDR/PDR prostate brachytherapy treatment planning

et al. 2015

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“…Based on prescribed dose levels for the target and OAR, the model penalizes deviations from these levels at each dose point. The model is easy to solve but the objective function value has been observed to correlate weakly with dosimetric indices (Gorissen et al 2013, Holm et al 2013b.…”

Section: Introductionmentioning

confidence: 99%

Mathematical optimization of high dose-rate brachytherapy—derivation of a linear penalty model from a dose-volume model

2018

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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.

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Mixed integer programming improves comprehensibility and plan quality in inverse optimization of prostate HDR brachytherapy

Cited by 51 publications

References 21 publications

Mathematical Optimization of HDR Brachytherapy

Mathematical Optimization of HDR Brachytherapy

A comparison of inverse optimization algorithms for HDR/PDR prostate brachytherapy treatment planning

Mathematical optimization of high dose-rate brachytherapy—derivation of a linear penalty model from a dose-volume model

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