A mathematical optimization model for spatial adjustments of dose distributions in high dose-rate brachytherapy

Morén, Björn; Larsson, Torbjörn; Tedgren, Åsa Carlsson

doi:10.1088/1361-6560/ab4d8d

Cited by 7 publications

(21 citation statements)

References 36 publications

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“…[53,55,56]. Another approach to handle DVMs is to approximate the Heaviside step functions (corresponding to the binary indicator variables) with smooth nonlinear sigmoid functions, 6,35,[68][69][70]…”

Section: B3 Properties and Solutions Methodsmentioning

confidence: 99%

“…An optimization model for IMRT that takes also the spatial dose distribution into account is proposed, 113 while for HDR BT such a model is proposed. 69,70 Both approaches take a tentative dose plan and tries to improve upon spatial properties.…”

Section: G Modeling Of Spatial Propertiesmentioning

confidence: 99%

“…Another approach to handle DVMs is to approximate the Heaviside step functions (corresponding to the binary indicator variables) with smooth nonlinear sigmoid functions, 6,35,68–70

\begin{matrix} f false(D o s e_{i} false) = 0.5 false(1 + \tanh ()(, β, (D o s e_{i} ‐ L^{T})) false), \end{matrix}

where

β

is a parameter to control the steepness of the function; see Fig. 2 for an illustration.…”

Section: Mathematical Modelsmentioning

confidence: 99%

“…The aim in Ref. [70] is to reduce PTV hot spots and cold spots in a tentative dose plan. Constraints are maintaining the dosimetric indices from the tentative plan and the purpose of the objective function is to improve the plan’s spatial properties.…”

Section: Mathematical Modelsmentioning

confidence: 99%

“…The complete models 70,113 are as follows, with the notation introduced in Tables II and VIII.

\begin{matrix} {min}_{t} & \sum_{b \in I_{f}} {(f_{b} false(t false) ‐ f_{b}^{0})}^{2} \\ + \sum_{c \in I_{c}} π_{c} max (0, g_{c} (t)) \\ + \sum_{i \in P} r_{i} {()(D o s e_{i} ‐ d o s e_{i}^{0})}^{2} \end{matrix}

\begin{matrix} subject to \\ L_{i} \leq D o s e_{i} \leq U_{i} & i \in I_{s} \end{matrix}

\begin{matrix} \sum_{j \in J} d_{italicij} t_{j} = D o s e_{i} & i \in P \end{matrix}

\begin{matrix} t \in X \end{matrix}

…”

Section: Mathematical Modelsmentioning

confidence: 99%

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Optimization in treatment planning of high dose‐rate brachytherapy — Review and analysis of mathematical models

2021

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Treatment planning in high dose-rate brachytherapy has traditionally been conducted with manual forward planning, but inverse planning is today increasingly used in clinical practice. There is a large variety of proposed optimization models and algorithms to model and solve the treatment planning problem. Two major parts of inverse treatment planning for which mathematical optimization can be used are the decisions about catheter placement and dwell time distributions. Both these problems as well as integrated approaches are included in this review. The proposed models include linear penalty models, dose-volume models, mean-tail dose models, quadratic penalty models, radiobiological models, and multiobjective models. The aim of this survey is twofold: (i) to give a broad overview over mathematical optimization models used for treatment planning of brachytherapy and (ii) to provide mathematical analyses and comparisons between models. New technologies for brachytherapy treatments and methods for treatment planning are also discussed. Of particular interest for future research is a thorough comparison between optimization models and algorithms on the same dataset, and clinical validation of proposed optimization approaches with respect to patient outcome.

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Section: B3 Properties and Solutions Methodsmentioning

confidence: 99%

Section: G Modeling Of Spatial Propertiesmentioning

confidence: 99%

“…Another approach to handle DVMs is to approximate the Heaviside step functions (corresponding to the binary indicator variables) with smooth nonlinear sigmoid functions, 6,35,68–70

\begin{matrix} f false(D o s e_{i} false) = 0.5 false(1 + \tanh ()(, β, (D o s e_{i} ‐ L^{T})) false), \end{matrix}

where

β

is a parameter to control the steepness of the function; see Fig. 2 for an illustration.…”

Section: Mathematical Modelsmentioning

confidence: 99%

Section: Mathematical Modelsmentioning

confidence: 99%

“…The complete models 70,113 are as follows, with the notation introduced in Tables II and VIII.

\begin{matrix} {min}_{t} & \sum_{b \in I_{f}} {(f_{b} false(t false) ‐ f_{b}^{0})}^{2} \\ + \sum_{c \in I_{c}} π_{c} max (0, g_{c} (t)) \\ + \sum_{i \in P} r_{i} {()(D o s e_{i} ‐ d o s e_{i}^{0})}^{2} \end{matrix}

\begin{matrix} subject to \\ L_{i} \leq D o s e_{i} \leq U_{i} & i \in I_{s} \end{matrix}

\begin{matrix} \sum_{j \in J} d_{italicij} t_{j} = D o s e_{i} & i \in P \end{matrix}

\begin{matrix} t \in X \end{matrix}

…”

Section: Mathematical Modelsmentioning

confidence: 99%

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Optimization in treatment planning of high dose‐rate brachytherapy — Review and analysis of mathematical models

2021

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Dosimetric impact of a robust optimization approach to mitigate effects from rotational uncertainty in prostate intensity‐modulated brachytherapy

et al. 2022

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Background: Intensity-modulated brachytherapy (IMBT) is an emerging technology for cancer treatment, in which radiation sources are shielded to shape the dose distribution. The rotatable shields provide an additional degree of freedom, but also introduce an additional, directional, type of uncertainty, compared to conventional high-dose-rate brachytherapy (HDR BT). Purpose: We propose and evaluate a robust optimization approach to mitigate the effects of rotational uncertainty in the shields with respect to planning criteria. Methods: A previously suggested prototype for platinum-shielded prostate 169 Yb-based dynamic IMBT is considered. We study a retrospective patient data set (anatomical contours and catheter placement) from two clinics, consisting of six patients that had previously undergone conventional 192 Ir HDR BT treatment. The Monte Carlo-based treatment planning software RapidBrachyMCTPS is used for dose calculations. In our computational experiments, we investigate systematic rotational shield errors of ±10 • and ±20 • , and the same systematic error is applied to all dwell positions in each scenario. This gives us three scenarios, one nominal and two with errors. The robust optimization approach finds a compromise between the average and worst-case scenario outcomes. Results: We compare dose plans obtained from standard models and their robust counterparts. With dwell times obtained from a linear penalty model (LPM), for 10 • errors, the dose to urethra (D 0.1cc ) and rectum (D 0.1cc and D 1cc ) increase with up to 5% and 7%, respectively, in the worst-case scenario, while with the robust counterpart, the corresponding increases were 3% and 3%. For all patients and all evaluated criteria, the worst-case scenario outcome with the robust approach had lower deviation compared to the standard model, without compromising target coverage. We also evaluated shield errors up to 20 • and while the deviations increased to a large extent with the standard models, the robust models were capable of handling even such large errors. Conclusions: We conclude that robust optimization can be used to mitigate the effects from rotational uncertainty and to ensure the treatment plan quality of IMBT.

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Technical note: Evaluation of a spatial optimization model for prostate high dose‐rate brachytherapy in a clinical treatment planning system

et al. 2023

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Background Spatial properties of a dose distribution, such as volumes of contiguous hot spots, are of clinical importance in treatment planning for high dose‐rate brachytherapy (HDR BT). We have in an earlier study developed an optimization model that reduces the prevalence of contiguous hot spots by modifying a tentative treatment plan. Purpose The aim of this study is to incorporate the correction of hot spots in a standard inverse planning workflow and to validate the integrated model in a clinical treatment planning system. The spatial function is included in the objective function for the inverse planning, as opposed to in the previous study where it was applied as a separate post‐processing step. Our aim is to demonstrate that fine‐adjustments of dose distributions, which are often performed manually in today's clinical practice, can be automated. Methods A spatial optimization function was introduced in the treatment planning system RayStation (RaySearch Laboratories AB, Stockholm, Sweden) via a research interface. A series of 10 consecutive prostate patients treated with HDR BT was retrospectively replanned with and without the spatial function. Results Optimization with the spatial function decreased the volume of the largest contiguous hot spot by on average 31%, compared to if the function was not included. The volume receiving at least 200% of the prescription dose decreased by on average 11%. Target coverage, measured as the fractions of the clinical target volume (CTV) and the planning target volume (PTV) receiving at least the prescription dose, was virtually unchanged (less than a percent change for both metrics). Organs‐at‐risk received comparable or slightly decreased doses if the spatial function was included in the optimization model. Conclusions Optimization of spatial properties such as the volume of contiguous hot spots can be integrated in a standard inverse planning workflow for brachytherapy, and need not be conducted as a separate post‐processing step.

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A mathematical optimization model for spatial adjustments of dose distributions in high dose-rate brachytherapy

Cited by 7 publications

References 36 publications

Optimization in treatment planning of high dose‐rate brachytherapy — Review and analysis of mathematical models

Optimization in treatment planning of high dose‐rate brachytherapy — Review and analysis of mathematical models

Dosimetric impact of a robust optimization approach to mitigate effects from rotational uncertainty in prostate intensity‐modulated brachytherapy

Technical note: Evaluation of a spatial optimization model for prostate high dose‐rate brachytherapy in a clinical treatment planning system

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