BackgroundIntensity-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). PurposeWe propose and evaluate a robust optimization approach to mitigate the effects of rotational uncertainty in the shields with respect to planning criteria. MethodsA previously suggested prototype for platinum-shielded prostate Yb-169-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 Ir-192 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 degrees and +/- 20 degrees, 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. ResultsWe compare dose plans obtained from standard models and their robust counterparts. With dwell times obtained from a linear penalty model (LPM), for 10 degrees errors, the dose to urethra (D0.1cc) and rectum (D0.1cc and D1cc) 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 degrees and while the deviations increased to a large extent with the standard models, the robust models were capable of handling even such large errors. ConclusionsWe conclude that robust optimization can be used to mitigate the effects from rotational uncertainty and to ensure the treatment plan quality of IMBT.

BackgroundSpatial 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. PurposeThe 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 todays clinical practice, can be automated. MethodsA 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. ResultsOptimization 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. ConclusionsOptimization 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.

PURPOSE: The aim was to evaluate a postprocessing optimization algorithms ability to improve the spatial properties of a clinical treatment plan while preserving the target coverage and the dose to the organs at risk. The goal was to obtain a more homogenous treatment plan, minimizing the need for manual adjustments after inverse treatment planning. MATERIALS AND METHODS: The study included 25 previously treated prostate cancer pa-tients. The treatment plans were evaluated on dose-volume histogram parameters established clin-ical and quantitative measures of the high dose volumes. The volumes of the four largest hot spots were compared and complemented with a human observer study with visual grading by eight oncologists. Statistical analysis was done using ordinal logistic regression. Weighted kappa and Fleiss kappa were used to evaluate intra-and interobserver reliability. RESULTS: The quantitative analysis showed that there was no change in planning target volume (PTV) coverage and dose to the rectum. There were significant improvements for the adjusted treatment plan in: V150% and V200% for PTV, dose to urethra, conformal index, and dose nonhomogeneity ratio. The three largest hot spots for the adjusted treatment plan were significantly smaller compared to the clinical treatment plan. The observers preferred the adjusted treatment plan in 132 cases and the clinical in 83 cases. The observers preferred the adjusted treatment plan on homogeneity and organs at risk but preferred the clinical plan on PTV coverage. CONCLUSIONS: Quantitative analysis showed that the postadjustment optimization tool could improve the spatial properties of the treatment plans while maintaining the target coverage. (c) 2022 The Authors. Published by Elsevier Inc. on behalf of American Brachytherapy Society. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )

Brachytherapy is a mature treatment modality. The literature is abundant in terms of review articles and comprehensive books on the latest established as well as evolving clinical practices. The intent of this article is to part ways and look beyond the current state-of-the-art and review emerging technologies that are noteworthy and perhaps may drive the future innovations in the field. There are plenty of candidate topics that deserve a deeper look, of course, but with practical limits in this communicative platform, we explore four topics that perhaps is worthwhile to review in detail at this time. First, intensity modulated brachytherapy (IMBT) is reviewed. The IMBT takes advantage of anisotropic radiation profile generated through intelligent high-density shielding designs incorporated onto sources and applicators such to achieve high quality plans. Second, emerging applications of 3D printing (i.e. additive manufacturing) in brachytherapy are reviewed. With the advent of 3D printing, interest in this technology in brachytherapy has been immense and translation swift due to their potential to tailor applicators and treatments customizable to each individual patient. This is followed by, in third, innovations in treatment planning concerning catheter placement and dwell times where new modelling approaches, solution algorithms, and technological advances are reviewed. And, fourth and lastly, applications of a new machine learning technique, called deep learning, which has the potential to improve and automate all aspects of brachytherapy workflow, are reviewed. We do not expect that all ideas and innovations reviewed in this article will ultimately reach clinic but, nonetheless, this review provides a decent glimpse of what is to come. It would be exciting to monitor as IMBT, 3D printing, novel optimization algorithms, and deep learning technologies evolve over time and translate into pilot testing and sensibly phased clinical trials, and ultimately make a difference for cancer patients. Todays fancy is tomorrows reality. The future is bright for brachytherapy.

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.

Cancer is a widespread class of diseases that each year affects millions of people. It is mostly treated with chemotherapy, surgery, radiation therapy, or combinations thereof. High doserate (HDR) brachytherapy (BT) is one modality of radiation therapy, which is used to treat for example prostate cancer and gynecologic cancer. In BT, catheters (i.e., hollow needles) or applicators are used to place a single, small, but highly radioactive source of ionizing radiation close to or within a tumour, at dwell positions. An emerging technique for HDR BT treatment is intensity modulated brachytherapy (IMBT), in which static or dynamic shields are used to further shape the dose distribution, by hindering the radiation in certain directions. 

The topic of this thesis is the application of mathematical optimization to model and solve the treatment planning problem. The treatment planning includes decisions on catheter placement, that is, how many catheters to use and where to place them, as well as decisions for dwell times. Our focus is on the latter decisions. The primary treatment goals are to give the tumour a sufficiently high radiation dose while limiting the dose to the surrounding healthy organs, to avoid severe side effects. Because these aims are typically in conflict, optimization models of the treatment planning problem are inherently multiobjective. Compared to manual treatment planning, there are several advantages of using mathematical optimization for treatment planning. First, the optimization of treatment plans requires less time, compared to the time-consuming manual planning. Secondly, treatment plan quality can be improved by using optimization models and algorithms. Finally, with the use of sophisticated optimization models and algorithms the requirements of experience and skill level for the planners are lower. The use of optimization for treatment planning of IMBT is especially important because the degrees of freedom are too many for manual planning. 

The contributions of this thesis include the study of properties of treatment planning models, suggestions for extensions and improvements of proposed models, and the development of new optimization models that take clinically relevant, but uncustomary aspects, into account in the treatment planning. A common theme is the modelling of constraints on dosimetric indices, each of which is a restriction on the portion of a volume that receives at least a specified dose, or on the lowest dose that is received by a portion of a volume. Modelling dosimetric indices explicitly yields mixed-integer programs which are computationally demanding to solve. We have therefore investigated approximations of dosimetric indices, for example using smooth non-linear functions or convex functions. Contributions of this thesis are also a literature review of proposed treatment planning models for HDR BT, including mathematical analyses and comparisons of models, and a study of treatment planning for IMBT, which shows how robust optimization can be used to mitigate the risks from rotational errors in the shield placement. 

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.

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.

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.

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.

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.