Background and purpose: Manual treatment planning for cervical brachytherapy is a challenging task; therefore, we investigated a method for inverse treatment planning using pseudo-structures to control the dwell distribution. Our hypothesis was that this method could produce treatment plans with a pear-shaped dose distribution and a high central dose, that comply with clinical constraints. Materials and methods: Data from 16 previously treated patients were used to compare three treatment planning methods: i) manual, ii) straightforward inverse, and iii) inverse with pseudo-structures. The treatment plans were compared using dose-volume histogram parameters and by analysing the dwell times, and the distribution of total reference air-kerma (TRAK) in the different parts of the applicator. Methods were evaluated in one treatment planning system and verified in a second treatment planning system. Results: The median dose to 90 % of the clinical tumor volume was 7.6 Gy, 7.8 Gy and 8.1 Gy for manual, pseudostructure and straightforward methods respectively. Distribution of TRAK for the different parts of the applicator for the three methods (manual, pseudo-structures, and straightforward), with combined intracavitary and interstitial treatments, were for vaginal part 39 %, 33 % and 15 %, for intra-uterine part 47 %, 50 % and 47 % and for interstitial part 13 %, 17 % and 38 % respectively. The results were similar in the second treatment planning system. Conclusion: The developed pseudo-structures worked as intended in shaping the dwell time distribution and in meeting the clinical constraints for both investigated treatment planning systems.

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.

We study a bi-objective covering problem stemming from a real-world application concerning the design of camera surveillance systems for large-scale outdoor areas. It is in this application prohibitively costly to surveil the entire area, and therefore necessary to be able to present a decision-maker with trade-offs between total cost and the portion of the area that is surveilled. The problem can be stated as a set covering problem with two objectives, describing cost and portion of covering constraints that are fulfilled. Finding the Pareto frontier for these objectives is very computationally demanding and we therefore derive a method for finding a good approximate frontier in a practically feasible computing time. The method is based on the epsilon-constraint reformulation, an established heuristic for set covering problems, and subgradient optimization.

We develop a model for asset liability management of pension funds, which is solved by stochastic programming techniques. Using data provided by the Bank of Uganda Defined Benefits Scheme, which is closed to new members, we obtain the optimal investment policies. Randomly sampled scenario trees using the mean and covariance structure of the return distribution are used for generating the coefficients of the stochastic program. Liabilities are modelled by remaining years of life expectancy and guaranteed period for monthly pension. We obtain the funding situation of the scheme at each stage, and the terminal cash injection by the sponsor required to meet all future benefit payments, in absence of contributing members.

We revisit the classic supporting hyperplane illustration of the duality gap for non-convex optimization problems. It is refined by dissecting the duality gap into two terms: the first measures the degree of near-optimality in a Lagrangian relaxation, while the second measures the degree of near-complementarity in the Lagrangian relaxed constraints. We also give an example of how this dissection may be exploited in the design of a solution approach within discrete optimization.

We study the Parliamentary Pension Scheme of Uganda, a hybrid cash balance scheme which is contributory. It has two categories of members, the staff of the Parliamentary Commission and the Members of Parliament. A long term projection of the schemes demographic and financial evolution is done to asses its sustainability and fairness with respect to the two categories of members. The projection of the schemes future members is done using non-linear regression. The distribution of future members by age states is done by Markov model using frequencies of state transition of the scheme members. We project the future contributions, accumulated funds, benefits, asset and liability values together with associated funding ratios. The results show that the fund is neither sustainable nor fair with respect to the two categories of members.

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.

Set covering problems are well-studied and have many applications. Sometimes the duality gap is significant and the problem is computationally challenging. We dissect the duality gap with the purpose of better understanding its relationship to problem characteristics, such as problem shape and density. The means for doing this is a set of global optimality conditions for discrete optimization problems. These decompose the duality gap into two terms: near-optimality in a Lagrangian relaxation and near-complementarity in the relaxed constraints. We analyse these terms for numerous instances of large size, including some real-life instances. We conclude that when the duality gap is large, typically the near-complementarity term is large and the near-optimality term is small. The large violation of complementarity is due to extensive over-coverage. Our observations should have implications for the design of solution methods, and especially for the design of core problems.

In aerodynamic development of ground vehicles, the use of Computational Fluid Dynamics (CFD) is crucial for improving the aerodynamic performance, stability and comfort of the vehicle. Simulation time and accuracy are two key factors of a well working CFD procedure. Using scale-resolving simulations, accurate predictions of the flow field and aerodynamic forces are possible, but often leads to long simulation time. For a given solver, one of the most significant aspects of the simulation time/cost is the temporal resolution. In this study, this aspect is investigated using the realistic vehicle model DrivAer with the notchback geometry as the test case. To ensure a direct and accurate comparison with wind tunnel measurements, performed at TU Berlin, a large section of the wind tunnel is included in the simulation domain. All simulations are performed at a Reynolds number of 3.12 million, based on the vehicle length. Three spatial resolutions were compared, where it could be seen that a hybrid element mesh consisting of 102 million cells only revealed small differences to the finest mesh investigated, well as showing excellent agreement with wind tunnel measurements. An investigation of the temporal resolution is performed, in order to see its effect on the simulation time/cost and accuracy of the results. The finest temporal resolution resulted in a Courant-Friedrichs-Lewy number less than unity, while the coarsest reached a CFL number of around 100. From these results, it is seen that it is possible to reduce the simulation time with more than 90 % (CFL 20) and still keep sufficient accuracy of the forces and important features of the flow field.

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.