Karl-Heinz Küfer

Trade-off bounds for the Pareto surface approximation in multi-criteria IMRT planning.

One approach to multi-criteria IMRT planning is to automatically calculate a data set of Pareto-optimal plans for a given planning problem in a first phase, and then interactively explore the solution space and decide on the clinically best treatment plan in a second phase. The challenge of computing the plan data set is to ensure that all clinically meaningful plans are covered and that as many clinically irrelevant plans as possible are excluded to keep computation times within reasonable limits. In this work, we focus on the approximation of the clinically relevant part of the Pareto surface, the process that constitutes the first phase. It is possible that two plans on the Pareto surface have a small, clinically insignificant difference in one criterion and a significant difference in another criterion. For such cases, only the plan that is clinically clearly superior should be included into the data set. To achieve this during the Pareto surface approximation, we propose to introduce bounds that restrict the relative quality between plans, the so-called trade-off bounds. We show how to integrate these trade-off bounds into the approximation scheme and study their effects. The proposed scheme is applied to two artificial cases and one clinical case of a paraspinal tumor. For all cases, the quality of the Pareto surface approximation is measured with respect to the number of computed plans, and the range of values occurring in the approximation for different criteria is compared. Through enforcing trade-off bounds, the scheme disregards clinically irrelevant plans during the approximation. Thereby, the number of plans necessary to achieve a good approximation quality can be significantly reduced. Thus, trade-off bounds are an effective tool to focus the planning and to reduce computation time.

Combinatorial auctions in freight logistics

Freight business is a huge market with strong competition. In many companies, planning and routing software has been introduced, and optimization potentials have been widely exploited. To further improve efficiency, especially the small and medium sized carriers have to cooperate beyond enterprise boundaries. A promising approach to exchange transportation requests between freight carriers is provided by combinatorial auctions and exchanges. They allow bundles of items to be traded, thereby allowing participants to express complex synergies. In this paper we discuss various goals for a combinatorial request exchange in freight logistics and provide the reasoning for our design decisions. All goals aim to improve usefulness in a practical environment of less-than-truckload (LTL) carriers.We provide experimental results for both generated and real-life data that show significant savings and are often close to a heuristic solution for the global optimization problem. We study how bundling and restricting the number of submitted bids affect the solution quality.

Comparative analysis of Pareto surfaces in multi-criteria IMRT planning.

In the multi-criteria optimization approach to IMRT planning, a given dose distribution is evaluated by a number of convex objective functions that measure tumor coverage and sparing of the different organs at risk. Within this context optimizing the intensity profiles for any fixed set of beams yields a convex Pareto set in the objective space. However, if the number of beam directions and irradiation angles are included as free parameters in the formulation of the optimization problem, the resulting Pareto set becomes more intricate. In this work, a method is presented that allows for the comparison of two convex Pareto sets emerging from two distinct beam configuration choices. For the two competing beam settings, the non-dominated and the dominated points of the corresponding Pareto sets are identified and the distance between the two sets in the objective space is calculated and subsequently plotted. The obtained information enables the planner to decide if, for a given compromise, the current beam setup is optimal. He may then re-adjust his choice accordingly during navigation. The method is applied to an artificial case and two clinical head neck cases. In all cases no configuration is dominating its competitor over the whole Pareto set. For example, in one of the head neck cases a seven-beam configuration turns out to be superior to a nine-beam configuration if the highest priority is the sparing of the spinal cord. The presented method of comparing Pareto sets is not restricted to comparing different beam angle configurations, but will allow for more comprehensive comparisons of competing treatment techniques (e.g., photons versus protons) than with the classical method of comparing single treatment plans.

The critical spot eraser-a method to interactively control the correction of local hot and cold spots in IMRT planning.

Common problems in inverse radiotherapy planning are localized dose insufficiencies like hot spots in organs at risk or cold spots inside targets. These are hard to correct since the optimization is based on global evaluations like maximum/minimum doses, equivalent uniform doses or dose-volume constraints for whole structures. In this work, we present a new approach to locally correct the dose of any given treatment plan. Once a treatment plan has been found that is acceptable in general but requires local corrections, these areas are marked by the planner. Then the system generates new plans that fulfil the local dose goals. Consequently, it is possible to interactively explore all plans between the locally corrected plans and the original treatment plan, allowing one to exactly adjust the degree of local correction and how the plan changes overall. Both the amount (in Gy) and the size of the local dose change can be navigated. The method is introduced formally as a new mathematical optimization setting, and is evaluated using a clinical example of a meningioma at the base of the skull. It was possible to eliminate a hot spot outside the target volume while controlling the dose changes to all other parts of the treatment plan. The proposed method has the potential to become the final standard step of inverse treatment planning.

Tactical Operating Theatre Scheduling: Efficient Appointment Assignment

Finding an appointment for elective surgeries in hospitals is a task that has a direct impact on the optimization potential for offline and online daily surgery scheduling. A novel approach based on bin packing which takes into account limited resource availability (e.g. staff, equipment), its utilization, clinical priority, hospital bed distribution and surgery difficulty is proposed for this planning level. A solution procedure is presented that explores the specific structure of the model to find appointments for elective surgeries in real time. Tests performed with randomly generated data motivated by a mid size hospital suggest that the new approach yields high quality solutions.

A new mathematical approach for handling DVH criteria in IMRT planning

The appropriate handling of planning criteria on the cumulative dose-volume histogram (DVH) is a highly problematic issue in intensity-modulated radiation therapy (IMRT) plan optimization. The nonconvexity of DVH criteria and globality of the resulting optimization problems complicate the design of suitable optimization methods, which feature numerical efficiency, reliable convergence and optimality of the results. This work examines the mathematical structure of DVH criteria and proves the valuable properties of isotonicity/antitonicity, connectedness, invexity and sufficiency of the Karush–Kuhn–Tucker condition. These properties facilitate the use of efficient and goal-oriented optimization methods. An exemplary algorithmic realization with feasible direction methods gives rise to a functional framework for interactive IMRT planning on DVH criteria. Numerical examples on real world planning cases prove its practical capability.

Improved stratification algorithms for step-and-shoot MLC delivery in intensity-modulated radiation therapy

In inverse planning for intensity-modulated radiotherapy (IMRT), the fluence distribution of each treatment beam is usually calculated in an optimization process. The delivery of the resulting treatment plan using multileaf collimators (MLCs) is performed either in the step-and-shoot or sliding window technique. For step-and-shoot delivery, the arbitrary beam fluence distributions have to be transformed into an applicable sequence of subsegments. In a stratification step the complexity of the fluence maps is reduced by assigning each beamlet to discrete intensity values, followed by the sequencing step that generates the subsegments. In this work, we concentrate on the stratification for step-and-shoot delivery. Different concepts of stratification are formally introduced. In addition to already used strategies that minimize the difference between original and stratified beam intensities, we propose an original stratification principle that minimizes the error of the resulting dose distribution. It could be shown that for a comparable total number of subsegments the dose-oriented stratification results in a better approximation of the original, unsequenced plan. The presented algorithm can replace the stratification routine in existing sequencer programs and can also be applied to interpolated plans that are generated in an interactive decision making process of multicriteria inverse planning programs.

Decision Support by Multicriteria Optimization in Process Development: An Integrated Approach for Robust Planning and Design of Plant Experiments

Abstract In simulation-based process design, model parameters, like thermodynamic data, are affected by uncertainties. Optimized process designs should, among different other objectives, also be robust to uncertainties of the model parameters. In industrial practise, it is important to know the trade-off between an increase in robustness and the other objectives – like minimizing costs or maximizing product purities. This contribution describes a practical procedure how to incorporate robustness as an objective into a multicriteria optimization framework. The general procedure is illustrated by a concrete example. Finally, we argue that the same approach is useable for an optimal design of plant experiments.

Analyzing the quality robustness of chemotherapy plans with respect to model uncertainties

Mathematical models of chemotherapy planning problems contain various biomedical parameters, whose values are difficult to quantify and thus subject to some uncertainty. This uncertainty propagates into the therapy plans computed on these models, which poses the question of robustness to the expected therapy quality. This work introduces a combined approach for analyzing the quality robustness of plans in terms of dosing levels with respect to model uncertainties in chemotherapy planning. It uses concepts from multi-criteria decision making for studying parameters related to the balancing between the different therapy goals, and concepts from sensitivity analysis for the examination of parameters describing the underlying biomedical processes and their interplay. This approach allows for a profound assessment of a therapy plan, how stable its quality is with respect to parametric changes in the used mathematical model.

A generalized projection-based scheme for solving convex constrained optimization problems

In this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the original optimization problem to a sequence of feasibility problems by iteratively constraining the objective function from above until the feasibility problem is inconsistent. For each of the feasibility problems one may apply any of the existing projection methods for solving it. In particular, the scheme allows the use of subgradient projections and does not require exact projections onto the constraints sets as in existing similar methods. We also apply the newly introduced concept of superiorization to optimization formulation and compare its performance to our scheme. We provide some numerical results for convex quadratic test problems as well as for real-life optimization problems coming from medical treatment planning.