Conic formulation of fluence map optimization problems.

The convexity of objectives and constraints in fluence map optimization (FMO) for radiation therapy has been extensively studied. Next to convexity, there is another important characteristic of optimization functions and problems, which has thus far not been considered in FMO literature: conic representation. Optimization problems that are conically representable using quadratic, exponential and power cones are solvable with advanced primal-dual interior-point algorithms. These algorithms guarantee an optimal solution in polynomial time and have good performance in practice. In this paper, we construct conic representations for most FMO objectives and constraints. This paper is the first that shows that FMO problems containing multiple biological evaluation criteria can be solved in polynomial time. For fractionation-corrected functions for which no exact conic reformulation is found, we provide an accurate approximation that is conically representable. We present numerical results on the TROTS data set, which demonstrate very stable numerical performance for solving FMO problems in conic form. With ongoing research in the optimization community, improvements in speed can be expected, which makes conic optimization a promising alternative for solving FMO problems.

Optimal treatment plan adaptation using mid-treatment imaging biomarkers.

Previous studies on personalized radiotherapy (RT) have mostly focused on baseline patient stratification, adapting the treatment plan according to mid-treatment anatomical changes, or dose boosting to selected tumor subregions using mid-treatment radiological findings. However, the question of how to find the optimal adapted plan has not been properly tackled. Moreover, the effect of information uncertainty on the resulting adaptation has not been explored. In this paper, we present a framework to optimally adapt radiation therapy treatments to early radiation treatment response estimates derived from pre- and mid-treatment imaging data while considering the information uncertainty. The framework is based on the optimal stopping in radiation therapy (OSRT) framework. Biological response is quantified using tumor control probability (TCP) and normal tissue complication probability (NTCP) models, and these are directly optimized for in the adaptation step. Two adaptation strategies are discussed: (1) uniform dose adaptation and (2) continuous dose adaptation. In the first strategy, the original fluence-map is simply scaled upwards or downwards, depending on whether dose escalation or de-escalation is deemed appropriate based on the mid-treatment response observed from the radiological images. In the second strategy, a full NTCP-TCP-based fluence map re-optimization is performed to achieve the optimal adapted plans. We retrospectively tested the performance of these strategies on 14 canine head and neck cases treated with tomotherapy, using as response biomarker the change in the 3'-deoxy-3'[(18)F]-fluorothymidine (FLT)-PET signals between the pre- and mid-treatment images, and accounting for information uncertainty. Using a 10% uncertainty level, the two adaptation strategies both yield a noteworthy average improvement in guaranteed (worst-case) TCP.

Optimal combined proton-photon therapy schemes based on the standard BED model.

This paper investigates the potential of combined proton-photon therapy schemes in radiation oncology, with a special emphasis on fractionation. Several combined modality models, with and without fractionation, are discussed, and conditions under which combined modality treatments are of added value are demonstrated analytically and numerically. The combined modality optimal fractionation problem with multiple normal tissues is formulated based on the biologically effective dose (BED) model and tested on real patient data. Results indicate that for several patients a combined modality treatment gives better results in terms of biological dose (up to [Formula: see text] improvement) than single modality proton treatments. For several other patients, a combined modality treatment is found that offers an alternative to the optimal single modality proton treatment, being only marginally worse but using significantly fewer proton fractions, putting less pressure on the limited availability of proton slots. Overall, these results indicate that combined modality treatments can be a viable option, which is expected to become more important as proton therapy centers are spreading but the proton therapy price tag remains high.

Optimal working zone division for safe track maintenance in The Netherlands.

After a sequence of serious accidents, the safety of rail track workers became an urgent and political problem in The Netherlands. It turned out that the rail track workers had one of the most dangerous jobs. The board of the Dutch Railways decided that the Dutch railway infrastructure had to be divided into so-called working zones. Moreover, to carry out maintenance activities, that particular working zone of the railway system had to be taken out of service. An essential problem was how to divide the Dutch railway infrastructure into working zones such that all parties involved are satisfied. Since many parties with conflicting interests were involved, this problem was extremely difficult. In this paper we show the division rules we developed, and which had been implemented in The Netherlands.