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 14.8% 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.

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.

Traditionally, optimization of radiation therapy (RT) treatment plans has been done before the initiation of RT course, using population-wide estimates for patients’ response to therapy. However, recent technological advancements have enabled monitoring individual patient response during the RT course, in the form of biomarkers. Although biomarker data remains subject to substantial uncertainties, information extracted from this data may allow the RT plan to be adapted in a biologically informative way. We present a mathematical framework that optimally adapts the treatment-length of an RT plan based on the acquired mid-treatment biomarker information, while accounting for the inexact nature of this information. We formulate the adaptive treatment-length optimization problem as a 2-stage problem, wherein the information about the model parameters gathered during the first stage influences the decisions in the second stage. Using Adjustable Robust Optimization (ARO) techniques we derive explicit optimal decision rules for the stage-2 decisions and solve the optimization problem. The problem allows for multiple worst-case optimal solutions. To discriminate between these, we introduce the concept of Pareto Adjustable Robustly Optimal solutions. In numerical experiments using lung cancer patient data, the ARO method is benchmarked against several other static and adaptive methods. In the case of exact biomarker information, there is sufficient space to adapt, and numerical results show that taking into account both robustness and adaptability is not necessary. In the case of inexact biomarker information, accounting for adaptability and inexactness of biomarker information is particularly beneficial when robustness (w.r.t. organ-at-risk (OAR) constraint violations) is of high importance. If minor OAR violations are allowed, a nominal folding horizon approach (NOM-FH) is a good performing alternative, which can outperform ARO. Both the difference in performance and the magnitude of OAR violations of NOM-FH are highly influenced by the biomarker information quality.

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The resource allocation problem is among the classical problems in operations research, and has been studied extensively for decades. However, current solution approaches are not able to efficiently handle problems with expensive function evaluations, which can occur in a variety of applications. We study the integer resource allocation problem with expensive function evaluations, for both convex and non-convex separable cost functions. We present several solution methods, both heuristics and exact methods, that aim to limit the number of function evaluations.The methods are compared in numerical experiments using both randomly generated instances and instances from two resource allocation problems occurring in radiation therapy planning. The best performing method depends on the problem type, and savings in number of function evaluations can be substantial.