Robust spatiotemporally integrated fractionation in radiotherapy

Ajdari, Ali; Ghate, Archis

doi:10.1016/j.orl.2016.05.007

Cited by 11 publications

(11 citation statements)

References 20 publications

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“…Lemma 2. At the optimal solution to (3.9), the constraints X 2 ≤ N max Y and X 2 ≥ Y are either inactive or the optimal solution occurs at corners (X (1) , Y (1) ) and (X (Nmax) , Y (Nmax) ).…”

Section: Solution Approachmentioning

confidence: 99%

“…If X 2 ≤ N max Y and X 2 ≥ Y are redundant constraints ((X * , Y * ) obtained by ignoring these constraints satisfy these constraints), then X 2 ≤ N max Y and X 2 ≥ Y are inactive constraints in optimality. Otherwise, consider the three corners p 1 = (0, 0), p 2 = (X (1) , Y (1) ) and p 3 = (X (Nmax) , Y (Nmax) ). As we move from p 1 toward p 2 or from p 1 toward p 3 , we can increase both X and Y .…”

Section: Proof Of Technical Lemmamentioning

confidence: 99%

“…In this paper we concentrate on the modeling the uncertainties arising in inter-patient variations, which we will use later in an optimization method for radiotherapy scheduling. In a recent unpublished manuscript [1] (appearing on web after the first version of current manuscript), the authors developed a similar model where the uncertain parameters is assumed to take values in a given interval. Unfortunately this optimization method may lead to an overly pessimistic solution, and furthermore they did not include the uncertainty in the tumor radio-sensitivity parameters (α and β).…”

Section: Introductionmentioning

confidence: 99%

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Robust and probabilistic optimization of dose schedules in radiotherapy

Badri¹,

Watanabe²,

Leder³

2015

Preprint

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We consider the effects of parameter uncertainty on the optimal radiation schedule in the context of the linear-quadratic model. Our interest arises from the observation that if interpatient variations in normal tissues and tumor sensitivities to radiation or sparing factor of the organ at risk (OAR) are not accounted for during radiation scheduling, the performance of the therapy may be strongly degraded or the OAR may receive a substantially larger dose than the maximum threshold. This paper proposes two radiation scheduling concepts to incorporate inter-patient variability into the scheduling optimization problem. The first approach is a robust formulation that formulates the problem as a conservative model that optimizes the worst case dose scheduling that may occur, assuming that the parameters vary within given intervals. The second method is a probabilistic approach, where the model parameters are given by a set of random variables. Our probabilistic formulation insures that our constraints are satisfied with a given probability, and that our objective function achieves a desired level with a stated probability. We used the same transformation as [37] to reduce the resulting optimization problem to two dimensions. We showed that the optimal solution in the absence of uncertainty in the tumor radio-sensitivity parameters (α and β) occurs at one of the corners of the feasible region. However if we incorporate uncertainty in α and β into the optimization problem, this result does not hold anymore. In this case, we showed that the optimal solution lies on the boundary of the feasible region and we implemented a branch and bound algorithm to find the global optimal solution. We demonstrated how the configuration of optimal schedules in the presence of uncertainty compares to optimal schedules in the absence of uncertainty (conventional schedule). We observed that if the number of fractions in the optimal conventional schedule is the same as the robust and stochastic solutions, it is preferable to administer equal or smaller total dose. In addition if there exist more (fewer) treatment sessions in the probabilistic or robust solution compared to the conventional schedule, a reduction in total dose squared (total dose) will be expected. Finally, we performed numerical experiments in the setting of head-and-neck tumors including several normal tissues to reveal the effect of parameter uncertainty on optimal schedules and to evaluate the sensitivity of the model to the choice of key model parameters.

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Section: Solution Approachmentioning

confidence: 99%

Section: Proof Of Technical Lemmamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust and probabilistic optimization of dose schedules in radiotherapy

Badri¹,

Watanabe²,

Leder³

2015

Preprint

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“…Literature on the fractionation optimization problem is predominantly based on the linearquadratic (LQ) model of cell kill, and the related biological effective dose (BED) model Fowler (1989), Hall and Giaccia (2012). Amongst others, Jones et al (1995), Armpilia et al (2004), Yang and Xing (2005), Mizuta et al (2012), Bertuzzi et al (2013), Unkelbach et al (2013a), Bortfeld et al (2015), Saberian et al (2015Saberian et al ( , 2016a, Badri et al (2016), Ajdari and Ghate (2017a) solve various forms of the fractionation problem, taking into account tumor repopulation, tumor specific biology, uncertainty and/or multiple normal tissues.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, spatiotemporal optimization has been gaining some attention (Unkelbach et al 2013b, Unkelbach and Papp 2015, Ajdari and Ghate 2016, 2017b, Saberian et al 2017, Adibi and Salari 2018. In these studies, the spatial and the temporal component are optimized simultaneously.…”

Section: Introductionmentioning

confidence: 99%

Adjustable robust treatment-length optimization in radiation therapy

Eikelder¹,

Ajdari²,

Bortfeld³

et al. 2019

Preprint

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Technological advancements in radiation therapy (RT) allow the collection of biomarker data on individual patient response during treatment. Although biomarker data remains subject to substantial uncertainties, information extracted from this data may allow the RT plan to be adapted in an 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, and also consider the inexact nature of this information. We formulate the adaptive treatment-length optimization problem as a 2-stage problem, where after the first stage we acquire information about model parameters and decisions in stage 2 may depend on this information. 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 Robust Optimal (PARO) solutions. In extensive numerical experiments based on liver cancer patient data, ARO is benchmarked against several other static and adaptive methods, including robust optimization with a folding horizon. Results show good performance of ARO both if acquired mid-treatment biomarker data is exact and inexact. We also investigate the effect of biomarker acquisition time on the performance of the ARO solution and the benefit of adaptation. Results indicate that a higher level of uncertainty in biomarker information pushes the optimal moment of biomarker acquisition backwards.

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