On the interplay between robustness and dynamic planning for adaptive radiation therapy*

Abstract

1 arXiv:1811.00391v1 [physics.med-ph] 1 Nov 2018 Boeck et al. Interfractional geometric uncertainties can lead to deviations of the actual delivered dose from the prescribed dose distribution. To better handle these uncertainties during the course of treatment, the authors propose a dynamic framework for robust adaptive radiation therapy in which a variety of robust adaptive treatment strategies are introduced and evaluated. This variety is a result of optimization variables with various degrees of freedom within robust optimization models that vary in their grade of conservativeness. The different degrees of freedom in the optimization variables are expressed through either time-and-uncertainty-scenario-independence, time-dependence or time-anduncertainty-scenario-dependence, while the robust models are either based on expected value-, worst-case-or conditional value-at-risk-optimization. The goal of this study is to understand which mathematical properties of the proposed robust adaptive strategies are relevant such that the accumulated dose can be steered as close as possible to the prescribed dose as the treatment progresses. We apply a result from convex analysis to show that the robust non-adaptive approach under conditions of convexity and permutation-invariance is at least as good as the time-dependent robust adaptive approach, which implies that the time-dependent problem can be solved by dynamically solving the corresponding time-independent problem. According to the computational study, non-adaptive robust strategies may provide sufficient target coverage comparable to robust adaptive strategies if the occurring uncertainties follow the same distribution as those included in the robust model. Moreover, the results indicate that time-and-uncertainty-scenario-dependent optimization variables are most compatible with worst-case-optimization, while timeand-uncertainty-scenario-independent find their best match with expected value optimization.In conclusion, the authors introduced a novel framework for robust adaptive radiation therapy and identified mathematical requirements to further develop robust adaptive strategies in order to improve treatment outcome in the presence of interfractional uncertainties.

On adaptation cost and tractability in robust adaptive radiation therapy optimization

“…Then, the optimal plan is computed from Eq. independent of the total number of fractions T , as demonstrated in our previous work 14 . The step‐by‐step derivation of Eq.…”

“…Here, robust optimization approaches are used to optimize the initial and adapted robust plans. In our previous studies, 6,14 expected‐value, worst‐case, and conditional‐value‐at‐risk (CVaR) optimization was used to evaluate robust approaches with varying grades of conservativeness. The results with the clearest trends in the previous studies were given by expected‐value and worst‐case optimization.…”

“…Theoretical studies focus on the problem formulation and optimization approach. According to our previous studies 5,6 , the concept of combining robust optimization approaches with adaptive replanning can handle interfractional geometric variations. In particular, this combination can outperform the conventional non-adaptive treatment approach in terms of CTV coverage and OAR protection.…”

“…Therefore, a comparative analysis of the traditional PTV concept with our proposed robust adaptive framework has been omitted here to avoid repetition of findings documented in the literature 4,6,15,16 . In Böck et al, 14 we investigated the connection between more or less conservative approaches to robust planning and optimization variables which are either time‐ and/or scenario dependent or static.…”

“…In our previous work 5,6 , robust optimization approaches were combined with adaptive reoptimization to establish mathematical models of frameworks for robust ART. These models were evaluated in simulation and mathematical studies in the context of offline robust ART.…”