  Interfractional geometric uncertainties can lead to deviations of the actual
delivered dose from the prescribed dose distribution. To better handle these
uncertainties during 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. We formulate
an adaptive framework with dependence on time and/or uncertainty or neither.
The framework is evaluated with either expected-value-, worst-case-, or
conditional-value-at-risk-(CVaR)-optimization. The goal of this study is to
identify the mathematical properties of the proposed robust adaptive strategies
in order to restore the planned dose distribution. We apply a result from
convex analysis to show that in our framework, the time-dependent problem has a
time-independent optimal solution. This implies that the time-dependent problem
can be solved by dynamically solving the corresponding time-independent
problem. This is especially relevant in a clinical context, since it implies
that adaptive radiation therapy can be implemented in clinical practice using
commercially available treatment planning systems. We demonstrate that
time-and-scenario-dependent variables are most compatible with
worst-case-optimization and that including dose prediction potentially improves
treatment compared to non-adaptive planning. Contrarily,
time-and-scenario-independent variables appear most compatible with
expected-value-optimization. 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.
