Towards fast and robust 4D optimization for moving tumors with scanned proton therapy

Robust optimization is becoming the gold standard for generating robust plans against various kinds of treatment uncertainties. Today, most robust optimization strategies use a pragmatic set of treatment scenarios (the so-called uncertainty set) consisting of combinations of maximum errors, of each considered uncertainty source (such as tumor motion, setup and image-conversion errors). This approach presents two key issues. First, a subset of considered scenarios is unnecessarily improbable which could potentially compromise the plan quality. Second, the resulting large uncertainty set leads to long plan computation times, which limits the potential for robust optimization as a standard clinical tool. In order to address these issues, a method is introduced which is able to preselect a limited set of relevant treatment error scenarios.

Uncertainties due to systematic setup errors, image-conversion errors and respiratory tumor motion are considered. A four-dimensional (4D)-equiprobability hypersurface is defined, which takes into account the joint probabilities of the above-mentioned uncertainty sources. Only scenarios that lie on the predefined 4D hypersurface are considered, guaranteeing statistical consistency of the uncertainty set. In this regard, twelve scenarios are selected that cover maximum spatial displacements of the tumor during breathing. Subsequently, additional scenarios are considered (sampled from the aforementioned 4D hypersurface) in order to cover any estimated residual range errors. Two different scenario-selection procedures were tested: (a) the maximum displacements (MD) method that only considers twelve scaled maximum displacement scenarios and (b) maximum displacements and residual range (MDR) method which, in addition to the scaled maximum displacement scenarios, considers additional maximum range uncertainty scenarios. The methods were tested for five lung cancer patients by performing comprehensive Monte Carlo robustness evaluations.

A plan computation time gain of 78% is achieved by applying the MD method, whilst obtaining a target robustness of D $$ larger than 95% of the prescribed dose, for the worst-case scenario. Additionally, the MD method has the potential to be fully automatic which makes it a promising candidate for fast automatic planning workflows. The MDR method produced plans with excellent target robustness (D $$ larger than 95% of the prescribed dose, even for the worst-case scenario), whilst still obtaining a significant plan computation time gain of 57%.

Two scenario-selection procedures were developed which achieved significant reduction of plan computation time and memory consumption, without compromising plan quality or robustness.