Scenario-free robust optimization algorithm for IMRT and IMPT treatment planning

Robust treatment planning algorithms for intensity modulated proton therapy (IMPT) and intensity modulated radiation therapy (IMRT) allow for uncertainty reduction in the delivered dose distributions through explicit inclusion of error scenarios. Due to the curse of dimensionality, application of such algorithms can easily become computationally prohibitive.

This work proposes a scenario-free probabilistic robust optimization algorithm that overcomes both the runtime and memory limitations typical of traditional robustness algorithms.

The scenario-free approach minimizes cost-functions evaluated on expected-dose distributions and total variance. Calculation of these quantities relies on precomputed expected-dose-influence and total-variance-influence matrices, such that no scenarios need to be stored for optimization. The algorithm is developed within matRad and tested in several optimization configurations for photon and proton irradiation plans. A traditional robust optimization algorithm and a margin-based approach are used as a reference to benchmark the performance of the scenario-free algorithm in terms of plan quality, robustness, and computational workload.

The implemented scenario-free approach achieves plan quality similar to traditional robust optimization algorithms, and it reduces the distribution of standard deviation within selected structures when variance reduction objectives are defined. Avoiding the storage of individual scenario information allows for the solution of treatment plan optimization problems, including an arbitrary number of error scenarios. The observed computational time required for optimization is close to a nominal, non-robust algorithm and substantially lower compared to the traditional robust approach. Estimated gains in relative runtime range from approximately $5$ - $600$ times with respect to the traditional approach.

This work introduces a novel scenario-free optimization approach relying on the precomputation of probabilistic quantities while preserving compatibility with state-of-the-art uncertainty modeling. The measured runtime and memory footprint are independent of the number of included error scenarios and similar to those of non-robust margin-based optimization algorithms, while achieving the required dose and robustness specifications under multiple different optimization conditions. These properties make the scenario-free approach suitable and beneficial for 3D and 4D robust optimization involving a high number of error scenarios and/or CT phases.