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

TL;DR

This study addresses uncertainty in external beam radiotherapy by introducing a scenario-free robust optimization method that bypasses explicit scenario storage. It relies on precomputed expected-dose influence $\mathbb{E}[\boldsymbol{D}]$ and a total-variance influence $\boldsymbol{\Omega}$ to evaluate dose objectives on the mean dose while applying variance-reduction terms separately, significantly reducing memory and runtime compared with traditional scenario-based methods. The approach achieves plan quality and robustness comparable to conventional robust optimization and scales to large numbers of error scenarios and 4D CT phases, enabling feasible 4D robust optimization and integration with multi-criteria planning. Validation on 3D and 4D box phantoms and two lung patient cases demonstrates similar or improved target coverage and reduced uncertainty in critical structures, with substantially lower optimization times, highlighting practical benefits for adaptive and high-dimensional uncertainty modeling in IMRT and IMPT.

Abstract

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 was 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 performances of the scenario-free algorithm in terms of plan quality, robustness and computational workload. The scenario-free approach achieves plan quality compatible with traditional robust optimization algorithms and it reduces the standard deviation within selected structures when variance reduction objectives are defined. Avoiding the storage of individual scenario information allows for the inclusion of an arbitrary number of error scenarios. The observed optimization time is independent on the number of included scenarios, compatible with a nominal, non-robust algorithm and significantly lower than the traditional robust approach. These properties make the scenario-free approach suitable for the optimization of robust plans involving a high number of error scenarios and CT phases as 4D robust optimization.

Figures (17)

• Figure 1: Expected dose (top) and corresponding SD (bottom) obtained with the scenario-free (left), traditional stochastic (middle) and nominal (right) optimization approaches. The target structure and the OAR are contoured in purple and red respectively. All the colorbar values are reported in Gy.
• Figure 2: Dosimetric quality and cost-function evolution for the validation of the scenario-free algorithm compared to the conventional stochastic implementation. (a) DVHs and SDVHs for the target structure and the two applied algorithms. The solid line represents the DVH computed for the expected dose distribution while the dashed and dotted lines correspond to the $25$-$75$ and the $5$-$95$ percentiles of single-scenario DVHs distributions. (b) Values of the cost-functions for each performed iteration for the two robust algorithms.
• Figure 3: DVH (a) and SDVH (b) comparison for the target structure when two different constraint values are applied to the "mean variance" term in the cost-function. The dotted vertical lines in the SDVH plot represent the mean standard deviation, i.e., the average value of the SD distribution.
• Figure 4: Expected dose and SD distributions obtained with the different approaches and scenario sampling techniques described in \ref{['subsection:MM_calc_prob_quantities']}. Top row: expected dose distributions obtained with the scenario-free algorithm and a randomly sampled set of scenarios (left), the scenario-free algorithm and a worst-case sampling approach (middle), the stochastic algorithm applied to the same set of randomly sampled scenarios (right). Bottom row: the corresponding standard deviation distributions. All colorbar values are reported in Gy.
• Figure 5: Robustness analysis for the different sampling and optimization approaches. (a) DVHs and SDVHs for the target structure and (b) SDVHs for the OAR reported for both the sampling procedures applied to the scenario-free approach and the additional stochastic approach. Target (c) DVHs and (d) SDVHs for the scenario-free optimization when different sample sizes are used. For the reported DVHs, the solid line represents the DVH computed for the expected dose distribution while the dashed and dotted lines correspond to the 25.0-75.0 and the 5.0-95.0 percentiles of single-scenario DVHs distributions. The dotted vertical lines in the SDVH plot represent the mean standard deviation, i.e., the average value of the SD distribution.