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Reducing the set of considered scenarios in robust optimization of intensity-modulated proton therapy

Ivar Bengtsson

TL;DR

The paper addresses the computational burden of robust IMPT optimization when many uncertainty scenarios are considered. It introduces scenario-subset strategies, including manual extremes, dose- and gradient-based distance measures, and diversity maximization, as well as adversarial methods to adaptively build a smaller yet representative scenario set within a minimax (SQP) framework. Key findings show that the optimal active set $\\mathcal{A}^{\\star}$ can be closely approximated in practice, with diversity- and gradient-based subsets often outperforming manual selections, and adversarial approaches delivering substantial speedups (commonly 6.7x to 17x) while preserving robustness. The work significantly advances practical robust IMPT planning by enabling faster solutions with maintained plan quality, though it notes limitations such as DVH evaluation and memory considerations, outlining directions toward data-driven or scenario-free strategies.

Abstract

Robust optimization is a commonly employed method to mitigate uncertainties in the planning of intensity-modulated proton therapy (IMPT). In certain contexts, the large number of uncertainty scenarios makes the robust problem impractically expensive to solve. Recent developments in research on IMPT treatment planning indicate that the number of ideally considered error scenarios may continue to increase. In this paper, we therefore investigate methods that reduce the size of the scenario set considered during the robust optimization. Six cases of patients with non-small cell lung cancer are considered. First, we investigate the existence of an optimal subset of scenarios that needs to be considered during robust optimization, and perform experiments to see if the set can be found in a reasonable time and substitute for the full set of scenarios during robust IMPT optimization. We then consider heuristic methods to estimate this subset or find subsets with similar properties. Specifically, we select a subset of maximal diversity in terms of scenario-specific features such as the dose distributions and function gradients at the initial point. Finally, we consider adversarial methods as an alternative to solving the full robust problem and investigate the impact on computation times. The results indicate that the optimal subset can be well approximated by solving the robust IMPT problem with conventional methods. Of the methods designed to approximate it within a practically useful time frame, the results of the diversity-maximization methods indicate that they may perform better than a manual selection of scenarios based on the patient geometry. In addition, the adversarial approaches decreased the computation time by at least half compared to the conventional approach.

Reducing the set of considered scenarios in robust optimization of intensity-modulated proton therapy

TL;DR

The paper addresses the computational burden of robust IMPT optimization when many uncertainty scenarios are considered. It introduces scenario-subset strategies, including manual extremes, dose- and gradient-based distance measures, and diversity maximization, as well as adversarial methods to adaptively build a smaller yet representative scenario set within a minimax (SQP) framework. Key findings show that the optimal active set can be closely approximated in practice, with diversity- and gradient-based subsets often outperforming manual selections, and adversarial approaches delivering substantial speedups (commonly 6.7x to 17x) while preserving robustness. The work significantly advances practical robust IMPT planning by enabling faster solutions with maintained plan quality, though it notes limitations such as DVH evaluation and memory considerations, outlining directions toward data-driven or scenario-free strategies.

Abstract

Robust optimization is a commonly employed method to mitigate uncertainties in the planning of intensity-modulated proton therapy (IMPT). In certain contexts, the large number of uncertainty scenarios makes the robust problem impractically expensive to solve. Recent developments in research on IMPT treatment planning indicate that the number of ideally considered error scenarios may continue to increase. In this paper, we therefore investigate methods that reduce the size of the scenario set considered during the robust optimization. Six cases of patients with non-small cell lung cancer are considered. First, we investigate the existence of an optimal subset of scenarios that needs to be considered during robust optimization, and perform experiments to see if the set can be found in a reasonable time and substitute for the full set of scenarios during robust IMPT optimization. We then consider heuristic methods to estimate this subset or find subsets with similar properties. Specifically, we select a subset of maximal diversity in terms of scenario-specific features such as the dose distributions and function gradients at the initial point. Finally, we consider adversarial methods as an alternative to solving the full robust problem and investigate the impact on computation times. The results indicate that the optimal subset can be well approximated by solving the robust IMPT problem with conventional methods. Of the methods designed to approximate it within a practically useful time frame, the results of the diversity-maximization methods indicate that they may perform better than a manual selection of scenarios based on the patient geometry. In addition, the adversarial approaches decreased the computation time by at least half compared to the conventional approach.

Paper Structure

This paper contains 20 sections, 7 equations, 8 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Mathematical preliminaries
  3. Purpose
  4. Scenario subset selection
  5. Manual selection of extreme scenarios
  6. Distance-based selection
  7. Dose-based differences
  8. Gradient-based differences
  9. Maximizing diversity
  10. Building the scenario set adversarially
  11. Numerical experiments
  12. Patient cases
  13. Experiment 1: Existence of $\mathcal{A}^\star$
  14. Experiment 2: Usefulness of $\mathcal{A}^\star$ and its estimates
  15. Experiment 3: Adversarial methods
  16. ...and 5 more sections

Figures (8)

  • Figure 1: The scenario-specific objective values for P101, for three values of $\varepsilon$ and the corresponding approximate solutions $x^\varepsilon_{\mathcal{S}}$ and $x^\varepsilon_{\mathcal{A}^\varepsilon}$.
  • Figure 2: Objective values per subset selection method and case, after 50 SQP iterations. For each compared subset $\mathcal{M}$, the solution after 50 iterations is denoted $x_\mathcal{M}^{50}$. The subset $\mathcal{A}^\varepsilon$ was computed as in experiment 1, with $\varepsilon = 10^{-7}$.
  • Figure 3: P101
  • Figure 4: P103
  • Figure 5: P104
  • ...and 3 more figures