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Trading robustness: a scenario-free approach to robust Multi-Criteria Optimization for Treatment Planning

Remo Cristoforetti, Philipp Süss, Tobias Becher, Niklas Wahl

TL;DR

The reported analysis highlighted the conflicting trade-off nature of plan robustness and dosimetric quality, demonstrating how robust MCO supports a more informed and flexible decision-making process in treatment planning.

Abstract

Treatment planning in radiotherapy is inherently a multi-criteria optimization (MCO) problem. Traditionally, the treatment's robustness is not formulated as a part of this decision making problem, but dealt with separately through margins or robust optimization. This work facilitates integration of robustness into multi-criteria optimization using a recently proposed efficient scenario-free (s-f) robust optimization approach: The s-f approach relies on the fast evaluation of the expected dose distribution and mean variance during optimization. This is achieved by precomputation of probabilistic quantities, which can then be used for repeated solving of subproblems in the two explored MCO approaches: Lexicographic Ordering (LO) and Pareto Front (PF) approximation. Different prioritization strategies within the LO approach are used to assess the impact of variance reduction while a 3-objective PF approximation, including a variance reduction objective, is generated to visualize and analyze trade-offs between the competing objectives. The robust optimization is performed including 100 scenarios modeling setup and range errors, as well as organ motion, on 3D- and 4DCT lung cancer patient datasets. Robustness analysis is performed to assess and explore the efficacy of all optimization strategies. The s-f approach enabled robust optimization in MCO with computational times comparable to nominal MCO. Both MCO strategies highlighted the interplay between dosimetric and variance reduction objectives. The LO approach showed how prioritization affects plan quality and robustness, while the PF analysis revealed a clear trade-off between robustness and organ-at-risk sparing. The reported analysis highlighted the conflicting trade-off nature of plan robustness and dosimetric quality, demonstrating how robust MCO supports a more informed and flexible decision-making process in treatment planning.

Trading robustness: a scenario-free approach to robust Multi-Criteria Optimization for Treatment Planning

TL;DR

The reported analysis highlighted the conflicting trade-off nature of plan robustness and dosimetric quality, demonstrating how robust MCO supports a more informed and flexible decision-making process in treatment planning.

Abstract

Treatment planning in radiotherapy is inherently a multi-criteria optimization (MCO) problem. Traditionally, the treatment's robustness is not formulated as a part of this decision making problem, but dealt with separately through margins or robust optimization. This work facilitates integration of robustness into multi-criteria optimization using a recently proposed efficient scenario-free (s-f) robust optimization approach: The s-f approach relies on the fast evaluation of the expected dose distribution and mean variance during optimization. This is achieved by precomputation of probabilistic quantities, which can then be used for repeated solving of subproblems in the two explored MCO approaches: Lexicographic Ordering (LO) and Pareto Front (PF) approximation. Different prioritization strategies within the LO approach are used to assess the impact of variance reduction while a 3-objective PF approximation, including a variance reduction objective, is generated to visualize and analyze trade-offs between the competing objectives. The robust optimization is performed including 100 scenarios modeling setup and range errors, as well as organ motion, on 3D- and 4DCT lung cancer patient datasets. Robustness analysis is performed to assess and explore the efficacy of all optimization strategies. The s-f approach enabled robust optimization in MCO with computational times comparable to nominal MCO. Both MCO strategies highlighted the interplay between dosimetric and variance reduction objectives. The LO approach showed how prioritization affects plan quality and robustness, while the PF analysis revealed a clear trade-off between robustness and organ-at-risk sparing. The reported analysis highlighted the conflicting trade-off nature of plan robustness and dosimetric quality, demonstrating how robust MCO supports a more informed and flexible decision-making process in treatment planning.
Paper Structure (28 sections, 5 equations, 4 figures, 2 tables)

This paper contains 28 sections, 5 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Materials and Methods
  3. Multi Criteria Optimization
  4. A posteriori approach: Pareto Front navigation
  5. A priori approach: Lexicographic Ordering
  6. The scenario-free approximation to robust optimization
  7. MCO Robust Optimization Strategies
  8. LO strategies
  9. Pareto Front Approximation
  10. Treatment planning application
  11. Objective functions and clinical goals
  12. Patient datasets
  13. Robustness Analysis
  14. Algorithm implementation
  15. Results
  16. ...and 13 more sections

Figures (4)

  • Figure 1: Comparison between optimized plans for 3.0 different LO optimization strategies. (Strategy 1, Step 4) Comparison between the nominal plan (left) and the scenario-free robust plan (right) for the last optimization step of the Strategy 1. (Strategy 2) Comparison between DVHs and expected dose distribution (left) and SDVHs and standard deviation maps (right) for the last dosimetric (Step 4) and variance reduction (Step 5) steps of Strategy 2. (Strategy 3) DVHs, expected dose distribution, SDVHs and standard deviation distribution of the last step of the optimization Strategy 3. For the DVH plots, the solid line corresponds to the DVH computed for the expected dose distribution, while the dotted lines correspond to the 25.0-75.0 percentiles. The colored DVH band spans the 5.0-95.0 percentiles over the scenarios distribution. For the SDVH of Strategy 2, solid lines for the target correspond to the SDVH for the corresponding step, strategy and plan, the dotted lines serve as a comparison reference for the nominal plan (Step 4) and the previous step (Step 5). All colorbar values are reported in Gy.
  • Figure 2: Robustness analyses performed for the Step 5 and Step 6 of the LO Strategy 4. Top left: SDVH analysis and SD distribution computed on the 3D-only set of error scenarios. The green dashed line corresponds to the target SDVH obtained at Step 4 for the same strategy and 3D error scenario dataset. Top right: SDVH and SD analysis for the same step but performed for the 4D scenario dataset only including the nominal CT-phases. Bottom: DVH and expected-dose distribution (left) and SDVH and SD distribution (right) performed for Step 6 on the complete combined set of 3D and 4D error scenarios. All the reported values are in Gy.
  • Figure 3: Representation of the Pareto front (a-d) for the considered case and correlation analysis for interpolated solutions on the surface (e-h). Black dots on the complete surface (b) and the three projections (a,c,d) correspond to points obtained through the sandwiching algorithm. The yellow and blue circles in (a-d) highlight Solution 1 and 2 respectively. SDVHs for the target (e), DVHs for the heart (f) and lung (g) for solutions obtained through interpolation of the Pareto surface. DVH ans SDVH lines with the same color correspond to the same solution. Scatter plot (h) relating $SD_{50}$ for the target and $V_{5}$ for the heart for the same set of sampled solutions. The set is color coded according to the $D_{20}$ metric for the lung of the corresponding solution.
  • Figure 4: Comparison between DVHs and dose distribution (left), SD distribution and SDVHs (right) for Solution 1 (top) and Solution 2 (bottom). For the DVH plots, the solid line represents the DVH computed for the expected dose distribution, the dotted lines correspond to the 25.0-75.0 % percentiles of the DVH distribution over the error scenarios, and the colored band corresponds to the 5.0-95.0 % percentiles. All reported values are in Gy.