Purpose: This work demonstrates the feasibility of using a robustness analysis for the determination of tolerance limits with probabilistic machine learning methods. Specifically, this study (1) evaluates the dosimetric sensitivity of linac-based cranial single-isocenter multi-target (SIMT) plans to systematic geometric errors, and (2) interprets these sensitivities with respect to the probability of meeting clinical objectives.
Methods: Dose distributions were evaluated for 5 SIMT plans having 3 to 15 brain metastases under simulated systematic translation and rotation errors of -5 to 5 mm and -3 to 3 degrees. All plans were created in Eclipse using four non-coplanar arcs without target margins. Ensembles of support vector machines (SVM) were used to create uncertainty-aware models for coverage as a function of translation error. Using Gaussian models to describe the probability of shifts, Monte Carlo methods were used to simulate the impact on coverage for each error model and calculate the likelihood of adequate treatment. Quantitative benchmarks for margin expansion, machine quality assurance tolerances, and acceptable target-to-isocenter distance were generated.
Results: SVM ensembles were used to characterize the coverage distribution specified by V₁₀₀, V₉₈ and V₉₅ for translational error models with σ(δr)∈(0, 3mm). Given our planning strategy, to achieve V₉₈>95% with probability 0.95, our heuristic recommends a total translational error <0.42 mm (2σ(δr)). Similarly, for p(V₉₅>95%)=0.90, we would recommend a tolerance of 1.16 mm. For estimates of translation and rotation errors δx=0.4 mm and δθ=0.5°, in order to maintain a combined error of δr <0.8 mm, our method recommends a maximum target-to-isocenter distance of 7.9 cm.
Conclusion: Robustness analyses can be followed through to meaningful clinical endpoints with the help of ensemble machine learning. Our results can help to inform appropriate target margins and mechanical tolerances for cranial SIMT. The techniques described here may easily be extended to other sources of uncertainty.