Abstract
Objective. To present an efficient uncertainty quantification method for range and set-up errors in Monte Carlo (MC) dose calculations. Further, we show that uncertainty induced by interplay and other dynamic influences may be approximated using suitable error correlation models. Approach. We introduce an importance (re-)weighting method in MC history scoring to concurrently construct estimates for error scenarios, the expected dose and its variance from a single set of MC simulated particle histories. The approach relies on a multivariate Gaussian input and uncertainty model, which assigns probabilities to the initial phase space sample, enabling the use of different correlation models. Through modification of the phase space parameterization, accuracy can be traded between that of the uncertainty or the nominal dose estimate. Main results. The method was implemented using the MC code TOPAS and validated for proton intensity-modulated particle therapy (IMPT) with reference scenario estimates. We achieve accurate results for set-up uncertainties (γ 2 mm/2% ≥ 99.01% (E[ d ]), γ 2 mm/2% ≥ 98.04% (σ( d ))) and expectedly lower but still sufficient agreement for range uncertainties, which are approximated with uncertainty over the energy distribution. Here pass rates of 99.39% (E[ d ])/ 93.70% (σ( d )) (range errors) and 99.86% (E[ d ])/ 96.64% (σ( d )) (range and set-up errors) can be achieved. Initial evaluations on a water phantom, a prostate and a liver case from the public CORT dataset show that the CPU time decreases by more than an order of magnitude. Significance. The high precision and conformity of IMPT comes at the cost of susceptibility to treatment uncertainties in particle range and patient set-up. Yet, dose uncertainty quantification and mitigation, which is usually based on sampled error scenarios, becomes challenging when computing the dose with computationally expensive but accurate MC simulations. As the results indicate, the proposed method could reduce computational effort while also facilitating the use of high-dimensional uncertainty models.
Highlights
Monte Carlo (MC) methods are considered the gold standard for dose calculation in radiotherapy treatment planning due to their accuracy (Weng et al 2003, Paganetti 2012)
We demonstrate the application of this method to approximate expected value and variance of dose, given a respective uncertainty model for set-up and range errors, which includes the choice of different beam and pencil beam correlation scenarios
We introduce an efficient approach for uncertainty quantification in MC dose calculations using historyweighting
Summary
Monte Carlo (MC) methods are considered the gold standard for dose calculation in radiotherapy treatment planning due to their accuracy (Weng et al 2003, Paganetti 2012). Particle therapy demands personalized robustness analyses and mitigation Such techniques may be based on explicit propagation of input uncertainties using probabilistic methods and statistical analysis (Bangert et al 2013, Kraan et al 2013, Park et al 2013, Perkó et al 2016, Wahl et al 2017, 2020) or worst-case estimates (Casiraghi et al 2013, McGowan et al 2015, Lowe et al 2016). Most of these methods further translate to robust and probabilistic optimization to extend the conventional, generic margin approach to uncertainty mitigation (Sobotta et al 2010, Fredriksson 2012, Liu et al 2012, Unkelbach et al 2018)
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