arXiv subjects

Niklas Wahl

Publications and source records attributed to Niklas Wahl.

22 records · Page 2Linked to original sources

arXiv2022

Multivariate error modeling and uncertainty quantification using importance (re-)weighting for Monte Carlo simulations in particle transport

Fast and accurate predictions of uncertainties in the computed dose are crucial for the determination of robust treatment plans in radiation therapy. This requires the solution of particle transport problems with uncertain parameters or initial conditions. Monte Carlo methods are often used to solve transport problems especially for applications which require high accuracy. In these cases, common non-intrusive solution strategies that involve repeated simulations of the problem at different points in the parameter space quickly become infeasible due to their long run-times. Intrusive methods however limit the usability in combination with proprietary simulation engines. In our previous paper [51], we demonstrated the application of a new non-intrusive uncertainty quantification approach for Monte Carlo simulations in proton dose calculations with normally distributed errors on realistic patient data. In this paper, we introduce a generalized formulation and focus on a more in-depth theoretical analysis of this method concerning bias, error and convergence of the estimates. The multivariate input model of the proposed approach further supports almost arbitrary error correlation models. We demonstrate how this framework can be used to model and efficiently quantify complex auto-correlated and time-dependent errors.

physics.med-ph↗

arXiv2021

Efficient uncertainty quantification for Monte Carlo dose calculations using importance (re-)weighting

The high precision and conformity of intensity-modulated particle therapy (IMPT) comes at the cost of susceptibility to treatment uncertainties in particle range and patient set-up. Dose uncertainty quantification and mitigation, which is usually based on sampled error scenarios, however becomes challenging when computing the dose with computationally expensive but accurate Monte Carlo (MC) simulations. This paper introduces 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. Exploring and adapting bivariate emittance parametrizations for the beam shape, accuracy can be traded between that of the uncertainty or the nominal dose estimate. The method was implemented using the MC code TOPAS and tested for proton IMPT plan delivery in comparison to a reference scenario estimate. We achieve accurate results for set-up uncertainties ($γ_{3mm/3\%} \geq 99.99\%$) and expectedly lower but still sufficient agreement for range uncertainties, which are approximated with uncertainty over the energy distribution ($γ_{3 mm/3\%} \geq 99.50\%$ ($E[\boldsymbol{d}]$), $γ_{3mm/3\%} \geq 91.69\%$ ($σ(\boldsymbol{d})$) ). Initial experiments on a water phantom, a prostate and a liver case show that the re-weighting approach lowers the CPU time by more than an order of magnitude. Further, we show that uncertainty induced by interplay and other dynamic influences may be approximated using suitable error correlation models.

physics.med-ph↗

arXiv2020

Analytical probabilistic modeling of dose-volume histograms

Radiotherapy is sensitive to executional and preparational uncertainties that propagate to uncertainty in dose and plan quality indicators like dose-volume histograms (DVHs). Current approaches to quantify and mitigate such uncertainties rely on explicitly computed error scenarios and are thus subject to statistical uncertainty and limitations regarding the underlying uncertainty model. Here we present an alternative, analytical method to approximate moments of the probability distribution of DVH-points and evaluate its accuracy on patient data. We use analytical probabilistic modeling (APM) to derive those moments for individual DVH-points based on the probability distribution over dose. Further we use the computed moments to parameterize distinct probability distributions over DVH-points (here normal or beta distributions) to compute percentiles/$α$-DVHs. The model is then evaluated on three patient cases in 30- and single-fraction scenarios by assuming the dose to follow a multivariate normal distribution obtained from APM. The results are compared to a sampling benchmark. The evaluation of the new probabilistic model against the sampling benchmark proves its correctness under perfect assumptions as well as good agreement in realistic conditions. Ca. 90% of all computed expected DVH-points and their standard deviations agree within 1% volume with their empirical counterpart from sampling, for both fractionated and single fraction treatments. $α$-DVHs achieve better agreement with empirical percentiles when assuming a beta instead of a normal distribution: While in both cases probabilities show large local deviations (up to $\pm$0.2), the respective $α$-DVH only showed small deviations (up to $\pm$5% volume for a normal, and up to 2% for a beta distribution). A previously published model by different authors yielded substantially deviating $α$-DVHs.

physics.med-ph↗

arXiv2020

Long short-term memory networks for proton dose calculation in highly heterogeneous tissues

A novel dose calculation approach was designed based on the application of LSTM network that processes the 3D patient/phantom geometry as a sequence of 2D computed tomography input slices yielding a corresponding sequence of 2D slices that forms the respective 3D dose distribution. LSTM networks can propagate information effectively in one direction, resulting in a model that can properly imitate the mechanisms of proton interaction in matter. The study is centered on predicting dose on a single pencil beam level, avoiding the averaging effects in treatment plans comprised of thousands pencil beams. Moreover, such approach allows straightforward integration into today's treatment planning systems' inverse planning optimization process. The ground truth training data was prepared with Monte Carlo simulations for both phantom and patient studies by simulating different pencil beams impinging from random gantry angles through the patient geometry. For model training, 10'000 Monte Carlo simulations were prepared for the phantom study, and 4'000 simulations were prepared for the patient study. The trained LSTM model was able to achieve a 99.29 % gamma-index pass rate ([0.5 %, 1 mm]) accuracy on the set-aside test set for the phantom study, and a 99.33 % gamma-index pass rate ([0.5 %, 2 mm]) for the set-aside test set for the patient study. These results were achieved for each pencil beam in 6-23 ms. The average Monte Carlo simulation run-time using Topas was 1160 s. The generalization of the model was verified by testing for 5 previously unseen lung cancer patients. LSTM networks are well suited for proton therapy dose calculation tasks. However, further work needs to be performed to generalize the proposed approach to clinical applications, primarily to be implemented for various energies, patient sites, and CT resolutions/scanners.

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