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@ARTICLE{Stammer:176997,
      author       = {P. Stammer$^*$ and L. Burigo$^*$ and O. Jäkel$^*$ and M.
                      Frank and N. Wahl$^*$},
      title        = {{E}fficient uncertainty quantification for {M}onte {C}arlo
                      dose calculations using importance (re-)weighting.},
      journal      = {Physics in medicine and biology},
      volume       = {66},
      number       = {20},
      issn         = {1361-6560},
      address      = {Bristol},
      publisher    = {IOP Publ.},
      reportid     = {DKFZ-2021-02230},
      pages        = {205003},
      year         = {2021},
      note         = {#EA:E040#LA:E040#},
      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 (γ2 $mm/2\%≥$
                      $99.01\%$ (E[d]),γ2 $mm/2\%≥$ $98.04\%$ (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.},
      keywords     = {Monte Carlo (Other) / importance sampling (Other) /
                      intensity modulated particle therapy (IMPT) (Other) / proton
                      therapy (Other) / range error (Other) / setup error (Other)
                      / uncertainty (Other)},
      cin          = {E040},
      ddc          = {530},
      cid          = {I:(DE-He78)E040-20160331},
      pnm          = {315 - Bildgebung und Radioonkologie (POF4-315)},
      pid          = {G:(DE-HGF)POF4-315},
      typ          = {PUB:(DE-HGF)16},
      pubmed       = {pmid:34544068},
      doi          = {10.1088/1361-6560/ac287f},
      url          = {https://inrepo02.dkfz.de/record/176997},
}