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@ARTICLE{Wahl:157338,
      author       = {N. Wahl$^*$ and P. Hennig and H.-P. Wieser$^*$ and M.
                      Bangert$^*$},
      title        = {{A}nalytical probabilistic modeling of dose-volume
                      histograms.},
      journal      = {Medical physics},
      volume       = {47},
      number       = {10},
      issn         = {2473-4209},
      address      = {College Park, Md.},
      publisher    = {AAPM},
      reportid     = {DKFZ-2020-01567},
      pages        = {5260-5273},
      year         = {2020},
      note         = {#EA:E040#LA:E040#2020 Oct;47(10):5260-5273},
      abstract     = {Radiotherapy, especially with charged particles, is
                      sensitive to executional and preparational uncertainties
                      that propagate to uncertainty in dose and plan quality
                      indicators, e. g., 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, in
                      particular expectation value and (co)variance, of the
                      probability distribution of DVH-points, and evaluate its
                      accuracy on patient data.We use Analytical Probabilistic
                      Modeling (APM) to derive moments of the probability
                      distribution over individual DVH-points based on the
                      probability distribution over dose. By using the computed
                      moments to parameterize distinct probability distributions
                      over DVH-points (here normal or beta distributions), not
                      only the moments but also percentiles, i. e., α-DVHs, are
                      computed. The model is subsequently evaluated on three
                      patient cases (intracranial, paraspinal, prostate) in 30-
                      and singlefraction scenarios by assuming the dose to follow
                      a multivariate normal distribution, whose moments are
                      computed in closed-form with APM. The results are compared
                      to a benchmark based on discrete random sampling.The
                      evaluation of the new probabilistic model on the three
                      patient cases against a sampling benchmark proves its
                      correctness under perfect assumptions as well as good
                      agreement in realistic conditions. More precisely, ca.
                      $90\%$ of all computed expected DVH-points and their
                      standard deviations agree within $1\%$ volume with their
                      empirical counterpart from sampling computations, for both
                      fractionated and single fraction treatments. When computing
                      α-DVHs, the assumption of a beta distribution achieved
                      better agreement with empirical percentiles than the
                      assumption of a normal distribution: While in both cases
                      probabilities locally showed large deviations (up to ±0.2),
                      the respective α -DVHs for α = {0:05; 0:5; 0:95} only
                      showed small deviations in respective volume (up to $±5\%$
                      volume for a normal distribution, and up to $2\%$ for a beta
                      distribution). A previously published model from literature,
                      which was included for comparison, exhibited substantially
                      larger deviations.With APM we could derive a mathematically
                      exact description of moments of probability distributions
                      over DVH-points given a probability distribution over dose.
                      The model generalizes previous attempts and performs well
                      for both choices of probability distributions, i. e., normal
                      or beta distributions, over DVH-points.},
      cin          = {E040},
      ddc          = {610},
      cid          = {I:(DE-He78)E040-20160331},
      pnm          = {315 - Imaging and radiooncology (POF3-315)},
      pid          = {G:(DE-HGF)POF3-315},
      typ          = {PUB:(DE-HGF)16},
      pubmed       = {pmid:32740930},
      doi          = {10.1002/mp.14414},
      url          = {https://inrepo02.dkfz.de/record/157338},
}