title: Variance-based sensitivity analysis of biological uncertainties in carbon ion therapy.
abstract: OBJECTIVE
  Biological models to estimate the relative biological effectiveness (RBE) or the equivalent dose in 2 Gy fractions (EQD2) are needed for treatment planning and plan evaluation in carbon ion therapy. We present a model-independent, Monte Carlo based sensitivity analysis (SA) approach to quantify the impact of different uncertainties on the biological models.
  
  
  METHODS
  The Monte Carlo based SA is used for the evaluation of variations in biological parameters. The key property of this SA is the high number of simulation runs, each with randomized input parameters, allowing for a statistical variance-based ranking of the input variations. The potential of this SA is shown in a simplified one-dimensional treatment plan optimization. Physical properties of carbon ion beams (e.g. fragmentation) are simulated using the Monte Carlo code FLUKA. To estimate biological effects of ion beams compared to X-rays, we use the Local Effect Model (LEM) in the framework of the linear-quadratic (LQ) model. Currently, only uncertainties in the output of the biological models are taken into account.
  
  
  CONCLUSIONS
  The presented SA is suitable for evaluation of the impact of variations in biological parameters. Major advantages are the possibility to access and display the sensitivity of the evaluated quantity on several parameter variations at the same time. Main challenges for later use in three-dimensional treatment plan evaluation are computational time and memory usage. The presented SA can be performed with any analytical or numerical function and hence be applied to any biological model used in carbon ion therapy.
authors.affiliation: Department of Radiation Oncology, Technische Universität München, Klinikum rechts der Isar, Ismaninger Str. 22, 81675 München, Germany. Electronic address: florian.kamp@lrz.tu-muenchen.de.
authors.forename: F
authors.initials: F
authors.lastname: Kamp
authors.affiliation: Department of Radiation Oncology, Technische Universität München, Klinikum rechts der Isar, Ismaninger Str. 22, 81675 München, Germany.
authors.forename: S
authors.initials: S
authors.lastname: Brüningk
authors.affiliation: Ludwig Maximilians University (LMU) Munich, Experimental Physics - Medical Physics, Am Coulombwall 1, 85748 Garching, Germany.
authors.forename: G
authors.initials: G
authors.lastname: Cabal
authors.affiliation: Medical Physics Unit CNAO Foundation, Strada Campeggi 53, 27100 Pavia, Italy; Heidelberg Ion-Beam Therapy Center, Im Neuenheimer Feld 450, 69120 Heidelberg, Germany.
authors.forename: A
authors.initials: A
authors.lastname: Mairani
authors.affiliation: Ludwig Maximilians University (LMU) Munich, Experimental Physics - Medical Physics, Am Coulombwall 1, 85748 Garching, Germany.
authors.forename: K
authors.initials: K
authors.lastname: Parodi
authors.affiliation: Department of Radiation Oncology, Technische Universität München, Klinikum rechts der Isar, Ismaninger Str. 22, 81675 München, Germany.
authors.forename: J J
authors.initials: JJ
authors.lastname: Wilkens
mesh_terms: D000465:Algorithms; D000704:Analysis of Variance; D063193:Heavy Ion Radiotherapy / Q000379:methods*; D009010:Monte Carlo Method; D011880:Radiotherapy Planning, Computer-Assisted; D035501:Uncertainty
keywords: Carbon ion therapy; RBE; Sensitivity analysis