title: A phenomenological biological dose model for proton therapy based on linear energy transfer spectra.
abstract: OBJECTIVE
  The relative biological effectiveness (RBE) of protons varies with the radiation quality, quantified by the linear energy transfer (LET). Most phenomenological models employ a linear dependency of the dose-averaged LET (LETd) to calculate the biological dose. However, several experiments have indicated a possible non-linear trend. Our aim was to investigate if biological dose models including non-linear LET dependencies should be considered, by introducing a LET spectrum based dose model.
  
  
  METHODS
  The RBE-LET relationship was investigated by fitting of polynomials from 1st to 5th degree to a database of 85 data points from aerobic in vitro experiments. We included both unweighted and weighted regression, the latter taking into account experimental uncertainties. Statistical testing was performed to decide whether higher degree polynomials provided better fits to the data as compared to lower degrees. The newly developed models were compared to three published LETdbased models for a simulated spread out Bragg peak (SOBP) scenario.
  
  
  RESULTS
  The statistical analysis of the weighted regression analysis favored a non-linear RBE-LET relationship, with the quartic polynomial found to best represent the experimental data (P = 0.010). The results of the unweighted regression analysis were on the borderline of statistical significance for non-linear functions (P = 0.053), and with the current database a linear dependency could not be rejected. For the SOBP scenario, the weighted non-linear model estimated a similar mean RBE value (1.14) compared to the three established models (1.13-1.17). The unweighted model calculated a considerably higher RBE value (1.22).
  
  
  CONCLUSIONS
  The analysis indicated that non-linear models could give a better representation of the RBE-LET relationship. However, this is not decisive, as inclusion of the experimental uncertainties in the regression analysis had a significant impact on the determination and ranking of the models. As differences between the models were observed for the SOBP scenario, both non-linear LET spectrum- and linear LETdbased models should be further evaluated in clinically realistic scenarios.
authors.affiliation: Department of Physics and Technology, University of Bergen, Bergen, Norway.
authors.forename: Eivind
authors.initials: E
authors.lastname: Rørvik
authors.affiliation: Department of Physics and Technology, University of Bergen, Bergen, Norway.|Department of Oncology and Medical Physics, Haukeland University Hospital, Bergen, Norway.
authors.forename: Sara
authors.initials: S
authors.lastname: Thörnqvist
authors.affiliation: Department of Oncology and Medical Physics, Haukeland University Hospital, Bergen, Norway.
authors.forename: Camilla H
authors.initials: CH
authors.lastname: Stokkevåg
authors.affiliation: Department of Physics and Technology, University of Bergen, Bergen, Norway.
authors.forename: Tordis J
authors.initials: TJ
authors.lastname: Dahle
authors.affiliation: Department of Physics and Technology, University of Bergen, Bergen, Norway.|Department of Oncology and Medical Physics, Haukeland University Hospital, Bergen, Norway.
authors.forename: Lars Fredrik
authors.initials: LF
authors.lastname: Fjaera
authors.affiliation: Department of Physics and Technology, University of Bergen, Bergen, Norway.
authors.forename: Kristian S
authors.initials: KS
authors.lastname: Ytre-Hauge
mesh_terms: D018499:Linear Energy Transfer; D017711:Nonlinear Dynamics; D061766:Proton Therapy; D011522:Protons; D012062:Relative Biological Effectiveness
chemical_list: D011522:Protons
keywords: LET spectrum; biological dose modelling; linear energy transfer; mixed field radiation; proton therapy; relative biological effectiveness