title: Energy deposition clustering as a functional radiation quality descriptor for modeling relative biological effectiveness.
abstract: OBJECTIVE
  To explore the use of the frequency of the energy deposition (ED) clusters of different sizes (cluster order, CO) as a surrogate (instead of, e.g., LET) classification of the physical characteristics of ionizing radiation at a nanometer scale, to construct a framework for the calculation of relative biological effectiveness (RBE) with cell survival as endpoint.
  
  
  METHODS
  The frequency of cluster order fCOis calculated by sorting the ED sites generated with the Monte Carlo track structure code LIonTrack into clusters based on a single parameter called the cluster distance dCbeing the maximum allowed distance between two neighboring EDs belonging to a cluster. Published cell survival data parameterized with the linear-quadratic (LQ) model for V79 cells exposed to 15 different radiation qualities (including brachytherapy sources, proton, and carbon ions) were used as input to a fitting procedure, designed to determine a weighting function wCOthat describes the capacity of a cluster of a certain CO to damage the cell's sensitive volume. The proposed framework uses both fCOand wCOto construct surrogate based functions for the LQ parameters α and β from which RBE values can be derived.
  
  
  RESULTS
  The results demonstrate that radiation quality independent weights wCOexist for both the α and β parameters. This enables the calculation of α values that correlate to their experimental counterparts within experimental uncertainties (relative residual of 15% for dC= 2.5 nm). The combination of both α and β surrogate based functions, despite the higher relative residuals for β values, yielded an RBE function that correlated to experimentally derived RBE values (relative residual of 16.5% for dC= 2.5 nm) for all radiation qualities included in this work.
  
  
  CONCLUSIONS
  The fCOcluster characterization of ionizing radiation at a nanometer scale can effectively be used to calculate particle and energy dependent α and β values to predict RBE values with potential applications to, e.g., treatment planning systems in radiotherapy.
authors.affiliation: Medical Radiation Sciences, Department of Immunology, Genetics and Pathology, Uppsala University, Akademiska Sjukhuset, Uppsala SE-75185, Sweden.
authors.forename: Fernanda
authors.initials: F
authors.lastname: Villegas
authors.affiliation: Medical Physics Unit, Department of Oncology, McGill University, Montreal, Quebec H4A 3J1, Canada and Research Institute of the McGill University Health Centre, Montreal, Quebec H3H 2R9, Canada.
authors.forename: Gloria
authors.initials: G
authors.lastname: Bäckström
authors.affiliation: Medical Radiation Sciences, Department of Immunology, Genetics and Pathology, Uppsala University, Akademiska Sjukhuset, Uppsala SE-75185, Sweden and Elekta Instrument AB, Box 7593, Stockholm SE-10393, Sweden.
authors.forename: Nina
authors.initials: N
authors.lastname: Tilly
authors.affiliation: Medical Radiation Sciences, Department of Immunology, Genetics and Pathology, Uppsala University, Akademiska Sjukhuset, Uppsala SE-75185, Sweden.
authors.forename: Anders
authors.initials: A
authors.lastname: Ahnesjö
mesh_terms: D002470:Cell Survival / Q000528:radiation effects; D016000:Cluster Analysis; D008954:Models, Biological; D009010:Monte Carlo Method; D011522:Protons; D012062:Relative Biological Effectiveness
chemical_list: D011522:Protons