title: A Monte Carlo approach to the microdosimetric kinetic model to account for dose rate time structure effects in ion beam therapy with application in treatment planning simulations.
abstract: OBJECTIVE
  Advanced ion beam therapeutic techniques, such as hypofractionation, respiratory gating, or laser-based pulsed beams, have dose rate time structures which are substantially different from those found in conventional approaches. The biological impact of the time structure is mediated through the β parameter in the linear quadratic (LQ) model. The aim of this study was to assess the impact of changes in the value of the β parameter on the treatment outcomes, also accounting for noninstantaneous intrafraction dose delivery or fractionation and comparing the effects of using different primary ions.
  
  
  METHODS
  An original formulation of the microdosimetric kinetic model (MKM) is used (named MCt-MKM), in which a Monte Carlo (MC) approach was introduced to account for the stochastic spatio-temporal correlations characteristic of the irradiations and the cellular repair kinetics. A modified version of the kinetic equations, validated on experimental cell survival in vitro data, was also introduced. The model, trained on the HSG cells, was used to evaluate the relative biological effectiveness (RBE) for treatments with acute and protracted fractions. Exemplary cases of prostate cancer irradiated with different ion beams were evaluated to assess the impact of the temporal effects.
  
  
  RESULTS
  The LQ parameters for a range of cell lines (V79, HSG, and T1) and ion species (H, He, C, and Ne) were evaluated and compared with the experimental data available in the literature, with good results. Notably, in contrast to the original MKM formulation, the MCt-MKM explicitly predicts an ion and LET-dependent β compatible with observations. The data from a split-dose experiment were used to experimentally determine the value of the parameter related to the cellular repair kinetics. Concerning the clinical case considered, an RBE decrease was observed, depending on the dose, ion, and LET, exceeding up to 3% of the acute value in the case of a protraction in the delivery of 10 min. The intercomparison between different ions shows that the clinical optimality is strongly dependent on a complex interplay between the different physical and biological quantities considered.
  
  
  CONCLUSIONS
  The present study provides a framework for exploiting the temporal effects of dose delivery. The results show the possibility of optimizing the treatment outcomes accounting for the correlation between the specific dose rate time structure and the spatial characteristic of the LET distribution, depending on the ion type used.
authors.affiliation: Physics Department, Università degli studi di Torino, Torino, Italy.|Istituto Nazionale di Fisica Nucleare (INFN), Torino, Italy.
authors.forename: Lorenzo
authors.initials: L
authors.lastname: Manganaro
authors.affiliation: Istituto Nazionale di Fisica Nucleare (INFN), Torino, Italy.
authors.forename: Germano
authors.initials: G
authors.lastname: Russo
authors.affiliation: Physics Department, Università degli studi di Torino, Torino, Italy.|Istituto Nazionale di Fisica Nucleare (INFN), Torino, Italy.
authors.forename: Roberto
authors.initials: R
authors.lastname: Cirio
authors.affiliation: Physics Department, Università degli studi di Torino, Torino, Italy.|Istituto Nazionale di Fisica Nucleare (INFN), Torino, Italy.
authors.forename: Federico
authors.initials: F
authors.lastname: Dalmasso
authors.affiliation: Istituto Nazionale di Fisica Nucleare (INFN), Torino, Italy.
authors.forename: Simona
authors.initials: S
authors.lastname: Giordanengo
authors.affiliation: Physics Department, Università degli studi di Torino, Torino, Italy.|Istituto Nazionale di Fisica Nucleare (INFN), Torino, Italy.
authors.forename: Vincenzo
authors.initials: V
authors.lastname: Monaco
authors.affiliation: Istituto Nazionale di Fisica Nucleare (INFN), Milano, Italy.
authors.forename: Silvia
authors.initials: S
authors.lastname: Muraro
authors.affiliation: Physics Department, Università degli studi di Torino, Torino, Italy.|Istituto Nazionale di Fisica Nucleare (INFN), Torino, Italy.
authors.forename: Roberto
authors.initials: R
authors.lastname: Sacchi
authors.affiliation: Istituto Nazionale di Fisica Nucleare (INFN), Torino, Italy.
authors.forename: Anna
authors.initials: A
authors.lastname: Vignati
authors.affiliation: Istituto Nazionale di Fisica Nucleare (INFN), Torino, Italy.
authors.forename: Andrea
authors.initials: A
authors.lastname: Attili
mesh_terms: D045744:Cell Line, Tumor; D006801:Humans; D007700:Kinetics; D008954:Models, Biological; D009010:Monte Carlo Method; D011829:Radiation Dosage; D011874:Radiometry; D011879:Radiotherapy Dosage; D011880:Radiotherapy Planning, Computer-Assisted; D012062:Relative Biological Effectiveness; D013269:Stochastic Processes
keywords: 
  MKM
  ; dose-rate; particle therapy; radiobiology; repair kinetics