title: Analysis of the track- and dose-averaged LET and LET spectra in proton therapy using the geant4 Monte Carlo code.
abstract: OBJECTIVE
  The motivation of this study was to find and eliminate the cause of errors in dose-averaged linear energy transfer (LET) calculations from therapeutic protons in small targets, such as biological cell layers, calculated using the geant 4 Monte Carlo code. Furthermore, the purpose was also to provide a recommendation to select an appropriate LET quantity from geant 4 simulations to correlate with biological effectiveness of therapeutic protons.
  
  
  METHODS
  The authors developed a particle tracking step based strategy to calculate the average LET quantities (track-averaged LET, LETt and dose-averaged LET, LETd) using geant 4 for different tracking step size limits. A step size limit refers to the maximally allowable tracking step length. The authors investigated how the tracking step size limit influenced the calculated LETt and LETd of protons with six different step limits ranging from 1 to 500 μm in a water phantom irradiated by a 79.7-MeV clinical proton beam. In addition, the authors analyzed the detailed stochastic energy deposition information including fluence spectra and dose spectra of the energy-deposition-per-step of protons. As a reference, the authors also calculated the averaged LET and analyzed the LET spectra combining the Monte Carlo method and the deterministic method. Relative biological effectiveness (RBE) calculations were performed to illustrate the impact of different LET calculation methods on the RBE-weighted dose.
  
  
  RESULTS
  Simulation results showed that the step limit effect was small for LETt but significant for LETd. This resulted from differences in the energy-deposition-per-step between the fluence spectra and dose spectra at different depths in the phantom. Using the Monte Carlo particle tracking method in geant 4 can result in incorrect LETd calculation results in the dose plateau region for small step limits. The erroneous LETd results can be attributed to the algorithm to determine fluctuations in energy deposition along the tracking step in geant 4. The incorrect LETd values lead to substantial differences in the calculated RBE.
  
  
  CONCLUSIONS
  When the geant 4 particle tracking method is used to calculate the average LET values within targets with a small step limit, such as smaller than 500 μm, the authors recommend the use of LETt in the dose plateau region and LETd around the Bragg peak. For a large step limit, i.e., 500 μm, LETd is recommended along the whole Bragg curve. The transition point depends on beam parameters and can be found by determining the location where the gradient of the ratio of LETd and LETt becomes positive.
authors.affiliation: Department of Radiation Physics, The University of Texas MD Anderson Cancer Center, 1515 Holcombe Boulevard, Houston, Texas 77030.
authors.forename: Fada
authors.initials: F
authors.lastname: Guan
authors.affiliation: Department of Radiation Physics, The University of Texas MD Anderson Cancer Center, 1515 Holcombe Boulevard, Houston, Texas 77030.
authors.forename: Christopher
authors.initials: C
authors.lastname: Peeler
authors.affiliation: Department of Experimental Radiation Oncology, The University of Texas MD Anderson Cancer Center, 1515 Holcombe Boulevard, Houston, Texas 77030.
authors.forename: Lawrence
authors.initials: L
authors.lastname: Bronk
authors.affiliation: Department of Nuclear Science and Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China and Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, Massachusetts 02114.
authors.forename: Changran
authors.initials: C
authors.lastname: Geng
authors.affiliation: Department of Radiation Physics, The University of Texas MD Anderson Cancer Center, 1515 Holcombe Boulevard, Houston, Texas 77030.
authors.forename: Reza
authors.initials: R
authors.lastname: Taleei
authors.affiliation: Department of Radiation Physics, The University of Texas MD Anderson Cancer Center, 1515 Holcombe Boulevard, Houston, Texas 77030.
authors.forename: Sharmalee
authors.initials: S
authors.lastname: Randeniya
authors.affiliation: Department of Radiation Physics, The University of Texas MD Anderson Cancer Center, 1515 Holcombe Boulevard, Houston, Texas 77030.
authors.forename: Shuaiping
authors.initials: S
authors.lastname: Ge
authors.affiliation: Department of Radiation Physics, The University of Texas MD Anderson Cancer Center, 1515 Holcombe Boulevard, Houston, Texas 77030.
authors.forename: Dragan
authors.initials: D
authors.lastname: Mirkovic
authors.affiliation: Department of Experimental Radiation Oncology, The University of Texas MD Anderson Cancer Center, 1515 Holcombe Boulevard, Houston, Texas 77030 and Department of Radiation Oncology, The University of Texas MD Anderson Cancer Center, 1515 Holcombe Boulevard, Houston, Texas 77030.
authors.forename: David
authors.initials: D
authors.lastname: Grosshans
authors.affiliation: Department of Radiation Physics, The University of Texas MD Anderson Cancer Center, 1515 Holcombe Boulevard, Houston, Texas 77030.
authors.forename: Radhe
authors.initials: R
authors.lastname: Mohan
authors.affiliation: Department of Radiation Physics, The University of Texas MD Anderson Cancer Center, 1515 Holcombe Boulevard, Houston, Texas 77030.
authors.forename: Uwe
authors.initials: U
authors.lastname: Titt
mesh_terms: D003198:Computer Simulation; D004307:Dose-Response Relationship, Radiation; D006801:Humans; D018499:Linear Energy Transfer / Q000502:physiology* / Q000528:radiation effects; D008954:Models, Biological; D015233:Models, Statistical; D009010:Monte Carlo Method; D061766:Proton Therapy / Q000379:methods*; D011879:Radiotherapy Dosage; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods*; D012984:Software; D011522:Protons
chemical_list: D011522:Protons