title: Discontinuous finite element space-angle treatment of the first order linear Boltzmann transport equation with magnetic fields: Application to MRI-guided radiotherapy.
abstract: OBJECTIVE
  The advent of magnetic resonance imaging (MRI) guided radiotherapy systems demands the incorporation of the magnetic field into dose calculation algorithms of treatment planning systems. This is due to the fact that the Lorentz force of the magnetic field perturbs the path of the relativistic electrons, hence altering the dose deposited by them. Building on the previous work, the authors have developed a discontinuous finite element space-angle treatment of the linear Boltzmann transport equation to accurately account for the effects of magnetic fields on radiotherapy doses.
  
  
  METHODS
  The authors present a detailed description of their new formalism and compare its accuracy to geant4 Monte Carlo calculations for magnetic fields parallel and perpendicular to the radiation beam at field strengths of 0.5 and 3 T for an inhomogeneous 3D slab geometry phantom comprising water, bone, and air or lung. The accuracy of the authors' new formalism was determined using a gamma analysis with a 2%/2 mm criterion.
  
  
  RESULTS
  Greater than 98.9% of all points analyzed passed the 2%/2 mm gamma criterion for the field strengths and orientations tested. The authors have benchmarked their new formalism against Monte Carlo in a challenging radiation transport problem with a high density material (bone) directly adjacent to a very low density material (dry air at STP) where the effects of the magnetic field dominate collisions.
  
  
  CONCLUSIONS
  A discontinuous finite element space-angle approach has been proven to be an accurate method for solving the linear Boltzmann transport equation with magnetic fields for cases relevant to MRI guided radiotherapy. The authors have validated the accuracy of this novel technique against geant4, even in cases of strong magnetic field strengths and low density air.
authors.affiliation: Department of Medical Physics, Cross Cancer Institute, 11560 University Avenue, Edmonton, Alberta T6G 1Z2, Canada and Department of Oncology, Medical Physics Division, University of Alberta, 11560 University Avenue, Edmonton, Alberta T6G 1Z2, Canada.
authors.forename: J
authors.initials: J
authors.lastname: St Aubin
authors.affiliation: Department of Medical Physics, Cross Cancer Institute, 11560 University Avenue, Edmonton, Alberta T6G 1Z2, Canada.
authors.forename: A
authors.initials: A
authors.lastname: Keyvanloo
authors.affiliation: Department of Medical Physics, Cross Cancer Institute, 11560 University Avenue, Edmonton, Alberta T6G 1Z2, Canada; Department of Oncology, Medical Physics Division, University of Alberta, 11560 University Avenue, Edmonton, Alberta T6G 1Z2, Canada; and Department of Physics, University of Alberta, Edmonton, Alberta T6G 2M9, Canada.
authors.forename: B G
authors.initials: BG
authors.lastname: Fallone
mesh_terms: D000388:Air; D000465:Algorithms; D020342:Finite Element Analysis; D006801:Humans; D016014:Linear Models; D060526:Magnetic Fields; D008279:Magnetic Resonance Imaging; D009010:Monte Carlo Method; D017785:Photons; D011880:Radiotherapy Planning, Computer-Assisted; D061089:Radiotherapy, Image-Guided