title: On the parametrization of lateral dose profiles in proton radiation therapy.
abstract: OBJECTIVE
  The accurate evaluation of the lateral dose profile is an important issue in the field of proton radiation therapy. The beam spread, due to Multiple Coulomb Scattering (MCS), is described by the Molière's theory. To take into account also the contribution of nuclear interactions, modern Treatment Planning Systems (TPSs) generally approximate the dose profiles by a sum of Gaussian functions. In this paper we have compared different parametrizations for the lateral dose profile of protons in water for therapeutical energies: the goal is to improve the performances of the actual treatment planning.
  
  
  METHODS
  We have simulated typical dose profiles at the CNAO (Centro Nazionale di Adroterapia Oncologica) beamline with the FLUKA code and validated them with data taken at CNAO considering different energies and depths. We then performed best fits of the lateral dose profiles for different functions using ROOT and MINUIT.
  
  
  RESULTS
  The accuracy of the best fits was analyzed by evaluating the reduced χ(2), the number of free parameters of the functions and the calculation time. The best results were obtained with the triple Gaussian and double Gaussian Lorentz-Cauchy functions which have 6 parameters, but good results were also obtained with the so called Gauss-Rutherford function which has only 4 parameters.
  
  
  CONCLUSIONS
  The comparison of the studied functions with accurate and validated Monte Carlo calculations and with experimental data from CNAO lead us to propose an original parametrization, the Gauss-Rutherford function, to describe the lateral dose profiles of proton beams.
authors.affiliation: Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, Pavia, Italy; Dipartimento di Fisica, Università di Pavia, Pavia, Italy; Department of Medical Physics, Ludwig Maximilians University, Munich, Germany.
authors.forename: V E
authors.initials: VE
authors.lastname: Bellinzona
authors.affiliation: Medical Physics Unit, Centro Nazionale di Adroterapia Oncologica, Pavia, Italy.
authors.forename: M
authors.initials: M
authors.lastname: Ciocca
authors.affiliation: Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, Pavia, Italy; Dipartimento di Fisica, Università di Pavia, Pavia, Italy.
authors.forename: A
authors.initials: A
authors.lastname: Embriaco
authors.affiliation: Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, Pavia, Italy. Electronic address: andrea.fontana@pv.infn.it.
authors.forename: A
authors.initials: A
authors.lastname: Fontana
authors.affiliation: Medical Physics Unit, Centro Nazionale di Adroterapia Oncologica, Pavia, Italy.
authors.forename: A
authors.initials: A
authors.lastname: Mairani
authors.affiliation: Dipartimento di Fisica, Università di Pavia, Pavia, Italy.
authors.forename: M
authors.initials: M
authors.lastname: Mori
authors.affiliation: Department of Medical Physics, Ludwig Maximilians University, Munich, Germany; Heidelberg Ion Beam Therapy Center, University Hospital Heidelberg, Heidelberg, Germany.
authors.forename: K
authors.initials: K
authors.lastname: Parodi
mesh_terms: D016011:Normal Distribution; D061766:Proton Therapy; D011829:Radiation Dosage; D011879:Radiotherapy Dosage; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods*; D012542:Scattering, Radiation
keywords: Lateral dose distribution; Proton therapy; TPS optimization