title: A pencil beam approach to proton computed tomography.
abstract: OBJECTIVE
  A new approach to proton computed tomography (pCT) is presented. In this approach, protons are not tracked one-by-one but a beam of particles is considered instead. The elements of the pCT reconstruction problem (residual energy and path) are redefined on the basis of this new approach. An analytical image reconstruction algorithm applicable to this scenario is also proposed.
  
  
  METHODS
  The pencil beam (PB) and its propagation in matter were modeled by making use of the generalization of the Fermi-Eyges theory to account for multiple Coulomb scattering (MCS). This model was integrated into the pCT reconstruction problem, allowing the definition of the mean beam path concept similar to the most likely path (MLP) used in the single-particle approach. A numerical validation of the model was performed. The algorithm of filtered backprojection along MLPs was adapted to the beam-by-beam approach. The acquisition of a perfect proton scan was simulated and the data were used to reconstruct images of the relative stopping power of the phantom with the single-proton and beam-by-beam approaches. The resulting images were compared in a qualitative way.
  
  
  RESULTS
  The parameters of the modeled PB (mean and spread) were compared to Monte Carlo results in order to validate the model. For a water target, good agreement was found for the mean value of the distributions. As far as the spread is concerned, depth-dependent discrepancies as large as 2%-3% were found. For a heterogeneous phantom, discrepancies in the distribution spread ranged from 6% to 8%. The image reconstructed with the beam-by-beam approach showed a high level of noise compared to the one reconstructed with the classical approach.
  
  
  CONCLUSIONS
  The PB approach to proton imaging may allow technical challenges imposed by the current proton-by-proton method to be overcome. In this framework, an analytical algorithm is proposed. Further work will involve a detailed study of the performances and limitations of this approach in terms of image quality. The paper shows how to account for the MCS in the reconstruction step with this new approach when an analytical reconstruction algorithm is used.
authors.affiliation: Université de Strasbourg, IPHC, 23 rue du Loess, Strasbourg 67037, France and CNRS, UMR7178, Strasbourg 67037, France.
authors.forename: Regina
authors.initials: R
authors.lastname: Rescigno
authors.affiliation: Université de Strasbourg, IPHC, 23 rue du Loess, Strasbourg 67037, France and CNRS, UMR7178, Strasbourg 67037, France.
authors.forename: Cécile
authors.initials: C
authors.lastname: Bopp
authors.affiliation: Université de Strasbourg, IPHC, 23 rue du Loess, Strasbourg 67037, France and CNRS, UMR7178, Strasbourg 67037, France.
authors.forename: Marc
authors.initials: M
authors.lastname: Rousseau
authors.affiliation: Université de Strasbourg, IPHC, 23 rue du Loess, Strasbourg 67037, France and CNRS, UMR7178, Strasbourg 67037, France.
authors.forename: David
authors.initials: D
authors.lastname: Brasse
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008962:Models, Theoretical; D009010:Monte Carlo Method; D019047:Phantoms, Imaging; D011522:Protons; D014054:Tomography / Q000295:instrumentation / Q000379:methods*; D014867:Water
chemical_list: D011522:Protons; D014867:Water