Moscow University Physics Bulletin

, Volume 71, Issue 4, pp 431–439 | Cite as

The dose kernels of pencil and differential pencil photon beams with the spectrum of treatment machines with a 60Co source in water and their analytical approximation

  • V. A. Klimanov
  • A. N. Moiseev
  • M. A. Kolyvanova
  • V. L. Romodanov
  • A. P. Chernyaev
Biophysics and Medical Physics


This article presents the results of calculations by the Monte-Carlo method in the EGSnrc toolkit of the spatial distributions of absorbed energy or dose kernels in water for a pencil beam or differential pencil beam (point spread function) with the spectrum of ROKUS-M treatment machines. The photon spectrum of the ROKUS-M machines was also calculated by the Monte-Carlo method. The calculated dose-kernel results were approximated separately for the radial distribution of the primary and the scattered component of dose kernels by sums of exponential functions divided by the squared radius for a differential pencil beam and by the radius for a pencil beam. This approximation makes direct implementation possible for wellknown model-based techniques for finding 3D dose distributions in external radiation therapy. A simple analytical procedure to verify approximation formulas is proposed. It is also applicable in independent checks of dose distributions along the treat beam axis, which is an important guideline of the Radiation Therapy Quality Assurance Program.


external radiation therapy photons ROKUS treatment machine pencil beam differential pencil beam 3D treatment planning collapsed cone convolution pencil beam algorithm 


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Copyright information

© Allerton Press, Inc. 2016

Authors and Affiliations

  • V. A. Klimanov
    • 1
    • 2
    • 3
  • A. N. Moiseev
    • 4
  • M. A. Kolyvanova
    • 2
    • 3
  • V. L. Romodanov
    • 5
  • A. P. Chernyaev
    • 2
  1. 1.Department of Medical PhysicsNational Research Nuclear University MEPhI (Moscow Engineering Physics Institute)MoscowRussia
  2. 2.Department of PhysicsMoscow State UniversityMoscowRussia
  3. 3.State Research Center Burnasyan Federal Medical Biophysical Center of the Federal Medical Biological AgencyMoscowRussia
  4. 4.Medical Rehabilitation CenterMinistry of Health of the Russian FederationMoscowRussia
  5. 5.Department of Experimental and Theoretical Physics of Nuclear ReactorsNational Research Nuclear University MEPhI (Moscow Engineering Physics Institute)MoscowRussia

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