Publishing house Radiotekhnika

"Publishing house Radiotekhnika":
scientific and technical literature.
Books and journals of publishing houses: IPRZHR, RS-PRESS, SCIENCE-PRESS

Тел.: +7 (495) 625-9241


Equivalent dose depth distribution in condition of photon beam irradiation


A.V. Belousov – Ph.D. (Phys.-Math.), Associate Professor, Faculty of Physics, Lomonosov Moscow State University E-mail: A.A.Belianov – Junior Research Scientist, Faculty of Physics, Lomonosov Moscow State University G.A.Krusanov – Post-graduate Student, Faculty of Physics, Lomonosov Moscow State University E-mail: A.P. Chernyaev – Dr.Sc. (Phys.-Math.), Professor, Head of Department, Faculty of Physics, Lomonosov Moscow State University

To take into account the differences in biological effectiveness of ionizing radiation the concept of equivalent dose is intro-duced. It is believed that the same equivalent dose irradiation, regardless of the type and energy of radiation, leads to the same biological effect. The equivalent dose is defined as the product of the absorbed dose to the coefficients depending on the type of radiation. At equal absorbed doses hard-ionizing radiation leads to a more presented effect than soft-ionizing one. To take into account the dependence on the linear energy transfer (LET) the normalization factor Q (quality factor) is used. If the object is located in a mixed radiation field the equivalent dose H is equal to the sum of the absorbed dose of radiation Di all types i, multiplied by the corresponding coefficients wi. The ratio of the absorbed dose to the equivalent can be regarded as an average value of the quality factor (or radiation weighting factor (RWF) depending on the method of calculating the equivalent dose of mixed radiation). Mixed radiation can be generated even when the volume is irradiated by monoenergetic radiation of constant composition. Such conditions are realized in the field of photon radiation. During the interaction of photons with matter streams of dif-ferent secondary particles are formed. When the threshold of photo-nuclear reactions is exceeded heavy charged particles with a high LET may be formed. Despite the low probability of the formation, due to the high values of the weighting coeffi-cients, these particles can make a significant contribution to the equivalent dose. The Monte Carlo computer simulation is used with the Geant4 toolkit. Water phantom is a homogeneous cube 30 × 30 × 30 cm. Water is commonly used in medical dosimetry as tissue-equivalent material. In the the cube along the beam axis a set of 300 "sensitive" layer of 2 × 2 × 0.1 cm is placed, each of which accumulates the data of occuring processes (released energy, step length). Phantom is irradiated by a photon beam with radius of 2 cm. The beam source is located at 40 cm from the center of the cube. To calculate the RWF the recommended values are applied (for photons of all energies – 1, for protons – 2, for alpha par-ticles, heavy ions and recoil nuclei – 20) and for calculating the value of Q the LET of all formed of secondary particles (electrons, heavy particles and recoil nuclei) is taken into account. It is shown that in the surface layers of thickness up to 10 mm the equivalent dose values are calculated by these two methods, within the error limits do not differ at all the above energies. Statistically significant discrepancy is observed at a depth of more than 5 cm. The maximum value is achieved at the energy of 22-25 MeV, which corresponds to a maximum cross section of the giant dipole resonance in the nuclei of oxygen, and for the surface layer is up to ~ 5, a layer at a depth of 9.5 mm is ~2. It is shown that in case of a monochromatic photon radiation is to be considered a significant difference between the equivalent and the absorbed dose, at least in surface areas. In particular, during radiotherapy with a prescribed intratu-moral dose radiation complications may occur on human skin. To quantify these risks intensive calculations should be carried out for the bremsstrahlung spectrum of medical accelerators.


  1. ICRP, 2007. The 2007 Recommendations of the International Commission on Radiological Protection. ICRP Publication 103. Ann. ICRP 37 (2–4).
  2. Belousov A.V., Kurakin A.A., CHernjaev A.P. Vlijanie fotojadernykh reakcijj na koehfficient kachestva tormoznykh fotonov // Medicinskaja radiologija i radiacionnaja bezopasnost, 2007. T. 52. № 2. S. 71–74.
  3. Belousov A.V., CHernjaev A.P. Model ucheta vklada vtorichnykh chastic v OBEH pervichnogo izluchenija // Izv. RAN. Ser. Fizicheskaja. 2008. T. 72. № 7. S. 1038–1041.
  4. Belousov A.V., CHernjaev A.P. Ocenka vklada fotonejjtronov v dozovuju nagruzku na pacienta pri luchevojj terapii // Almanakh klinicheskojj mediciny. 2008. T. XVII. CH. 1. S. 282–284.
  5. Belousov A.V., Osipov A.S., CHernjaev A.P. Koehfficient kachestva smeshannogo izluchenija, inducirovannogo tormoznymi fotonami vysokikh ehnergijj // Uchenye zapiski fizicheskogo fakulteta MGU. 2012. № 2. S. 122701-1 – 122701-7.
  6. Belousov A.V., Varzar S.M., Gordienko T.V. i dr. Biologicheskaja ehffektivnost fotonov vysokikh ehnergijj // Biomedicinskaja radioehlektronika. 2012. № 12. S. 46–53.
  7. Belousov A.V., Chernyaev A.P., Osipov A.S. A model considering secondary particles contribution in RBE of primary bremsstrahlung // Biomedicine and Biotechnology. 2013. V. 1. № 2. P. 6-8.
  8. Belousov A.V., Osipov A.S., CHernjaev A.P. Ocenka srednego radiacionnogo vzveshivajushhego faktora pri obluchenii tonkikh sloev tkanejj tormoznymi fotonami // Medicinskaja fizika. 2013. № 3 (59). S. 37–41.
  9. Belousov A.V., Bliznyuk U.A., Chernyaev A.P. Evaluation of the Average Weighting Factor in Thin Layer Irradiation by Bremsstrahlung // Biomedicine and Biotechnology. 2014. V. 2. № 4. P. 80–84.
  10. Belousov A.V., Kalachev A.A., Krusanov G.A. Chernyaev A.P. Estimation of absorbed and equivalent doses of photon radiation in thin layers // Moscow University Physics Bulletin. 2015. V. 70. № 5. P. 416–422.
  11. Agostinelli S. et al. Geant4 – A Simulation Toolkit // Nuclear Instruments and Methods A. 2003. V. 506. P. 250–303.
  12. Allison J. et al. Geant4 Developments and Applications // IEEE Transactions on Nuclear Science. 2006. V. 53. № 1. P. 270–278.
  13. Breton V. et al. Extending Geant4 at the Physics-Medicine-Biology frontier // Trends in Computational Science and Engineering 3. 2013. P. 21–41.
  14. Superkompjuter «LOMONOSOV»: http://
  15. Voevodin Vl.V., ZHumatijj S.A., Sobolev S.I., Antonov A.S., Bryzgalov P.A., Nikitenko D.A., Stefanov K.S., Voevodin Vad.V. Praktika superkompjutera «Lomonosov» // Otkrytye sistemy. M.: Izd. dom «Otkrytye sistemy». 2012. N 7. S. 36–39.


© Издательство «РАДИОТЕХНИКА», 2004-2017            Тел.: (495) 625-9241                   Designed by [SWAP]Studio