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


Mathematical model of low-intensity laser therapeutic effect on intervertebral hernia

DOI 10.18127/j15604136-201906-09


G.N. Zmievskoy –  Ph.D. (Phys.-Math.), Associate Professor, Department «Biomedical Technical Systems», Bauman Moscow State Technical University
M.A. Kuznetsov – Student, Department «Biomedical Technical Systems», Bauman Moscow State Technical University

The causes of the appearance of an intervertebral hernia are considered, the therapeutic methods of its treatment are compared with the advantages of low-intensity laser therapy. Laser therapy, unlike other therapeutic methods, is characterized by the practical absence of contraindications. The advantages include the painlessness of laser therapy, the possibility of combination with other types of treatment, and the reduction of the rehabilitation period after surgical treatment.
Development of a mathematical model of the effect of low-intensity laser radiation on pathological tissue.
The developed mathematical model is presented as the result of a numerical solution of the radiation transfer equation in the Kubelka-Munk approximation for a three-layer biological tissue (skin, muscle tissue, choroid). To solve the system of differential equations in the Mathcad program, the numerical Runge-Kutta method was used. The manifestation of the effect of stimulating blood circulation is associated with an increase in the diameter of the vessels of the spinal cord under the action of laser radiation.
The obtained phenomenological dependence of the therapeutic effect on the exposure time shows that exceeding the irradiation time by more than 10 minutes is impractical, since there is no further increase in blood supply to the intervertebral discs. This corresponds to the experimental data presented in a number of previous works.
The results can be used in medical practice for a priori determination of the dose of laser radiation incident on the surface of the body, necessary to optimize the therapeutic effect.

  1. Pulbere O.P. Gryzha mezhpozvonkovogo diska. Interv'yu so specialistom. [Elektronnyj resurs] // URL: (data obrashcheniya: 12.01.17).
  2. Vinogradov E.N. Udalenie mezhpozvonkovoj gryzhi [Elektronnyj resurs] // URL: (data obrashcheniya: 17.03.17).
  3. Lazeroterapiya Informacionnyj portal «Masterskaya zdorov'ya» // [Elektronnyj resurs] URL: (data obrashcheniya: 20.03.17).
  4. Pushkareva A.E. Metody matematicheskogo modelirovaniya v optike biotkani. SPb.: SPbGU ITMO. 2008. 103 s.
  5. Bashkatov A.N., Genina E.A., Tuchin V.V. Optical properties of skin, subcutaneous, and muscle tissues: Review. Saratov: State University. DOI: 10.1142/S1793545811001319 // Journal of Innovative Optical Health Sciences. 2011. № 1. P. 9–38.
  6. Genina E.A. Optika biotkanej. Kurs lekcij. Saratov: Izd-vo SGU. 2013. 188 s.
  7. Bujlin V.A., Laryushin A.I., Nikitina M.V. Sveto-lazernaya terapiya: Rukovodstvo dlya vrachej. Tver': OOO «Izd. «Triada». 2004. 256 s.
  8. Zaharov S.D., Ivanov A.V. Svetokislorodnyj effekt – fizicheskij mekhanizm aktivacii biosistem kvazimonohromaticheskim izlucheniem. M.: FIAN im. P.N. Lebedeva. 2006. 51 s.
  9. Muller G., Sliney D.H. Dosimetry of laser radiation in medicine and biology // SPIE Institute Series. 1989. V. IS5. R. 38‒46.
  10. Zmievskoj G.N. Dozimetricheskie aspekty nizkointensivnoj fototerapii pri kogerentnyh i nekogerentnyh vozdejstviyah // Izmeritel'naya tekhnika. 2005. № 10. S. 53‒58.
June 24, 2020
May 29, 2020

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