Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya
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Vestnik Sankt-Peterburgskogo Universiteta. Seriya 10. Prikladnaya Matematika. Informatika. Protsessy Upravleniya, 2021, Volume 17, Issue 4, Pages 381–388
DOI: https://doi.org/10.21638/11701/spbu10.2021.406
(Mi vspui504)
 

Applied mathematics

Mathematical modeling of pressure distribution during deformations of the intervertebral disc

D. A. Chubarov, V. P. Tregubov, N. K. Egorova

St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
References:
Abstract: Based on the analysis of the mechanical models of the intervertebral disc given in the literature, it is concluded that the finite element computational grids used in them do not reflect the real structure of the intervertebral disc. In this regard, a mechanical model of the intervertebral disc was built, the structure of which is close to its real structure. The proposed model was used to determine the dynamics of the pressure distribution in the intervertebral disc when one of the vertebrae is rotated by a given angle. To determine the resulting bulges of each cell in the structure of the fibrous ring, the Rayleigh method and its modification were used. This made it possible to rationally calculate the volumes of cells. When calculating the pressure in each cell, its linear dependence on the deflection value of the cell was used. As a result of the proposed algorithm, the pressure dynamics in each cell of the intervertebral disc model was determined when the angle between the vertebrae changed.
Keywords: mechanical model, intervertebral disc, pressure distribution, mathematical modeling.
Received: July 19, 2021
Accepted: October 13, 2021
Document Type: Article
UDC: 531.51-7
MSC: 92C10, 70E55
Language: Russian
Citation: D. A. Chubarov, V. P. Tregubov, N. K. Egorova, “Mathematical modeling of pressure distribution during deformations of the intervertebral disc”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 17:4 (2021), 381–388
Citation in format AMSBIB
\Bibitem{ChuTreEgo21}
\by D.~A.~Chubarov, V.~P.~Tregubov, N.~K.~Egorova
\paper Mathematical modeling of pressure distribution during deformations of the intervertebral disc
\jour Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr.
\yr 2021
\vol 17
\issue 4
\pages 381--388
\mathnet{http://mi.mathnet.ru/vspui504}
\crossref{https://doi.org/10.21638/11701/spbu10.2021.406}
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    Вестник Санкт-Петербургского университета. Серия 10. Прикладная математика. Информатика. Процессы управления
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    References:22
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