Geodesic
Mathematical modeling of pressure distribution during deformations of the intervertebral disc
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 17 (2021) no. 4, pp. 381-388
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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. 
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     title = {Mathematical modeling of pressure distribution during deformations of the intervertebral disc},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
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D. A. Chubarov; V. P. Tregubov; N. K. Egorova. Mathematical modeling of pressure distribution during deformations of the intervertebral disc. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 17 (2021) no. 4, pp. 381-388. http://geodesic.mathdoc.fr/item/VSPUI_2021_17_4_a5/

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