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4D Investigation of Vortex Fluid Motion Inside the Eyeball

Authors: Skladchikov S.A., Savenkova N.P., Vysikaylo P.I., Avetisov S.E., Lipatov D.V., Novoderеzhkin V.V. Published: 03.11.2021
Published in issue: #5(98)/2021  
DOI: 10.18698/1812-3368-2021-5-73-88

 
Category: Physics | Chapter: Theoretical Physics  
Keywords: vortex formations, convective diffusion flows, mathematical simulation

The eye is a complex system of boundaries and fluids with different viscosities within the boundaries. At present, there are no experimental possibilities to thoroughly observe the dynamic 4D processes after one or another method of eye treatment is applied. The complexity of cumulative, i.e., focusing, and dissipative, i.e., scattering, convective and diffusion 4D fluxes of fluids in the eye requires 4D analytical and numerical models of fluid transfer in the human eyeball to be developed. The purpose of the study was to develop and then verify a numerical model of 4D cumulative-dissipative processes of fluid transfer in the eyeball. The study was the first to numerically evaluate the values of the characteristic time of the drug substance in the vitreous cavity until it is completely washed out, depending on the injection site; to visualize the paths of the vortex motion of the drug in the vitreous cavity; to determine the main parameters of the 4D fluid flows of the medicinal substance in the vitreous cavity, depending on the presence or absence of vitreous detachment from the wall of the posterior chamber of the eye. The results obtained are verified by the experimental data available to doctors. In the eye, as a partially open cumulative-dissipative system, Euler regions with high rates of cumulative flows and regions with low speeds or stagnant Lagrange flow zones are defined

References

[1] Yusupaliev U., Savenkova N.P., Troshchiev Yu.V., et al. Vortex rings and plasma toroidal vortices in homogeneous unbounded media. II. The study of vortex formation process. Bull. Lebedev Phys. Inst., 2011, vol. 38, no. 9, pp. 275--282. DOI: https://doi.org/10.3103/S1068335611090065

[2] Savenkova N.P., Anpilov S.V., Kuzmin R.N., et al. Reduction cell multiphase 3d model. Applied Physics, 2012, no. 3, pp. 111--115.

[3] Savenkova N., Laponin V. A numerical method for finding soliton solutions in nonlinear differential equations. Moscow Univ. Comput. Math. Cybern., 2013, vol. 37, no. 2, pp. 49--54. DOI: https://doi.org/10.3103/S0278641913020076

[4] Kuz’min R.N., Laponin V.S., Savenkova N.P., et al. Mathematical modeling of the formation of a solitary wave on a liquid surface. Inzhenernaya fizika [Engineering Physics], 2014, no. 8, pp. 19--24 (in Russ.).

[5] Yusupaliyev U., Savenkova N.P., Shuteyev S.A., et al. Computer simulation of vortex self-maintenance and amplification. Moscow Univ. Phys., 2013, vol. 68, no. 4, pp. 317--319. DOI: https://doi.org/10.3103/S0027134913040115

[6] Bychkov V.L., Savenkova N.P., Anpilov S.V., et al. Modeling of vorticle objects created in Gatchina discharge. IEEE Trans. Plasma Sci., 2012, vol. 40, iss. 12, pp. 3158--3161. DOI: https://doi.org/10.1109/TPS.2012.2210566

[7] Vysikaylo P.I. Cumulative point --- L1 between two positively charged plasma structures (3-D strata). IEEE Trans. Plasma Sci., 2014, vol. 42, iss. 12, pp. 3931--3935. DOI: https://doi.org/10.1109/TPS.2014.2365438

[8] Alekseev I.B., Belkin V.E., Samoylenko A.I., et al. Vitreous. Anatomy, pathology and methods of surgical treatment (review). Novosti glaukomy, 2015, no. 1, pp. 69--73 (in Russ.).

[9] Makhacheva Z.A. Anatomiya steklovidnogo tela [Anatomy of vitreous body]. Moscow, Rusprint Publ., 2006.

[10] Starkov G.L. Patologiya steklovidnogo tela pri biomikroskopicheskom issledovanii. Avtoref. dis. d-ra med. nauk [Vitreous body pathology at biomicroscopic study. Dr. Med. Sc. Diss. Abs.]. Novokuznetsk, 1964 (in Russ.).

[11] Busacca A., Goldmann H., Schiff-Wertheimer S. Biomicroscopie du corps vitre et Du Fond de l’oeil. Paris, Masson & Cie, 1957.

[12] Koeppe L. Die Mikroskopie des Lebenden Auges. Berlin, Springer, 1922. DOI: https://doi.org/10.1007/978-3-642-91818-6

[13] Rao S., Kulkarni M., Cooper S., et al. Analysis of proteins of bovine lens, vitreous, and aqueous by electrophoresis and by Oudin’s gel diffusion technique. Brit. J. Ophthal., 1955, vol. 39, iss. 3, pp. 163--169. DOI: http://dx.doi.org/10.1136/bjo.39.3.163

[14] Worst J.G.F., Los L.I. Cisternal anatomy of the vitreous. Amsterdam, Kugler, 1955.

[15] Khusainov R.R., Tsibul’skii V.R., Yakushev V.L. Simulation of eye deformation in the measurement of intraocular pressure. Comput. Math. and Math. Phys., 2011, vol. 51, no. 2, pp. 326--338. DOI: https://doi.org/10.1134/S0965542511020096

[16] Yakushev V.L. Statement of the problem of intraocular pressure measurement modeling by a pneumotonometric method. Mech. Solids, 2011, vol. 46, no. 6, pp. 937--945. DOI: https://doi.org/10.3103/S0025654411060136

[17] Bogomolova M.S., Petrov I.B. Numerical modeling of dynamic processes in an eye during the procedure of surgeon cataract laser extraction. Vestnik RGU im. I. Kanta, 2007, no. 10, pp. 37--43 (in Russ.).