Modeling fluid injection into a porous spherical composite with anisotropy

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Abstract

Porous spherical composites are widely found both in natural objects and in technical applications. To describe the mechanical behavior of such structures, it is necessary to take into account the interaction of solid and fluid phases, since the fluid inside the porous body supports and redistributes part of the external load. This paper proposes a model of a spherical composite including a porous core and an elastic transversely isotropic shell. The developed model is applied for stress and strain analysis in different loading regimes, including the effect of external normal pressure and the injection of an additional volume of fluid, for example, when modeling intravitreal injections in biomedical research. The analysis has shown that when modeling intravitreal injections and describing the eyeball as a poroelastic composite, the drop in intraocular pressure with increasing degree of anisotropy is less significant than in the case of a model with an elastic shell under the influence of internal pressure alone. The increase in the degree of anisotropy is more significant for the pressure reduction in the porous core in the mode of external normal pressure application than the injection of additional fluid volume. The study also investigates the influence of the geometry and mechanical properties of the porous core on the variation of the shell thickness. The results obtained provide a comprehensive understanding of the stress distribution and fluid pressure, which allows to consider the influence of shell anisotropy, core porosity and their mechanical characteristics on the behavior of spherical composites.

About the authors

Denis V. Kucherenko

St. Petersburg University

ORCID iD: 0000-0001-5946-5943
SPIN-code: 8184-0670
Russia, 199034, St. Petersburg, Universitetskaya nab., 7-9

References

  1. Бауэр С. М., Замураев Л. А., Котляр К. Е. Модель трансверсально-изотропного сферического слоя для расчета изменения внутриглазного давления при интрасклеральных инъекциях // Российский журнал биомеханики. 2006. Т. 10, № 2. С. 43–49. EDN: JWTIDD
  2. Powers J. J., Wirth B. D. A review of TRISO fuel performance models // Journal of Nuclear Materials. 2010. Vol. 405, iss. 1. P. 74–82. https://doi.org/10.1016/j.jnucmat.2010.07.030
  3. Pasquini L., Molinari A., Fantazzini P., Dauphen Ya., Cuif J.-P., Levy O., Dubinsky Z., Caroselli E., Prada F., Goffredo S., Di Giosia M., Reggi M., Falini G. Isotropic microscale mechanical properties of coral skeletons // Journal of the Royal Society Interface. 2015. Vol. 12, iss. 106. Art. 20150168. https://doi.org/10.1098/rsif.2015.0168
  4. Wu Y.-C., Lee T.-M., Chiu K.-H., Shaw S.-Y., Yang C.-Y. A comparative study of the physical and mechanical properties of three natural corals based on the criteria for bone–tissue engineering scaffolds // Journal of Materials Science: Materials in Medicine. 2009. Vol. 20. P. 1273–1280. https://doi.org/10.1007/s10856-009-3695-3
  5. Du R., Eychmuller A. Metal-based aerogels and porous composites as efficient catalysts: Synthesis and catalytic performance // Catalysts. 2023. Vol. 13, iss. 11. Art. 1451. https://doi.org/10.3390/catal13111451
  6. Hashin Z., Monteiro P. J. M. An inverse method to determine the elastic properties of the interphase between the aggregate and the cement paste // Cement and Concrete Research. 2002. Vol. 32, iss. 8. P. 1291–1300. https://doi.org/10.1016/S0008-8846(02)00792-5
  7. Cheng A. H.-D. Poroelasticity. Switzerland : Springer, 2016. 877 p. (Theory and Applications of Transport in Porous Media, vol. 27.). https://doi.org/10.1007/978-3-319-25202-5
  8. Маслов Л. Б. Конечно-элементные пороупругие модели в биомеханике. СПб. : Лань, 2013. 236 с.
  9. Coudrillier B., Tian J., Alexander S., Myers K. M., Quigley H. A., Nguyen T. D. Glaucoma-related changes in the mechanical properties and collagen micro-architecture of the human sclera // PloS One. 2015. Vol. 10, iss. 7. Art. e0131396. https://doi.org/10.1371/journal.pone.0131396
  10. Meek K. M. The cornea and sclera // Collagen: Structure and Mechanics / ed. by P. Fratzl. Boston, MA : Springer US, 2008. P. 359–396. https://doi.org/10.1007/978-0-387-73906-9_13
  11. Bonfiglio A., Repetto R., Siggers J. H., Stocchino A. Investigation of the motion of a viscous fluid in the vitreous cavity induced by eye rotations and implications for drug delivery // Physics in Medicine & Biology. 2013. Vol. 58, iss. 6. Art. 1969. https://doi.org/10.1088/0031-9155/58/6/1969
  12. Ruffini A., Casalucci A., Cara C., Ethier C. R., Repetto R. Drug distribution after intravitreal injection: A mathematical model // Investigative Ophthalmology & Visual Science. 2024. Vol. 65, iss. 4. Art. 9. https://doi.org/10.1167/iovs.65.4.9
  13. Avery R. L., Pieramici D. J., Rabena M. D., Castellarin A. A., Nasir M. A., Giust M. J. Intravitreal bevacizumab (Avastin) for neovascular age-related macular degeneration // Ophthalmology. 2006. Vol. 113, iss. 3. P. 363–372. https://doi.org/10.1016/j.ophtha.2005.11.019
  14. Doshi R. R., Bakri S. J., Fung A. E. Intravitreal injection technique // Seminars in Ophthalmology. 2011. Vol. 26, iss. 3. P. 104–113. https://doi.org/10.3109/08820538.2010.541318
  15. Nagel E., Vilser W., Lanzl I. M. Retinal vessel reaction to short-term IOP elevation in ocular hypertensive and glaucoma patients // European Journal of Ophthalmology. 2001. Vol. 11, iss. 4. P. 338–344. https://doi.org/10.1177/112067210101100404
  16. Бауэр С. М., Венатовская Л. А., Воронкова Е. Б. Модели механики деформируемого тела в задачах офтальмологии // Вестник Санкт-Петербургского университета. Математика. Механика. Астрономия. 2023. Т. 10, вып. 4. С. 686–712. https://doi.org/10.21638/spbu01.2023.407, EDN: UJNCGP
  17. Иомдина Е. Н., Полоз М. В. Биомеханическая модель глазного яблока человека: описание и верификация // Математическая биология и биоинформатика. 2014. Т. 9, № 1. С. 286–295. https://doi.org/10.17537/2014.9.286, EDN: SIHWUT
  18. Бауэр С. М., Венатовская Л. А., Воронкова Е. Б., Смирнов А. Л. Задача об осесимметричной деформации ортотропного сферического слоя в трехмерной постановке // Вестник Санкт-Петербургского университета. Математика. Механика. Астрономия. 2016. Т. 3, вып. 3. С. 449–456. https://doi.org/10.21638/11701/spbu01.2016.313, EDN: WLSQNJ
  19. Bauer S. M., Voronkova E. B. Nonclassical shell theories in ocular biomechanics // Advanced Structured Materials. 2015. Vol. 45. P. 81–97. https://doi.org/10.1007/978-3-319-02535-3_4, EDN: UEMWQF
  20. Bekerman I., Gottlieb P., Vaiman M. Variations in eyeball diameters of the healthy adults // Journal of Ophthalmology. 2014. Vol. 2014. Art. 503645. https://doi.org/10.1155/2014/503645
  21. Boote C., Sigal I. A., Grytz R., Hua Y., Nguyen T. D., Girard M. J. A. Scleral structure and biomechanics // Progress in Retinal and Eye Research. 2020. Vol. 74. Art. 100773. https://doi.org/10.1016/j.preteyeres.2019.100773
  22. Иомдина Е. Н. Механические свойства тканей глаза человека // Биомеханика: достижения и перспективы / под ред. А. К. Цатуряна, А. А. Штейна. Москва : Изд-во Московского ун-та, 2006. С. 183–200. (Современные проблемы биомеханики. Вып. 11).
  23. Иомдина Е. Н., Бауэр С. М., Котляр К. Е. Биомеханика глаза: теоретические аспекты и клинические приложения. Москва : Реал Тайм, 2015. 208 с.
  24. Zhang Y., Li Z., Liu L., Han X., Zhao X., Mu G. Comparison of riboflavin/ultraviolet-A cross-linking in porcine, rabbit, and human sclera // BioMed Research International. 2014. Vol. 2014. Art. 194204. https://doi.org/10.1155/2014/194204
  25. Swindle K. E., Hamilton P. D., Ravi N. In situ formation of hydrogels as vitreous substitutes: viscoelastic comparison to porcine vitreous // Journal of Biomedical Materials Research Part A. 2008. Vol. 87A, iss. 3. P. 656–665. https://doi.org/10.1002/jbm.a.31769

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