Numerical simulation of the fluid dynamics in a 3D spherical model of partially liquefied vitreous due to eye movements under planar interface conditions

Document Type : Research Paper


School of mechanical Engineering, Shiraz University, Shiraz, Iran


Partially liquefied vitreous humor is a common physical and biochemical degenerative change in vitreous body which the liquid component gets separated from collagen fiber network and leads to form a region of liquefaction. The main objective of this research is to investigate how the oscillatory motions influence flow dynamics of partial vitreous liquefaction (PVL). So far computational fluid dynamics modeling of the PVL has not yet been well studied. To this end, a spherical model of the vitreous is subjected to harmonic motion and the numerical simulations are performed for various planar interface conditions in linear viscoelastic regimes. A numerical solver is developed in the OpenFOAM toolbox which is based on finite volume method and uses the PIMPLE algorithm and the dynamic mesh technique. This solver also uses modified classic volume-of-fluid approach to capture the interface effects and dynamic characteristics of two-phase viscoelastic-Newtonian fluid flow. The numerical model is validated by comparing the obtained results with the analytical solution which excellent agreement was observed. The results showed that the intensity of secondary flow in the vertical direction was much higher for the PVL with a higher liquefied fraction. Also, the obtained maximum stresses were dependent on the liquefied fraction of the PVL and located on the equatorial plane at the cavity wall near the interface layer and within the vitreous gel.


1.   Friedrich S., Cheng Y., Saville B., 1997, Finite elementmodeling of drug distribution in the vitreous humor of the rabbit eye, Annals of Biomedical Engineering, 25:303–314.
2.   Kathawate J. and  Acharya S., 2008, Computational modeling of intravitreal drug delivery in the vitreous chamber with different vitreous substitutes, International Journal of Heat and Mass Transfer, 51(23-24): 5598-5609.
3.   Lee B., Litt M., Buchsbaum G., 1992, Rheology of the vitreous body, Part I: viscoelasticity of human vitreous. Biorheology, 29(5-6): 521-533.
4.   Nickerson C.S., Park J., Kornfield J.A., Karageozian H., 2008, Rheological properties of the vitreous and the role of hyaluronic acid, Journal of biomechanics, 41(9):1840-1846.
5.   Swindle K.E., Hamilton P.D., Ravi N., 2008,  In  situ formation  of  hydrogels  as  vitreous  substitutes:  Viscoelastic comparison  to  porcine  vitreous,  Journal of Biomedical Materials Research, Part A, Vol. 87A: 656-65.
6.   Sharif-Kashani P., Hubschman J.P., Sassoon D., Kavehpour H.P., 2011, Rheology of the vitreous gel: effects of macromolecule organization on the viscoelastic properties. Journal of biomechanics 44(3): 419-423.
7.   Piccirelli M., 2011, MRI of the Orbit during Eye Movement, Doctoral dissertation, ETH Zurich.
8.   Rossi T., Querzoli G., Pasqualitto G., Iossa M., Placentino L., Repetto R., Stocchino A., Ripandelli G., 2012, Ultrasound imaging velocimetry of the human vitreous, Experimental eye research, 99: 98-104.
9.   Bonfiglio A., Lagazzo A., Repetto R., Stocchino A., 2015, An experimental model of vitreous motion induced by eye rotations, Eye and Vision 2(1): 10.
10. Sebag J., 1987, Age-related changes in human vitreous structure. Graefe's archive for clinical and experimental ophthalmology, 225(2): 89-93.
11. Asaria R.H.Y. and Gregor Z.J. ,2002, Simple retinal detachments: identifying the at-risk case, Eye, 16(4) :404.
12. Balazs E.A. and Flood M.T., 1978, Age-related changes in the physical and chemical state of human vitreous, Third International Congress for Eye Research, Osaka, Japan.
13. Balazs E.A. and Denlinger J.L., 1982, Aging changes in the vitreus, in Aging and Human Visual Function, Alan R. Liss, New York, 45-57.
14. Takahashi K., Arai K., Hayashi S., Tanaka Y., 2006, Degree of degraded proteoglycan in human vitreous and the influence of peroxidation, Nippon Ganka Gakkai Zasshi, 110(3): 171-179.‏
15. Zhang Q., Filas B.A., Roth R., Heuser J., Ma N., Sharma S., ... & Shui Y.B., 2014, Preservation of the structure of enzymatically-degraded bovine vitreous using synthetic proteoglycan mimics, Investigative ophthalmology & visual science, 55(12): 8153-8162.‏
16. David T., Smye S., Dabbs T., James T., 1998, A model for the fluid motion of vitreous humour of the human eye during saccadic movement, Physics in Medicine & Biology 43(6): 1385.
17. Lee E., Lee Y.H., Pai Y.T., Hsu J.P., 2002, Flow of a viscoelastic shear-thinning fluid between two concentric rotating spheres, Chemical Engineering Science, 57(3): 507-514.
18. Meskauskas J., Repetto R., Siggers J.H., 2011, Oscillatory motion of a viscoelastic fluid within a spherical cavity, Journal of Fluid Mechanics, 685: 1-22.
19. Repetto R., Tatone A., Testa A., Colangeli E., 2011, Traction on the retina induced by saccadic eye movements in the presence of posterior vitreous detachment, Biomechanics and modeling in mechanobiology, 10(2): 191-202.
20. Abouali O., Modareszadeh A., Ghaffariyeh A., Tu J., 2012, Numerical simulation of the fluid dynamics in vitreous cavity due to saccadic eye movement, Medical engineering & physics, 34(6): 681-692.
21. Modareszadeh A. and Abouali O., 2014, Numerical simulation for unsteady motions of the human vitreous humor as a viscoelastic substance in linear and non-linear regimes, Journal of Non-Newtonian Fluid Mechanics 204: 22-31.
22. Eisner G., 1975, Zur anatomie des glaskörpers. Albrecht von Graefes Archiv für klinische und experimentelle Ophthalmologie, 193(1): 33-56.
23. Tolentino F.I., Schepens C.L., Freeman H.M., 1975, Vitreoretinal Disorders 121-129. Philadelphia, Pa: WB Saunders Co.
24. Sebag J. and Balazs E.A., 1984 Pathogenesis of cystoid macular edema: an anatomic consideration of vitreoretinal adhesions, Survey of ophthalmology, 28: 493-498.
25. Kishi S. and Shimizu K., 1990, Posterior precortical vitreous pocket. Archives of Ophthalmology, 108(7): 979-982.
26. Sebag J., 1987, Age-related changes in human vitreous structure. Graefe's archive for clinical and experimental ophthalmology, 225(2): 89-93.
27. Kummer M.P., Abbott J.J., Dinser S., Nelson B.J., 2007, Artificial vitreous humor for in vitro experiments. In Engineering in Medicine and Biology Society, 29th Annual International Conference of the IEEE, 6406-6409.
28. Macosko C.W., 1994, Rheology: principles, measurements and applications. New York: VCH Publishers.
29. Giesekus H., 1982, A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility. Journal of Non-Newtonian Fluid Mechanics, 11(1-2): 69-109.
30. Hirt C.W. and Nichols B.D., 1981, Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of computational physics, 39(1): 201-225.
31. Rusche H., 2003, Computational fluid dynamics of dispersed two-phase flows at high phase fractions, Doctoral dissertation, Imperial College London, University of London.
32. Benson D.J., 2002, Volume of fluid interface reconstruction methods for multi-material problems, Applied Mechanics Reviews, 55(2): 151-165.
33. Piro D.J. and Maki K.J., 2013, An adaptive interface compression method for water entry and exit, University of Michigan.
34. Weller H.G., Tabor G., Jasak H., Fureby C., 1998, A tensorial approach to computational continuum mechanics using object-oriented techniques. Computers in physics, 12(6): 620-631.
35. Patankar S., 1980, Numerical Heat Transfer and Fluid Flow, Series in computational and physical processes in mechanics and thermal sciences, Hemisphere Publishing Company, ISBN 9780891165224
36. Versteeg H.K. and Malalasekera W., 2007, An introduction to computional fluid dynamics: The finite volume method.
37. Issa R.I., 1985, Solution of the implicitly discretised fluid flow equations by operator-splitting, J. Comput. Phys. 62: 40-65.
38. Ferziger J.H. and Peric M., 2012, Computational methods for fluid dynamics. Springer Science & Business Media, third edition.
39. Damián S.M., 2013, An extended mixture model for the simultaneous treatment of short and long scale interfaces, Doktorarbeit, Universidad Nacional Del Litoral, Facultad de Ingenieria y Ciencias Hidricas.
40. Jasak H., Weller H.G., Gosman A.D., 1999, High resolution NVD differencing scheme for arbitrarily unstructured meshes, International journal for numerical methods in fluids, 31(2): 431-449.
41. Ajiz M.A. and Jennings A. ,1984, A robust incomplete Choleski-conjugate gradient algorithm, International Journal for numerical methods in engineering, 20(5): 949-966.
42. Lee J., Zhang J., Lu C.C., 2003, Incomplete LU preconditioning for large scale dense complex linear systems from electromagnetic wave scattering problems, Journal of Computational Physics, 185(1): 158-175.
43. Habla F., Obermeier A., Hinrichsen O., 2013, Semi-implicit stress formulation for viscoelastic models: Application to three-dimensional contraction flows, Journal of Non-Newtonian Fluid Mechanics, 199: 70-79.
44. Guénette R. and Fortin M., 1995, A new mixed finite element method for computing viscoelastic flows, Journal of non-newtonian fluid mechanics, 60(1): 27-52.
45. White F.M. and Corfield I., 1974, Viscous fluid flow, vol. 3.
Volume 50, Issue 2
December 2019
Pages 387-394
  • Receive Date: 20 October 2019
  • Revise Date: 11 December 2019
  • Accept Date: 12 December 2019