The vitreous undergoes physical and biochemical changes with age. The most important of such degenerative changes is vitreous liquefaction or synchysis, in which pockets of liquid known as lacunae form in the vitreous gel. The movement mechanism and characteristics of vitreous liquefaction are quite complex. In this study, the flow dynamics of partial vitreous liquefaction (PVL) as two-phase viscoelastic-Newtonian fluid flow are investigated in the human eye. A reliable three-dimensional (3D) numerical procedure is developed for capturing the interface effects and dynamic characteristics of these two-phase complex fluid flows. In the present work, two different configurations of the PVL including liquefied pocket in the central and the posterior portions of the vitreous cavity are considered. The effects of lens indentation on the flow field and interface deformation of PVL inside the vitreous cavity are investigated. The results show that the curvature of the vitreous cavity due to the lens capsule increases shear and normal stresses in comparison with those for the PVL in a sphere as a simplified model. It is observed that the presence of lens indentation and the location of liquefied region are two factors that can produce conditions of asymmetry inside the vitreous body. In a realistic model of vitreous cavity, although the velocity magnitude inside the liquefied vitreous region increases when the liquefied pocket is in the posterior portion of the vitreous cavity, the stress values and the asymmetric condition of flow field become more significant for the liquefied pocket located close to the posterior lens curvature.

1.
A.
Penkova
,
S.
Zhang
,
M.
Humayun
,
S.
Fraser
,
R.
Moats
, and
S. S.
Sadhal
, “
Measurement of the hydraulic conductivity of the vitreous humor
,”
J. Porous Media
23
(
2
),
195
206
(
2020
).
2.
E.
Young
, “
Numerical simulations of the mechanics of vitrectomy
,” Ph.D. thesis (
University of California
, Los Angeles,
2015
).
3.
S.
Rahbar
and
M.
Shokooh-Saremi
, “
Mathematical modeling of laser linear thermal effects on the anterior layer of the human eye
,”
Opt. Laser Technol.
99
,
72
80
(
2018
).
4.
J.
Sebag
, “
Age-related changes in human vitreous structure
,”
Graefe's Arch. Clin. Exp. Ophthalmol.
225
(
2
),
89
93
(
1987
).
5.
R. H. Y.
Asaria
and
Z. J.
Gregor
, “
Simple retinal detachments: Identifying the at-risk case
,”
Eye
16
(
4
),
404
(
2002
).
6.
A. F.
Silva
,
M. A.
Alves
, and
M. S.
Oliveira
, “
Rheological behaviour of vitreous humour
,”
Rheol. Acta
56
(
4
),
377
386
(
2017
).
7.
R.
Repetto
and
M.
Dvoriashyna
, “
Mathematical models of vitreous humour dynamics and retinal detachment
,” in
Ocular Fluid Dynamics
(
Birkhäuser
,
Cham
,
2019
), pp.
303
325
.
8.
G.
Eisner
, “
Zur anatomie des glaskorpers
,”
Arch. Klin. Exp. Ophthalmol.
193
(
1
),
33
56
(
1975
).
9.
P.
O'Malley
, “
The pattern of vitreous syneresis: A study of 800 autopsy eyes
,” in
Advances in Vitreous Surgery
(
Charles C Thomas
,
1976
), pp.
17
33
.
10.
A.
Oksala
, “
Ultrasonic findings in the vitreous body at various ages
,”
Arch. Klin. Exp. Ophthalmol.
207
(
4
),
275
280
(
1978
).
11.
J.
Sebag
, “
Fibrous structure of the human vitreous body
,”
Bulletins et Memoires de la Societe Francaise D'ophtalmologie
96
,
395
397
(
1985
).
12.
J.
Sebag
and
E. A.
Balazs
, “
Human vitreous fibres and vitreoretinal disease
,”
Trans. Ophthalmol. Soc. U. K.
104
,
123
128
(
1985
).
13.
M. M.
Le Goff
,
V. J.
Hindson
,
T. A.
Jowitt
,
P. G.
Scott
, and
P. N.
Bishop
, “
Characterization of optic in and evidence of stable dimerization in solution
,”
J. Biol. Chem.
278
(
46
),
45280
45287
(
2003
).
14.
D.
Natali
,
J. O.
Pralits
,
A.
Mazzino
, and
S.
Bagheri
, “
Stabilizing effect of porosity on a flapping filament
,”
J. Fluids Struct.
61
,
362
375
(
2016
).
15.
D.
Natali
,
R.
Repetto
,
J. H.
Tweedy
,
T. H.
Williamson
, and
J. O.
Pralits
, “
A simple mathematical model of rhegmatogenous retinal detachment
,”
J. Fluids Struct.
82
,
245
257
(
2018
).
16.
J.
Vroon
,
J.
de Jong
,
A.
Aboulatta
,
A.
Eliasy
,
F.
van der Helm
,
J.
van Meurs
,
D.
Wong
, and
A.
Elsheikh
, “
Numerical study of the effect of head and eye movement on progression of retinal detachment
,”
Biomech. Model. Mechanobiol.
17
(
4
),
975
983
(
2018
).
17.
D.
Wong
,
Y.
Chan
,
T.
Bek
,
I.
Wilson
, and
E.
Stefansson
, “
Intraocular currents, Bernoulli's principle and non-drainage scleral buckling for rhegmatogenous retinal detachment
,”
Eye
32
(
2
),
213
(
2018
).
18.
E. A.
Balazs
and
M. T.
Flood
, “
Age-related changes in the physical and chemical structure of human vitreous
,” in
Third International Congress of Eye Research
(
1978
).
19.
N. K.
Tram
and
K. E.
Swindle-Reilly
, “
Rheological properties and age-related changes of the human vitreous humor
,”
Front. Bioeng. Biotechnol.
6
,
199
(
2018
).
20.
E. A.
Balazs
and
J. L.
Denlinger
, “
Aging changes in the vitreous
,” in
Aging and Human Visual Function
(
Alan R Liss
,
1982
), pp.
45
57
.
21.
B.
Lee
,
M.
Litt
, and
G.
Buchsbaum
, “
Rheology of the vitreous body. Part I: Viscoelasticity of human vitreous
,”
Biorheology
29
(
5–6
),
521
533
(
1992
).
22.
J.
Bayat
,
H.
Emdad
, and
O.
Abouali
, “
Numerical simulation of the fluid dynamics in a 3D spherical model of partially liquefied vitreous due to eye movements under planar interface conditions
,”
J. Comput. Appl. Mech.
50
(
2
),
387
394
(
2019
).
23.
J.
Bayat
,
H.
Emdad
, and
O.
Abouali
, “
Numerical investigation of partially liquefied vitreous dynamics as two-phase viscoelastic-Newtonian fluid flow in a planar cavity due to oscillatory motion
,”
Int. J. Multiphase Flow
127
,
103259
(
2020
).
24.
J.
Bayat
,
H.
Emdad
, and
O.
Abouali
, “
3D numerical investigation of the fluid mechanics in a partially liquefied vitreous humor due to saccadic eye movement
,”
Comput. Biol. Med.
125
,
103955
(
2020
).
25.
O.
Abouali
,
A.
Modareszadeh
,
A.
Ghaffariyeh
, and
J.
Tu
, “
Numerical simulation of the fluid dynamics in vitreous cavity due to saccadic eye movement
,”
Med. Eng. Phys.
34
(
6
),
681
692
(
2012
).
26.
A.
Bonfiglio
,
R.
Repetto
,
J. H.
Siggers
, and
A.
Stocchino
, “
Investigation of the motion of a viscous fluid in the vitreous cavity induced by eye rotations and implications for drug delivery
,”
Phys. Med. Biol.
58
(
6
),
1969
1982
(
2013
).
27.
K.
Isakova
,
J. O.
Pralits
,
R.
Repetto
, and
M. R.
Romano
, “
A model for the linear stability of the interface between aqueous humor and vitreoussubstitutes after vitreoretinal surgery
,”
Phys. Fluids
26
(
12
),
124101
(
2014
).
28.
S.
Garcia-Gonzalez
and
R.
Fernandez-Feria
, “
Stability analysis of the interface between two weak viscoelastic liquids under periodic oscillations
,”
Phys. Fluids
29
(
1
),
013101
(
2017
).
29.
A.
Khoobyar
,
A.
Penkova
,
M. S.
Humayun
, and
S. S.
Sadhal
, “
Mathematical model of macromolecular drug transport in a partially liquefied vitreous humor
,”
J. Heat Transfer
(published online,
2021
).
30.
J. E.
Hall
,
Guyton and Hall Textbook of Medical Physiology
(
Elsevier Health Sciences
,
2010
).
31.
J.
Wallman
,
M. D.
Gottlieb
,
V.
Rajaram
, and
L. A.
Fugate-Wentzek
, “
Local retinal regions control local eye growth and myopia
,”
Science
237
(
4810
),
73
77
(
1987
).
32.
D. O.
Mutti
,
R. I.
Sholtz
,
N. E.
Friedman
, and
K.
Zadnik
, “
Peripheral refraction and ocular shape in children
,”
Invest. Ophthalmol. Visual Sci.
41
(
5
),
1022
1030
(
2000
).
33.
R. A.
Stone
and
D. I.
Flitcroft
, “
Ocular shape and myopia
,”
Ann. Acad. Med. Singapore
33
(
1
),
7
15
(
2004
).
34.
W.
Becker
, “
The neurobiology of saccadic eye movements
.
Metrics,” Rev. Oculomotor Res.
3
,
13
67
(
1989
).
35.
M. J.
Crochet
and
R.
Keunings
, “
On numerical die swell calculation
,”
J. Non-Newtonian Fluid Mech.
10
(
1–2
),
85
94
(
1982
).
36.
R. I.
Tanner
, “
A theory of die-swell
,”
J. Polym. Sci. Part A-2
8
(
12
),
2067
2078
(
1970
).
37.
M. F.
Tomé
,
N.
Mangiavacchi
,
J. A.
Cuminato
,
A.
Castelo
, and
S.
McKee
, “
A finite difference technique for simulating unsteady viscoelastic free surface flows
,”
J. Non-Newtonian Fluid Mech.
106
(
2–3
),
61
106
(
2002
).
38.
G. S.
Beavers
and
D. D.
Joseph
, “
The rotating rod viscometer
,”
J Fluid Mech
69
,
475
511
(
1975
).
39.
R. A.
Figueiredo
,
C. M.
Oishi
,
A. M.
Afonso
,
I. V. M.
Tasso
, and
J. A.
Cuminato
, “
A two-phase solver for complex fluids: Studies of the Weissenberg effect
,”
Int. J. Multiphase Flow
84
,
98
115
(
2016
).
40.
X. L.
Luo
, “
Numerical simulation of Weissenberg phenomena—The rod-climbing of viscoelastic fluids
,”
Comput. Methods Appl. Mech. Eng.
180
(
3–4
),
393
412
(
1999
).
41.
J.
Yoo
,
D. D.
Joseph
, and
G. S.
Beavers
, “
Higher-order theory of the Weissenberg effect
,”
J. Fluid Mech.
92
(
3
),
529
590
(
1979
).
42.
A.
Albadawi
,
D.
Donoghue
,
A.
Robinson
,
D.
Murray
, and
Y.
Delaure
, “
Influence of surface tension implementation in volume of fluid and coupled volume of fluid with level set methods for bubble growth and detachment
,”
Int. J. Multiphase Flow
53
,
11
28
(
2013
).
43.
H.
deGuillebon
and
H.
Zauberman
, “
Experimental retinal detachment: Biophysical aspects of retinal peeling and stretching
,”
Arch. Ophthalmol.
87
(
5
),
545
548
(
1972
).
44.
H. L.
Kain
, “
A new model for examining chorioretinal adhesion experimentally
,”
Arch. Ophthalmol.
102
(
4
),
608
611
(
1984
).
45.
M.
Kita
and
M. F.
Marmor
, “
Retinal adhesive force in living rabbit, cat, and monkey eyes. Normative data and enhancement by mannitol and acetazolamide
,”
Investigative ophthalmology & visual science
33
(
6
),
1879
1882
(
1992
).
46.
A.
Ross
,
R. C.
Blake
, and
R. S.
Ayyala
, “
Surface tension of aqueous humor
,”
J. Glaucoma
19
(
7
),
456
459
(
2010
).
47.
H.
Giesekus
, “
A simple constitutive equation for polymer fluids based on the concept of deformation-dependent tensorial mobility
,”
J. Non-Newtonian Fluid Mech.
11
,
69
109
(
1982
).
48.
R. B.
Bird
,
R. C.
Armstrong
, and
O.
Hassager
, “
Dynamics of polymeric liquids
,” in
Fluid Mechanics
(
John Wiley
,
New York
,
1987
), Vol.
1
.
49.
C. W.
Macosko
,
Rheology: Principles, Measurements and Applications
(
VCH Publishers
,
New York
,
1994
).
50.
C. W.
Hirt
and
B. D.
Nichols
, “
Volume of fluid (VOF) method for the dynamics of free boundaries
,”
J. Comput. Phys.
39
,
201
225
(
1981
).
51.
H.
Rusche
, “
Computational fluid dynamics of dispersed two-phase flows at high phase fractions
,” Doctoral dissertation (
Imperial College London, University of London
,
2003
).
52.
D. J.
Benson
, “
Volume of fluid interface reconstruction methods for multi-material problems
,”
Appl. Mech. Rev.
55
,
151
165
(
2002
).
53.
D. J.
Piro
and
K. J.
Maki
,
An Adaptive Interface Compression Method for Water Entry and Exit
(
University of Michigan
,
2013
).
54.
G.
Tryggvason
,
B.
Bunner
,
A.
Esmaeeli
,
D.
Juric
,
N.
Al-Rawahi
,
W.
Tauber
,
J.
Han
,
S.
Nas
, and
Y. J.
Jan
, “
A front-tracking method for the computations of multiphase flow
,”
J. Comput. Phys.
169
,
708
759
(
2001
).
55.
E.
Uzgoren
,
J.
Sim
, and
W.
Shyy
, “
Marker-based, 3-D adaptive Cartesian grid method for multiphase flow around irregular geometries
,”
in 46th AIAA Aerospace Sciences Meeting and Exhibit
(AIAA,
2009
), p.
1239
.
56.
E. A.
Hassan
,
E.
Uzgoren
,
H.
Fujioka
,
J. B.
Grotberg
, and
W.
Shyy
, “
Adaptive Lagrangian–Eulerian computation of propagation and rupture of a liquid plug in a tube
,”
Int. J. Numer. Methods Fluids
67
,
1373
1392
(
2011
).
57.
H. G.
Weller
,
G.
Tabor
,
H.
Jasak
, and
C.
Fureby
, “
A tensorial approach to computational continuum mechanics using object-oriented techniques
,”
Comput. Phys.
12
(
6
),
620
631
(
1998
).
58.
S.
Patankar
,
Numerical Heat Transfer and Fluid Flow
, Series in Computational and Physical Processes in Mechanics and Thermal Sciences (
Hemisphere Publishing Company
,
1980
), ISBN: 9780891165224.
59.
R. I.
Issa
, “
Solution of the implicitly discretised fluid flow equations by operator-splitting
,”
J. Comput. Phys.
62
,
40
65
(
1986
).
60.
J. H.
Ferziger
and
M.
Peric
,
Computational Methods for Fluid Dynamics
, 3rd ed. (
Springer Science & Business Media
,
2012
).
61.
S. M.
Damián
, “
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
,
2013
).
62.
F.
Habla
,
A.
Obermeier
, and
O.
Hinrichsen
, “
Semi-implicit stress formulation for viscoelastic models: Application to three-dimensional contraction flows
,”
J. Non-Newtonian Fluid Mech.
199
,
70
79
(
2013
).
63.
R.
Guénette
and
M.
Fortin
, “
A new mixed finite element method for computing viscoelastic flows
,”
J. Non-Newtonian Fluid Mech.
60
(
1
),
27
52
(
1995
).
64.
H. K.
Versteeg
and
W.
Malalasekera
,
An Introduction to Computational Fluid Dynamics: The Finite Volume Method
(
Pearson Education
,
2007
).
65.
H.
Jasak
,
H. G.
Weller
, and
A. D.
Gosman
, “
High resolution NVD differencing scheme for arbitrarily unstructured meshes
,”
Int. J. Numer. Methods Fluids
31
(
2
),
431
449
(
1999
).
66.
A.
Modareszadeh
and
O.
Abouali
, “
Numerical simulation for unsteady motions of the human vitreous humor as a viscoelastic substance in linear and non-linear regimes
,”
J. Non-Newtonian Fluid Mech.
204
,
22
31
(
2014
).
67.
M. A.
Ajiz
and
A.
Jennings
, “
A robust incomplete Choleski-conjugate gradient algorithm
,”
Int. J. Numer. Methods Eng.
20
(
5
),
949
966
(
1984
).
68.
J.
Lee
,
J.
Zhang
, and
C. C.
Lu
, “
Incomplete LU preconditioning for large scale dense complex linear systems from electromagnetic wave scattering problems
,”
J. Comput. Phys.
185
(
1
),
158
175
(
2003
).
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