Experimental tests on human corneas reveal distinguished reinforcing collagen lamellar structures that may be well described by a structural constitutive model considering distributed collagen fibril orientations along the superior-inferior and the nasal-temporal meridians. A proper interplay between the material structure and the geometry guarantees the refractive function and defines the refractive properties of the cornea. We propose a three-dimensional computational model for the human cornea that is able to provide the refractive power by analyzing the structural mechanical response with the nonlinear regime and the effect the intraocular pressure has. For an assigned unloaded geometry we show how the distribution of the von Mises stress at the top surface of the cornea and through the corneal thickness and the refractive power depend on the material properties and the fibril dispersion. We conclude that a model for the human cornea must not disregard the peculiar collagen fibrillar structure, which equips the cornea with the unique biophysical, mechanical, and optical properties.

1.
Kokott
,
W.
, 1938, “
Über die Mechanisch-Funktionelle Strukturen des Auges
,”
Albrecht von Graefes Arch. Ophthalmol.
,
138
, pp.
424
485
. 0376-0200
2.
Daxer
,
A.
, and
Fratzl
,
P.
, 1997, “
Collagen Fibril Orientation in the Human Corneal Stroma and Its Implication in Keratoconus
,”
Invest. Ophthalmol. Visual Sci.
,
38
, pp.
121
129
. 0146-0404
3.
Löpping
,
B.
, and
Weale
,
R. A.
, 1965, “
Changes in Corneal Curvature Following Ocular Convergence
,”
Vision Res.
,
5
, pp.
207
215
. 0042-6989
4.
Boote
,
C.
,
Dennis
,
S.
,
Huang
,
Y.
,
Quantock
,
A. J.
, and
Meek
,
K. M.
, 2005, “
Lamellar Orientation in Human Cornea in Relation to Mechanical Properties
,”
J. Struct. Biol.
1047-8477,
149
, pp.
1
6
.
5.
Boote
,
C.
,
Dennis
,
S.
, and
Meek
,
K. M.
, 2004, “
Spatial Mapping of Collagen Fibril Organisation in Primate Cornea: An X-ray Diffraction Investigation
,”
J. Struct. Biol.
1047-8477,
146
, pp.
359
367
.
6.
Newton
,
R. H.
, and
Meek
,
K. M.
, 1998a, “
Circumcorneal Annulus of Collagen Fibrils in the Human Limbus
,”
Invest. Ophthalmol. Visual Sci.
,
39
, pp.
1125
1134
. 0146-0404
7.
Newton
,
R. H.
, and
Meek
,
K. M.
, 1998b, “
The Integration of the Corneal and Limbal Fibrils in the Human Eye
,”
Biophys. J.
,
75
, pp.
2508
2512
. 0006-3495
8.
Aghamohammadzadeh
,
H.
,
Newton
,
R. H.
, and
Meek
,
K. M.
, 2004, “
X-Ray Scattering Used to Map the Preferred Collagen Orientation in the Human Cornea and Limbus
,”
Structure (London)
0969-2126,
12
, pp.
249
256
.
9.
Maurice
,
D. M.
, 1969, “
The Cornea and Sclera
,”
The Eye
,
2nd ed.
,
H.
Davison
, ed.,
Academic
,
New York
, pp.
489
600
.
10.
Buzard
,
K. A.
, 1992, “
Introduction to Biomechanics of the Cornea
,”
Refract. Corneal Surg.
,
8
, pp.
127
138
. 1042-962X
11.
Höltzel
,
D. A.
,
Altman
,
P.
,
Buzard
,
K.
, and
Choe
,
K.
, 1992, “
Strip Extensiometry for Comparison of the Mechanical Response of Bovine, Rabbit, and Human Corneas
,”
J. Biomech. Eng.
0148-0731,
114
, pp.
202
215
.
12.
Pinsky
,
P. M.
, and
Datye
,
D. V.
, 1991, “
A Microstructurally-Based Finite Element Model of the Incised Human Cornea
,”
J. Biomech.
0021-9290,
24
, pp.
907
922
.
13.
Pinsky
,
P. M.
, and
Datye
,
D. V.
, 1992, “
Numerical Modeling of Radial, Astigmatic, and Hexagonal Keratotomy
,”
Refract. Corneal Surg.
,
8
, pp.
164
172
. 1042-962X
14.
Velinsky
,
S. A.
, and
Bryant
,
M. R.
, 1992, “
On The Computer-Aided and Optimal Design of Keratorefractive Surgery
,”
Refract. Corneal Surg.
,
8
, pp.
173
182
. 1042-962X
15.
Bryant
,
M. R.
, and
McDonnell
,
P. J.
, 1996, “
Constitutive Laws for Biomechanical Modeling of Refractive Surgery
,”
J. Biomech. Eng.
0148-0731,
118
, pp.
473
481
.
16.
Pinsky
,
P. M.
,
van der Heide
,
D.
, and
Chernyak
,
D.
, 2005, “
Computational Modeling of Mechanical Anisotropy in the Cornea and Sclera
,”
J. Cataract Refractive Surg.
0886-3350,
31
, pp.
136
145
.
17.
Holzapfel
,
G. A.
,
Gasser
,
T. C.
, and
Ogden
,
R. W.
, 2000, “
A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models
,”
J. Elast.
0374-3535,
61
, pp.
1
48
.
18.
Alastrué
,
V.
,
Calvo
,
B.
,
Peña
,
E. M.
, and
Doblaré
,
M.
, 2006, “
Biomechanical Modeling of Refractive Corneal Surgery
,”
ASME J. Biomech. Eng.
0148-0731,
128
, pp.
150
160
.
19.
Pandolfi
,
A.
, and
Manganiello
,
F.
, 2006, “
A Model for the Human Cornea: Constitutive Formulation and Numerical Analysis
,”
Biomech. Model. Mechanobiol.
,
5
, pp.
237
246
. 1617-7959
20.
Pandolfi
,
A.
,
Fotia
,
G.
, and
Manganiello
,
F.
, 2008, “
Finite Element Simulations of Laser Refractive Corneal Surgery
,”
Eng. Comput.
, in press.
21.
Anderson
,
K.
,
El-Sheikh
,
A.
, and
Newson
,
T.
, 2004, “
Application of Structural Analysis to the Mechanical Behaviour of the Cornea
,”
J. R. Soc., Interface
1742-5689,
1
, pp.
3
15
.
22.
Li
,
L. Y.
, and
Tighe
,
B.
, 2006, “
The Anisotropic Material Constitutive Models for the Human Cornea
,”
J. Struct. Biol.
,
153
, pp.
223
230
. 1047-8477
23.
Elsheikh
,
A.
, and
Wang
,
D.
, 2007, “
Numerical Modelling of Corneal Biomechanical Behaviour
,”
Comput. Methods Biomech. Biomed. Eng.
,
10
, pp.
85
95
. 1025-5842
24.
Meek
,
K. M.
,
Blamires
,
T.
,
Elliott
,
G. F.
,
Gyi
,
T. J.
, and
Nave
,
C.
, 1987, “
The Organisation of Collagen Fibrils in the Human Corneal Stroma: A Synchrotron X-Ray Diffraction Study
,”
Curr. Eye Res.
0271-3683,
6
, pp.
841
846
.
25.
Meek
,
K. M.
, and
Newton
,
R. H.
, 1999, “
Organization of Collagen Fibrils in the Corneal Stroma in Relation to Mechanical Properties and Surgical Practice
,”
J. Refract. Surg.
,
15
, pp.
695
699
. 1081-597X
26.
Gasser
,
T. C.
,
Ogden
,
R. W.
, and
Holzapfel
,
G. A.
, 2006, “
Hyperelastic Modelling of Arterial Layers With Distributed Collagen Fibre Orientations
,”
J. R. Soc., Interface
1742-5689,
3
, pp.
15
35
.
27.
Radner
,
W.
,
Zehetmayer
,
M.
,
Aufreiter
,
R.
, and
Mallinger
,
R.
, 1998, “
Interlacing and Cross-Angle Distribution of Collagen Lamellae in the Human Cornea
,”
Cornea
,
17
, pp.
537
543
. 0277-3740
28.
Hjortdal
,
J. O.
, 1996, “
Regional Elastic Performance of the Human Cornea
,”
J. Biomech.
0021-9290,
29
, pp.
931
942
.
29.
Bryant
,
M. R.
,
Szerenyi
,
K.
,
Schmotzer
,
H.
, and
McDonnell
,
P. J.
, 1994, “
Corneal Tensile Strength in Fully Healed Radial Keratotomy Wounds
,”
Invest. Ophthalmol. Visual Sci.
,
35
, pp.
3022
3031
. 0146-0404
30.
Jayasuriya
,
A. C.
,
Scheinbeim
,
J. I.
,
Lubkin
,
V.
,
Bennett
,
G.
, and
Kramer
,
P.
, 2003, “
Piezoelectric and Mechanical Properties in Bovine Cornea
,”
J. Biomed. Mater. Res. A
,
66A
, pp.
260
265
. 1549-3296
31.
Wollensak
,
G.
,
Spoerl
,
E.
, and
Seiler
,
T.
, 2003, “
Stress-Strain Measurements of Human and Porcine Corneas After Riboflavin-Ultraviolet-a-Induced Cross-Linking
,”
J. Cataract Refractive Surg.
0886-3350,
29
, pp.
1780
1785
.
32.
Zeng
,
Y.
,
Yang
,
J.
,
Huang
,
K.
,
Lee
,
Z.
, and
Lee
,
X.
, 2001, “
A Comparison of Biomechanical Properties Between Human and Porcine Cornea
,”
J. Biomech.
0021-9290,
34
, pp.
533
537
.
33.
Kampmeier
,
J.
,
Radt
,
B.
,
Birngruber
,
R.
, and
Brinkmann
,
R.
, 2000, “
Thermal and Biomechanical Parameters of Porcine Cornea
,”
Cornea
,
19
, pp.
355
363
. 0277-3740
34.
Boyce
,
B. L.
,
Jones
,
R. E.
,
Nguyen
,
T. D.
, and
Grazier
,
J. M.
, 2007, “
Stress-Controlled Viscoelastic Tensile Response of Bovine Cornea
,”
J. Biomech.
0021-9290,
40
, pp.
2367
2376
.
35.
Holzapfel
,
G. A.
,
Sommer
,
G.
,
Gasser
,
T. C.
, and
Regitnig
,
P.
, 2005a, “
Determination of the Layer-Specific Mechanical Properties of Human Coronary Arteries With Non-Atherosclerotic Intimal Thickening, and Related Constitutive Modelling
,”
Am. J. Physiol. Heart Circ. Physiol.
,
289
, pp.
H2048
H2058
. 0363-6135
36.
Holzapfel
,
G. A.
,
Stadler
,
M.
, and
Gasser
,
T. C.
, 2005b, “
Changes in the Mechanical Environment of Stenotic Arteries During Interaction With Stents: Computational Assessment of Parametric Stent Design
,”
J. Biomech. Eng.
0148-0731,
127
, pp.
166
180
.
37.
Holzapfel
,
G. A.
, 2000, “
Nonlinear Solid Mechanics
,”
A Continuum Approach for Engineering
.
Wiley
,
Chichester
.
38.
Demiray
,
H.
, 1972, “
A Note on the Elasticity of Soft Biological Tissues
,”
J. Biomech.
0021-9290,
5
, pp.
309
311
.
39.
1998,
Handbook of Grid Generation
,
J. F.
Thompson
,
B. K.
Soni
, and
N. P.
Weatherill
, eds.,
CRC
,
Boca Raton, FL
.
40.
Manganiello
,
F.
, 2006, “
A Computational Model of the Human Cornea: A Predictive Approach to Refractive Surgery
,” Ph.D. thesis, Politecnico di Milano, Italy.
41.
Dubbelman
,
M.
,
Sicam
,
V. A.
, and
Van der Heijde
,
G. L.
, 2006, “
The Shape of the Anterior and Posterior Surface of the Aging Human Cornea
,”
Vision Res.
0042-6989,
46
, pp.
993
1001
.
42.
Holzapfel
,
G. A.
, and
Gasser
,
T. C.
, 2001, “
A Viscoelastic Model for Fiber-Reinforced Composites at Finite Strains: Continuum Basis, Computational Aspects and Applications
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
190
, pp.
4379
4403
.
43.
Elsheikh
,
A.
, and
Anderson
,
K.
, 2005, “
Comparative Study of Corneal Strip Extensometry and Inflation Tests
,”
J. R. Soc., Interface
,
2
, pp.
177
185
. 1742-5689
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