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Research Papers

Three-Dimensional Modeling and Computational Analysis of the Human Cornea Considering Distributed Collagen Fibril Orientations

[+] Author and Article Information
Anna Pandolfi1

Dipartimento di Ingegneria Strutturale, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italypandolfi@stru.polimi.it

Gerhard A. Holzapfel

Institute of Biomechanics, and Center of Biomedical Engineering, Graz University of Technology, Kronesgasse 5-I, 8010 Graz, Austria; Department of Solid Mechanics, Royal Institute of Technology (KTH), Osquars Backe 1, 100 44 Stockholm, Swedenholzapfel@tugraz.at

1

Corresponding author.

J Biomech Eng 130(6), 061006 (Oct 09, 2008) (12 pages) doi:10.1115/1.2982251 History: Received October 03, 2007; Revised May 06, 2008; Published October 09, 2008

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.

FIGURES IN THIS ARTICLE
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Copyright © 2008 by American Society of Mechanical Engineers
Topics: Cornea , Stress
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Figures

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Figure 1

Schematics of fibril orientation in the human cornea (left eye): (a) model proposed by Meek and Newton (25) and Newton and Meek (6)—the vertical and horizontal fibrils bend in the proximity of the limbus to form an annular reinforcement; (b) model proposed by Aghamohammadzadeh (8)—additional fibrils may have their origins in a set of anchoring lamellae that bend in and out of the peripheral cornea

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Figure 2

Fibril-reinforced structure of the cornea, as assumed in the present finite element model, compare also with Fig. 1: (a) orientation of the two families of collagen fibrils in the outermost layer of the cornea. Each pair of fibrils is visualized at the integration points of the elements; (b) contour levels of the dispersion parameter κi for both families of collagen fibrils; (c) contour levels of the ratio R between the strongly oriented fibrils and the dispersed fibrils for both families of collagen fibrils.

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Figure 3

Finite element mesh used in the calculations (2500 nodes and 1728 eight-node brick elements), top view, and NT meridian section of the discretized model: (a) unloaded configuration, identified through an iterative procedure (thickness at the apex: 0.627 mm, thickness at the limbus: 0.756 mm, and elevation at the apex: 2.52 mm); (b) deformed configuration, at physiological IOP (16 mm Hg) (thickness at the apex: 0.579 mm, thickness at the limbus: 0.620 mm, and elevation at the apex: 2.940 mm). The in-plane diameter is 11.61 mm.

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Figure 4

Variation of the refractive power (according to Eq. 18) with IOP for fixed and rotating boundaries at the limbus

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Figure 5

Intraocular pressure versus apical displacement. Comparison between experimental data documented by Anderson (21) and the finite element results used for the calibration of the material parameters, as summarized in Table 1.

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Figure 6

von Mises stress σM maps for different values of the k1 stiffness parameter in the NT direction: (a) k1=0.005 MPa, (b) k1=0.02 MPa (baseline), (c) k1=0.04 MPa, and (d) k1=0.08 MPa. The physiological IOP is 16 mm Hg and the stresses are in MPa.

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Figure 7

Maximum principal Cauchy stress σI maps across the corneal thickness for different values of the k1 stiffness parameter in the NT direction: (a) k1=0.005 MPa, (b) k1=0.02 MPa (baseline), (c) k1=0.04 MPa, and (d) k1=0.08 MPa. The physiological IOP is 16 mm Hg and the stresses are in MPa.

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Figure 8

von Mises stress σM maps for different values of the k2 parameter in the NT direction: (a) k2=100, (b) k2=400 (baseline), (c) k2=800, and (d) k2=1600. The physiological IOP is 16 mm Hg and the stresses are in MPa.

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Figure 9

Maximum principal Cauchy stress σI maps across the corneal thickness for different values of the k2 parameter in the NT direction: (a) k2=100, (b) k2=400 (baseline), (c) k2=800, and (d) k2=1600. The physiological IOP is 16 mm Hg and the stresses are in MPa.

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Figure 10

Variation of the refractive power (according to Eq. 18) along the NT and SI meridians by (a) altering the stiffness parameter k1 and (b) the parameter k2, for the fibril set oriented in the NT direction. The physiological IOP is 16 mm Hg.

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Figure 11

von Mises stress σM maps: (a) IOP 16 mm Hg and (b) IOP 40 mm Hg, for different assumptions of the κ parameter (see Table 2). Stresses are in MPa.

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Figure 12

Maximum principal Cauchy stress σI maps: (a) IOP 16 mm Hg and (b) IOP 40 mm Hg, for different assumptions of the κ parameter (see Table 2). Stresses are in MPa.

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Figure 13

Variation of the refractive power (according to Eq. 18) versus the intraocular pressure for different assumptions of the κ parameter (see Table 2): (a) NT meridian power and (b) SI meridian power

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Figure 14

Intraocular pressure versus apical displacement for different assumptions of the κ parameter (see Table 2)

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