Research paper
Biomechanical analysis of the keratoconic cornea

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Abstract

Keratoconus is a non-inflammatory disease characterized by irregular thinning and gradual bulging of the cornea, which results in distortion of the corneal surface that causes blurred vision. We conducted three-dimensional finite element (FE) simulations to analyze the biomechanical factors contributing to the distorted shape of a keratoconic cornea. We assumed orthotropic linear elastic tissue mechanical properties, and simulated localized tissue thinning (reduction from 0.5 mm to 0.35 or 0.2 mm). We analyzed tissue deformations, stresses and theoretical dioptric power maps predicted by the models, for intraocular pressure (IOP) of 10, 15 20 and 25 mmHg. The analyses revealed that three factors affect the shape distortion of keratoconic corneas: (i) localized thinning, and (ii) reduction in the tissue’s meridian elastic modulus or (iii) reduction in the shear modulus perpendicular to the corneal surface, whereas thinning showed the most predominant effect. Maximal stress levels occurred at the centers of the bulged regions, at the thinnest points. The IOP levels had little influence on dioptric power in the healthy cornea, but a substantial influence in keratoconic conditions. The present FE studies allowed characterization of the biomechanical interactions in keratoconus, toward understanding the aetiology of this poorly studied malady.

Introduction

The cornea, a transparent tissue that covers the front of the eye, performs approximately 2/3 of the optical refraction and focuses light towards the lens and the retina. Thus, even slight variations in the shape of the cornea can significantly diminish visual performance. Normally, collagen fibers in the central cornea are dominantly arranged in the medial-lateral and inferior–superior directions. As one moves from the central cornea toward the periphery (limbus), a circumferential orientation is also noticeable (Meek and Boote, 2004). Accordingly, the corneal tissue is a heterogeneous structure with strongly anisotropic mechanical properties, which induce a flattening response in the limbus region when the cornea is subjected to physiological intraocular pressure (IOP) (Shin et al., 1997).

Keratoconus is a disease of the cornea characterized by non-inflammatory deterioration of the corneal structure, mainly in the form of localized loss, of up to 75% thickness, of corneal tissue (Bron, 1988, Edmund, 1989). This leads to deformation of the cornea, from a normal spherical shape to a more conic shape, owing to bulging of the tissue at the abnormally thin regions (Fig. 1). The change of shape causes optical aberrations that may be correctable by means of glasses or hard contact lenses at mild conditions, or require corneal transplantation in more severe cases. Keratoconus is a relatively common condition, with estimates ranging from 4 to 600 cases per a population of 100,000 people (Rabinowitz, 1998).

The aetiology of keratoconus is unclear, and it is currently considered incurable, but the literature lists several factors that are likely to be involved in the onset and progress of the disease, including genetics, overexposure to sunlight, improper fittings of contact lenses, excessive eye rubbing, and continual (chronic) eye irritation (Rabinowitz, 1998). It is reported though, that localized loss of corneal thickness, and likely also degradation of corneal mechanical properties, cause gradual tissue protrusion, which results in a more conical appearance of the cornea that imposes blurred vision (Edmund, 1988, Edmund, 1989). Hence, keratoconus is most likely a disease that involves substantial biological–mechanical interactions; pathological changes of the tissue structure alter the mechanical properties of cornea, which in turn affect the gross shape of the cornea under IOP.

Published biomechanical models of the cornea employed the finite element (FE) method to study mechanical strain and stress distributions in corneal tissue (Buzard, 1992, Bryant and McDonnell, 1996, Pinsky and Dayte, 1991). In addition to stress–strain analyses, FE as well as the boundary element numerical method have been employed to determine temperature distributions in the eye, and in the cornea in particular (Ng and Ooi, 2006, Ooi et al., 2007a, Ooi et al., 2007b). Recently, computational models of the cornea were expanded to simulate keratoconic corneas (Anderson et al., 2004, Pandolfi and Manganiello, 2006). However, it is still unclear from these modeling studies whether changes in corneal mechanical properties are sufficient to cause a conical appearance of the cornea, or whether the localized non-inflammatory thinning of the cornea is the trigger. Since keratoconus was associated with connective tissue disorders, and collagen metabolism disorders in particular (Rabinowitz, 1998), identification of the primary mechanical cause for the conical corneal shape is critical for understanding the aetiology of keratoconus.

In the present study we developed more accurate biomechanical models of normal and keratoconic corneas by employing a more realistic representation of the corneal geometry and anisotropic mechanical properties. Cases of keratoconous were simulated by global or localized tissue “weakening”, as well as localized asymmetric thinning distortions of the cornea, considered separately or together in the models, in order to determine their relative individual/combined influences on the shape of the cornea. In addition, the relationship between corneal topography due to mechanical deformations and the dioptric power maps, which are the relevant clinical imaging method for diagnosis and severity assessment, were also explored.

Section snippets

The computational model

Computational modeling of the cornea based on the FE method is used herein to predict the mechanical performance of normal and keratoconic human corneas and to provide a detailed account of their response to various changes in tissue mechanical properties, geometry and IOP. The following general assumptions were made: (i) The normal unloaded cornea is assumed to be symmetric, half-sphere shaped at the central region, and clamped at the sclera, which is a reasonable approximation of the shape of

Results

The normal distribution maps of corneal displacement and dioptric power for simulation of a healthy cornea subjected to IOP of 15 mmHg (case #1) are shown in Fig. 4. The maximal tissue displacement, 56 μm, occurred at the apex of the cornea. Likewise, the maximal dioptric power, 44.7 D (which is within the normal range; (Aydin et al., 2007)) occurred at the corneal apex (Table 3). The distribution of principal stresses along a cross section A–A through the center of the cornea (depicted by a

Discussion

In this study, we employed FE simulations and coupled dioptric power map calculations to determine the mechanical behavior and optical performance of normal and keratoconic corneas. Corneal thinning, though considerably variable among patients (∼25%–75%), is probably the most important characteristic of keratoconus (Mandell and Polse, 1969, Foster and Yamamoto, 1978). Histopathology of the thinned regions demonstrates that they contain a decreased number of collagen lamella, slippage between

Conclusions

The analyses revealed that three factors affect the shape distortion of keratoconic corneas: (i) localized tissue thinning, (ii) reduction in the tissue’s meridian elastic modulus Eφφ, and (iii) reduction in the shear modulus perpendicular to the corneal surface Grφ. Tissue thinning was found to be the most influential factor contributing to the bulged shape of the keratoconic cornea, and the center of the bulge closely followed the thinnest tissue region. Maximal stress levels also occurred at

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    The first two authors contributed equally.

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