A microstructural model of cross-link interaction between collagen fibrils in the human cornea

Experimental in-vitro investigation on Epi-Off-Crosslinking on porcine corneas

Aim

To evaluate quantitatively the effects of the Epi-Off-CXL irradiance dose on the stromal stiffening of pig corneas.

Setting

Laboratory of Biological structures (LaBS), Politecnico di Milano, Milano, Italy.

Methods

Inflation tests have been carried on 90 excised and de-epithelized pig corneas, monitoring the change of configuration of the corneal dome at specific pressures. Test have been carried out twice on each cornea, once before and once after Epi-Off-CXL performed at a constant irradiance of 9 mW/cm² and variable UV-A exposure times. Corneas were grouped according to the exposure time (2.5, 5, 10, 15 and 20 min), proportional to the irradiation dose (1.35, 2.7, 5.4, 8.1, and 10.8 J/cm²). A theoretical model based on linearized shell theory has been used to estimate the increment of the corneal stiffness.

Results

The linearized shell theory allowed to establish a quantitative relation between the increment of the stiffness parameters and the irradiation dose. Relative to the pre-treatment values, in all experiments the post-treatment corneal stiffness revealed a pronounced increase. In general, the stiffness gain increased with the exposure time. No significant differences in stiffening was observed between tests conducted at 2.5, 5, and 10 min exposure.

Conclusions

Qualitatively, the effectiveness of accelerated CXL treatments observed in pig corneas complies very well with in-vivo clinical results in humans, suggesting that experimental data in pigs can be very useful for the design of the procedure in humans. A larger irradiation dose provides a larger increment of the corneal stiffness. Due to the biological variability of the tissues, however, it is difficult to distinguish quantitatively the level of the reinforcement induced by accelerated protocols (low doses with < = 10 min exposure), less prone to induce damage in the corneal tissue. Therefore, the definition of personalized treatments must be related to the actual biomechanics of the cornea.

Stress-Strain Index Map: A New Way to Represent Corneal Material Stiffness

Purpose

To introduce a new method to map the mechanical stiffness of healthy and keratoconic corneas.

Methods

Numerical modeling based on the finite element method was used to carry out inverse analysis of simulated healthy and keratoconic corneas to determine the regional variation of mechanical stiffness across the corneal surface based on established trends in collagen fibril distribution. The Stress–Strain Index (SSI), developed and validated in an earlier study and presented as a parameter that can estimate the overall stress–strain behavior of corneal tissue, was adopted in this research as a measure of corneal stiffness. The regional variation of SSI across the corneal surface was estimated using inverse analysis while referring to the common features of collagen fibrils’ distribution obtained from earlier x-ray scattering studies. Additionally, for keratoconic corneas, a method relating keratoconic cone features and cornea’s refractive power to the reduction in collagen fibril density inside the cone was implemented in the development of SSI maps. In addition to the simulated cases, the study also included two keratoconus cases, for which SSI maps were developed.

Results

SSI values varied slightly across corneal surface in the simulated healthy eyes. In contrast, both simulated and clinical keratoconic corneas demonstrated substantial reductions in SSI values inside the cone. These SSI reductions depended on the extent of the disease and increased with more considerable simulated losses in fibril density in the cone area. SSI values and their regional variation showed little change with changes in IOP, corneal thickness, and curvature.

Conclusion

SSI maps provide an estimation of the regional variation of biomechanical stiffness across the corneal surface. The maps could be particularly useful in keratoconic corneas, demonstrating the dependence of corneal biomechanical behavior on the tissue’s microstructure and offering a tool to fundamentally understand the mechanics of keratoconus progression in individual patients.

On the Connection Between Geometry and Statically Determined Membrane Stresses in the Human Cornea

Under the action of the intraocular pressure (IOP), the human cornea is stressed and deforms acquiring a quasi-spherical configuration. If the stressed configuration is known, and the cornea is regarded as a membrane, disregarding flexural behaviors with an equilibrium analysis only is possible to estimate the distribution of the average stress across the thickness. In the cornea, the action of the intraocular pressure is supported by collagen fibrils, immersed into an elastin-proteoglycan matrix, and organized in a very precise architecture to provide the necessary confinement and transparency to the light. With the goal of understanding the static consequences of shape modifications due to pathological dilatation (ectasia), we present a simplified stress analysis of the human cornea modeled as a membrane. A numerical investigation over 40 patient-specific corneas (20 normal and 20 ectatic) is carried out to establish a relationship between the physiological geometry and the distribution of the membrane stresses, and to assess the possibility to obtain information on the stress state based on topographic images only. Comparative analyses reveal that, with respect to normal corneas, in ectatic corneas the pattern of the principal stress lines is modified markedly showing a deviation from the hypothetical dominant orientation of the collagen fibrils. The rotation of the principal stress with respect to the fibril orientation can be thought as responsible of the transmission of a large amount of shear stresses onto the elastin-proteoglycan matrix. The anomalous loading of the matrix could be correlated to the evolution of time-dependent shape modifications leading to ectasia.

Cornea modelling

Background

Biomechanics introduces numerous technologies to support clinical practice in ophthalmology, with the goal of improving surgical outcomes and to develop new advanced technologies with minimum impact on clinical training. Unfortunately, a few misconceptions on the way that computational methods should be applied to living tissues contributes to a lack of confidence towards computer-based approaches.

Methods

Corneal biomechanics relies on sound theories of mechanics, including concepts of equilibrium, geometrical measurements, and complex material behaviors. The peculiarities of biological tissues require the consideration of multi-physics, typical of the eye environment, and to adopt customized geometrical models constructed on the basis of advanced optical imaging and in-vivo testing.

Results

Patient-specific models are able to predict the outcomes of refractive surgery and to exploit the results of in-vivo test to characterize the material properties of the corneal tissue.

Conclusions

Corneal biomechanics can become an important support to clinical practice, provided that methods are based on the actual multi-physics and use customized geometrical and mechanical models.