Modelling Light Propagation in Ocular Tissues

The cornea is the transparent part of the eye’s outer sheath and the primary refractive element in the optical system of the eye. Indeed, its curved interface with the air provides three-fourths of the eye’s focusing power (the remainder being provided by the lens). Maintenance of its curvature and clarity is therefore essential for good vision. An understanding of the physical basis of corneal transparency has been a subject of interest amongst physicists, basic scientists and ophthalmologists. Impairment of corneal clarity is a significant cause of visual morbidity worldwide. Several highly mathematical treatises have been presented in support of different theories of corneal transparency in the normal cornea relating structure to function.

The scheme of the eye. Source: a-diagram-of-vertical-section-of-human-eye-and/.

The structural elements that give the cornea the strength to preserve its proper curvature while withstanding the intraocular pressure (typically 14 to 18 mm Hg) are located within its stromal region, which constitutes 90\% of the cornea’s thickness. The cornea stroma is composed of dense, regularly packed collagen fibrils arranged in layers or lamellae. Fibrils are narrow, uniform in diameter and precisely organised. These properties are vital to maintain transparency and to provide the biomechanical prerequisites necessary to sustain shape and provide strength. There is a vast literature trying to figure out why cornea is transparent, but there is a consensus that every model trying to explain corneal transparency should consider the shape, size and organization of extracellular matrix in the corneal stroma and its elements such as collagen fibrils and proteoglycans, and their refractive indexes.

A cross–section scheme of the human cornea. Source: Batista, A., “Two–photon imaging of the cornea using femtosecond laser microscopes and tomographs”, PhD Dissertation, Faculty of Natural Sciences and Technology of the Saarland University, Germany, 2018.

The main goal of our project is to identify the conditions leading to corneal opacity and how those conditions can be detected early on the Optical Coherence Tomography (OCT) signal. To achieve that, we aim to developed a suitable model of the corneal stroma capable of representing the multiple lamellae with different orientations and the interlacing between lamellae and to use the Discontinuous Galerkin method to simulate the corneal transparency and generate OCT scans from backscattered light for comparison with actual measurements.

The preliminary results obtained so far are very promising and are in line with recent literature. We considered a numerical simulation of light scattering in the human’s cornea aiming to mimicking the OCT imaging system with the help of a two-dimensional model of backscattered light intensity is proposed and its time evolution is considered both for healthy and pathological tissues. As we may the backscattering is more intensive in case where the organization of the fibrils is not uniform, that corresponds to a lack of transparency of the ill cornea.

Time evolution of scattered electric field intensity. Left hand side corresponds to healthy cornea, whereas right hand side states for case of corneal illness. Source: Sunčica Sakić Master Thesis.

This work is funded by the projects UID/MAT/00324/2019, PTDC/MAT-APL/28118/2017 and POCI-01-0145-FEDER-028118.

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