Mathematical modelling of corneal transparency problem

My name is Sunčica Sakić and I am finishing Master studies in Applied Mathematics (Technomathematics) at University of Novi Sad (UNS). In my opinion, the studies at UNS produce a strong base for research in a variety of real-world applications. In order to make my view wider and achieve professional goals, I decided to participate in the student exchange program Erasmus+. I spent the last semester at the Department of Mathematics of University of Coimbra (UC).

Life in charming Coimbra left a great impression on me, while the studying at UC, the university with remarkable history, helped me to extend my knowledge at multidisciplinary level and improve my skills considerably.

At UC I was doing research for my master thesis on topic ‘Modelling light propagation in ocular tissues’. This thesis theme emerged from a bigger interdisciplinary research project whose main aim is to identify the conditions leading to corneal opacity and how those conditions can be detected early on the Optical Coherence Tomography (OCT) scan. The OCT is a popular non-invasive mean of ocular tissue imaging whose key idea lays in measuring the magnitude and echo time delay of backscattered light from internal microstructures in tissue caused by discontinuities in its refractive index.

The goal of thesis was to generate a virtual OCT scan of a part of cornea with the aid of an appropriate mathematical model. The mathematical model was described by two-dimensional Maxwell’s equations in time domain which were adapted to dielectric and optical properties of eye’s structures. These equations I solved numerically applying Runge-Kutta discontinuous Galerkin method, which uses discontinuous Galerkin Finite Element Method for spatial discretization while Runge-Kutta method is employed for temporal integration. In this way I got the simulations of light scatter in a small part of corneal tissue for case of healthy eye tissue and tissue affected by a disease. Afterwards, I made a comparison of obtained results. Especially, one of the most demanding tasks was to construct a suitable mesh for a given problem setup that supports simulations of high resolution and simultaneously limits the computational costs. In that purpose I had been exploring several software packages for mesh generation.

I truly appreciate having had opportunity to give contribution to a project with significant application in medicine, as well as to collaborate with scientists from UC. This semester provided me an excellent experience and with no doubts, the University of Coimbra was a perfect choice for a student exchange.