Prof. Dr. A. Araújo (University of Coimbra):

The human retina is a complex structure in the eye that is responsible for the sense of vision. It is part of the central nervous system, composed by several layers, among which the outer nuclear layer that comprises the cells bodies of light sensitive photoreceptor cells (rods and cones). There are a number of eye-related pathologies that can be identified by the detailed analysis of the retinal layers. These pathologies can be diagnosed more conclusively with the help of the increasingly popular noninvasive optical imaging technique optical coherence tomography (OCT). In this talk we report a methodology to assess cell level alterations on the human retina responsible for functional changes observable in the OCT data in healthy ageing and in disease conditions, in the absence of structural alterations.

In particular, we will discuss the mathematical model that describes the electromagnetic wave's propagation through the eye's structures in order to create a virtual OCT scan. We use a leap-frog type discontinuous Galerkin method for the discretization of the time-dependent Maxwell's equations and we will focus on deriving stability and convergent estimates of fully discrete schemes. We consider anisotropic permittivity tensors, which arise naturally in our application of interest. An important aspect in computational electromagnetic problems is the implementation of the boundary conditions.

This work is being developed in the Institute for Biomedical Imaging and Life Sciences (IBILI) of the Faculty of Medicine of the University of Coimbra and in the Laboratory for Computational Mathematics of the Centre for Mathematics of the University of Coimbra, in the framework of a research project in the field of Biomedical Engineering. This project gathered a group of experts in mathematics, physics, engineers and medical doctors and was supported by FCT, the Portuguese funding agency for science, research and technology.

Joint work with
Silvia Barbeiro[1], Rui Bernardes[3], Francisco Caramelo[2], Antonio Correia[3], Maria Isabel Marques[2], Miguel Morgado[2,4], Luis Pinto[1], Miriam Santos[3] and Pedro Serranho[2,5]

[1] CMUC, Department of Mathematics, University of Coimbra, Portugal
[2] IBILI, Faculty of Medicine, University of Coimbra, Portugal
[3] AIBILI-Association for Innovation and Biomedical Research on Light and Image, Coimbra, Portugal
[4] Department of Physics, University of Coimbra, Portugal
[5] Mathematics Section, Department of Science and Technology, Universidade Aberta, Lisbon, Portugal