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Universidade de Coimbra Universidade de Coimbra Universidade de Coimbra
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LCM Laboratory for Computational Mathematics

Optical modelling of the human retina in health and disease: from structure to function

Problem Description

This is a project in the field of Biomedical Engineering which brings together researchers with multidisciplinary backgrounds from the Faculty of Sciences and Technology and from the Faculty of Medicine of the University of Coimbra.

Diabetes mellitus is one of the most prevalent diseases in developed countries, estimated to affect 8.5% of the European population, according to recently collected data. A resulting complication of diabetes, diabetic macular edema (DME), is a major cause of visual loss in diabetic patients. DME is defined as an increase in retinal thickness due to fluid accumulation that can be intra- or extra-cellular. In intra-cellular edema, cells have increased fluid intake, becoming enlarged. Extra-cellular edema, in contrast, results from fluid accumulation outside the cell, generally as a consequence of the breakdown of the blood-retinal barrier and subsequent leakage into the retinal space. Distinguishing which case is present or more prevalent in a patient’s eye at an early stage is usually not straightforward.



OCT

Optical coherence tomography (OCT) is a noninvasive imaging modality undergoing a fast growth of application in the field of ophthalmology because of its unique ability of noninvasive imaging of the ocular fundus, allowing to access the structure of the human retina in vivo. Using OCT, patients with DME can be identified, when contrasted with healthy controls, as they exhibit an increased retinal thickness. However, OCT is still unable to directly assess changes at the cellular level. In this work, we aim to identify and understand the microscopic changes that lead to the differences in the OCT data between healthy and diseased cases, which are not possible to detect through direct observation.

Modelling & Computational Challenges

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). One of the main tasks is to model and numerically solve local scattering effects within the retina, considering different settings for each layer. Depending on the considered layer several structures will be considered and the local setting will vary with respect to size of each structure, distance between them and/or respective refractive indexes, in accordance with healthy or pathological status as described in the literature. 

In order to better understand the information carried in an optical coherence tomography, it is crucial to study in detail the behaviour of the electromagnetic wave as it travels through the sample. Several different models have been developed to describe the interactions of the electromagnetic field with biological structures. The first models were based on single-scattering theory, which is restricted to superficial layers of highly scattering tissue in which only single scattering occurs. Simulating the full complexity of the retina, in particular the variation of the size and shape of each structure, distance between them and the respective refractive indexes, requires a more rigorous approach that can be achieved by solving Maxwell’s equations. 

Research at LCM

Our method combines a light scattering simulation using a Monte Carlo (MC) routine (a stochastic method) with a model of the outer nuclear layer (ONL). This layer was chosen as it consistently presents the characteristics of DME and because spherical scatterers can adequately model it, which helps to simplify the simulation. By varying the model’s parameters, we expect to reproduce data gathered from healthy and DME eyes and potentially infer which changes at the cellular level are responsible for the OCT data differences between groups.



OCT2

The parameters describing the interaction of light with the medium were estimated with a nodal Discontinuous Galerkin Finite Element Method (DG-FEM) model of Maxwell’s equations. For the time integration, we used an improved fourth order, 14-stage low-storage Runge-Kutta. In order to avoid undesirable reflections caused by nonabsorbing boundary conditions, that invade the simulation domain and interfere with the observation of the phenomenon of interest, we consider the perfectly matched layer boundary conditions. The validation of the proposed methodology was done by comparison with Mie’s theory, considering the light scattering for a single sphere, using the same parameters as inputs for both models.

Papers & Reports

    Project Team

    • Adérito Araújo (LCM/CMUC)
    • Ana Sílvia F.C. Silva (FCTUC)
    • António L. Correia (IBILI/FCTUC)
    • António Morgado (IBILI/FMUC)
    • Francisco Caramelo (IBILI/FMUC)
    • José Cunha-Vaz (IBILI/FMUC/AIBILI)
    • Luís Pinto (IBILI/FCTUC)
    • Maria Margarida Marques (IBILI/FMUC)
    • Maria da Conceição Fonseca (IBILI/FMUC/AIBILI/HUC)
    • Maryam Ghalati (LCM/CMUC)
    • Paulo Jorge Menezes (ISR/FCTUC)
    • Pedro Serranho (IBILI/UA)
    • Rui Bernardes (IBILI/FMUC/AIBILI)
    • Sílvia Barbeiro (LCM/CMUC)
    • Torcato Santos (IBILI/AIBILI)

    Project Reference:

    FCT Research Project - PTDC/SAU-ENB/119132/2010

    Minerva 1290 UC Universidade de Coimbra
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